PREFACE

New electromechanical transducers with high energy output, high strains, high mechanical compliance, lightweight, damage-tolerance and low cost can enable needed advances in a variety of applications, such as robotics, automation and biomedical devices. The perceived need for improved transducer performance, which has progressively emerged in the last few decades, has drawn considerable efforts for the develop-ment of devices relying on materials with intrinsic transduction properties. These materials, often termed “ smart ” or “ intelligent ” , include improved piezoelectrics and magnetostrictive or shape-memory materials. While these technologies have addressed niche applications and continue to make incremental improve-ments, newer emerging electromechanical transduction technologies, based on so-called electroactive polymers (EAP), have gained a considerable attention. EAP offer the potential for performance exceed-ing other smart materials, while retaining the cost and versatility inherent in polymer materials. EAP are currently being developed and significantly studied as possible “ artificial muscles ” , i.e. functional surrogates of natural muscles, aimed at mimicking performances of biological actuation machines.

Within the EAP family, a specific class of materials, known as “ dielectric elastomers ” , is drawing particular interest at present, because of its already demonstrated good overall performance, as well as its simplicity of structure and robustness due to the use of stable and commercially available polymer materials. Dielectric elastomer transducers are rapidly emerging as high-performance “ pseudo-muscular ” actuators, useful for different kinds of tasks. Further, in addition to actuation, dielectric elastomers have also been shown to offer unique possibilities for improved generator and sensing devices.

Dielectric elastomer technology was introduced during late 1990s, pioneered by SRI International. While encouraging results have already been achieved, dielectric elastomers are quite new and are still being explored extensively. Dielectric elastomer transduction is enabling an enormous range of new applications that were precluded by any other EAP or smart-material technology until a few years ago.

With such a great potential, it is no surprise that research efforts focused on dielectric elastomers are growing rapidly. This is demonstrated by the increasing number of related publications in scientific journals, conferences and workshops, as well as the academic research projects and industrial contracts. Furthermore, while the technology is still new and growing, the technical maturity achieved so far has led to a new company that is focused exclusively on commercially exploiting the potential of dielectric elastomers. This company, Artificial Muscle, Inc., was founded in 2004.

This book intends to provide a comprehensive and updated insight on dielectric elastomer transduc-tion, by covering all its fundamental aspects. The book is organized in five main sections, dealing with transduction principles, basic materials properties, design of efficient device architectures, material and device modelling, along with applications already demonstrated or envisaged. These topics are treated by a collection of chapters written by the inventors of this technology and by the most renowned interna-tional contributors in the field. The broad and far-reaching range of the covered contents is expected to make this text as the first reference handbook on dielectric elastomer transduction. This book has been conceived as a source aimed at conveying the essence of this emerging EAP technology, serving as a comprehensive reference on the current state-of-the-art and, at the same time, proposing future research avenues and possibly stimulating new ideas.

Federico Carpi, University of Pisa Danilo De Rossi, University of Pisa

Roy Kornbluh, SRI International Ronald Pelrine, SRI International

Peter Sommer-Larsen, Risø National Laboratory

July, 2007

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Dedicated to our colleague Alberto Mazzoldi

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LIST OF CONTRIBUTORS

Mohamed Benslimane Micro Technology Group (IS-TCR) Danfoss A/S Jegstrupvej 3 Hasselager DK-8361, Denmark

Federico Carpi Interdepartmental Research Centre ‘ E. Piaggio ’ University of Pisa via Diotisalvi, 2 Pisa 56100, Italy

Claudia Caudai Interdepartmental Research Centre ‘ E. Piaggio ’ University of Pisa via Diotisalvi, 2 Pisa 56100, Italy

Hyouk Ryeol Choi School of Mechanical Engineering Sungkyunkwan University 300 Cheoncheon-dong, Jangan-gu, Suwon, Gyeonggi-do 440-746,

Korea

François Conti Artificial Intelligence Laboratory Department of Computer Science 9105 Stanford University Stanford, CA 94309-12685, USA

Danilo De Rossi Interdepartmental Research Centre ‘ E. Piaggio ’ University of Pisa via Diotisalvi, 2 Pisa 56100, Italy

Steven Dubowsky Department of Mechanical Engineering Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139, USA

Charlie Duncheon Artificial Muscle, Inc. 925 Hamilton Avenue Menlo Park, CA 94025, USA

Joe Eckerle SRI International 333 Ravenswood Avenue Menlo Park, CA 94025, USA

Joseph Eckerle SRI International 333 Ravenswood Avenue Menlo Park, CA 94025, USA

Gualtiero Fantoni Department of Mechanical Engineering University of Pisa Pisa, Italy

Mary I. Frecker Department of Mechanical Engineering The Pennsylvania State University 0326 Leonhard Building University Park, PA 16802, USA

Gabriele Frediani Interdepartmental Research Centre ‘ E. Piaggio ’ University of Pisa via Diotisalvi, 2 Pisa 56100, Italy

Fabia Galantini Interdepartmental Research Centre ‘ E. Piaggio ’ University of Pisa via Diotisalvi, 2 Pisa 56100, Italy

Stefano Galatolo Department of Applied Mathematics ‘ U. Dini ’ University of Pisa Via Buonarroti 1 Pisa 56127, Italy

Giuseppe Gallone Interdepartmental Research Centre ‘ E. Piaggio ’ University of Pisa via Diotisalvi, 2 Pisa 56100, Italy Department of Chemical Engineering University of Pisa Pisa, Italy

Nakhiah C. Goulbourne Department of Mechanical Engineering Virginia Tech 310 Durham Hall Blacksburg, VI 24061, USA

Soon Mok Ha Department of Materials Science and

Engineering

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List of Contributors ix

University of California Los Angeles, CA, USA

Hugh Herr Biomechatronics Group MIT Media Laboratory Room E15-419, 77 Massachusetts Avenue Cambridge, MA 02139, USA

Richard P. Heydt SRI International 333 Ravenswood Avenue Menlo Park, CA 94025, USA

Claudio Iseli EMPA, Swiss Federal Laboratories for Materials

Testing and Research Laboratory for Mechanical Systems Engineering Ueberlandstrasse 129 CH-8600 Dübendorf, Switzerland

Kwangmok Jung School of Mechanical Engineering Sungkyunkwan University Suwon, Korea

Lukas Kessler EMPA, Swiss Federal Laboratories for Materials

Testing and Research Laboratory for Mechanical Systems Engineering Ueberlandstrasse 129 Dübendorf CH-8600, Switzerland

Guggi Kofod Applied Condensed-Matter Physics Department of Physics University of Potsdam Haus 19, Raum 2.15, Am Neuen Palais 10 Potsdam D-14469, Germany

Ja Choon Koo School of Mechanical Engineering Sungkyunkwan University 300 Cheoncheon-dong Jangan-gu, Suwon,

Gyeonggi-do 440-746, Korea

Roy Kornbluh SRI International 333 Ravenswood Avenue Menlo Park, CA 94025, USA

Gabor Kovacs EMPA, Swiss Federal Laboratories for Materials

Testing and Research Laboratory for Mechanical Systems Engineering

Ueberlandstrasse 129 Dübendorf CH-8600, Switzerland

Anne Ladegaard Skov Department of Chemical Engineering The Technical University of Denmark Lyngby, Denmark

Sangwon Lee Korea Institute of Industrial Technology

(KAITECH) Chonan 330-825, Korea

Youngkwan Lee Department of Chemical Engineering Sungkyunkwan University 300 Cheoncheon-dong Jangan-gu, Suwon, Gyeonggi-do 440-746, Korea

Patrick Lochmatter EMPA, Swiss Federal Laboratories for Materials

Testing and Research Laboratory for Mechanical Systems Engineering Ueberlandstrasse 129 Dübendorf CH-8600, Switzerland

Federico Lorussi Interdepartmental Research Centre ‘ E. Piaggio ’ University of Pisa via Diotisalvi, 2 Pisa 56100, Italy

Peter Lotz Institute for Electromechanical Design Darmstadt University of Technology Merckstrasse 25 Darmstadt 64283, Germany

John D.W. Madden Department of Electrical and Computer

Engineering and the Advanced Materials and Process Engineering Laboratory

University of British Columbia 5500-2332 Main Mall Vancouver, BC V6T 1Z4, Canada

Marc Matysek Institute for Electromechanical Design Darmstadt University of Technology Merckstrasse 25 Darmstadt 64283, Germany

Edoardo Mazza Department of Mechanical Engineering ETH, Swiss Federal Institute of Technology Zürich, Switzerland

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x List of Contributors

EMPA, Swiss Federal Laboratories for Materials Testing and Research

Laboratory of Mechanics for Modelling and Simulation

Abt. 119 Ueberlandstrasse 129 Dübendorf CH-8600, Switzerland

Eric M. Mockensturm Department of Mechanical Engineering The Pennsylvania State University 0157C Hammond Building University Park, PA 16802, USA

Amit P. Mulgaonkar Department of Materials Science and Engineering V Bldg., Room 3121H University of California Los Angeles, CA 90095-1595, USA

Jae-do Nam Department of Polymer Science and Engineering Sungkyunkwan University 300 Cheoncheon-dong, Jangan-gu, Suwon, Gyeonggi-do 440-746, Korea

Qibing Pei Department of Materials Science and

Engineering University of California 6531 Boelter Hall, 420 Westwood Plaza Los Angeles, CA 90095-1595, USA

Ronald Pelrine SRI International 333 Ravenswood Avenue Menlo Park, CA 94025, USA

Jean-Sébastien Plante Department of Mechanical Engineering Massachusetts Institute of Technology Cambridge, MA, USA

Harsha Prahlad SRI International 333 Ravenswood Avenue Menlo Park, CA 94025, USA

Marcus Aaron Rosenthal Artificial Muscle, Inc. 925 Hamilton Avenue Menlo Park, CA 94025, USA

Helmut F. Schlaak Institute for Electromechanical Design Darmstadt University of Technology Merckstrasse 25 Darmstadt 64283, Germany

Peter Sommer-Larsen Polymer Department Risø National Laboratory PO Box 49 Roskilde DK-4000, Denmark

Scott Stanford SRI International 333 Ravenswood Avenue Menlo Park, CA 94025, USA

Michael Wissler EMPA, Swiss Federal Laboratories for Materials

Testing and Research Laboratory for Materials and Engineering Ueberlandstrasse 129 Dübendorf CH-8600, Switzerland Department of Mechanical Engineering ETH, Swiss Federal Institute of Technology Zürich, Switzerland

Wei Yuan Department of Materials Science and

Engineering University of California Los Angeles, CA, USA

Rui Zhang Swiss Federal Laboratories for Materials, Testing

and Research (EMPA) Laboratory for Mechanical Systems

Engineering Duebendorf, Switzerland

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INTRODUCTION: HISTORY OF DIELECTRIC ELASTOMER ACTUATORS

Ronald Pelrine and Roy Kornbluh

SRI International, Menlo Park, CA, USA

Dielectric elastomers , the name most commonly given to a new class of electroactive polymer actuators discovered in the early 1990s, are an exciting new actuator technology. The field is growing rapidly, whether measured by number of research papers, performance of the technology, or diversity of poten-tial applications. This first book devoted exclusively to dielectric elastomers therefore seems timely, and the introduction is a good place to step back and take a big picture look at where the field has been and where it is going.

Dielectric elastomers are a technology that could have been discovered decades earlier. The notion of opposite charges attracting and like charges repelling has been known since the earliest days of electric-ity (indeed, the effect on dielectric materials is known as Maxwell stress referring to the work by James Maxwell on the foundations of the electromagnetic theory). The materials needed to show actuation, such as polymer films and carbon black, have been available since at least the 1940s if not earlier. In fact, Bar-Cohen and Breazeal [1] note that experiments done with electric charges on natural rubber by W. Roentgen date back to 1880 while M. Sacerdote measured the strain response of dielectrics to applied electric fields in 1899.

But just because a technology could be discovered does not mean that it will be discovered. As with other technologies, several seemingly disparate threads had to come together before dielectric elastom-ers could be realized. Certainly, long-term interest in piezoelectric and electrostrictive materials helped to set the stage for dielectric elastomer development. An important step in this regard was the excellent work by Scheinbeim, Zhang, Zhenyi and others in investigating electrostrictive polymers such as semi-crystalline polyurethanes [2] . As with piezoelectric and electrostrictive ceramic work before it, inves-tigations into electrostrictive polymers treated Maxwell stress as a secondary factor that needed to be subtracted out from the more important electrostrictive measurements rather than a potentially powerful actuation mode worth pursuing in itself. Nonetheless, early electrostrictive polymer work was important in the evolution of dielectric elastomers in that it showed the potential of electroactive polymers beyond piezoelectric polymer materials such as polyvinylidene fluoride (PVDF), and it illustrated some of the important issues in electrode compliance that arise in high strain actuator materials.

Separate from the electrostrictive polymer work, several other developments came together in the early 1990s to lead to dielectric elastomer discoveries. One such development was the heavy interest in robotics in the late 1980s, with seminal work by Kornbluh [3] , Ian Hunter, and others arguing for inves-tigations into new actuation technologies for artificial muscles for robots. This work was important because it showed that, from a mechanical engineering perspective, there was no man-made analogue to natural muscle in performance. It was a very different perspective, and led to very different lines of research, than one might have focused on higher frequency applications such as sound generation. The work by Kornbluh, Higuchi [4] and others was also significant in that it suggested that electrostatic forces on micro scales might be used for such artificial muscles. Indeed, it is fair to say that dielectric elastomers might never have been discovered as a technology without the observation by many micro-electromechanical systems (MEMS) researchers that very small gaps, and very thin films, can have much higher electric breakdown strength than corresponding macro structures.

These separate research threads came together in fundamental work by Pelrine and others at SRI International in the early 1990s [5, 6] showing that actuation using polymers with Maxwell ’ s stress alone was an exciting option for actuation. In retrospect, the idea that something as simple as an elas-tomer sandwiched between electrodes could give good actuation response was audacious given what was known at the time. But in quick succession it was shown that virtually all insulating elastomer films exhibit a visible response using graphite electrodes, with various silicone elastomers leading the pack.

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xii Introduction

From the beginning, dielectric elastomer research has been an international affair, and indeed the early work at SRI, a US organization, was sponsored by the Micromachine Center, an organization funded by the Japanese government (MITI/NEDO). In Europe, researchers such as Sommer-Larsen and De Rossi were already investigating new artificial muscle approaches in the early 1990s [7] and were quick to recognize the potential of dielectric elastomers. This growing interest was facilitated by the growth in the larger electroactive polymer community including developments in both electrostrictive and ionic polymers.

One other technical development is worth mentioning both because it was important in itself and because of what it says about the field. Throughout much of the 1990s, the peak dielectric elastomer per-formance was roughly constant and exemplified by silicones, with peak strains of 10–30%. To be sure, important discoveries in materials, actuator design, and basic theory were made throughout the 1990s, but performance improvements seemed to have levelled off. That situation changed in 1999 with the discovery of acrylic as a dielectric elastomer. Acrylic easily broke the 100% strain mark, and brought higher visibility to the field. Even a lay person could immediately recognize that there was something remarkable in seeing a material double in size at the flick of a switch. The ability to be able to easily purchase large quantities of high quality, high performing film also greatly enhanced research. This has been particularly true in applications and device development where the necessity to fabricate custom films might be an obstacle to many research groups.

Acrylic was discovered by Pelrine testing the adhesive on the back of a discarded child-proof lock. In one sense the discovery was serendipitous, but in a deeper sense dielectric elastomers have such a simple structure, and so many elastomers are commercially available, that trial-and-error tests of many different commercial films and chemistries has been an effective strategy. As the field matures, one can expect a greater reliance on materials synthesized and optimized specifically as dielectric elastomers rather than for other commercial purposes. Nonetheless, historically many of the most important breakthroughs in materials have come from exploratory testing of new materials long after the physics were ‘ understood ’ . Ceramic superconductors and neodymium–iron magnets come to mind as two historically recent exam-ples. Given the rich chemistries involved, it seems highly likely that dielectric elastomers will be identi-fied with performance far superior to that of current acrylics designed as pressure sensitive adhesives, or silicones designed as sealants. But whether the next-generation materials will be designed and syn-thesized as super dielectric elastomers by intent, or discovered as part of a directed search of existing materials, is uncertain.

What is more certain is that rapid progress is being made in the technology on multiple fronts, much of it described in this book. Basic understanding of materials, failure mechanisms, and environmental aspects is growing. This fundamental understanding is taking place against a backdrop of intense appli-cation and device design interest. While the initial discoveries and research were motivated by the desire to develop improved muscle-like actuators, dielectric elastomers have also been shown to have great potential for applications as generators and sensors. Dielectric elastomers can potentially replace exist-ing actuator, generator, and sensor technologies, or they may enable entirely new applications that are impractical using existing technologies (variable surfaces might be an example here). Dielectric elastom-ers are potentially competitive in such a broad range of applications that it is not surprising that commer-cial participation in dielectric elastomer research and development (R & D) has grown from nearly zero in the early 1990s to a major component today.

These trends will continue and will likely accelerate if dielectric elastomers can make the transition from research topic to practical use. Many challenges remain such as in lifetime, environmental toler-ance, and manufacturing. Yet promising results on the practical side of the technology are being gradually realized, and one can be optimistic that the very flexibility and range of the technology in chemistries, device design, and potential applications will eventually bring it into common use. In the meantime, as a research community there is exciting work to be done, and beyond the academic interest this work may eventually have an important impact on society at large. With that in mind, we hope this book can further the field, and provide a reference for, and insights into, dielectric elastomers in years to come.

This book overviews both the technology itself and a representative selection of developing applica-tions. This book is divided into five sections, roughly laid out starting from fundamentals and ending at the application end of the R & D spectrum. The first section focuses on fundamentals of dielectric elas-tomers. This section describes how dielectric elastomers work and how they fit into the larger picture of electroactive polymers. The second section looks at dielectric elastomer materials, including both polymers

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Introduction xiii

and electrodes. Properties of existing materials are described, as well as directions for new material research. The third section discusses dielectric elastomer devices such as actuator configurations, and gen-erator and sensor modes. If it was not already obvious from the first two sections of the book, this third section illustrates the tremendous scope in how dielectric elastomers may be designed and used. In order for a technology to be really understood and applied, however, it is necessary to have a strong technology base, including modelling, the topic of the fourth section. Going forward, one can expect modelling to have increasing importance to the engineering side of dielectric elastomer technology. The fifth section on applications brings all the previous sections together to show how dielectric elastomers may be used for practical applications. New applications and their development using dielectric elastomers is a fascinating area, and they are often a motivating factor for more fundamental work described in earlier sections.

The authors of these chapters are from nearly 20 research institutes and companies in more than eight countries, attesting to the growing interest in dielectric elastomers. We believe we speak for the authors in extending a special thanks to Dr Federico Carpi and his colleagues at the University of Pisa for conceiving of this book and making it happen. The dedication and interest of researchers such as Dr Carpi are the best assurance that the field of dielectric elastomers will continue to blossom in the years ahead.

References

[1] Bar-Cohen, Y. and Breazeal, C. (2003). Biologically inspired intelligent robotics. Proceedings of the SPIE Smart Structures and Materials Symposium, EAPAD Conference, Paper 5051–02 , 3–6 March, San Diego, CA,

pp. 14–28.

[2] Zhenyi , M. , Scheinbeim , J. I. , Lee , J. W. and Newman , B. A. ( 1994 ). High field electrostrictive response of

polymers . J. Polym. Sci B Polym. Phy. 32 , 2721 – 2731 .

[3] Kornbluh, R., Eckerle, J. and Andeen, G. (1991). Artificial muscle: the next generation of robotic actuators.

SME Paper MS91-331, presented at the 4th World Conference of Robotics Research , Pittsburgh, PA.

[4] Niino, T., Egawa, S., Kimura, H. and Higuchi, T. (1994). Electrostatic artificial muscle: compact, high-power

linear actuators with multiple-layer structures. Proceedings of the IEEE Micro Electro Mechanical Systems Workshop ’ 94 , Oiso, Japan, pp. 130–135.

[5] Pelrine, R., Eckerle, J. and Chiba, S. (1992). Review of artificial muscle approaches, invited paper. Proceedings of the 3rd International Symposium on Micro Machine and Human Science , Nagoya, Japan, pp. 1–19. See

also Pelrine, R., et al. FY 1992 and FY 1993 reports for SRI project Artificial Muscle for Small Robots,

MicroMachine Center, MBR99 Bldg. 6F 67, Kanda-sakumagashi, Chiyoda-ku, Tokyo, 101-0026 Japan.

[6] Kornbluh, R., Pelrine, R., and Joseph, J. (1995). Elastomeric dielectric artificial muscle actuators for small

robots. Proceedings of the 3rd IASTED International Conference on Robotics and Manufacturing , June,

Cancun, Mexico, pp. 1–6.

[7] Sommer-Larsen, P., Ed. (1996). Artificial Muscles, a Feasibility Study of Polymer Based Materials for Actuator Purposes . Risø National Laboratory, Denmark.

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Section I

Fundamentals

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Sec1-I047488.indd 2 12/11/2007 9:58:49 AM

ELECTROMECHANICAL TRANSDUCTION EFFECTS IN DIELECTRIC ELASTOMERS: ACTUATION, SENSING, STIFFNESS MODULATION AND ELECTRIC ENERGY GENERATION

Ronald Pelrine and Roy Kornbluh

SRI International, Menlo Park, CA, USA

Abstract

Dielectric elastomers (DEs) are electromechanical transducers that convert or transduce electrical energy to or from

mechanical energy. In an actuator mode, DEs convert electrical to mechanical energy, whereas in a generator mode

they perform the reverse function and convert mechanical to electrical energy. This chapter derives the fundamental

equations describing DE transduction. The equations show quantitatively how electrical parameters such as electric

field and dielectric constant are related to mechanical parameters such as stress and strain. The basic equations can

be extended to examine more subtle considerations such as film stability and leakage, as well as applied to devices

such as sensors and variable stiffness devices that transduce mechanical energy both to and from electrical energy.

The analysis conveniently uses an energy approach because ideal DEs are lossless, but more realistic energy loss

mechanisms such as leakage and viscoelasticity are also discussed.

Keywords : Actuators, dielectric elastomers, electromechanical transducers, energy, generators, leakage, sensors,

stability, variable stiffness.

1.1 INTRODUCTION

Dielectric elastomers (DEs) are fundamentally a transducer technology, meaning they convert energy from one form to another. More specifically, DE devices are electromechanical transducers that convert electrical energy to mechanical energy. Transducers that convert electrical to mechanical energy are actuators. DEs use a reversible electromechanical transduction mechanism, so in addition to converting electrical to mechanical energy, they can also convert in the reverse direction; that is, they can change mechanical energy to electrical energy. In this type of operation, DEs are acting in a generator mode.

Actuators and generators, currently based principally on electromagnetic transduction, are pervasive in modern industrial societies. Indeed, actuators are used in almost every modern system, including planes, computers, cars, washing machines, loudspeakers and so forth. Later chapters of this book will focus on a wide range of potential applications where DEs may compete with existing actuators and generators. In this chapter, the focus will be on the fundamental aspects of DEs as transducers, but the wide range of potential applications is a strong motivation beyond the interesting science and physic involved.

1.2 FUNDAMENTALS OF DE TRANSDUCTION

The basic structure of DEs, shown in Fig. 1.1(a) , is quite simple. A polymer film, typically but not nec-essarily an elastomer, is sandwiched between two electrodes. As noted above, DEs transduce mechanical energy, and in order for that to be accomplished the electrodes must typically stretch and contract with the polymer. Thus, the electrodes in a DE transducer are compliant, with the level of compliance deter-mined by the specifics of the DE transducer such as the magnitude of strain that must be accommodated.

The behaviour and physics of DEs can be derived in a number of ways. Methods involving tensors are perhaps the most general, and several excellent analysis using tensors have been developed [1] . But

Chapter 1

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4 Chapter 1

the very generality of tensor approaches can sometimes obscure the simplicity of the underlying phys-ics. Here an energy approach will be used to develop the important equations for DEs in an attempt to emphasize the basic physics. Later chapters, such as in Section IV on modelling DEs, can then describe more detailed analysis.

The DE film, including electrodes, is recognized electrically as a capacitor. The electrical description can be simplified by assuming an ideal structure with zero resistance in the electrode, and infinite resistance in the polymer. The polymer is further assumed to be a perfect dielectric with relative dielectric constant � , and to be perfectly elastic with no dissipative mechanical losses. With these assumptions the electrical and mechanical aspects of the system are separately and together lossless in the sense that energy is conserved during changes of state. Later these assumptions can be relaxed to better understand real materials.

The stored electrical energy on a DE film is a convenient starting point to examine the physics. The capacitance C of the DE capacitor can be written as

C

A

z�

� �0

(1.1)

where � 0 is the permittivity of free space, A is the area where the opposite electrodes overlap (called the ‘ active area ’ ), and z is the polymer thickness. The electrical energy of a capacitor U e with charge Q can be written according to the well-known formula:

U

Q

Cz A Qe 0( )� � �0 5

0 52

1 2.. � �

(1.2)

Figure 1.1(b) shows a change in state relative to Fig. 1.1(a) . We imagine the change to be infini-tesimal, and denote the difference in area as d A , the difference in thickness as d z and the difference in charge as d Q . Figure 1.1 shows the change as resulting in a greater area and decreased thickness, but at this stage of analysis the changes are assumed to be arbitrary, that is, both d A and d z could be positive or negative. Using Eq. (1.2), the change in electrical energy d U e is written as

d d { ( ) d } { ( ) d }e 0 0UQ

CQ A Q z z A Q A� � �� �

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟ 0 5 0 51 2 2 2. .� � � � (1.3)

d d deUQ

CQ

Q

C zz� �

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎧⎨⎪⎪

⎩

0 5 12.

⎪⎪⎪

⎫⎬⎪⎪

⎭⎪⎪

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

⎧⎨⎪⎪

⎩⎪⎪

⎫⎬⎪⎪

⎭⎪�

(d

0 5 12. Q

C AA

⎪⎪ (1.4)

d d1

zd de eU

Q

CQ U z

AA� �

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟ −

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎧⎨⎪⎪⎩

1

⎪⎪⎪

⎫⎬⎪⎪⎭⎪⎪

(1.5)

Noting that ( Q / C ) � V where V is the voltage on the capacitor, we see that the first term on the right-hand side of Eq. (1.5) is just the voltage times the charge added or subtracted from the film. That is, the

Charge Q

Charge Q � dQ

�

� � � � � � �

� � � � � � � � � � �

� � � � � �

� � � � � � � � � � �

Compliantelectrodes(top andbottom)

(a)

(b)

Polymer

z

z � dz

A

A � dA

Figure 1.1 Charged DE film (a) in an initial stage and (b) in an incrementally changed final state. Changes exag-gerated for clarity.

Ch01-I047488.indd 4 12/10/2007 8:15:40 PM

Electromechanical Transduction Effects in Dielectric Elastomers 5

term ( Q / C )d Q � V d Q is just the electrical energy that has flowed on or off the film from an external power source during the incremental change in state. The flow of charge and energy must be from an external source in this model because the polymer is assumed to be a perfect insulator.

The second term in Eq. (1.5) represents the conversion of electrical to mechanical energy or work. It depends on the existing stored electrical energy of the film U e times a factor which depends only on changes in the film ’ s geometry. If d W is the incremental mechanical work done on the polymer by the electric field pressure, we can therefore write

d1

zd

1deW U z

AA� �

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟ −

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎧⎨⎪⎪⎩⎪⎪

⎫⎬⎪⎪⎭⎪⎪

(1.6)

Note the sign change in Eq. (1.6) relative to the sign of the second two terms in Eq. (1.5) because we have defined the work as being done on the polymer rather than that done on the electric field or charges. Equation (1.6) shows the incremental work, an important quantity in DE transduction.

To better understand physically what the terms represent, suppose there is no charge flowing to or from the film so that d Q � 0. In this case, the change in electrical energy can be expressed as

d dz

d d constant charge)ee eU W

Uz

U

AA� � �

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟ (

(1.7)

We can understand what the two terms on the right-hand side of Eq. (1.7) represent by first considering an imaginary polymer that can change thickness z but must keep a constant area A . This is the situation for a conventional parallel plate in which the ‘ polymer ’ dielectric is just air or vacuum. In this case, the second term on the right is zero, so that the first term just represents the change in energy of a parallel plate capacitor as the plates are moved closer together or farther apart. Physically this term arises because opposite charges attract, so as the plates become closer, d z � 0 and the electrical energy is reduced.

The second term in Eq. (1.7) is a bit less intuitive but can also be understood physically. Consider an imaginary polymer that can change area but not thickness. This is similar in some respects to compliant conductors, such as liquid mercury, being placed on opposite sides of a rigid insulating plate, such as a glass slide. The thickness change d z � 0, so the second term represents the change in electrical energy as the charge is allowed to spread out. Physically this term arises because like charges repel, so that compressing them into a smaller area, d A � 0, increases stored electrical energy.

1.3 THE CONSTANT VOLUME ASSUMPTION AND RESULTANT MAXWELL STRESS

For elastomers, a significant simplification of Eq. (1.5) can be achieved by using the constant volume assumption for elastomers [2] . In an elastomer the bulk compressibility of the material is usually much greater than its elastic modulus, so to a very good approximation one can assume

Az � �Vol constant (1.8)

where Vol is the volume of the elastomer. This approximation is generally very accurate for real elas-tomers, and is a fair approximation for some polymers that are not elastomers. For incremental changes, Eq. (1.8) can be expressed as

A z z Ad d� � 0

(1.9)

1 1

zz

AA

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟d d� �

(1.10)

Substituting Eq. (1.10) into Eq. (1.5) now gives equivalent expressions for d U e as

d d1

d constant volume)e eUQ

CQ U

AA� �

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟2 (

(1.11)

Ch01-I047488.indd 5 12/10/2007 8:15:40 PM

6 Chapter 1

d d1

zd constant volume)e eU

Q

CQ U z� �

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟2 ( (1.12)

where, again, the first term on the right-hand side of both equations represents electrical energy flowing into or out of the film from an external source, and the second terms on the right represent the mechanical work done on the electric field ( � d W using the definition in Eq. (1.6)). Equations (1.11) and (1.12) are useful for understanding the two important modes of DEs. Considering Eq. (1.11), for example, one sees that if the area is increasing (d A � 0), electrical energy is decreasing. That is, electrical energy is being con-verted into mechanical work, and the film is operating in an actuator mode. Any increase in area of a DE, whether as a result of electric field pressure stretching the film or as the result of external forces, causes electrical energy to be converted to mechanical work, provided of course that there is charge on the film.

Conversely, if the active film area is decreasing ( dA � 0), such as from film contraction, electrical energy is increasing from Eq. (1.11). Mechanical energy is being converted to electrical energy in this case, and the film is operating in a generator mode [3] . Similar observations can, of course, be made about thickness changes using Eq. (1.12). The description between area and thickness is completely analogous except for a sign reversal as can be seen by comparing Eq. (1.11) with Eq. (1.12).

So far in the derivation we have focused primarily on changes in electrical energy, and have only noted that when no electrical energy is flowing from or onto the film, the electrical energy is con-verted to (or from) mechanical work by the incremental change in state. That is, the change in electrical energy must equal the mechanical work done by or on the electric charges via the field pressure. To better understand the mechanical variables involved, consider the resultant Maxwell stress p exerted by the electric field. The resultant Maxwell stress, sometimes called the effective pressure or actuation pressure, can be defined by the equation:

� �Ap z Wd d (1.13)

With this definition, p is the compressive stress or pressure exerted over an area A through a displace-ment d z necessary to provide mechanical work equal to the actual work on the polymer. Taking into account the sign, this is also equal to the change in electrical energy d U e with constant charge. Equation (1.13) can be rewritten directly in terms of U e as

pA

U

z�

1 d

dconstant charge)e

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟ ( (1.14)

In Eq. (1.14) one must be cautious about what is held fixed during the change d z . The actual normal pres-sure or stress from the field in the z -direction would be obtained if A (and Q ) were held fixed. However, if the volume constraint in Eq. (1.8) is considered, there is really only one relevant spatial variable in the physical problem. It is a one-degree-of-freedom system with regard to spatial variables given the con-stant volume assumption. The variable can be considered z or A according to convenience, but once one is chosen the other is strictly specified according to Eq. (1.8). Thus, the resultant Maxwell stress of greatest interest is obtained by differentiating U e with respect to z when U e is changed according to a constant vol-ume system. In this case, Eq. (1.12) with d Q � 0 is the appropriate expression to use to derive the result-ant Maxwell stress as

pA

U

zU

Az

U� � �

1 d

d

1

Vole

ee

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟2

2

(1.15)

The resultant Maxwell stress can be put into a more familiar form by noting that

U CV AzV

z

V

ze 0 0 Vol� � � �0 5 0 5 0 5 02

2 2

. . .� � � �⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟ ..5 2� �0 VolE (1.16)

where E is the electric field. Substituting U e from Eq. (1.16) into Eq. (1.15) gives the expression for p as

p E� � �0

2 (1.17)

Ch01-I047488.indd 6 12/10/2007 8:15:40 PM

Electromechanical Transduction Effects in Dielectric Elastomers 7

This is a well-known result in the field of DEs. Readers familiar with air-gap electrostatic actuators using rigid parallel plates might note that the resultant Maxwell stress in Eq. (1.17) is twice the cor-responding normal stress per unit area in a parallel plate capacitor device. The additional factor of 2 is because DEs have a second coupled degree-of-freedom to convert electrical to mechanical energy com-pared with air-gap parallel plates. More specifically, the electrodes in a DE can spread out in area in addition to becoming closer together, and, as noted in the discussion following Eq. (1.7), both changes reduce electrical energy. The two modes of conversion can be treated separately, with compressive stress in the z -direction and tensile stresses in the planar directions, but since the two modes are coupled via the constant volume condition in an elastomer, it is more convenient to speak of a single effective pressure or resultant Maxwell stress rather than two separate components. Strictly speaking, the resultant Maxwell stress is not the true normal stress on the polymer (it is twice the true normal stress), but since the planar tensile stresses are directly coupled to the thickness direction, the film is driven mechanically just as if the resultant Maxwell stress were applied normally with no tensile stresses. In this chapter, the resultant Maxwell stress will be referred to as the effective pressure or simply the pressure, but it should be noted that this simplification is accurate only to the degree that the constant volume condition holds.

The effective pressure in Eq. (1.17) is directly related to the force output of a DE actuator. Note that for a given effective pressure, the higher the dielectric constant, the lower the electric field needed to achieve that pressure. Since E � V / z , it follows that the higher the dielectric constant, the lower the voltage needed to achieve a given pressure and actuator force with a given film thickness. This observa-tion has led to significant investigations into materials with high dielectric constants in order to reduce operating voltage [4] such as those described in Chapter 6 of this book. However, one can also see that the pressure increases with the square of the electric field, so a high breakdown voltage, even with a modest dielectric constant, can result in high effective pressures.

1.4 ANALYSIS OF SEVERAL IMPORTANT DE CONDITIONS

Equations (1.11), (1.12) and (1.17) can be used to determine the mechanical energy output of a DE film in the actuator mode, or the electrical energy generated in the generator mode, under a number of conditions. For example, if charge is constant, d Q � 0, from Eq. (1.11) one can derive

d / (d / )e eU U A A� �2

(1.18)

ln lnef

ei

U

U

Af

Ai

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟� �2

(1.19)

U

U

Ai

Afef

ei

�⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

2

(1.20)

where the subscripts i and f in Eqs. (1.19) and (1.20) refer to initial and final states of the polymer. Hence, with a constant charge system, the change in electrical stored energy is simply equal to the square of the area ratio between initial and final states. If U ei is known from Eq. (1.1) or Eq. (1.16), the resulting final energy U ef can be found from Eq. (1.20) and the area change. Since d Q � 0, the mechanical energy W converted to or from electrical energy is then found from Eq. (1.20) as the opposite of the change in U e . That is,

W U U UAi

AfU U

Ai

Af� � � � � �ei ef ei ei ei

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

⎧2 2

1⎨⎨⎪⎪⎪

⎩⎪⎪⎪

⎫⎬⎪⎪⎪

⎭⎪⎪⎪

(1.21)

More complex conditions when d Q is not zero can also be analysed. One condition of interest is the case of a constant electric field. This case is significant because the simplest assumption for a DE is that the polymer has a breakdown electric field that is constant, independent of strain. The constant field case therefore represents optimal performance in getting the most energy from the material for

Ch01-I047488.indd 7 12/10/2007 8:15:40 PM

8 Chapter 1

these types of polymers. Equation (1.17) can be used to analyse the constant field case [5] . With con-stant field, p is also constant and therefore using Eq. (1.13) we have

d dW Ap z� �

(1.22)

W Ap z p A z pz

z� � � � � �{ d } { d }Vol

d∫ ∫ ∫⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎧⎨⎪⎪⎩⎪⎪

⎫⎬⎪⎪⎭⎪⎪

(1.23)

W pzf

zip

Af

Ai� � �Vol ln Vol ln

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

(1.24)

where Eqs. (1.23) and (1.24) have made use of the constant volume condition Az � Vol � constant. Another common case of interest is a constant voltage drive. In this case, d Q is not zero. However,

the second term from Eq. (1.11) is still equal to the mechanical work done on the electric field. This is opposite in sign from the work done on the polymer d W so

d deW UA

A� 21⎛

⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

(1.25)

The expression in Eq. (1.25) can be simplified in the constant volume case by noting that

U CVA

zV

AVe 0 0

Vol� � �0 5 0 5 0 52 2

22. . .� � � �

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

(1.26)

And with constant voltage, using Eq. (1.26) into Eq. (1.25) gives

dVol

d0WA

VA

A� 2 0 512

2. � �⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

⎧⎨⎪⎪

⎩⎪⎪

⎫⎬⎪⎪

⎭⎪⎪

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟ �� � �0

VoldV

AA2

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

(1.27)

WV

Af Ai U U� � � �0 52

2 2.� �0

ef eiVol

( )⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

(1.28)

In the constant voltage case, electrical energy is flowing onto or off the film from an external source, so there is no a priori connection between the change in the stored electrical energy and the work done by the electric field. If U fl is the electrical energy that flows onto the film from an external source , then

U U Wef ei flU� � �

(1.29)

U ( )fl ef ei� �2 U U

(1.30)

where Eq. (1.30) is derived from Eq. (1.29) using Eq. (1.28) to substitute for W . The right-hand side of Eq. (1.28) thus reflects the fact that half the electrical energy flowing onto the film is converted to work on the polymer, while the other half changes the stored electrical energy. This observation is closely related to the fact that without recovery of the electrical energy of the film at the end of the actuation, the maximum theoretical efficiency for a constant voltage drive actuator is 50%. One can see this by noting that if U ei is negligible, the energy that flows onto the film is twice the final stored energy and twice the work output. Thus, at most, with a constant voltage drive without energy recovery, the work output is half the input energy.

1.5 STRAIN RESPONSE AND STABILITY

Equation (1.17) gives the pressure exerted on the polymer by the electric field, but does not specify the mechanical response of the polymer. In general the mechanical response of the polymer is quite complex,

Ch01-I047488.indd 8 12/10/2007 8:15:41 PM

Electromechanical Transduction Effects in Dielectric Elastomers 9

and full treatment typically requires finite element modelling including elasticity, viscoelasticity, creep, loading, boundary conditions and so forth. This is particularly true when DEs are driven into highly non-linear regimes, as is quite possible for materials that have demonstrated over 300% strains. Some insight can be gained, however, by considering the simplified case of an unloaded film with free boundary con-ditions. It is assumed in this case that the active area covers the entire surface of the film. We further assume that material is linear with a constant modulus Y so that the strain in z , S z , can be expressed as

Sp

Y YE

Y

V

zz � � � � � �� � � �0 0

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

2

2

(1.31)

Suppose z 0 is the initial film thickness. Then one can write z � z 0 (1 �S z ) so that Eq. (1.31) becomes

SY

V

z Szz

� ��

� �0

0[ ( )]

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟1

2

(1.32)

S SY

V

zz z( ) 0

0

1 2

2

� � �� �⎛

⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

(1.33)

S S SY

V

zbz z z

3 2

2

2� � � � �� �0

0

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

(1.34)

where for convenience we have defined a quantity b � � ( � 0 � / Y )( V / z 0 ) 2 . The parameter b can be thought

of as a first order approximation to the strain as seen from Eq. (1.34). Equation (1.34) is a rather cumbersome 3rd power polynomial in S z . It can be solved exactly or

numerically for S z , but it is more instructive to consider the stability of the film based on Eq. (1.34). Imagine the quantity b on the right-hand side of Eq. (1.34) changed incrementally, such as from a slight change in voltage V or initial film thickness. The incremental change in thickness strain d S z is then written as

{ }d d3 4 12S S S bz z z� � �

(1.35)

or

d

d

1S

b S Sz

z z

�� �{ }3 4 12

(1.36)

Note that as S z → � 1/3, the quantity in { } in Eq. (1.36) goes to zero and therefore d S z /d b approaches infinity. This means that as the thickness strain approaches � 1/3, that is, 33% reduction of the initial thickness, the film becomes less and less stable relative to changes in the physical variables, and when S z reaches � 1/3, the film collapses in thickness until breakdown or some other violation of the model assumptions occurs [6] . With constant voltage drive, the instability occurs physically because as the film decreases in thickness, the field pressure increases, and beyond S z � � 1/3, the field pressure is increasing faster than the elastic restoring forces can balance to maintain static equilibrium.

The instability at S z � � 1/3 with this model is closely related to the pull-in phenomena known in air-gap electrostatics. It should be emphasized that the instability at S z � � 1/3 only occurs given the model assumptions, and in particular the assumption of constant modulus Y . In practice Y is usually not constant over such a large range in thickness strain. Nonetheless, while detailed values may be different from this simple model, pull-in phenomena can and does occur in DEs, and it is the cause of failure in a number of situations. Often one can see very local regions of polymer actuate to much greater strains than surrounding regions, and this is an experimental indication that pull-in may be an issue. Pull-in can be avoided by making sure that the elastic restoring forces increase faster than the field pressure during operation of the DE.

Ch01-I047488.indd 9 12/10/2007 8:15:41 PM

10 Chapter 1

1.6 DE SENSORS

DEs can be used in a number of ways as sensors or sensor arrays [7] . If the applied field or voltage is sufficiently small relative to the thickness and stiffness of the film, the actuated strain is negligible. For example, if 1 kV causes a 10% strain in DE film, Eq. (1.31) indicates that at 10 V the actuated strain will be on the order of one ten-thousandth of this value, or about 0.001%. Thus, the actuated strain is negligible, but if the film is stretched by external forces the percentage changes in voltage are not. The voltage on the film can be written as

VQ

C

Q

A z

Q

A� � �

( / )

Vol

( )0 0� � � �

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟ 2

(1.37)

where the last equality is written using the constant volume assumption. It can be seen from Eq. (1.37) that if Q is constant, the voltage varies according to 1/ A 2 . Such an effect can be used to sense strain by measuring the change in voltage. Elastomer strains can be quite large, so strain sensors based on this effect can measure large strains, in addition to being conformal, easily patterned in arrays, and low cost.

Sensors based on Eq. (1.37) can measure AC strains, but DC and very low frequency strains using this approach are problematic because leakage and other effects change Q over time. An alternate way to use DEs in a sensor mode is to measure capacitance of the film directly. Capacitance varies according to Eq. (1.1) or its constant volume analogue, C � � 0 � A 2 /Vol. This method can measure DC changes in strain, and various capacitance measuring circuits are well-known in the electrical engineering literature.

Other techniques using DE-related methods are also known, such as measuring changes in electrode resistance with strain. DE sensors are of interest in and of themselves, but it is worth noting that they are also a natural option wherever DE actuators or generators are being used.

1.7 STIFFNESS MODULATION

The AC sensor mode based on changes in voltage with constant charge uses both actuator and generator modes. That is, the film is expanding at some times but contracting at others, so that energy is convert-ing back and forth between electrical and mechanical energy. Variable stiffness, or stiffness modulation, also operates this way [8] . But whereas sensors typically use very small signal voltages and charges, variable stiffness relies on the full power capabilities of the device. As shall be shown, stiffness modu-lation in DEs depends on the electrical loading of the system, as it does with piezoelectrics and other electromechanical transducers.

There are many ways to modulate stiffness of a device. In this chapter, stiffness modulation using the basic transduction mechanism of DEs is analysed. Let U m be the elastic mechanical energy stored in the material. For simplicity assume the material is perfectly elastic. If the material is stretched or com-pressed an amount d z in thickness by an external force applied adiabatically (i.e. reversibly such that quasi-static equilibrium is maintained), an amount of external work d W e is done on the DE:

F z Wd d e�

(1.38)

where F is the net force applied in the z -direction. The stiffness of the system in the z -direction, K z , is the rate of change of F with z . That is,

K

F

zz �d

d (1.39)

To find F , we consider the energy balance of the system. The material is assumed elastic, and there are no internal electrical or mechanical energy losses in the material. The energy d W e input to the system therefore must be equal to the increase in stored mechanical and electrical energy, d U m � d U e , plus the incremental electrical energy that flows out of the material. The electrical energy that flows out of the material, d U f , is just d U f � � V d Q � � ( Q / C )d Q as noted in the discussion following Eq. (1.5). Hence,

F z W U U V Q U Uz

zd d d d d d de m e m e� � � � � � 21⎛

⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

(1.40)

Ch01-I047488.indd 10 12/10/2007 8:15:41 PM

Electromechanical Transduction Effects in Dielectric Elastomers 11

where the last equality uses Eq. (1.12) with the constant volume assumption. F is now found as

F

U

z

U

z� �

d

dm e2

(1.41)

The stiffness of the system can now be found using Eqs. (1.39) and (1.41):

K

U

z

U z

zK

U z

zz z� � � �d

d

d( / )

d

d( / )

dm e

0e

2

22 2

(1.42)

where K z 0 � d 2 U m /d z 2 is the mechanical stiffness with zero charge. First consider a constant charge electrical loading. One can express U e � 0.5 z 2 ( � 0 � Vol) � 1 Q 2 and Q is constant independent of z , so that Eq. (1.42) becomes

K KU z

zK

Qz z z� � � �0

e0

0

d( / )

d ( Vol)2

2

� � (1.43)

The term on the right-hand side of Eq. (1.43) is always positive, and therefore a constant charge on a DE film always makes the film stiffer. This result can seem counter-intuitive in the sense that charge placed on a film makes it contract in thickness and so in a sense makes it seem softer. However, the con-fusion is that deflection is a force whereas stiffness only refers to the rate of change of force. The pres-ence of charge can indeed reduce the amount of force needed for a given deflection, but if the slope of the force versus displacement is greater, then the stiffness is greater. This is illustrated in Fig. 1.2 which shows a qualitative graph of the external force needed to achieve a given contraction or expansion of z , with and without charge Q . In this graph, z 0 is taken as the zero force or relaxed thickness of the film with Q � 0. When Q � 0, the thickness at zero external force contracts to a value less than z 0 , such as that specified by the negative z -axis strain in Eq. (1.31). However, note that although the zero force point on the thickness axis is less, the slope of F versus z is greater with the Q � 0 curve.

Next consider the stiffness with constant voltage. In this case, U e � 0.5 CV 2 � 0.5( � 0 � Vol) z � 2 V 2 where the constant volume constraint A � Vol/ z has been used. Substituting this expression for U e into Eq. (1.42) gives

K K

U z

zK

V

zz z z� � � ��0

e0

0d( / )

d

( Vol)2 3

2

4

� �

(1.44)

Equation (1.44) says that the stiffness of the film in thickness is reduced with constant voltage applied to the electrodes. Physically, in the previous constant charge case, the field and field pressure of the film decreased as the thickness decreased and area increased. By contrast, in the constant voltage case, as the film decreases in thickness and increases in area, the field pressure increases to reduce the net stiffness of the film in thickness compression. As the thickness of the film increases , however, at con-stant voltage the field decreases . Hence, the effects of the field on mechanical stiffness decrease for increasing thickness z , as seen from the second term in Eq. (1.44).

Unstable

z0 z

Q, V � 0

Constant QF

Constant V

Figure 1.2 DE thickness versus applied force under different electrical conditions.

Ch01-I047488.indd 11 12/10/2007 8:15:41 PM

12 Chapter 1

Note that if the second term on the right-hand side of Eq. (1.44) gets sufficiently negative, the film stiffness goes to zero and becomes negative for decreasing z . This is consistent with the earlier discussion regarding film stability. A negative stiffness implies the film is unstable, and this regime must typically be avoided in a DE. However, in practice it is worth noting that K z 0 typically increases as z approaches zero. Otherwise the force needed to compress the film to zero thickness (infinite area) would only be twice that needed to compress the film to half the unstrained thickness and twice the area. Nonetheless, although the stability situation is usually not as bad as one might conclude based on constant K z 0 , the possibility of an unstable or marginally stable condition can have implications for DE design and must be considered.

1.8 SUMMARY

The basic energy relations of DE transduction have been described in this chapter. If an electric charge or voltage is on a film that is expanding in area, the film is converting electrical to mechanical energy and operating in an actuator mode. If a charged film is contracting in area, energy is being converted from mechanical energy to electrical energy and the film is operating in a generator mode. A key sim-plification in the energy equations can be achieved for true elastomers and other soft polymers where volume can be assumed constant. These equations can be used to analyse a number of important condi-tions for DEs, such as constant charge or constant voltage conditions, optimal energy transduction at constant field, and stability as a function of strain. DEs can also be used in devices that operate in both actuator and generator modes, such as sensors and variable stiffness devices. The energy relations can give the designer insight into the fundamental behaviour of these devices as well. In particular, constant charge increases the stiffness of a DE film, whereas constant voltage decreases its overall stiffness. Later chapters in this book describe the use of DEs in many types of devices. But fundamentally, DEs are an electromechanical transducer technology, and the equations developed in this chapter may give a better understanding of detailed applications.

References

[1] Zhang, Q. and Scheinbeim, J. (2001). Electric EAP. In Electroactive Polymer (EAP) Actuators as Artificial Muscles – Reality, Potential and Challenges , 1st edn, Chapter 4, Ed. Bar-Cohen, Y., SPIE Press, Bellingham,

Washington, DC.

[2] Kofod, G., Kornbluh, R., Pelrine, R. and Sommers-Larsen, P. (2001). Actuation response of polyacrylate die-

lectric elastomers. In Smart Structures and Materials 2001: Electroactive Polymer Actuators and Devices , Ed.

Bar-Cohen, Y., Proc. SPIE , 4329 , pp. 141–147.

[3] Pelrine, R., Kornbluh, R., Eckerle, J., Jeuck, P., Oh, S., Pei, Q. and Stanford, S. (2001). Dielectric elastom-

ers: generator mode fundamentals and applications. In Smart Structures and Materials 2001: Electroactive Polymer Actuators and Devices , Ed. Bar-Cohen, Y., Proc. SPIE , 4329 , pp. 148–156.

[4] Szabo, J. P., Hiltz, J. A., Cameron, C. G., Underhill, R. S., Massey, J., White, B. and Leidner, J. (2003). In

Elastomeric composites with high dielectric constant for use in Maxwell stress actuators. In Smart Structures and Materials 2003: Electroactive Polymer Actuators and Devices (EAPAD) , Ed. Bar-Cohen, Y., Proc. SPIE ,

5051 , July, pp. 180–190.

[5] Pelrine , R. , Kornbluh , R. , Pei , Q. and Joseph , J. ( 2000 ). High-speed electrically actuated elastomers with over

100% strain . Science , 287 ( 5454 ), 836 – 839 .

[6] Pelrine , R. , Kornbluh , R. , Joseph , J. and Marlow , J. ( 1998 ). Analysis of the electrostriction of polymer dielec-

trics with compliant electrodes as a means of actuation . Sens. Act. A-Phys . , 64 , 77 – 85 .

[7] Kornbluh, R., Pelrine, R., Pei, Q., Heydt, R., Stanford, S., Oh, S. and Eckerle, J. (2002). Electroelastomers:

applications of dielectric elastomer transducers for actuation, generation and smart structures. In Smart Structures and Materials 2002: Industrial and Commercial Applications of Smart Structures Technologies , Ed.

McGowan, A., Proc. SPIE , 4698 , pp. 254–270.

[8] Choi, H., Ryew, S., Jung, Kwangmok, J., Jaewook, K., Hunmo, N., Jaedo, T., Atsuo, M., Ryutaro, K. and

Tanie, K. (2002). Biomimetic actuator based on dielectric polymer. In Proc. of SPIE – Volume 4695 Smart Structures and Materials 2002: Electroactive Polymer Actuators and Devices (EAPAD), Ed. Bar-Cohen, Y.,

July, pp. 138–149.

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DIELECTRIC ELASTOMERS AS HIGH-PERFORMANCE ELECTROACTIVE POLYMERS

John D.W. Madden

Electrical and Computer Engineering and the Advanced Materials and Process Engineering Laboratory, University of British Columbia, Vancouver, BC, Canada

Abstract

In this chapter the properties of dielectric elastomers are compared with other actuators – both new materials such as

electroactive polymers, and more established technologies such as piezoelectrics, electric motors, combustion engines

and muscle. Dielectric elastomers cannot readily compete with combustion engines and electric motors in performing

continuous high power work, such as steady propulsion. However, relative to other muscle-like technologies dielectric

elastomers have advantages in their very large strains, high work densities, good frequency responses, high degree of

electromechanical coupling and the availability of the materials. Practical issues to be considered when implementing

dielectric elastomers include supplying their high voltage, the design of the pre-straining mechanism and cycle life.

Keywords: Actuator, artificial muscle, carbon nanotube, conducting polymer, dielectric elastomer, electroactive

polymers, ionic polymer–metal composite, motor, review, shape memory alloys.

2.1 CONVENTIONAL ACTUATORS AND THE NEED FOR NEW APPROACHES

In the most simplistic sense a good actuator only needs to exhibit very high power per unit volume (power density) or power per unit mass (specific power). Mechanical work can be delivered at the desired rate up to the limit of the actuator’s power output. Piezoelectrics, internal combustion engines and high-revving electric motors are outstanding in this regard, with specific powers in excess of 500 W/kg [1].

Combustion engines are hard to beat for use in automobiles because not only do they have a power density of 1 kW/kg, they also consume very high energy density fuels (40 MJ/kg � freely available air), thereby using only a relatively small fraction of the vehicle volume. However, combustion engines and high-revving electric motors have a relatively narrow range of rotational speeds over which their output is optimal. This makes them well suited for constant speed processes such as the propulsion of ships, highway driving or steady pumping. Transmissions enable operating speed range to be extended.

When the required motions become more complex, effective implementation of combustion engines and high-revving electric motors becomes increasingly problematic. Creating an elbow joint that needs to move, stop, and then maintain force or stiffness is not particularly easy to achieve, and the complex-ity of the transmission overcomes the benefits of high power density. Hydraulics or pneumatics can be used as the transmission, as is done in excavator arms for example, but the efficiency is low and the fine control of speed and position are often poor. Honda have used servo motors combined with harmonic drives to create high torque in their impressive ASIMO humanoid robot [2]. The mechanism works beautifully but dissipation in the harmonic drive reduces efficiency. Furthermore, the motors do not have a catch state – they expend energy to hold a constant force. An alternative actuator technology that is better suited for positioning and intermittent operation is thus desirable.

Piezoceramics [3] are very well suited for controlling position at small length scales. In these mate-rials an electric field acts on permanent dipoles within the material, leading to deformations of the crystalline domains and strains of about 0.1%. The extent of deformation is proportional to the applied voltage. The material acts as a capacitor at moderate to low frequencies. Holding a fixed voltage leads

Chapter 2

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14 Chapter 2

to the maintenance of a fixed position without energy expenditure. In other words these actuators have a catch state. Although the specific power is high, it is a challenge to couple the mechanical work out of the structure when relatively large displacements are needed compared to the size of the actuator. Lamination of the piezoceramic to a passive backing (a bilayer) leads to bending due to differential expansion of the structure. These and similar approaches are very commonly used to amplify displace-ments, but because the strains are so small, even mechanical amplification often leads to relatively small deformations relative to the size of the device.

Piezoelectrics work well for nanopositioning since the position control and the high bandwidth of the actuators allow sub-atomic positioning resolutions to be achieved and kilohertz rates of scan-ning. Stepping mechanisms can be used to create larger displacements, as in camera lens positioners. However, the efficiency of such mechanisms can be relatively low because much of the energy in step-ping devices is used for clamping, and the bandwidth is reduced by the ratio of the single step time to the total number of steps in the range of travel. Larger stroke is desirable for many applications. Although piezoceramics have extremely high power to mass ratios, the challenge is getting the work out, especially where large displacements are needed.

Dielectric elastomer actuator performance is not sufficient at present to replace automobile engines and constant speed machines (fans, machine tools, etc.). Although power densities are approaching the right range, cycle life has so far been limited to about one million cycles. Dielectric elastomers do how-ever offer large stroke and a catch state, which, along with the relatively high power density, make them good alternatives to combustion engines, piezoelectrics and high-revving electric motors in situations where complex, non-periodic motions are required. In the sections that follow other promising actua-tors are discussed and their properties compared with those of dielectric elastomers. The properties of skeletal muscle are first briefly presented since its prowess is well established and provides a good benchmark. Table 2.1 compares the properties of dielectric elastomers to muscle, relaxor ferroelectric polymers, conducting polymers and shape memory alloys. More details on these and other technologies can be found in a number of reviews [3–5].

2.2 MUSCLE

Dielectric elastomers and other contractile materials are often referred to as artificial muscle technolo-gies. The mechanisms employed in these materials are not nearly as elegant as those in muscle, which uses the combined ratcheting motion of many proteins to create force and displacement [6]. A similar-ity is that, like muscle, artificial muscles consist of materials that change in length in response to input

Table 2.1 Actuator comparisons [10].

Property Mammalian Skeletal Muscle

Dielectric Elastomers

Relaxor Ferroelectric Polymers

Conducting Polymers

NiTi Shape Memory Alloys

Strain (%) 20–40 10 to �100 3–10 [15] 2–12 1–8Stress (MPa) 0.1–0.35 0.1–2 typical,

3–9 maximum20–45 1–100 [24] 200

Work density (kJ/m3)

8–40 10–150 typical, 3400 maximum

�1000 70–100 �1000

Density (kg/m3) 1037 �1000 �2000 �1300 6450Strain rate (%/s) >50 450 in VHB,

34 000 in silicone�2000 @ 0.1% strain

1–12 300

Continuous power (W/kg)

50–280 �500 �1000 150 �1000

Electromechanical coupling (%)

�40 efficiency 30 typical, 90 maximum

10–40 �10 �5

Cycle life �109 106 @ 50% strain

– 800 000 best to date

300 @ 5%, 107 @ 0.5%

Modulus (MPa) 10–60 0.1–3 400–1200 �500 20 000–80 000Voltage (V) �1 V �1000 �1000 2 Low

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Dielectric Elastomers as High-Performance Electroactive Polymers 15

stimulus. Mammalian skeletal muscle is relatively efficient (up to 40%), produces substantial strains (�20%) and reasonable forces (350 kPa blocking force, per cross-sectional area) [3].

There are a number of properties of muscle that are desirable in artificial muscle technologies, but have yet to be fully emulated [3, 6]. Its exceptional cycle life (�109 in the heart) is made possible by constant regeneration of the proteins. It is able to vary stiffness, a feature that is very useful in common tasks such as catching a ball. Stiffness in dielectric elastomers, conducting polymers and some other artificial muscle technologies can change as a function of voltage, but to a much smaller extent, and not independently of position [7, 8]. Muscle is composed of bundles of fibres that can be selectively acti-vated to produce a graded force in a process known as recruitment [6] – a feature not yet present in arti-ficial muscles, and that is effective because the stiffnesses of the inactive fibres are minimal. Another feature that is rarely exploited is built-in feedback. Displacement and force measurement are built into muscle (muscle spindles and Golgi tendon organs [6]) which provide input to reflex loops.

A very important advantage of muscle, and one that it shares with the internal combustion engine, is that it is driven using high energy density fuels (20–40 MJ/kg). This is much higher than the specific energy of batteries (typically �1 MJ/kg). Although batteries also store chemical energy, they are much lower in energy density in large part because they do not generally exploit the free availability of oxygen. Fuel cells allow this exploitation, and promising actuator approaches are emerging in which the active materials themselves (shape memory alloys and carbon nanotubes) act as electrodes in a fuel cell [9].

Muscle’s widespread use in nature demonstrates that it is scaleable from the large (blue whales) to the very small (transport of structures within a cell employs a related mechanism). We have yet to find actua-tors that can be widely used to replace muscle in the pumps, valves and limbs that it actuates within us. A muscle-like actuator, combined with control mechanisms and energy sources, would be greatly ben-eficial in creating bio-mimetic structures (e.g. robots and efficient fish-like submersibles), toys, medical devices (active catheters), automobiles (door locks, wipers) and motors for consumer electronics (autofo-cus devices).

Dielectric elastomers [3] are probably the closest of any artificial technology to reproducing muscles’ basic properties, particularly when strain and stress levels are compared. In dielectric elastomers strain (10–100%) is similar to or higher than in muscle, as is stress (0.1–8 MPa). Work density in mammalian skeletal muscle may reach 40 kJ/m3, compared to between 10 and 150 kJ/m3 in silicone and VHB based elastomers, respectively. The continuous power output of dielectric elastomers also matches or exceeds that of our skeletal muscle, with human muscle producing about 50 W/kg, compared to about 400 W/kg in the elastomers. In fact the specific power generated by dielectric elastomers is similar to that of high-revving electric motors. These figures of merit are compared in Table 2.1.

Overall, dielectric elastomers look set to outperform muscle. Some additional factors need to be con-sidered however. One is that dielectric elastomers need to be pre-strained in order to maximize perform-ance. This pre-strain provides mechanical amplification and increases dielectric strength. Pre-strains are often large (�100%), and require high stresses (MPa range) [7]. Structures including springs (in spring rolls) [10] and so-called bow-ties are used to maintain the pre-strain. These take up substantial space and often weigh much more than the dielectric elastomer itself. Work density can be reduced by a fac-tor of 10 or more as a result. For example, the energy density in one spring roll [11] is calculated based on its effective stress and strain [3] to be less than 2 kJ/m3. In this calculation packaging and the cross-sectional area consumed by the spring are added to the cross-sectional area of the elastomers itself. The packaging challenge posed by the pre-straining mechanisms can be resolved at least in part by stretch-ing the dielectric elastomers and then locking the pre-strain in place by creating an additional polymer within the elastomer matrix [12].

Dielectric elastomers are electrically powered. In the absence of widely available and cost effective fuel cell technology, batteries are generally relied upon to store energy in autonomous devices. As men-tioned, the energy density of batteries is at least 20 times lower than that of sugars and fats used by mus-cle, meaning that to go the same distance with the same efficiency, 20 � more fuel mass must be carried.

Cycle life in dielectric elastomers is reasonable, but at �106 for moderate to large strains [3] is still much lower than is possible in muscle itself.

Dielectric elastomers have two advantages relative to mammalian skeletal muscle, namely that they exhibit a catch state and that they can be used as generators [13]. They are also easier for us to build and sustain.

Comparison with muscle enables us to assess whether or not a technology can, from a mechanical per-spective at least, replace muscle function in the pumps, valves and motors found within organisms, and

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16 Chapter 2

perhaps also in artificial devices that are similar in scale, such as humanoid and animal-like robots, sub-mersibles, pumps and valves. The answer is not completely clear cut because of the many factors that go into selecting actuators. However, what is clear is that the energy densities and speeds of dielectric elas-tomers are sufficient to allow them to be of the same size or smaller than muscles doing the same task, provided that pre-straining mechanisms and packaging are not excessive. Some limitations of dielectric elastomers relative to muscle include its current reliance on low energy density sources and relatively short cycle life. In general muscle has a number of properties that improve its function and efficiency, and that perhaps can be developed in artificial actuators, including recruitment, regeneration and variable stiffness.

Dielectric elastomers are not the only materials that actuate in response to applied voltage, producing displacements akin to those of muscle. A selection of other technologies are now described and com-pared to dielectric elastomers. The aim is to describe advantages and disadvantages of each relative to dielectric elastomers.

2.3 RELAXOR FERROELECTRIC POLYMERS

Electrostrictive polymers [14] are another class of materials that convert energy in an applied electric field into mechanical work. There are a number of variations including ferroelectric polymers, liquid crystal polymers and graft elastomers. Here the focus is on relaxor ferroelectric polymers, which so far have exhibited the best properties overall [14].

Ferroelectric polymers, of which polyvinylidenefluoride (PVDF) is the best known, undergo an elec-trostatically induced change in conformation in response to an applied field. Polar fluorines on the PVDF backbone align themselves with the field, causing the chains that are aligned perpendicular to the direction of the field to expand in length [14], as somewhat simplistically represented in Fig. 2.1. The relatively large stiffness of the ferroelectric polymers (�100 � larger than in dielectric elastomers) means that strains induced by Maxwell forces are relatively small.

The relationship between polarization and field is hysteretic in ferroelectrics, much like the B–H curve in a ferromagnet. Hysteresis and the accompanying loss are reduced by introducing defects along the chain, thereby preventing the formation of extended domains. The resulting electromechanical cou-pling in the defect containing materials, known as relaxor ferroelectrics, is 10–40% [3]. This is not quite as high as is achievable in dielectric elastomers, but is in the same range as muscle. As in dielectric elas-tomers, the coupling needs to be divided by two (or more) to obtain the actual amount of mechanical energy that can be extracted from the input electrical energy, since some of the input electrical energy

Conducting coatings

Stiffpolymer

No voltage Voltage applied

V

Exploded views

Figure 2.1 Ferroelectric polymers. The application of an electric field to a film of aligned PVDF molecules is expected to lead to a reorientation of the polar fluorines from a non-polar phase, as depicted. This change in con-formation turns out to produce extension along the chain direction and contraction orthogonal to it. The relative positioning of adjacent molecules turns out to be important in explaining the response [14]. Dimensional changes in the top diagrams are exaggerated to make them easier to view.

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Dielectric Elastomers as High-Performance Electroactive Polymers 17

goes into deforming the active material itself [3]. Strains are in the range of 3–10% [14, 15]. These are lower than in dielectric elastomers, so increased mechanical amplification is generally required. However, stiffness and stress (up to 45 MPa) are much higher than in dielectric elastomers, enabling high work densities (�1 MJ/m3) [14]. Again voltages are high, with fields ranging from 10 to 150 MV/m. The properties of relaxor ferroelectrics are compared with those of other actuators in Table 2.1. Frequency response and power densities are similar to or higher than those in dielectric elastomers. High frequency operation could lead to heat dissipation problems, particularly in large devices [3].

PVDF is a commercially available piezoelectric polymer, but defects need to be created (e.g. via gamma irradiation) [14]. Alternatively defects can be introduced into the backbone during synthesis (e.g. monomers whose size prevents the formation of large domains) [14]. These materials can be cus-tom ordered but are not yet commercially available. Dielectric elastomers are more readily obtained. Commercially available silicone or acrylics can be used without modification. The caveat is that com-mercially available elastomers will need to be pre-strained in order to maximize their deformations, or chemically modified to lock in pre-strain.

Where space and thus work density are important, relaxor ferroelectrics are probably preferred since high energy densities do not require a pre-straining mechanism. In situations where relatively large displacements are required dielectric elastomers have the advantage of larger strain. In general both dielectric elastomers and relaxor ferroelectrics are extremely promising actuator materials. Thus far, applications of dielectric elastomers are more developed, and commercialization is more advanced (e.g. Artificial Muscle Incorporated, Menlo Park, California).

2.4 IONIC ACTUATORS

Low voltage operation is often desirable, particularly in autonomous battery or fuel cell driven applica-tions. High voltage can often still be used in such situations, but will require the use of additional electron-ics, adding to cost and volume requirements. Dielectric elastomers generally require voltages in excess of 1 kV, which can be obtained using relatively compact DC to DC converters (�1 cm3, EMCO High Voltage, Sutter Creek, CA) or with potentially very compact piezoelectric transformers [16]. Extra packaging may also be needed for high voltage devices in order to reduce the risk of electrical shorts to the surround-ings, which even at low power can be undesirable in devices including medical implants or toys. Use of thinner actuators with higher dielectric constants will likely lead to a reduction in the required operating voltages of dielectric elastomers. This process leads to increased capacitance and therefore increased cur-rent, so will ultimately require reduced resistance in the conductive coating in order to maintain speed and power. Increasing conductivity without increasing stiffness (so that actuation is not impeded) is likely to prove difficult. Alternative actuator technologies are available whose primary advantage is their low volt-age operation. Some of these are now described, followed by a comparison with dielectric elastomers.

Significant dimensional changes can be induced in a number of materials using low voltages. Here three materials are presented: conducting polymers, carbon nanotubes and ionic polymer–metal composites (IPMC). All rely on reversible ion transport. Ions are able to penetrate the materials and approach within a nanometre of the electrically conducting surfaces. Local fields that are similar to or even higher than those employed in dielectric elastomers are generated, providing driving forces to per-form mechanical work despite the lower voltage.

2.4.1 Conducting polymers

In conducting polymers the polymer itself is electronically conductive [17]. When a potential is applied to the polymer through an electrolyte, electrons are added to or removed from the polymer. This charge is balanced by a flux of ions that is able to penetrate inside the polymer. Often only one ion is small enough to fit within the polymer, and thus dominates transport. When ions are inserted it is found that the polymer swells [18]. This swelling appears to take place perpendicular to the chain direction – changing the distance between chains [3, 19]. The mechanism described is depicted in Fig. 2.2. To first order, the strain is proportional to the number of ions per unit volume inserted or removed. Repeatable strains have typically been �2%, but recently have exceeded 8% [20–22]. The lower strain compared to dielectric elastomers or muscle means that greater mechanical amplification is often required [23]. Conducting polymers are relatively stiff materials, with elastic moduli in the 100 MPa to

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18 Chapter 2

several GPa range. Actuation has been observed at stresses of up to 100 MPa [24], although it is more typically less than 10 MPa. Work densities approach 100 kJ/m3, and are thus similar to typical values in dielectric elastomers, but an order of magnitude lower than the best achieved [8, 24]. Application of a force on the film leads to the generation of a voltage [25], enabling the material itself to act as a sensor. Unlike dielectric elastomers, no applied voltage is needed for this voltage, or the associated current, to be measured [26]. However, the relatively small coupling makes conducting polymers poor generators. Table 2.1 lists some properties of conducting polymer actuators.

2.4.2 Carbon nanotube actuators

Carbon nanotubes are a recently discovered form of carbon that is composed of graphite like sheets rolled into tubes [27]. Single walled nanotubes are often about 1 nm in diameter, while tubes with mul-tiple concentric walls can have diameters of 10 nm or larger. Carbon nanotubes can be metallic or semi-conducting. Immersion of films or fibres composed of many nanotubes in an electrolyte and application of a voltage attracts charges to the tube/solution interface. Strains that are typically between 0.1% and 0.6% are observed, which are thought be the result of electrostatic forces and changes in electron density [9, 28–31]. Such small relative changes in length (�100 � smaller than in dielectric elastomers) make mechanical amplification essential for most applications, and add to the challenge of implementing these actuators. Although strains are small, stresses in individual nanotubes are expected to be enormous. Each nanotube has a modulus of �640 GPa [27], so the stresses in each tube are anticipated to be �600 MPa. If fibres can be made that can withstand such stresses without substantial creep, and with a modulus similar to that of the individual tube, then enormous work densities are possible (�10 MJ/m3 assuming 0.6% strain). At present work densities [31] are closer to 100 kJ/m3.

2.4.3 Ionic polymer/metal composites

IPMC are composed of ion conducting polymer films such as Nafion® (Dupont) which are coated on each side with very high surface area electrodes [32–34]. The ionically conducting polymer has a charged backbone (typically negative in charge), with the charge being balanced by oppositely charged mobile ions, such as Na�. There is usually water present also. The charged regions of the polymer form hydrophilic clusters with water channels. Application of a voltage charges the porous metal electrodes

V�

Conductingpolymer

electrolyte

Counter electrode

V�

Force

Anionsin

electrolyte

Neutralpolymerchains

Exploded views

Chargedpolymer

�anions

Figure 2.2 Conducting polymer actuation. The insertion of ions between polymer chains is commonly believed to contribute to the macroscopic expansion of conducting polymers observed upon application of a voltage in an electrolyte. In the case depicted, anions (PF �

6 ) are inserted between polymer chains (polypyrrole) when a positive voltage is applied (bottom view), leading to swelling. Contraction occurs when the voltage is reversed (top view). The scale of the deformations is exaggerated.

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Dielectric Elastomers as High-Performance Electroactive Polymers 19

[33], redistributes ions and creates electrostatic interactions within clusters [32], resulting in actuation. These actuators bend by swelling on one side and contracting on the other, and thus mechanical ampli-fication is built in. Strains are on the order of 0.5–3%, and stresses typically 3 MPa or less [3].

The ionic actuators described operate at low voltages, are relatively high in stiffness and provide moderate to small strains when compared to dielectric elastomers. The key advantage of these ionic actuators relative to dielectric elastomers is their low voltage operation. IPMCs employ up to about 7 V. Carbon nanotubes and conducting polymer normally operate at about 2 V or less. These voltages are three orders of magnitude lower than those used in dielectric elastomers, and make battery opera-tion relatively simple. However, there are a number of drawbacks and challenges associated with these materials. Under typical operating conditions none of these ionic actuators have electromagnetic cou-pling in excess of 1% – compared to 30% or more in dielectric elastomers. In principle relatively high coupling can be achieved, but it requires operation at high stresses (�1 GPa for nanotubes and conduct-ing polymers) and either a large modulus or high strain. These have yet to be achieved, though rapid progress is being made on the carbon nanotube front [35]. Despite the poor coupling, the efficiency can be ��1% because much of the input electrical energy is stored and can then be recovered (in IPMCs this only applies at low voltages when parasitic currents are small, i.e. ��2 V). Even when efficiency can be increased, the coupling remains low, so a large transfer of energy to and from the materials is needed each cycle. Current into and out of the actuators can be �100 times higher than if the coupling were close to unity, putting a large load on the power supply. The large current demands good conduc-tion paths, including in the ionic phase. In conducting polymers in particular this is a challenge since the mobility of ions inside the polymer is not particularly high, and thus, unless the conducting polymer is less than about 1 �m in thickness, the response is slow (often seconds of more). Currents in dielectric elastomers, in contrast, are tiny due to the combination of high operating voltage and good coupling, so even relatively poor conductivity electrodes allow good frequency response. Finally, all ionic actuators operate best when using wet electrolytes, which generally need to be encapsulated [3].

Dielectric elastomers generally can perform well relative to ionic electroactive polymers, particularly where large strain and relatively high efficiency are important. In situations where low voltage is criti-cal however, dielectric elastomers are not currently an option.

2.5 SHAPE MEMORY ALLOYS

Shape memory alloys are worth mentioning in this overview of actuator technologies because, despite a number of drawbacks, they are unmatched in work density and, as is not so well known, can be extremely high in power to mass [3, 4]. These metal alloys undergo temperature driven phase transfor-mation. Temperature change is frequently achieved using a current pulse, particularly in nickel–titanium alloys, where resistivity is reasonable. A change in crystal structure results in dimensional changes that are typically between 1% and 8%. These strains can be induced under very high loads, leading to high work densities (�1 MJ/m3). Furthermore, by employing effective cooling (e.g. operating in a water bath and employing short current pulses to induce heating), millisecond time scale impulse responses can be induced by heating, followed by quick cooling from nucleate boiling. Typically the shape memory alloy contracts at high temperature, and a tensile stress is needed to return it to its elongated state following cooling. A simplified version of the shape memory cycle is shown in Fig. 2.3. Mechanical elongation can be avoided when a two-way shape memory effect is induced [3].

The properties of NiTi shape memory alloys are summarized in Table 2.1. Apart from the smaller strain, shape memory alloy performance generally exceeds that of dielectric elastomers. However, shape memory alloys suffer from low efficiency (�5%). Furthermore, these actuators are difficult to position control because of their hysteretic and stress dependent response. Rates of actuation can be low when used in air. Finally, lifetime is relatively short at high strain. Materials are readily available and produced in quantity.

2.6 DISCUSSION AND CONCLUSIONS

Dielectric elastomers are not ready to compete with combustion engines and electric motors to continu-ously run machines, particularly over a large number of cycles. However, they are better suited for inter-mittent tasks such as gross position control and in replacing muscle. The high work density, power density and electromechanical coupling, combined with exceptional strain, and ready availability of materials

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20 Chapter 2

make dielectric elastomers extremely attractive for widespread application. The high voltages used are a potential obstacle in some applications, particularly where additional costs associated with voltage conver-sion are necessary. A further challenge is to maintain the outstanding work densities, power densities and strains in practical devices by limiting the volumes and constraints of pre-straining mechanisms, mechani-cal couplings and packaging. These obstacles may be minimized by employing novel voltage converters (e.g. piezoelectric transformers) and by locking in pre-strain using chemical methods.

When low voltage is essential conducting polymers, carbon nanotubes and IPMC actuators can be used. Otherwise none of these actuators exhibit any clear performance advantages at present, and have the disadvantages of much smaller electromechanical coupling and strain.

Relaxor ferroelectrics and shape memory alloys may offer improved work and power densities, which can be beneficial for many applications. On the other hand, dielectric elastomers offer higher efficiency, particularly relative to shape memory alloys, and larger strains.

Dielectric elastomers have proven themselves in the laboratory to be high performance actuator tech-nologies, comparing favourably with both conventional and emerging actuators. A key challenge now is to identify applications and create designs that effectively employ this high performance.

References

[1] Hollerbach, J., Hunter, I. W., Ballantyne, J., Khatib, O., Craig, J. and Lozano, P. (1992). A Comparative Analysis of Actuator Technologies for Robotics. MIT Press, Cambridge, MA, pp. 299–342.

[2] ASIMO. The Honda humanoid robot. http://world.honda.com/ASIMO/ http://world.honda.com/ASIMO/

[3] Madden, J. D. W., Vandesteeg, N. A., Anquetil, P. A., Madden, P. G. A., Takshi, A., Pytel, R. Z., Lafontaine,

S. R., Wieringa, P. A. and Hunter, I. W. (2004). Artificial muscle technology: physical principles and naval

prospects. IEEE J. Oceanic Eng., 29(3), 706–728.

[4] Hunter, I. W. and Lafontaine, S. (1992). A comparison of muscle with artificial actuators. IEEE. Solid State

Actuator, Sensor and Microsystems Workshop, Hilton Head, SC, pp. 178–185.

[5] Bar-Cohen, Y. (2004). Electroactive Polymer (EAP) Actuators as Artificial Muscle, 2nd edn. SPIE,

Bellingham, WA, p. 765.

[6] King, A. M., Loiselle, D. S. and Kohl, P. (2004). Force generation for locomotion of vertebrates: skeletal

muscle overview. IEEE J. Oceanic Eng., 29(3), 684–691.

[7] Kofod, G. (2001). Dielectric Elastomer Actuators. Ph.D. Thesis, Technical University of Denmark.

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Austenite

Twinned martensite Deformed martensite

Raisetemperature

Stress

Lower temperature

Figure 2.3 Shape memory effect. Reversible deformation in nickel–titanium alloys is generally produced by cool-ing the material from the austenitic phase. A twinned martensite structure results. Application of stress leads to deformation. Increased temperature returns the martensite to the original austenitic phase, generating strain. The cycle is repeated to produce actuation. Two-way shape memory effects are also possible in which physical deforma-tion of the twinned state is not required.

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Dielectric Elastomers as High-Performance Electroactive Polymers 21

[9] Ebron, V. H., Yang, Z. W., Seyer, D. J., Kozlov, M. E., Oh, J. Y., Xie, H., Razal, J., Hall, L. J., Ferraris,

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1580–1583.

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lastomer roll actuators and their application for biomimetic walking robots [5051-31]. Proceeding of SPIE,

5051, 281–290.

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[12] Soon Mok, H., Wei, Y., Qibing, P., Ron, P. and Scott, S. (2006). In New High-Performance Electroelastomer Based on Interpenetrating Polymer Networks, Ed. Bar-Cohen, Y. Proc. SPIE, p. 616808.

[13] Ron, P., Roy, D. K., Joseph, E., Philip, J., Seajin, O., Qibing, P. and Scott, S. (2001). In Dielectric Elastomers: Generator Mode Fundamentals and Applications, Ed. Bar-Cohen, Y. Proc. SPIE, pp. 148–156.

[14] Zhang, Q., Huang, C., Xia, F. and Su, J. (2004). Electric EAP. In Electroactive Polymer Actuators as Artificial Muscle, Ed. Bar-Cohen, Y, Proc. SPIE Press, Bellingham, Washington, pp. 95–170.

[15] Huang, C., Klein, R., Xia, F., Li, H., Zhang, Q. M., Bauer, F. and Cheng, Z. Y. (2004). Poly(vinylidene fluo-

ride-trifluoroethylene) based high performance electroactive polymers. IEEE Trans. Diel. Elec. Insu., 11(2),

299–311 [see also IEEE Transactions on Electrical Insulation].

[16] Uchino, K. (2000). Ferroelectric Devices. CRC Press, Boca Raton, p. 308.

[17] Skotheim, T. A., Elsenbaumer, R. L. and Reynolds, J. R. (1998). Handbook of Conducting Polymers. Marcel

Dekker, New York.

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and volume changes in polypyrrole during redox. J. Phys. Chem., 96(25), 10507–10514.

[19] Herod, T. E. and Schlenoff, J. B. (1993). Doping induced strain in polyaniline: stretchoelectrochemistry.

Chem. Mater., 5, 951–955.

[20] Della Santa, A., DeRossi, D. and Mazzoldi, A. (1997). Characterization and modeling of a conducting poly-

mer muscle-like linear actuator. Smart Mater. Struct., 6, 23–34.

[21] Zama, T., Hara, S., Takashima, W. and Kaneto, K. (2005). Comparison of conducting polymer actuators

based on polypyrrole doped with Bf4(–), Pf6(–), Cf3so3–, and Clo4. Bull. Chem. Soc. Jpn., 78(3), 506–511.

[22] Cole, M. and Madden, J. D. (2005). The effect of temperature on polypyrrole actuation. Materials Research

Society Proceedings, 889, pp. 105–110.

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and Hunter, I. W. (2004). Application of polypyrrole actuators: feasibility of variable camber foils. IEEE J. Oceanic Eng., 29(3), 738–749.

[24] Spinks, G. M., Mottaghitalab, V., Bahrami-Saniani, M., Whitten, P. G. and Wallace, G. G. (2006). Carbon-

nanotube-reinforced polyaniline fibers for high-strength artificial muscles. Adv. Mater., 18(5), 637.

[25] Takashima, W., Uesugi, T., Fukui, M., Kaneko, M. and Kaneto, K. (1997). Mechanochemoelectrical effect of

polyaniline film. Synth. Met., 85(1–3), 1395–1396.

[26] Wu, Y., Alici, G., Madden, J. D. W., Spinks, G. M. and Wallace, G. G. (2007). Soft mechanical sensors

through reverse actuation in polypyrrole. Adv. Funct. Mater., 17(16), 3216–3224.

[27] Baughman, R. H., Zakhidov, A. A. and de Heer, W. A. (2002). Carbon nanotubes – the route toward applica-

tions. Science, 297(5582), 787–792.

[28] Baughman, R. H., Cui, C. X., Zakhidov, A. A., Iqbal, Z., Barisci, J. N., Spinks, G. M., Wallace, G. G.,

Mazzoldi, A., De Rossi, D., Rinzler, A. G., Jaschinski, O., Roth, S. and Kertesz, M. (1999). Carbon nanotube

actuators. Science, 284(5418), 1340–1344.

[29] Gartstein, Y. N., Zakhidov, A. A. and Baughman, R. H. (2002). Charge-induced anisotropic distortions of

semiconducting and metallic carbon nanotubes. Phys. Rev. Lett., 89(4), 45503–45507.

[30] Spinks, G. (2004). EAP Activity in Australia and New Zealand. WW-EAP Newsletter, December, 5–7.

[31] Mirfakhrai, T., Oh, J., Kozlov, M., Fok, E. C. W., Zhang, M., Fang, S., Baughman, R. H. and Madden, J. D. W.

(2007). Electrochemical actuation of carbon nanotube yarns. Smart Mater. Struct., 16, S243.

[32] Nemat-Nasser, S. and Thomas, C. W. (2004). Ionomeric polymer–metal composites. In Electroactive Polymer (EAP) Actuators as Artificial Muscle, Eds. Bar-Cohen, Y., 2nd edn. SPIE Press, Bellingham, WA,

pp. 171–230.

[33] Shahinpoor, M. and Kim, K. J. (2004). Ionic polymer–metal composites: III. Modeling and simulation as

biomimetic sensors, actuators, transducers, and artificial muscles. Smart Mater. Struct., 13(6), 1362–1388.

[34] Bennett, M. D. and Leo, D. J. (2004). Ionic liquids as novel solvents for ionic polymer transducers. In Smart Structures and Materials: Electroactive Polymer Actuators and Devices, Ed. Bar-Cohen, Y. SPIE Press, San

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sizing an ancient technology. Science, 306(5700), 1358–1361.

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Section II

Materials

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Sec2-I047488.indd 24 12/11/2007 9:59:09 AM

PHYSICAL AND CHEMICAL PROPERTIES OF DIELECTRIC ELASTOMERS

Anne Ladegaard Skov 1 and Peter Sommer-Larsen 2

1 Department of Chemical Engineering, The Technical University of Denmark, Lyngby, Denmark 2 Polymer Department, Risø National Laboratory, Roskilde, Denmark

Abstract

The basic physical and chemical properties of elastomers are essential for their use in dielectric elastomer actuators.

The elastic modulus, the dielectric constant, and the dielectric breakdown strength determine the ultimate static per-

formance of an actuator, whereas viscoelasticity influences the dynamic behaviour. The chemical and thermal prop-

erties determine the environmental compliance of the actuator including temperature service range and resistance

towards various solvents. The properties influencing processing are more subtle but the chemical nature and the

viscoelastic properties are important for the ability to form smooth films, for release from moulds, and for bonding

between elastomer and electrode material. The elasticity of elastomers is generally speaking governed by the length

of elastic active chains – that is the average molecular weight of chains between crosslinks and a contribution from

entanglements. Interpenetrating networks and swelling prior to crosslinking are routes to networks with tailored,

chemical, static, and dynamic mechanical properties.

Keywords : Acrylate elastomer, elastic modulus, elastomers, entanglement, interpenetrating networks, network,

polyurethane, relaxation time, silicone, styrene–butadiene rubber, swelling.

3.1 INTRODUCTION

Elastomers are used in many applications and range from extremely soft gel-like materials to hard and brittle rubbers, and it is obvious that such materials have very different physical properties. Traditional elastomers are formed from crosslinking of a polymer either by use of a crosslinker or by means of radiation, and the properties of the polymer and the crosslinker (or the amount of radiation) govern to large extent the properties of the resulting elastomer. In order to design dielectric elastomer actuators it is necessary to keep in mind the possibilities and limitations of the applied elastomeric material. Different aspects of the choice of material as well as the preparation procedure are discussed in the present chapter.

3.1.1 Elastomers

The empirical definition of an elastomer is a macromolecular material that deforms substantially when exposed to small mechanical loads. Furthermore, the material almost recovers its original shape shortly after the load has been released. A more physical definition is that an elastomer is a crosslinked poly-mer material above its glass transition temperature. Three common types of elastomers are chemically crosslinked (vulcanized) rubbers, physically crosslinked thermoplastic elastomers, and polymers of suf-ficiently high chain length, where entanglements serve as physical crosslinks.

A wealth of information exists on the mechanical properties of elastomers as described in the follow-ing chapters. The dielectric properties and especially electric breakdown properties are less understood. It generally holds for any polymer that polar groups increase the dielectric constant, and at the same time increase ionic conductance and lower chain mobility and hence raise the glass transition temperature ( T g ). Poly(dimethylsiloxane) (PDMS) is an example of a polymer with low relative dielectric constant – typically between 2.5 and 3 – high dielectric breakdown strength and high chain mobility. Polyurethanes

Chapter 3

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26 Chapter 3

(PUs), which contain several polar groups compared to PDMS, follow the general trend: they have rela-tive dielectric constant in the range 3–10, they have much higher ionic conductivity at especially elevated temperatures and hence lower dielectric strength. Finally, PUs have glass transition temperatures much above those of silicones. The acrylate elastomer used in VHB ™ 4910 from 3M ™ deviates from the gen-eral trends by possessing extremely high dielectric strength when stretched, and at the same time, a rela-tive high dielectric constant, which is mostly independent of stretching [1] .

The variations in time of the dielectric constant and elastic modulus share a common origin. The effects are dominated by relaxations of the polymer – reorientation of the polymer chains under stress or in an electric field. The � -relaxation is associated with the glass transition of amorphous polymers. As the temperature service ranges of elastomers are well above T g , the relaxation typically occurs in microseconds or faster, and the relaxation poses no restriction to the speed of dielectric elastomer actu-ators or influences their properties. In polymer melts, entanglements form an important contribution to the viscoelastic properties and the disentanglement time – the time it takes a polymer chain to reptate out of its tube [2] – defines a slow relaxation process in milliseconds to seconds. In a network, the chains are fixed through chemical crosslinks; they can no more relax through reptation along their tube, and most of the entanglements are trapped. Only free ends – so-called dangling ends – and substructures attached to those can relax through a kind of breathing motion. This motion requires a strong deformation of the chain and is order of magnitudes slower than reptation motion in a melt [3] .

These relaxations of dangling ends are responsible for the slow – seconds to days – viscoelastic response observed in most elastomers. Chapter 17 illustrates how viscoelasticity affects the dynamic behaviour of acrylate elastomer actuators.

The dielectric constant is proportional to the density of polarizable groups and decreases with increas-ing temperature due to thermal expansion. The affine model for rubber elasticity (see below) states that the elastic modulus is proportional to the density of elastic active polymer chains and the temperature. For a room temperature vulcanized PDMS the decrease in density due to thermal expansion approxi-mately balances the temperature proportionality. The modulus is almost constant over a wide temperature range.

3.2 THE ELASTIC MODULUS

Elastomers possess properties of both solids and liquids, and therefore elastomers have many applica-tions in the field of soft solids, e.g. as vibration sinks in electronics, medical implants, or adhesives. Permanent, chemical, physical, or topological crosslinks contribute to the elastic behaviour, whereas long polymer chains contribute to the viscous behaviour of the material. The elasticity of elastomers are generally speaking governed by the length of elastic active chains – that is the average molecular weight of chains between crosslinks ( M x ) measured in quantities of the molecular entanglement weight ( M E ), which is a temperature-dependent characteristic material property. Generally speaking, elastomers with M x / M E � 1 are rigid and elastomers with M x / M E � 1 are soft. Traditionally the elasticity is measured by the elastic modulus ( G ) or the Young ’ s modulus ( Y ). For an elastomer, the relation between the two is

Y G� 3 (3.1)

The premise for traditional theories of rubber elasticity is that network chains stretch as simple Gaussian random coils and that their contributions to the modulus are additive. Models of elastomers in the ‘ phantom ’ limit (in which the chains are assumed to be devoid of material properties) were developed by James and Guth [4] . In such a phantom network, it is assumed that the chains move freely through one another, and that the only contribution to the elasticity arises from the network connectivity. The phantom model predicts the modulus to be proportional to the inverse of the molecular weight of the elastic active chain:

G RTf M

RTphx

� � � �( )� ��

12⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

(3.2)

where � is the moles of junctions per unit volume given by 2 � /f with f being the functionality of the crosslinker, � is the moles of elastic chains per unit volume, R is the gas constant, T is the absolute tem-perature, and � is the density of the elastomer.

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Physical and Chemical Properties of Dielectric Elastomers 27

In an affine network, on the other hand, the end-to-end chain vectors are assumed to transform aff-inely with the macroscopic deformation. The affine model does not take into account the functionality of the crosslinking agent:

G RTM

RTafx

� ��� (3.3)

It can be seen that for high functionalities, the affine and the phantom model coincide. The phantom and affine limits of deformation are two extreme cases, and experimental stress–strain measurements suggest that low-molecular PDMS networks exhibit properties between these two limits. The network is predicted to be more affine-like at small deformations and more phantom-like at larger deformations. Contributions to the modulus from topological constraints along the contour of the polymer chains are not considered in the two above models, and these so-called entanglements contribute significantly to the elastic modulus when the molecular weight of the PDMS prepolymer is increased. Langley [5] and Graessley [6] developed a phenomenological model with an additional term introduced to allow for the contribution from entanglements. The result of the model can be expressed as

G h RT G TLG o E� � �( )� � (3.4)

where h is an empirical parameter between 0 and 1, G o is the plateau modulus of the melt of uncrosslinked, high-molecular-weight prepolymer, and T E is the proportion of the maximum concentra-tion of topological constraints that contribute to the modulus, the so-called trapping factor. This result indicates that with increased molecular weight of PDMS, a plateau is obtained by

G G TM o E�� � (3.5)

The molecular entanglement weight M E is determined from the equilibrium modulus of long, linear chains G o as

GM

RToE

��

(3.6)

The time dependence of soft materials is usually described in terms of the storage modulus G ′ ( � ) and the loss modulus G ″ ( � ), where � is the frequency of the applied stress in oscillatory shear experiments. The time-dependent behaviour of elastomers may be very complex. For the completely crosslinked rub-ber, the material behaves as an ideal spring, i.e. G ′ ( � ) � G and G ″ ( � ) � 0, which means that the elas-tic modulus is constant and that there is no viscous dissipation in the material. However, real elastomers will always have some extent of viscous dissipation since ideal crosslinking is very hard to obtain. Very soft elastomers will in general have a storage modulus approaching the entanglement modulus of the corresponding linear polymer as given by Eq. (3.6). The time-dependent properties are often described by the so-called loss function:

tan( )( )( )

( )� �

��

��

�

G

G (3.7)

When tan( � ) � 1, the material is mainly elastic, and when tan( � ) � 1, the material is mainly viscous at the given frequency. For certain applications, it is favourable for the material to be viscous at a given frequency and to be elastic at another frequency, e.g. in applications where conformability and stabil-ity are wanted. This can for example be obtained by choosing network reactants with certain chemical structures and lengths. There exist a variety of elastomers and common commercially available elasto-mers operating at room temperature include polyisoprenes (also known as synthetic rubber), silicones, polyurethanes, and polyacrylates. Within the different types of elastomers, one can obtain very different properties by adding side groups to the polymer, which influences the glass forming properties and the dynamics of the elastomer. Another way to alter the properties of elastomers is to swell the elastomer in a compatible solvent. This is an easy method to obtain fast-responding, soft materials.

Styrene–butadiene rubber (SBR) is the most important synthetic rubber and the most widely used rubber in the world. SBRs are obtained by the emulsion polymerization of butadiene and styrene in varying ratios. Unlike natural rubber, SBR does not crystallize upon stretching and therefore it has low

Ch03-I047488.indd 27 12/10/2007 8:17:59 PM

28 Chapter 3

tensile strength unless reinforced. The major use for SBR is in tires and tire products. Silicone elasto-mers possess extraordinary properties due to the special characteristics of the silicon–oxygen bonds in their backbone. The silicon–oxygen bond is much stronger than the carbon–carbon bond of organic polymers, which makes silicones better electric insulators and more resistant to oxidation. Furthermore, the silicon–oxygen chain is easily twisted, and the organic side groups can rotate freely around the bonds, which gives rise to very flexible materials even at room temperature. This can be visualized by each silicone molecule occupying its own space, preventing close contact with its neighbours and as a result, silicones have weak forces of attraction, low freezing points, and low surface tension. These properties have rendered silicones ideal for variety of specialized uses where high tear strength is not required. Silicone elastomers retain their elasticity, strength, and flexibility in temperatures rang-ing from approximately −60ºC to higher than 300ºC, which clearly makes silicone elastomers capable of working under extreme conditions. Speciality grades are even elastic down to −60ºC. Other elasto-mers such as isoprenes become brittle below room temperature and degrade or decomposite at elevated temperatures. Polyurethane (PU) networks find large applicability in a wide range of areas including medical devices, mattresses, and components to the automotive industry. PU elastomers are of interest because of their versatility and variety of properties and uses. They can be used as liquids or solids in a number of manufacturing methods.

A new trend in polymeric networks has emerged, the so-called interpenetrating networks (IPNs), where mixtures of two or more crosslinked networks are held physically together via entanglements. The combination of two dissimilar polymers provides a convenient route for the modification of prop-erties to meet specific needs. The combination of varied chemical types of polymeric networks in dif-ferent compositions, often resulting in controlled different morphologies, has produced IPNs with properties that show synergism between the two components. Plastic material may attain improved toughness with an elastomeric component as the minor phase and a reinforced elastomer may result if the phase proportions are reversed [7] . An example of IPNs is the poly(ether urethane)/poly(ethyl meth-acrylate) (PU/PEMA) system where Young ’ s moduli in the range of 1 MPa (100% PUR) to 800 MPa (100% PEMA) were observed depending on the mixing ratio of the two components [8] . By altering the ratio of the two components one can also change the dynamic response of the elastomer since the two polymers will relax at two different frequencies due to the large difference in their glass transition temperatures, which is illustrated in Fig. 3.1 .

3.3 THE VULCANIZATION

The crosslinking reaction (also known as vulcanization) of polymers into elastomers can be per-formed in several ways. The traditional way of producing hard rubbers is radical vulcanization where the crosslinks are introduced randomly along the chain. However, if more controlled properties and soft materials are wanted, end-linked addition curing systems are favourable since the distance between crosslinks can be controlled and there are no byproducts. The reaction scheme for a platinum-catalysed silicone rubber is shown in Fig. 3.2 . The distance between crosslinks can also be controlled in conden-sation curing systems such as OH-chemistry, but during the crosslinking water will be produced and side reactions may occur. End-linked curing systems consist in general of a crosslinker with 3 or more reactive groups per chain (denoted by functionality f , f 3), a polymer with a reactive group positioned

tan(d)

v

A

BA � B

Figure 3.1 Illustration of the loss function of two networks (A and B) and the loss function of an IPN of the two networks.

Ch03-I047488.indd 28 12/10/2007 8:18:00 PM

Physical and Chemical Properties of Dielectric Elastomers 29

at both ends, and a catalyst. The properties of the resulting elastomer can furthermore be optimized by adding volatile or non-volatile solvent, chain extenders, resins, or other polymers interfering either chemically or physically with the network [9] .

In general, the reactants are all linear and during the vulcanization, the viscosity of the reaction mix-ture is increased. It is well known that the zero-shear-rate viscosities of linear polymer melts depend on the molecular weight in a non-simple way. For molecular weights below a critical molecular weight ( M c ) there is linear dependency but for molecular weights above M c , the scaling is stronger:

�o c( , ) ( ) ,M T K T M M M� �

�o c( , ) ( ) ,.M T K T M M M� �3 4 (3.8)

where K ( T ) is a temperature-dependent material constant. During the vulcanization, the viscosity of the reaction mixture will change dramatically, because the molecules grow longer and more branched and thereby one can get an idea of the degree of crosslinking. The viscosity and the elastic modulus are closely related, so one can follow the development of the elastic modulus as function of reaction time. In Fig. 3.3 , the time development of a silicone network with three different amounts of inert, high-viscosity silicone oil, i.e. non-volatile solvent, is shown. At the steep parts of the curves, the gelation point is obtained. The gelation point is defined as the time when there is a transition from mainly vis-cous to mainly elastic, i.e. when G ′ ( t ) � G ″ ( t ) and it usually occurs at where the curve is steepest [10] . Elastomers below the gelation threshold may seem stable, but on longer timescales such as weeks they will flow, i.e. G ′ ( t � ) � 0. For elastomers above the gelation threshold, the elastic modulus will reach a plateau on long timescales, i.e. G ′ ( t � ) � G o . However, for most traditional networks the reaction time is not a real parameter. For certain silicone networks catalysed by platinum catalyst, the vulcaniza-tion can be stopped by cooling down the reaction mixture and thereby inhibit the catalyst, which stops the network formation at a given time to give certain properties of the elastomer. However, the result-ing elastomer cannot be applied at elevated temperatures without the vulcanization proceeding further to the final harder elastomer. In the same way as with reaction time, the stoichiometry can be used to

OSi

HC

O

CH2

Si

O

Si OO

H

Si OSiO

O Si

H2C

O Si O

Si OO

CH2

Si OSiO

PtCl Cl

ClCl

Cl

Cl

2�

Figure 3.2 The reaction path of silicone network reacted from endlinked PDMS.

Ch03-I047488.indd 29 12/10/2007 8:18:00 PM

30 Chapter 3

obtain networks below and above the gelation threshold. This is shown in Fig. 3.4 where the moduli of silicone networks with different stoichiometries are measured. The stoichiometric imbalance is a more versatile parameter to optimize a material rather than the reaction time, and from the figure it is obvi-ous that the stoichiometric imbalance has large influence on the properties of the elastomer. With the same reactants one can obtain elastomers ranging from extremely soft and fragile to hard and durable. Another issue is the stability of the material since for most applications it is important to have exceeded the gelation point such that the material is stable with time, i.e. G ( � � 0) > 0. Systems just below the gelation threshold will usually behave as elastomers under normal usage but on long timescales such as several days or weeks, they will flow since the elasticity arises from entanglements between hyper-branched structures without the continuous three-dimensional structure and the material can therefore flow upon storage.

00

0.5

1

2 Model and experimental data

1.5

0.5 1 1.5 2 2.5 3 3.5Stoichiometric imbalance

�105

Equ

ilibr

ium

mod

ulus

(P

a)

Figure 3.4 The equilibrium modulus as function of the stoichiometric imbalance for a silicone network. Data points with error bars. The punctured line is model results [15].

101100

101

102

103

104

102 103 104

Time (s)

G�(

Pa)

0%5%20%

Figure 3.3 The vulcanization of a silicone network with different amounts of high-viscosity, inert silicone oil. The oil increases the distance between reactive groups without decreasing the overall viscosity of the reaction mixture, and therefore it decreases the reaction speed.

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Physical and Chemical Properties of Dielectric Elastomers 31

3.4 SWOLLEN NETWORKS

One can obtain very favourable properties of elastomers by swelling, either before or after the vul-canization. The most applicable method is to mix the reactants with the swelling agent before the vul-canization process (pre-swelling) since swelling afterwards can cause uneven elastomers as a result of small imperfections within the initial ‘ dry ’ elastomer. However, it can be favourable to swell the cured elastomer since pre-swelling may lead to extra soft and fragile networks. This is due to the dilution of trapped entanglements, which is significant for pre-swelling [11] . When pre-swelling is applied, the two contributions to the elastic modulus, namely the crosslink ( G c ) and the entanglement ( G E ) contribution, respectively, with the volume fraction of polymer in the elastic network, � , as

G G n

c E� �� �, (3.9)

where n is a parameter with value n � 2.4 for well-entangled networks [12] . If swelling is performed after curing, one may expect

G G G� � �c E � (3.10)

Soft elastomers reacted from unstoichiometric reacting mixtures generally consist of a large fraction of so-called dangling material, i.e. material chemically attached to the network but which is not elastic-ally active, except on short timescales. This fraction will give rise to dynamics with a characteristic relaxation time which scales as

�� e d E/k M M (3.11)

Here, k is a constant and M d is the average molar weight of dangling material. From this it is obvious that the swelling plays a tremendous role on the dynamics of the resulting swollen elastomer. The relax-ation time of the elastically active network fraction is also decreased due to dynamic dilution effects [13] as well as the so-called strangulation or tight-mesh effect [14] .

Another method to produce soft elastomers is to pre-swell the elastomer reactants by a volatile solv-ent and then remove the solvent after vulcanization. Thereby one has reduced the entanglement contri-bution [11] :

GG G

G T G n� � � � �c,o E,oc E o

1 (3.12)

where is the volume fraction of elastomer in the swollen system. The dynamic properties will however be comparable to a traditional network without any swelling

agent present during or after the vulcanization.

3.5 PROCESSING

Elastomers can be processed in different ways. The processing may however interfere with the resulting properties, e.g. solvent casting leads to softer elastomers than obtained from coating the reaction mix-ture without any volatile solvent present. This is due to the reduction in the concentration of physical entanglements in the elastomer when volatile solvent is present [11] . Furthermore, the mixing process may influence the elastic modulus of the network since it introduces local or overall alignment of the molecules. In Fig. 3.5 , it is illustrated how the molecules are aligned upon shear during the crosslinking

Flow(a) (b)

Figure 3.5 The network formation reaction depends on the curing conditions. (a) When no mixing is applied, the molecules are randomly distributed throughout the reaction volume. (b) When mixing is applied, the molecules will get aligned.

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32 Chapter 3

reaction and therefore a softer network is formed compared to the bulk reacted material since the con-centration of entanglements are lowered. From this, it is clear that the processing of the elastomers influences the properties of the elastomer and it can therefore be used as a parameter to optimize the material.

References

[1] Kofod , G. , Sommer-Larsen , P. , Kornbluh , R. and Pelrine , R. ( 2003 ). Actuation response of polyacrylate die-

lectric elastomers . J. Intell. Mater. Syst. Struct. , 14 , 787 .

[2] Doi , M. ( 2001 ). Introduction to polymer physics . Clarendon Press/Oxford University Press, Oxford, UK .

[3] Sommer-Larsen, P. and Larsen, A. (2004). Materials for dielectric elastomer actuators. The International Society for Optical Engineering , San Diego, CA, Proc. SPIE , 5385 , 68.

[4] James , H. M. and Guth , E. ( 1947 ). Theory of the increase in rigidity of rubber during cure . J. Chem. Phys. , 15 , 669 .

[5] Langley , N. R. and Ferry , J. D. ( 1968 ). Dynamic mechanical properties of cross-linked rubbers. VI.

Poly(dimethylsiloxane) networks . Macromolecules , 1 , 353 .

[6] Dossin , L. M. and Graessley , W. W. ( 1979 ). Rubber elasticity of well-characterized polybutadiene networks .

Macromolecules , 12 , 123 .

[7] Frisch , H. L. , Frisch , K. C. and Klempner , D. ( 1981 ). Advances in interpenetrating polymer networks . Pure Appl. Chem. , 53 , 1557 .

[8] Hourston , D. J. and Schafer , F. U. ( 1996 ). Poly(ether urethane)/poly(ethyl methacrylate) interpenetrating

polymer networks: morphology, phase continuity and mechanical properties as a function of composition .

Polymer , 37 , 3521 .

[9] Larsen , A. L. , Sommer-Larsen , P. and Hassager , O. ( 2004 ). Some experimental results for the end-linked

polydimethylsiloxane network system . e-Polymers , 050 .

[10] Chambon , F. and Winter , H. H. ( 1987 ). Linear viscoelasticity at the gel point of a crosslinking PDMS with

imbalanced stoichiometry . J. Rheol. , 31 , 683 .

[11] Larsen, A. L., Sommer-Larsen, P. and Hassager, O. (2004). How to tune rubber elasticity. Smart Structures and Materials 2004: Electroactive Polymer Actuators and Devices (EAPAD) , Proc. SPIE , 5385 , 108.

[12] Venkatraman , S. ( 1993 ). Deformation behavior of poly(dimethyl siloxane) networks. 1. Applicability of vari-

ous theories to modulus prediction . J. Appl. Polym. Sci. , 48 , 1383 .

[13] Milner , S. T. and Mcleish , T. C. B. ( 1997 ). Parameter-free theory for stress relaxation in star polymer melts .

Macromolecules , 30 , 2159 .

[14] Degennes , P. G. ( 1986 ). Conjectures on the transport of a melt through a gel . Macromolecules , 19 , 1245 .

[15] Larsen , A. L. , Hansen , K. , Sommer-Larsen , P. , Hassager , O. , Bach , A. , Ndoni , S. and Jorgensen , M. ( 2003 ).

Elastic properties of nonstoichiometric reacted PDMS networks . Macromolecules , 36 , 10063 .

Ch03-I047488.indd 32 12/10/2007 8:18:01 PM

HIGH-PERFORMANCE ACRYLIC AND SILICONE ELASTOMERS

Roy Kornbluh and Ronald Pelrine

SRI International, Menlo Park, CA, USA

Abstract

One of the strengths of dielectric elastomer technology is the wide range in material properties that can be used.

Polymers as soft as gels and as hard as relatively rigid thermoplastics can act as the dielectric layer in dielectric elas-

tomers. Simple analysis reveals desired material requirements for high performance, dielectric elastomer transduc-

tion, such as high breakdown strength, low modulus, high permittivity and good elastic properties. One must often

make trade-offs among desired properties in selecting the ideal material. A great many polymers have been shown to

have good performance (e.g. strain response greater than 10%). Compared with other polymers, polymer dielectrics

based on commercially available silicones and acrylic elastomers show good overall performance characteristics

and continue to be used for the most applications and studies. Comparing the two, silicones have very high speeds

and exceptional temperature tolerance, but acrylics have higher strains and energy density. The limitation on acrylic

speed of response is due to viscoelasticity. Chemical and processing modifications are possible to improve acrylic

speed of response, and along with the discovery and development of new silicones is an active area of research.

Keywords : Actuation pressure, acrylate, acrylic, efficiency, elastomers, energy density, polydimethyl siloxane,

silicone, speed of response, strain.

4.1 INTRODUCTION

The very name ‘ dielectric elastomer ’ conveys the importance of the dielectric polymer layer in determin-ing the performance of the dielectric elastomer transducer. While the performance of these transducers is dependent on the electric and mechanical properties of the dielectric polymer layer, one of the unique aspects of dielectric elastomers is that many different polymer layers may be used. The polymer may range from extremely soft thermoset gels to relatively rigid thermoplastics, which may not even be considered ‘ elastomers ’ . It is even possible to select a polymer whose properties are tailored for the desired applica-tion. In this chapter, we first look at the basic equations that relate the polymer material properties to the performance of dielectric elastomer transducers. Then we provide a brief overview of the performance of a range of polymers. This basic background sets the stage for an in-depth discussion of the performance of two of the more successful classes of dielectric elastomers, silicones and acrylics. While much of the discussion focuses on actuators, the same factors influence the application to generators. Application of silicones and acrylics to generators is gaining increasing interest and is discussed in detail in Chapter 15.

4.2 BASIC MODEL OF OPERATION

Dielectric elastomers are based on the interaction between the electrostatic charges on opposite sides of the elastomeric film. Derivation of the electrostatic model is described by Pelrine et al. [1] and elsewhere in this book. Here we just summarize.

The actuation pressure p is given by

p EV

z� ��� ��0 0

2

2⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

(4.1)

Chapter 4

Ch04-I047488.indd 33 12/10/2007 8:19:48 PM

34 Chapter 4

where E is the electric field, � is the dielectric constant, � 0 is the permittivity of free space, V is the volt-age and z is the polymer thickness. For small strains with free boundary conditions, the polymer thick-ness strain s z is given by

S

p

Y

V z

Yz � � � ���0 /( )2

(4.2)

where Y is the modulus of elasticity. The model for large strains with more realistic constrained bound-ary conditions, such as those required to drive a load, is more complex. However, this simple case illustrates the influence of the electrical and mechanical properties of the polymer on actuation per-formance. The model also assumes that the elastomer is an ideal rubber, that is, the rubber is incom-pressible and has a Poisson ’ s ratio of 0.5.

One of the more useful metrics for comparing actuator materials, independent of size, is the energy density of the material. The actuator energy density is the maximum mechanical energy output per cycle and per unit volume of material. While the actual energy output of the material depends on the loading condition, the case where the actuator does no external work is often used to compare different materi-als without regard to loading conditions. In this case, the energy is actually the internal elastic energy of deformation. For small strains with free boundary conditions and no load, the actuator energy density e a of the material can be written as

e Ys

V z

Yza0 /

� �22 4( ) ( )��

(4.3)

Conventionally, the elastic energy density e Ysze12

(� ) 2 is often used. However, for large strains with a linear stress–strain relation, this formula must be modified because as the thickness strain becomes increasingly negative, the film flattens out and the area over which the pressure must be applied increases. A more detailed derivation for large strains gives the formula for the elastic energy density of materials with a linear stress–strain relation as

e Y s sz ze ln� � �[ ( )]1 (4.4)

This equation agrees with the more common formula at small strains but is significantly higher for strains greater than 20%.

The validity of the electrostatic model and the above equations has been well established (e.g. [2] ). It can be clearly seen from the equations that dielectric elastomer performance depends on the macroscopic permittivity of the polymer as well as on its modulus of elasticity. Further, it is clear that it is desirable to have a high electrical breakdown strength in order for the response to be as large as possible.

Beyond these fundamental guidelines for quasistatic operation, there are several other material fea-tures that might be optimized for improved dynamic response. These features include:

● high bulk resistance and low electrical loss factor for high efficiency; ● low viscoelastic damping for high efficiency; ● good electrical fatigue properties for high durability; ● good mechanical fatigue properties and low creep.

There are also several features that are of practical consideration in selecting a material for ease of fabrication and a given application:

● good tolerance to temperature and humidity; ● ease of processing into thin uniform films with few defects for manufacturability and high yield.

4.3 OVERVIEW OF POLYMER PERFORMANCE

As the number of researchers working on dielectric elastomers increase, so too does the variety of poly-mers under consideration. Table 4.1 , adapted from [2] shows the performance of a variety of polymers using the circular actuation test. This table is not exhaustive nor does it reflect the greatest performance achieved with each class of polymer. However, it does serve to show that good response was achieved with a variety of polymers and also shows why much early work has focused on silicones. It will also be obvious by reviewing this table why acrylics were to become of great interest.

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High-Performance Acrylic and Silicone Elastomers 35

4.4 SILICONES AND ACRYLICS

We have obtained the best overall results with silicone rubber films (based on a polydimethyl siloxane backbone) and an acrylate elastomer, specifically that of the 3M Company (St. Paul, Minnesota, USA) VHB 1 acrylic series.

Table 4.2 summarizes the measured performance of the best silicones and acrylics. Although, as the earlier data in Table 4.1 demonstrates, good response was achieved in some sili-

cones and other polymers, the data in Table 4.2 demonstrate a significant improvement. While some of the improvement can be attributed to the discovery of new materials and improved electrodes, much of the improvement in material performance is due to the discovery of the importance of prestrain, that is, the initial strain loading condition. The introduction of a high amount of prestrain (produced by stretching and holding the film in tension before measurements are made) can significantly increase the maximum strain and pressures that can be generated within a given film [3] . Figure 4.1 shows the effect of vari-ous amounts of prestrain on the measured strain response of a silicone film. Note that the amount of prestrain can also determine the maximum stress generated within the film, since the maximum electric field that the film can withstand before breakdown may be increased. As per Eq. (4.1), the maximum pressure depends on the square of the applied electric field.

In acrylic, the effect of prestrain on breakdown strength is even more dramatic. From no prestrain to a biaxial prestrain of 500% � 500%, the practical breakdown field in dielectric elastomers increased by almost 10 times [4] .

Table 4.1 Maximum response of representative elastomers in early research by SRI International.

Polymer (Specific Type)

Elastic Energy Density (J/cm 3 )

Pressure (MPa)

Strain (%)

Young ’ s Modulus* (MPa)

Electric Field (V/mm)

Dielectric Constant (at 1 kHz)

Coupling Efficiency, k 2 (%)

Silicone Nusil CF19-2186

0.15 0.72 32 1.0 235 2.8 54

Silicone Dow Corning HS3 (centrifuged to remove particulates)

0.038 0.13 41 0.125 72 2.8 65

Polyurethane Deerfield PT6100S

0.20 3.8 11 17 160 7.0 21

Silicone Dow Corning Sylgard 186

0.10 0.50 32 0.7 144 2.8 54

Fluorosilicone Dow Corning 730 (centrifuged to remove particulates)

0.051 0.29 28 0.5 80 6.9 48

Fluoroelastomer LaurenL143HC

0.016 0.39 8 2.5 32 12.7 15

Polybutadiene Aldrich PBD

0.025 0.41 12 1.7 76 4.0 22

Isoprene Natural Rubber Latex

0.010 0.19 11 0.85 67 2.7 21

*Average engineering modulus at the maximum strain.

1 All product or company names mentioned in this document are the trademarks of their respective holders.

Ch04-I047488.indd 35 12/10/2007 8:19:48 PM

36 Chapter 4

Table 4.2 Performance of best Silicones and acrylics.

Parameter Acrylics Silicones Comment

Maximum actuation strain (%)

380 120 Strain in generator and sensing modes can be greater than that in actuation

Maximum actuation pressure (MPa)

8.2 3.0 Blocked stress

Maximum specific energy density in actuation (MJ/m 3 )

3.4 0.75 Greatest energy density of all field-activated materials; can theoretically be greater in generator mode

Maximum frequency response (Hz)

� 50 000 � 50 000 Small-strain acoustic measurements; frequency response is very dependent on strain and size; full response of acrylic is generally much lower, due to viscoelasticity (see mechanical loss factor below)

Maximum electric field (MV/m)

440 350 Maximum fields are realizable only in uniform films with few defects

Relative dielectric constant

4.5–4.8 2.5–3.0 Measured at 1 kHz; small drop-off at higher frequencies

Dielectric loss factor 0.005 � 0.005 Measured at 1 kHz Elastic modulus (MPa) 0.1–3.0 0.1–2.0 Elastic modulus is typically nonlinear with

respect to strain; these values are averages over a typical range of strain

Mechanical loss factor 0.18 0.05 Loss factor of acrylics varies with strain and other conditions

Maximum electromechanical coupling, k 2

0.9 0.8 Similar to that of the best field-activated materials such as single-crystal piezoelectric ceramics

Maximum overall efficiency (%)

� 80 � 80 Assumes ideal driving electronics; the efficiency depends on the actuation frequency

Durability (cycles) � 10 000 000 � 10 000 000 Durability is highly dependent on how close the driving voltage is to the maximum field

Operating range (°C) � 10 to 90 � 100 to 260 Short-term range; long-term range has yet to be determined

0.00

�0.05

�0.10

�0.15

�0.20

�0.25

�0.30

�0.35

�0.40

�0.45

Rel

ativ

e st

rain

(S

z)

0 50 100 150 200 250 300 350 400 450

Electric field (MV/m)

Nusil CF 19-2186,biaxially prestrained bythe following amounts inboth x and y :

15%

33%

35%

45%

93%

115%

Figure 4.1 Effect of prestrain on strain response (NuSil Corp., Carpinteria, California, USA; CF19-2186) (adapted from [5] ).

Ch04-I047488.indd 36 12/10/2007 8:19:48 PM

High-Performance Acrylic and Silicone Elastomers 37

It should be noted that the stretch need not be uniform in both in-plane directions. In the latter case, the film tends to actuate primarily in the direction with lower strain. The principal reason for this observed effect is due to the increase in the local elastic modulus of the material in the direction of the higher prestrain. The film would tend to deform more in the softer, less prestrained direction. Geometric edge constraints can also produce strains almost exclusively in one direction. For example, if the actuation area is a thin line that spans the width of the rigid frame, then the in-plane strain will be produced almost exclusively in the transverse in-plane direction (orthogonal to the long direction of the line), provided that the actuated stress does not exceed the prestrain stress in the width direction. When such a geometric constraint is combined with anisotropic prestrain, extremely large strains in a single direction have been observed. We have used this approach to produce linear strains of more than 100% in silicones and more than 300% in acrylics. An example of an acrylic film loaded in this manner is shown in Fig. 4.2 . The use of anisotropic prestrain to enhance actuation in a given desired direction is the basis of several actuator configurations discussed in Chapter 8.

4.5 DYNAMIC RESPONSE

Although, as Table 4.2 indicates, both silicones and acrylics have demonstrated response at high fre-quencies, the dynamic response of silicones and acrylics can differ greatly. It is therefore worth looking more closely at dynamic response issues. This discussion is adapted from [5] .

4.5.1 Efficiency

The overall efficiency of an actuator is affected by the electrical and mechanical losses within the material as well as losses in the electric driver circuitry. These losses in the drive circuitry reflect, to some extent, the ability of the actuator to convert a high percentage of the applied electrical energy to mechanical work and thus depend on the fundamental properties of the actuator. Table 4.3 shows the necessary material properties and derived parameters of our best dielectric elastomers. Note that the elastic modulus and loss factor are, in general, functions of frequency and, to a lesser extent, of

Table 4.3 Efficiency-related characteristics of dielectric elastomer films.

Material Effective Modulus (MPa)

Relative Dielectric Constant

Dielectric Loss Factor tan d e

Mechanical Loss Factor tan d m

Electro-mechanical Coupling Factor, k 2 (%)

Overall Maximum Efficiency h t (%)

Dow Corning HS3 silicone (centrifuged)

0.1 2.8 at 1 kHz 0.005 at 1 kHz 0.05 at 80 Hz 79 82 at 80 Hz

NuSil CF19-2186 silicone

1.0 2.8 at 1 kHz 0.005 at 1 kHz 0.05 at 80 Hz 63 79 at 80 Hz

3M VHB 4910 acrylic

3.0 4.8 at 1 kHz � 0.005 at1 kHz

0.18 at 20 Hz 90 80 at 20 Hz

(a) (b)

Figure 4.2 Linear-motion-stretched film actuator showing approximately 200% linear strain: (a) voltage off and (b) voltage on.

Ch04-I047488.indd 37 12/10/2007 8:19:49 PM

38 Chapter 4

amplitude and initial strain conditions. The values in Table 4.3 represent average values over the range of frequencies achievable with our measurement apparatus. The effect of frequency on the viscoelastic properties of the polymers is shown in Fig. 4.3 . The elastic modulus does not vary significantly over the range of frequencies tested. These measurements were made with an EnduraTEC (Minnetonka, Minnesota, USA) Dynamic Mechanical Analyzer (DMA). The DMA consists primarily of a servo-controlled voice coil and force transducer mounted to a rigid frame. A computer automatically sweeps through a range of frequencies and derives the modulus and loss factor from the dimensions of the sample polymer and the preset amplitude. In this case, the prestrain can be applied in only one direc-tion, so the loading conditions are not the same as those for our stretched film samples. However, this approximation is not expected to affect the qualitative conclusions.

The efficiency is related to the electrical and mechanical loss factors, � e and � m , respectively, as

�

� ��

� �ee

mmtan tan

��

��

1

1

1

1( ),

( ) (4.5)

It appears that the mechanical losses dominate the electrical losses, although more data are needed to measure the electrical dissipation factor at low frequencies. At low frequencies, the leakage of charge across the polymer film can dominate the electrical losses. In such cases, the electrical efficiency may be approximated by

�

� � �er 0

��

1

1 2 2( / (( ) ))Y E f (4.6)

where � is the bulk resistivity of the polymer and f is the frequency in hertz. That the electrical effi-ciency is dependent on frequency is not surprising. The relative amount of energy lost from electrical leakage increases with the amount of time that the voltage is applied across the electrodes during an actuation cycle.

The efficiency of the electric driver circuit can be included in the overall efficiency by consideration of the electromechanical coupling efficiency k 2 . (The square of k is used for consistency with the con-ventional nomenclature for piezoelectrics.) The electromechanical coupling factor is defined as follows:

k2 ��

nergy converted into mechanical work per cycle

Electriccal energy applied per cycle (4.7)

Materials with low coupling efficiencies are difficult to operate efficiently even if there is no intrin-sic energy loss mechanism (low electrical and mechanical loss factors) because low coupling requires a large amount of electrical energy to be removed or recovered from the actuator relative to the work output. Even with high-efficiency (e.g. 90% efficient) recovery circuits, if the coupling is too low, too much energy is lost in the recovery electronics, relative to the work output per cycle.

Coupling efficiency is often difficult to measure directly, but we can use the electrostatic model (in which the permittivity of the material does not change) to estimate the dielectric elastomer coupling efficiency, based on the capacitance change for the given strain (assuming no losses). This analysis, given by [2] , yields

k s sz z

2 22� � � (4.8)

20 40 60 800Frequency (Hz)

Acrylic

Silicone

0

0.2

0.4

0.6

0.8

1E

last

ic m

odul

us (

MP

a)

Loss

ang

le (

degr

ees)

20 40 60 800Frequency (Hz)

Acrylic

Silicone

252015

10

5

0

Figure 4.3 Measurements of the elastic modulus and loss factor of silicone (Nusil CF19-2186) and acrylic poly-mer (3M VHB 4910) samples in uniaxial loading.

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High-Performance Acrylic and Silicone Elastomers 39

The efficiency of the actuator, based on the coupling factor and the efficiency of the electric driver cir-cuit in recovering charge, is

��d

rec

�� �

k

k

2

21 1[ ( )] (4.9)

where � rec is the efficiency of the driver circuit. Note that if no charge recovery is used ( � rec � 0), the maximum efficiency of the actuator is � d � k 2 .

(The mechanical and electrical losses usually are included in k 2 , that is, multiply k 2 of Eq. (4.8) by � e � m ; however, in order to isolate the effect of energy recovery, we have treated them separately.)

The overall efficiency is

� � � �t e m d�

(4.10)

Typical estimated efficiencies of the best dielectric elastomer materials are shown in Table 4.3 . The overall efficiency, based on Eq. (4.10), assumes 90% energy recovery and uses the average values for electrical and mechanical issues. Note that the coupling efficiencies are given under conditions of maxi-mum strain and are likely to be greater than the efficiencies produced in practical actuators. Nonetheless, the overall efficiencies are competitive with or better than those of other field-activated materials.

4.5.2 Speed of response

The speed of response cannot easily be calculated from the measurable material properties because many different factors come into play, including the actuator size and configuration as well as the driv-ing electronics. Nonetheless, some simple observations and calculations can provide rough estimates. We also present some simple direct measurements of the speed of response.

We first note that the electromechanical response is produced by the electrostatic forces on the elec-trodes, so no significant delay should be associated with an intrinsic response mechanism of the pol-ymer. This assumption is supported by the fact that the dielectric constant of the materials does not change appreciably over the range of 100 Hz to 100 kHz.The fundamental limitation in response speed would then be due to the speed at which the pressure wave can propagate through the material (basi-cally the speed of sound). Since the individual polymer layers are thin, this propagation time can be less than a millionth of a second. More typically, the limitation on the speed of response is due to the mechanical resonance of the actuator and driven load.

Other response speed limitations arise from the RC time constant of the actuator. Typical surface resistivities of our electrodes are on the order of tens to hundreds to thousands of ohms, so the RC time constant need not be a limiting factor for most small devices. For example, a 10 cm 2 area of silicone film that is 50 � m thick could achieve a 1 kHz response bandwidth with electrodes whose surface resistivities exceed 10 5 � . The speed of response, based on the RC time constant, is size dependent (the capacitance scales with the film area). However, the individual electrodes could be comprised of many individual film areas that are electrically connected in parallel, so as to effectively reduce the surface resistivity of the individual electrodes. For example, electrically connecting in parallel the electrodes of many indi-vidual film layers of a multilayer actuator would have this effect. However, this approach could also be used on individual electrodes: thin higher conductivity traces could be used to distribute charge over the surface of an electrode and thereby reduce the effective resistance. This ‘ structured electrode ’ approach is described in more detail by Kornbluh et al. [2] . Since the RC time constant can be manipulated by the actuator design, it is not a fundamental limitation on the speed of response of the technology.

Figures 4.4 and 4.5 show the frequency response of acrylic and silicone, respectively. The materi-als were actuated to produce in-plane strains with a circular area at the centre of a stretched film. This setup is nearly identical to that used to measure the circular strain response described in Section 4.5.1. A sinusoidal voltage from a high-voltage amplifier (Lasermetrics 8403) was applied to the electrodes. The strain response was observed optically through a digital video system. At high frequencies the ampli-tude of the strain response could be measured by the length of the blurred path of a small feature on the electrode.

The silicone produced an essentially flat strain response up to about 400 Hz, with a resonance peak at about 1425 Hz. The response rolls off above this resonance point, as would be expected with the intro-duction of higher modes. The observed resonant peak corresponds closely to that predicted from the

Ch04-I047488.indd 39 12/10/2007 8:19:50 PM

40 Chapter 4

fundamental resonance of the in-plane strain response, based on a simplified lumped parameter model (where we have assumed that the characteristic length is equal to the diameter of the circular area and the driven load of inactive material that has a mass equal to half that of the active material).

This correspondence suggests that mechanical resonance of the system due to the elasticity and mass (density) of the material is indeed the limiting factor in response speed. The results also suggest that the elastic modulus and loss factor do not increase significantly at frequencies up to 3 or 4 kHz, which in turn suggests that we can maintain good efficiency at frequencies up to this limit.

The results from the acrylic tell a different story. The frequency drop-off cannot be explained solely by the increase in the mechanical loss factor with frequency. The effect of the loss factor on the relative amplitude is given by

Strain

Strain at low frequency tan m

��

1

1 2 0 5[ ] .� (4.11)

This curve, based on data from the loss factor measured by the DMA, is included in Fig. 4.4. Equation (4.11) is strictly valid only for small amplitude strains, but the error at the strains in these speed of response measurements should not be significant. It is possible that the resistance of the electrodes increases dramatically with strain, and thus that the RC time constant of the material is a limiting fac-tor in these particular measurements. This possibility is supported by the observations that larger elec-troded areas have an even slower speed of response and that this speed of response appears to decrease even further as the material expands. Since the acrylic has exceptional performance, it is desirable to better understand what limits its speed of response.

It should be noted that the loss factor for acrylic is highly dependent on the amount of prestrain. In general, more highly strained acrylic will have lower losses. The tests here were conducted with

Frequency (Hz)

Measured

Predicted based on measured loss factor1.2

1

0.8

0.6

0.4

0.2

0

Nor

mal

ized

res

pons

e

1 10 100 1000 10 000

Baseline strain at 1 Hzsx � sy � 15%

Figure 4.4 Frequency response of an acrylic stretched film actuator.

1 10 100 1000 10 000Frequency (Hz)

00.5

1.51

22.5

33.5

44.5

Nor

mal

ized

res

pons

e

Baseline strain at 1 Hzsx � sy � 12%

Figure 4.5 Frequency response of a silicone stretched film actuator.

Ch04-I047488.indd 40 12/10/2007 8:19:50 PM

High-Performance Acrylic and Silicone Elastomers 41

300% � 300% biaxial prestrain. It has also been observed that the losses in acrylic are temperature dependent with higher temperatures generally showing lower losses. In fact, 3M makes materials simi-lar to VHB that are sold as damping materials. Each material is optimized for a relatively narrow tem-perature range.

4.5.3 Creep and stress relaxation

In addition to the higher frequency effects discussed above, dielectric elastomer materials are subject to creep or stress relaxation.

Creep and stress relaxation are known to be particularly small in silicones (for an elastomer). For acrylic, creep and stress relaxation can be significant. The requirement for high prestrain further exacer-bates creep and stress relaxation. Creep and stress relaxation can affect the usage of acrylics in some appli-cations requiring high precision. Fortunately, many actuator designs, such as those that use push–pull or antagonistic pairs configurations can minimize creep. Such designs are discussed elsewhere in this book.

4.6 ENVIRONMENTAL CONSIDERATIONS

An actuator must maintain acceptable performance over the range of environmental conditions it might encounter. In most cases, the environmental conditions of interest are temperature and humidity. In some other applications, such as usage in space, factors such as radiation (e.g. solar), outgassing and chemical compatibility may be important.

Dielectric elastomers such as acrylics and silicones have not yet been rigorously tested for perform-ance and lifetime over a range of temperatures and humidities, although some studies have been per-formed. Further, projections can be based on knowledge of the basic physical phenomena. The physical basis of the electromechanical response of dielectric elastomers is electrostatics. Electrostatic forces do not themselves vary with temperature or other environmental factors, so that one can focus on the mechanical and electrical properties of dielectric elastomers in estimating their environmental toler-ance. If these properties are not themselves adversely affected by environmental conditions, then the actuator itself will not be affected.

Silicones are intriguing because they not only exhibit good performance, but also exhibit stable mechanical properties over a fairly wide range of temperatures. For example, one silicone (CF19-2186, NuSil Corporation, Carpinteria, California, USA) has been shown to have similar performance over a temperature range of � 65 ºC to 240 ºC [6] . While we do not expect the material to sustain its maximum performance over such a temperature range, we do expect that acceptable performance can be sustained over the range of temperatures seen in many applications. Another silicone rubber was shown to be capable of operation at temperatures below � 100°C [6] .

Silicones are also known to have low rates of moisture absorption, so changes in humidity should not affect performance significantly.

Acrylic dielectric elastomer does not have as large a temperature range as the silicones. They have been shown to operate over a range of � 10°C to 80°C, enough for many applications.

To some extent, it is possible to select a dielectric elastomer material with a desired temperature range. For example, if high-temperature operation is important, one would likely select a silicone rather than an acrylic.

While normal atmospheric variations in the humidity are not expected to greatly affect the perform-ance of some dielectric elastomer materials, long-term immersion might require coatings of mois-ture-proof materials. It is of course critical that the actuator be designed so that moisture cannot create a short circuit across the electrodes. Since the electrodes are exposed to high voltage, even a small amount of moisture could create a short.

4.7 FUTURE IMPROVEMENTS AND DISCUSSION

While the discovery of commercially available silicones and acrylics as the basis of top performing classes of materials was reported in 1995 and 2000 for silicone and acrylic, respectively, these materi-als continue to attract the most interest for applications. There has also been interest in improving com-mercially available silicones and acrylics specifically for improved dielectric elastomer performance.

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42 Chapter 4

These improvements address desirable material factors such as those discussed in Section 4.2. Both sili-cones and acrylic have rich chemistries, and can be made with widely different properties. Thus, further modifications even within these basic classes of elastomer may greatly enhance dielectric elastomer performance. For example, Larsen et al. [7] discussed how to tune rubber elasticity by manipulating the amount of cross-linking and mechanical processing and therefore the resulting stress–strain curve. This ‘ tuning ’ can allow for optimizing the breakdown and modulus, and could be of particular value in opti-mizing performance for given specific applications.

The mixing of small high-dielectric-constant particles, such as certain ceramics, in an effort to increase the permittivity of the resulting composite elastomer has been reported by several groups (e.g. [8] ). Unfortunately, increases in dielectric constant are typically accompanied by an undesirable decrease in breakdown strength and an increase in electrical losses. Thus, while the performance of such polymers at a given voltage or field is good, the overall maximum strains or stresses produced by such materials are typically not as high as the lower-dielectric-constant materials already in use.

Of all the elastomer properties, possibly the electric breakdown strength is the most important, since the output is proportional to the electric field to a power of two as discussed in Section 4.2.

As noted, prestrain has been shown to enhance the electric breakdown field tremendously in VHB 4910. Unfortunately, high prestrain has some drawbacks such as requiring special frames or structures to main-tain and the possibility of tearing. Some researchers have attempted to get the benefits of prestrain without the drawbacks. Pei [9] ‘ locked in ’ the prestrain by soaking the material in a monomer material, which is allowed to diffuse the VHB 4910 completely, and then cross-linked by increasing the temperature.

Pei [9] also showed that certain chemical additives could be added to acrylic in order to reduce the viscoelastic damping. He showed an increase in the half-power frequency bandwidth by more than a factor of two by using such additives.

Even without the future improvements discussed here, silicones and acrylics continue to be the basis of most successful dielectric elastomer devices to date. The improvements to these materials can further the successful use of these materials in future devices.

References

[1] Pelrine , R .E. , Kornbluh , R. D. and Joseph , J. P. ( 1998 ). Electrostriction of polymer dielectrics with compliant

electrodes as a means of actuation . Sens. Act. A Phys. , 64 ( 1 ), pp. 77 – 85 .

[2] Kornbluh, R., Pelrine, R., Joseph, J., Heydt, R., Pei, Q. and Chiba, S. (1999). High-field electrostriction of

elastomeric polymer dielectrics for actuation. In Smart Structures and Materials 1999: Electroactive Polymer Actuators and Devices , Ed. Bar-Cohen, Y., Proc. SPIE , 3669 , 149–161.

[3] Pelrine , R. , Kornbluh , R. , Pei , Q. and Joseph , J. ( 2000 ). High-speed electrically actuated elastomers with over

100% strain . Science , 287 ( 5454 ), pp. 836 – 839 .

[4] Kofod, G., Kornbluh, R., Pelrine, R. and Sommer-Larsen, P. (2001). Actuation response of polyacrylate die-

lectric elastomers. In Smart Structures and Materials: Electroactive Polymer Actuators and Devices (EAPAD) , Ed. Bar-Cohen, Y., Proc. SPIE , 4329 , 141–147.

[5] Kornbluh, R., Pelrine, R., Pei, Q., Oh, S. and Joseph. J. (2000). Ultrahigh strain response of field-actuated

elastomeric polymers. In Smart Structures and Materials 2000: Electroactive Polymer Actuators and Devices (EAPAD) , Ed. Bar-Cohen, Y., Proc. SPIE , 3987 , June, 51–64.

[6] Kornbluh, R. D., Flamm, D. S., Prahlad, H., Nashold, K. M., Chhokar, S., Pelrine, R., Huestis, D. L., Simons, J.,

Cooper, T. and Watters, D. G. (2003). Shape control of large lightweight mirrors with dielectric elastomer actua-

tion. In Smart Structures and Materials 2003: Electroactive Polymer Actuators and Devices (EAPAD) , Ed. Bar-

Cohen, Y., Proc. SPIE , 5051 , 143–158.

[7] Larsen, A. L., Sommer-Larsen, P. and Hassager, O. (2004). How to tune rubber elasticity. In Smart Structures and Materials: Electroactive Polymer Actuators and Devices (EAPAD) , Ed. Bar-Cohen, Y., Proc. SPIE , 5385 ,

108–117.

[8] Szabo , J. P. , Hiltz , J. A. , Cameron , C. G. , Underhill , R. S. , Massey , J. , White , B. and Leidner , J. ( 2003 ).

Elastomeric composites with high dielectric constant for use in Maxwell stress actuators . Proc. SPIE Smart Struct./NDE , 5051 , pp. 180 – 190 .

[9] Pei, Q., Pelrine, R., Rosenthal, M. A., Stanford, S., Prahlad, H. and Kornbluh, R. D. (2004). Recent progress

on electroelastomer artificial muscles and their application for biomimetic robots. In Smart Structures and Materials 2004, Electroactive Polymer Actuators and Devices (EAPAD) , Ed. Bar-Cohen, Y., Proc. SPIE , 5384 ,

41–50.

Ch04-I047488.indd 42 12/10/2007 8:19:50 PM

INTERPENETRATING POLYMER NETWORKS AS HIGH PERFORMANCE DIELECTRIC ELASTOMERS

Soon Mok Ha 1 , Wei Yuan 1 , Qibing Pei 1 , Ronald Pelrine 2 and Scott Stanford 2

1 Department of Materials Science and Engineering, University of California, Los Angeles, CA, USA 2 SRI International, Menlo Park, CA, USA

Abstract

Interpenetrating polymer networks (IPNs) are introduced as new dielectric elastomer artificial muscles. The IPN

films were prepared by diffusing polymerizable additive into highly prestrained VHB acrylic elastomer films and

subsequently curing the additive to form the second elastomeric network. The resulting free-standing IPN films con-

tain one network at high tension balanced by the other network under compression. Extraordinarily high actuation

performance has been obtained at zero external prestrain. Strains up to 300% in area expansion have been achieved

at an electrical field of 420 MV/m. The IPN films can potentially enable a number of soft, all-polymer actuators

containing no rigid structural elements.

Keywords : Dielectric elastomer, interpenetrating polymer networks, polymer actuator, prestrain.

5.1 INTRODUCTION

Since Pelrine et al. reported giant electrically induced strain from dielectric elastomers, also known as electroelastomers, it has become obvious that prestrain significantly enhances performance by increas-ing the dielectric breakdown strength [1–3] particularly with acrylic elastomers. Even though the elec-trically induced strain can be as high as 380%, the overall performance of the dielectric elastomers is substantially lower when packaged to support the required high prestrain. Disparities in performance between the active material and the packaged actuators are due to a large fraction of the rigid structure needed to hold prestrain [4, 5] . In addition, the lifetimes of the multilayer actuators are limited due to the stress concentration at the interfaces between the soft polymer film and the rigid supporting struc-ture. The prestrained films also exhibit stress relaxation which affects the subsequent actuation [6] . For these reasons, the challenge is to eliminate prestrain stresses in the actuator while retaining prestrain ’ s performance benefits. One attractive approach is ‘ locked-in prestrain ’ where the film is stretched, its pre-strain locked in, and subsequently released. This approach follows two parallel paths: (1) impregnating the dielectric elastomer with a curable additive (the chemical approach) and (2) laminating a second layer to the dielectric elastomer (the mechanical approach). This chapter reviews the chemical approach, the interpenetrating polymer networks (IPNs), to new dielectric elastomers enabling the design of high performance actuators without mechanical prestrain. More specifically, the chapter will focus on the development of IPN dielectric elastomers based on the VHB network and the additive network formed with different functionality monomer.

5.2 CONCEPTS FOR IPN DIELECTRIC ELASTOMERS

An IPN is defined as a combination of two or more polymers that form a network, in which at least one polymer is polymerized and/or crosslinked in the immediate presence of the others. Therefore, IPNs involve specific techniques of mixing owing to their crosslinked nature. The six basic kinds of IPNs are described in the literature [7] : simultaneous interpenetrating networks (SIN), latex IPN, gradient

Chapter 5

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44 Chapter 5

IPN, thermoplastic IPN, semi-IPN, and sequential IPN. Among the various IPNs, sequential IPN is the most suitable to prepare an internally locked-in prestrain of the first network by the second. Classically, sequential IPNs include many potential materials where the synthesis of one network follows the other. First, a matrix polymer network is synthesized. Then, the other monomer plus crosslinker and activator are diffused into matrix networks and polymerized in situ. In this approach, acrylic elastomers were used as the initial elastomeric network in order to take advantage of the high dielectric breakdown field obtained in highly prestrained acrylic elastomer films. Polymerizable and crosslinkable liquid mono-mers were introduced into highly prestrained acrylic films and cured to form the second elastomeric network [8, 9] . When the interpenetrating elastomeric network films were allowed to relax at zero external stress, the acrylic network would contract, compressing the additive network. The resulting free-standing films consist of two networks in balance; one in high tension and the other in high com-pression. Consequently, the molecular, nanometre, and micrometre-scale alignments may be preserved in the resulting free-standing films. A schematic explanation of this approach is shown in Fig. 5.1 .

5.3 SYNTHESIS OF IPN DIELECTRIC ELASTOMER

5.3.1 Materials

An acrylic copolymer elastomer, which is commercially available as a 1-mm thick adhesive film (3 M, VHB 4910), was used as the dielectric elastomer network. The film is extremely compliant and has a quite uniform surface. In forming an additive network in the acrylic network, a difunctional acrylate monomer or a trifunctional methacrylate monomer was used. The thermally curable 1,6-hexanediol dia-crylate (HDDA) was purchased from Sartomer Co. It has two acrylate functional groups per molecule, a molecular weight of 226 Da, and a viscosity of 9 cps at room temperature. The thermally curable, trifunctional trimethylolpropane trimethacrylate (TMPTMA) purchased from Sigma Aldrich, has a molecular weight of 338 Da. Benzoyl peroxide was used as a thermally activated initiator for free-radi-cal polymerization. Benzoyl peroxide is soluble in HDDA and TMPTMA.

5.3.2 Preparation of IPN in highly prestrained elastomer films

The fabrication of IPN composite films began with the biaxial stretching of acrylic films. The struc-tures to support the stretched films are made of Masonite to minimize thermal deformation. The films were stretched to five times its original length and width, i.e. 400% biaxial prestrain. The film thickness after the prestrain was 40 µm for VHB 4910. The diacrylate and trimethacrylate monomers were added into the prestrained VHB films. Benzoyl peroxide, a thermal initiator for free-radical polymerization, was also added. The films were then placed in a vacuum oven and heated up to 85°C to induce the free-radical polymerization of the monomers.

5.4 VHB-BASED IPN DIELECTRIC ELASTOMERS

5.4.1 Preserved prestrain with curable additive

In the experiment, various amounts of HDDA and TMPTMA were added separately into a highly pre-strained VHB film. Upon curing, an interpenetrating network of poly(HDDA) or poly(TMPTMA)

(a) (d)(b) (c)

Figure 5.1 Schematic illumination of the fabrication process of an IPN dielectric elastomer film: (a) an acrylic film before processing; (b) after 400% biaxial prestrain, the film area expands by 24 folds; (c) curable additives are added into the prestrained film and cured, forming an interpenetrating network of a highly crosslinked polymer; and (d) after external stress is removed, the interpenetrating network preserves most of the prestrain of the acrylic film.

Ch05-I047488.indd 44 12/10/2007 8:20:18 PM

Interpenetrating Polymer Networks as High Performance Dielectric Elastomers 45

formed in the highly prestrained VHB network. As the IPN composite film was released from the pre-strain structure, a contraction occurred in the prestrained VHB network, compressing the poly(HDDA) or poly(TMPTMA) network. The composite film reached a stable geometry when the tension in the VHB network balanced with the compression in the poly(HDDA) or poly(TMPTMA) network. This VHB network remained substantially strained compared to its original geometry. The preservation of the prestrain of the VHB network was measured using the distance between black dots marked on the cured film. The resulting preserved prestrain versus weight percentage of additive is plotted in Fig. 5.2 .

As expected, the prestrain preservation is strongly dependent on the amount of additive used. The preserved prestrain increases rapidly above a threshold concentration of additive. This may be explained by the percolation theory [10] . When the amount of additive is increased to a critical value, the polymer forms a crosslinked network of its own. This network effectively supports the prestrain of the preexistent VHB network. The threshold concentrations, the onset of the rapid increase of preserved prestrain, are approximately 14% for HDDA and 8.4% for TMPTMA. The lower threshold concentration of TMPTMA can be attributed to its trifunctionality that facilitates the formation of its three-dimensional network in the acrylic elastomers [11] .

5.4.2 Microstructures

Scanning electron micrographs displayed in Fig. 5.3 showed submicron size cracks. These cracks may be due to the broken additive network, which is less compliant than the VHB network. Figure 5.3 (b) and (c) compares the VHB-poly(HDDA) and the VHB-poly(TMPTMA) films containing the similar molar concentration of crosslinking acrylate or methacrylate functional groups. In an HDDA molecule, the first acrylate group is used for polymerization and the second acrylate is the crosslinkable group that

00

50

100

150

200

250

300

350

400

450

10 20 30 40 50

Weight percentage of monomer

Pre

serv

ed p

rest

rain

(%

)VHB-poly(HDDA)

VHB-poly(TMPTMA)

Figure 5.2 Preserved prestrain of VHB 4910 films after being released from prestrain structure. The preserved prestrain is calculated based on the original geometry of the VHB films before prestrain. Preserved prestrains of 0% and 400% correspond to zero and full prestrain preservation, respectively.

(c)

100 nm

(b)

100 nm

(a)

100 nm

Figure 5.3 Scanning electron micrograph (SEM) images of the VHB films for (a) 400% biaxial prestrained VHB 4910 without additive, (b) cured VHB 4910 with 35.94% by weight of poly(HDDA) before releasing, and (c) VHB 4910 with 23.38% by weight of poly(TMPTMA) before releasing.

Ch05-I047488.indd 45 12/10/2007 8:20:18 PM

46 Chapter 5

bonds polymer chains together. In TMPTMA, each molecule contains two crosslinkable groups. In Fig. 5.3 , the VHB-poly(HDDA) film exhibits a much rougher surface morphology and larger cracks than the VHB-poly(TMPTMA). The IPN films with high concentrations of additive appear turbid, indicating that the two networks are chemically independent from each other. For the same concentration of crosslink-able groups, the VHB-poly(HDDA) film is found to be more turbid than the VHB-poly(TMPTMA) film. The turbidity can be attributed to the phase separation of the additive network from the VHB network. The degree of phase separation is observed to increase proportionally with the turbidity of the IPN film.

5.4.3 Mechanical properties before release

The stress–strain behaviour of VHB-poly(HDDA) and VHB-poly(TMPTMA) was measured, assuming little chemical crosslinking occurred between the two networks. Results show that the acrylic network remained intact during the formation of the IPN. Any variation in the stress–strain behaviour would occur due to the presence of an additive network. Figure 5.4 shows the stress–strain response of the cured composite films before the films were released to free-standing. The VHB network is under 400% biaxial prestrain, whereas the additive network is at zero prestrain. There is no experimental data to prove that poly(HDDA) and poly(TMPTMA) aligns itself with the prestrained VHB network.

As shown in Fig. 5.4 , the stress–strain response is nonlinear for VHB without any additive, but it becomes increasingly linear with higher concentrations of poly(HDDA) and poly(TMPTMA). The non-linearity may be due to a combination of chain uncoiling and bond stretching [12] . At higher stretch-ing ratios, the chemical bonds are stretched very far apart and the VHB network begins to break. With increasing concentrations of additive, the films become stiffer, particularly at high stretch ratios. At small stretch ratios ( � � 1.05), the VHB-poly(HDDA) films in Fig. 5.4 (a) are not much stiffer, or even softer, than the pure VHB films. This is further discussed in the next paragraph.

To evaluate the effects of additive on film stiffness, we need to estimate the Young ’ s moduli of the films. In cases the deflections are no longer small in comparison with the thickness of the plate but are still small as compared with the other dimensions, a useful formula for an approximate calcula-tion of the Young ’ s moduli can be obtained by applying the theory of a large deflection developed by Timoshenko [13] . At small stretch ratios, the Young ’ s modulus E , of a clamped circular plate under a uniform applied pressure P is given by

EPa

hh h

��

��

3 1

160 442

1

4 2

42

03

( )

.

�

��

�0 ⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

(5.1)

2

4

6

8

10

12

14

01 1.1 1.2 1.3 1.4 1.5 1.6

w/o additive

w/ 18.33%

w/ 20.16%

w/ 21.91%

w/ 35.94%

Stretch ratio (l)

(a)

2

4

6

8

10

12

14

0

w/o additive

w/ 9.70%

w/ 10.32%

w/ 11.84%

w/ 23.49%

1 1.1 1.2 1.3 1.4 1.5 1.6

Stretch ratio (l)

(b)

Hyd

raul

ic P

ress

ure

(kP

a)

Figure 5.4 Hydraulic pressure versus stretch ratio curves for prestrained VHB 4910 (a) containing different con-centrations of poly(HDDA) and (b) poly (TMPTMA) before being released from prestrain structure. The numbers in the insets are in weight per cent of the additive network in the IPN films.

Ch05-I047488.indd 46 12/10/2007 8:20:19 PM

Interpenetrating Polymer Networks as High Performance Dielectric Elastomers 47

where h , � 0 , a , and v are film thickness, deflection at the film centre, radius of plate, and Poisson ’ s ratio, respectively.

Figure 5.5 shows the intriguing effects of additive content on the pseudo-Young ’ s modulus of the pre-strained films before release. Note that at zero deflection or at a stretch ratio of 1, the films have built-in tension. The Young ’ s moduli, which by definition are values at minimal external tension, thus only reflect the stiffness of the films at this condition, and do not correspond to the Young ’ s moduli of the films. Therefore, we call the calculated values ‘ pseudo-Young ’ s moduli ’ . The pseudo-Young ’ s modulus, while not the true modulus of the material, is a convenient parameter to measure relative stiffness of the film as the additive content is changed. The pseudo-Young ’ s modulus of VHB 4910 under 400% biaxial prestrain is 18.42 MPa, which increases to 38.76 MPa when the poly(TMPTMA) content is increased to 23.49%. This characteristic effect should result from augmentative proportions of additive network. The additive monomers are polymerized in the presence of the preexistent VHB matrix. As shown in Fig. 5.5 , the pseudo-Young ’ s modulus of VHB-poly(HDDA)first decreases from 18.42 MPa to 13.3 MPa as the poly(HDDA) content is increased from 0% to 21.91%. The pseudo-Young ’ s modulus then continues to increase with increasing weight percentages of poly(HDDA). The poly(HDDA) content correspond-ing to the modulus minimum falls near the high end of the percolation transition concentration range shown in Fig. 5.2 .

The preparation of the VHB-poly(HDDA) and VHB-poly(TMPTMA) composite films is similar to the synthesis of sequential IPN in which monomers of the additive are polymerized to completion in the presence of the matrix polymer. This characteristic reaction may result in discrete interpenetrating net-works, and enhance the mechanical strength. However, there are cases of high degree of network inter-locking. It has been proposed that in the latter stages of polymerization, additive monomers were either remaining or locally polymerized owing to greater diffusion limitation [14, 15] . This effect would lead to decreased Young ’ s modulus: the unreacted and locally polymerized monomers increase the total film thickness without contributing much to the total elastic modulus [16] . Pseudo-Young ’ s modulus minima observed in Fig. 5.5 may be resulted from a similar effect of unreacted or locally polymerized additive monomers. When the stretch ratio is rather large, the total mechanical strength will increasingly depend on the stiffer poly(HDDA) or poly(TMPTMA) network.

5.4.4 Mechanical properties after release

The stress–strain behaviours of the IPN composite films after they were released to free-standing were measured. In the free-standing composite films, the VHB network is under tension due to preserved prestrain.

Figure 5.6 shows the biaxial stretch ratios by the hydraulic pressure of the prestrain preserved, of free-standing composite films. The results of the VHB-poly(HDDA) and VHB-poly(TMPTMA) are similar to those of the unreleased films shown in Fig. 5.4 . The VHB-poly(HDDA) films in Fig. 5.6 (a)

10

15

20

25

30

35

40

45

0 10 20 30 40Weight percentage of monomer

Pse

udo-

You

ng’s

mod

ulus

(M

Pa) VHB-poly(HDDA) at 1.03

VHB-poly(TMPTMA) at 1.03

Figure 5.5 Calculated pseudo-Young ’ s moduli of prestrained VHB 4910 films with or without additive. The VHB films were biaxially prestrained by 400%, admixed with additive and cured. The moduli are calculated based on a stretch ratio of 1.03.

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48 Chapter 5

seem to be considerably softer than the VHB-poly(TMPTMA) films shown in Fig. 5.6 (b) even with respect to equivalent preserved prestrain. These results could be explained by comparing the bridge-length between functional groups (or crosslinks). The flexible hexylene segment in poly(HDDA) makes the network more pliable than that of the TMPTMA, which has a much shorter bridge-length. At small stretch ratios, the VHB-poly(HDDA) films appear much softer than the VHB films without poly(HDDA). However, the IPN films are stiffer when film thickness is considered.

As shown in Fig. 5.7 , the Timoshenko equation for free-standing composite films was used to calcu-late the Young ’ s moduli. The Young ’ s modulus of non-prestrained VHB 4910 is 181.53 kPa. Although the Young ’ s moduli of IPN composite films do not theoretically depend on the weight percentage of poly(HDDA) in the range of 18.3–23.6%, experimental data obtained show that the Young ’ s moduli of VHB-poly(TMPTMA) films increase rather rapidly with an increasing amount of poly(TMPTMA).

5.4.5 Actuation of IPN films without external prestrain

According to passive mechanical analysis, the films with a larger amount of additive would require a much higher energy to obtain large strains (stretch ratio >1.2). The electrically induced strains would thus be diminished. To support this argument, the electrical strains of free-standing IPN composite films with various amounts of additive were measured. The results are displayed in Fig. 5.8 . The strains were meas-ured with increasing driving voltage until dielectric breakdown is reached in the film. As expected, the

2

4

6

8

10

12

14

01 1.2 1.4 1.6 1.8 2 2.2

w/o additive

w/ 18.33%

w/ 20.16%

w/ 21.91%

w/ 23.58%

Stretch ratio (l)

(a)

2

4

6

8

10

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01 1.2 1.4 1.6 1.8 2 2.2

w/o additive

w/ 9.70%

w/ 10.32%

w/ 11.84%

w/ 23.49%

Stretch ratio (l)

(b)

Hyd

raul

ic P

ress

ure

(kP

a)

Figure 5.6 Hydraulic pressure versus stretch ratio curves for (a) different concentrations of VHB-poly(HDDA) and (b) VHB-poly(TMPTMA) after being released from prestrain structure.

0

5

10

15

20

25

30

35

40

0 10 20 30Weight percentage of monomer

You

ng’s

mod

ulus

(M

Pa)

VHB-poly(HDDA) at 1.03

VHB-poly(TMPTMA) at 1.03

Figure 5.7 Calculated Young ’ s moduli of IPN films as a function of weight percentage of additive. The VHB films were biaxially prestrained by 400%, admixed with HDDA or TMPTMA, cured, and released to free-standing. The moduli were calculated based on � � 1.03.

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Interpenetrating Polymer Networks as High Performance Dielectric Elastomers 49

IPN composite films show lower electrically induced strains with increasing amounts of additive. This is consistent with the increasing film stiffness observed with increasing additive content at large stretch ratios shown in Fig. 5.6 . For the VHB-poly(HDDA) shown in Fig. 5.8 (a), the IPN film with 18.33% poly(HDDA) shows the highest electrical strain of 233%, with a breakdown electric field of 300 MV/m. Its preserved prestrain was found to be 275%. The IPN formed film with 35.94% poly(HDDA) is too rigid to obtain high strain. The VHB-poly(TMPTMA) film with 9.7 wt% additive exhibits a preserved strain of 243.75%, with a maximum electrically induced strain of 300%. This result deserves further attention. As shown in Fig. 5.6 , although the VHB-poly(TMPTMA) film is more rigid than the VHB-poly(HDDA) film with 18.33 wt% of additive, it exhibits a higher electrical strain. It also has a dielec-tric breakdown strength of 420 MV/m, substantially higher than that of the VHB-poly(HDDA) film. The improved breakdown field in VHB-poly(TMPTMA) film can be attributed to the more uniform IPN film morphology and the smaller, fewer cracks present in the additive network (compare Fig. 5.3 (b) and (c)). The rather rough surface and submicron size cracks in the VHB-poly(HDDA) shown in Fig. 5.3 (b), are responsible for the diminished dielectric strength [17] . The electrically induced strain up to 300% in area is comparable to that of the highly prestrained, VHB 4910 films. Figure 5.9 shows the expansion of a diaphragm actuator using free-standing IPN composite films.

00 50 100 150

Electric field (MV/m)200 250 300

50

100

150

200

250S

trai

n (a

rea%

)

w/ 18.33%

w/ 20.16%

w/ 21.91%

w/ 23.58%

w/ 35.94%

(a)0 50 100 150

Electric field (MV/m)200 250 350 400 450300

0

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300

Str

ain

(are

a%)

w/ 9.70%

w/ 10.32%

w/ 10.86%

w/ 11.36%

w/ 11.84%

(b)

Figure 5.8 Electric field induced strain (area expansion) for (a) VHB-poly(HDDA) and (b) VHB-poly(TMPTMA) films containing various concentrations of additive. The films have been released from the prestrain structure and mounted, at minimal external stress, onto a diaphragm structure for the strain measurement.

(a)

(c)

(b)

(d)

VHB-poly(HDDA)

VHB-poly(TMPTMA)

Figure 5.9 Diaphragm actuators based on IPN composite films. The films are under a constant, small tension main-tained by the air pressure in the diaphragm chamber. VHB-poly(HDDA) containing 18.3 wt% HDDA (a) at 0 MV/m and (b) at 300 MV/m; VHB-poly(TMPTMA) film containing 9.7 wt% TMPTMA (c) at 0 MV/m and (d) at 420 MV/m.

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50 Chapter 5

5.5 CONCLUSIONS AND FUTURE DEVELOPMENTS

High performance IPNs based on VHB acrylic elastomers, poly(HDDA), and poly(TMPTMA) have been prepared for dielectric elastomer artificial muscles. The IPNs are formed in the highly prestrained VHB acrylic elastomer network to effectively support the prestrain of the VHB network. The VHB-poly(HDDA) composite film with 18.3 wt% poly(HDDA) preserves 275% prestrain of the acrylic elastomer and exhib-its an electrically induced strain up to 233% in area expansion, whereas the VHB-poly(TMPTMA) com-posite film with 9.7 wt% poly(TMPTMA) retains 243.75% prestrain and exhibits a 300% electrical strain.

These dielectric elastomer actuators driven by IPN composite do not have the problems caused by prestrain.

A number of further improvements can be made so that substantially more significant commer-cial applications can be realized. First of all, there are a broad range of elastomers, thermoplastic or crosslinked, could be employed as the first network. For instance, the use of silicone elastomers could reduce the viscoelastic loss generally observed with the acrylic elastomers and increase the response speed of the actuators. One could also use thermoplastic polyurethane that has higher response speed and higher dielectric permeability than the acrylics. Secondly, the additive forming the second network could use a silicone compound which forms a highly elastic network. Additives with high dielectric constant are attractive alternatives. Thirdly, there are several different approaches to prepare the sequen-tial IPN with internal tension–compression balance: e.g. an additive is impregnated before the first net-work is prestrained; an additive is admixed with a thermoplastic elastomer in solution from which thin film is processed and prestrained. Finally, there are other suitable approaches to prestrain the films and cure the additive based on availability of corresponding facilities and equipment.

There are also issues that need to be addressed, including design actuators that uniquely exploit the mechanical and electromechanical characteristics of the IPN films, improvement of the performance of packaged actuators in terms of cycle life, response speed, and environmental compatibility.

References

[1] Bar-Cohen, Y., Ed. (2004). Electroactive Polymer (EAP) Actuator as Artificial Muscles: Reality, Potential, and Challenges , 2nd edn. SPIE Press, Bellingham, WA.

[2] Kofod , G. , Kornbluh , R. , Pelrine , R. and Sommer-Larsen , P. ( 2001 ). Actuation response of polyacrylate

dielectric elastomers . Proc. SPIE Int. Soc. Opt. Eng. , 4329 , 141 – 147 .

[3] Pelrine , R. , Kornbluh , R. , Pei , Q. and Joseph , G. ( 2000 ). High-speed electrically actuated elastomers with

strain greater than 100% . Science , 287 , 836 – 839 .

[4] Kornbluh , R. , Pelrine , R. , Pei , Q. , Heydt , R. , Stanford , S. , Oh , S. and Eckerle , J. ( 2002 ). Electroelastomers:

applications of dielectric elastomer transducers for actuation, generation, and smart structures . Proc. SPIE Int. Soc. Opt. Eng. , 4698 , 254 – 270 .

[5] Pei , Q. , Rosenthal , M. , Stanford , S. , Prahlad , H. and Pelrine , R. ( 2004 ). Multiple-degrees-of-freedom electro-

elastomer roll actuators . Smart Mater. Struct. , 13 , N86 – N92 .

[6] Sommer-Larsen , P. , Kofod , G. , Shridhar , M. H. , Benslimane , M. and Gravesen , P. ( 2002 ). Performance of

dielectric elastomer actuators and materials . Proc. SPIE Int. Soc. Opt. Eng. , 4695 , 158 – 166 .

[7] Sperling , L. H. ( 1981 ). Interpenetrating Polymer Networks and Related Materials . Plenum , New York .

[8] Ha , S. M. , Yuan , W. , Pei , Q. , Pelrine , R. and Stanford , S. ( 2006 ). Interpenetrating polymer networks for high-

performance electroelastomer artificial muscles . Adv. Mater. , 18 , 887 – 891 .

[9] Ha , S. M. , Yuan , W. , Pei , Q. , Pelrine , R. and Stanford , S. ( 2006 ). New high-performance electroelastomer

based on interpenetrating polymer networks . Proc. SPIE Int. Soc. Opt. Eng. , 6168 , 616808 .

[10] Stauffer , D. and Ahrarony , A. ( 1994 ). Introduction to Percolation Theory . Taylor & Francis , New York .

[11] Ha, S. M., Yuan, W., Pei, Q., Pelrine R. and Stanford, S. (2007). Smart Mater. Struct. , 16 , S280–S287.

[12] Sperling , L. H. ( 1986 ). Physical Polymer Science . John Wiley & Sons , New York .

[13] Timoshenko , S. ( 1959 ). Theory of Plates and Shells . McGraw-Hill Book Co. , New York .

[14] Fan, J., Hu, X. and Yue, C. Y. (2001). Interpenetrating polymer networks based on modified cyanate ester

resin. Plast. Rubber Compos. , 30, 448–454.

[15] Sperling, L. H. and Mishra, V. (1995). The current status of interpenetrating polymer networks. Polym. Adv. Technol. , 7, 197–208.

[16] de Gennes , P. G. ( 1979 ). Scaling Concepts in Polymer Physics . Cornell University Press , New York .

[17] Lucas, J. R. (2001). High Voltage Engineering , revised edition. Open University of Sri Lanka, Nawala,

Nugegoda.

Ch05-I047488.indd 50 12/10/2007 8:20:21 PM

ENHANCING THE DIELECTRIC PERMITTIVITY OF ELASTOMERS

Federico Carpi 1 , Giuseppe Gallone 1, 2 , Fabia Galantini 1 and Danilo De Rossi 1

1 Interdepartmental Research Centre ‘ E. Piaggio ’ , University of Pisa, Pisa, Italy 2 Department of Chemical Engineering, University of Pisa, Pisa, Italy

Abstract

The electromechanical transduction properties of any dielectric elastomer are intrinsically regulated by the dielec-

tric permittivity of the material. This parameter proportionally controls both the achievable active stresses and

strains. Accordingly, a suitable increase of the material permittivity may provide a valuable means to improve the

performance of a dielectric elastomer actuator. This chapter provides a brief overview of the most used methods,

mainly based on purely physical approaches, currently available for increasing the dielectric permittivity of rubber-

like insulators.

Keywords : Composite, dielectric constant, dielectric elastomer, dielectric permittivity, dielectric strength, filler,

mixing rule.

6.1 INTRODUCTION

As reported in Chapter 1, the electromechanical response of a dielectric elastomer actuator is deter-mined by the actual compressive stress p [1] :

p E� � �0

2 (6.1)

where � 0 � 8.854 pF/m is the dielectric permittivity of vacuum, E is the applied electric field and � is the relative dielectric permittivity of the elastomer. Accordingly, an increase of the material permittivity provides a valuable mean to improve the performance of a dielectric elastomer actuator. The aim of the present chapter is to provide an overview of the available methods for increasing the permittivity of a dielectric elastomer.

Modifying a polymer matrix in order to increase its dielectric permittivity means acting on the dipolar moments of the material and, therefore, on its polarization vector P . This vector is related to the field vector E by the following expression:

P E( ) ( ( ) ) ( )� � � � �� �0 1

(6.2)

where � is the angular frequency of the AC electric field. Deviations from the linear behaviour expressed by Eq. (6.2) are likely to be observed at sufficiently high electric fields, when also higher order terms of E( )� must be taken into account. The frequency dependence of Eq. (6.2) reflects the possible existence of dispersive behaviours somewhere in the electromagnetic spectrum. In any case, the relative dielectric permittivity is a frequency dependent complex quantity:

� � � � � �*( ) ( ) ( )� � � �j (6.3)

� � ( � ) and � � ( � ) being its real and imaginary parts, respectively. The real part �� ( � ) is always different from zero and represents the contribution to the polarization responsible for the energy storage into the material. In order to stress its substantial independence from the electric field, it is often referred to as the relative dielectric constant of a material. The imaginary part �� ( � ), usually called loss factor , accounts for possible dissipative effects and its frequency spectrum differs from zero only in coincidence to dispersive regions. Sometimes, the dissipative behaviour is characterized by means of the so-called loss tangent , which is defined as tg � ( � ) � �� ( � )/�� ( � ).

Chapter 6

Ch06-I047488.indd 51 12/10/2007 8:20:56 PM

52 Chapter 6

In a homogeneous medium, the polarization P and thus also � �*( ) , arises as a combination of vari-ous contributions. One main contribution comes from the deformational polarizability of the mater ial, which is the mutual displacement of oppositely charged particles, like electrons nuclei and ions, under the action of the applied field. Associated with such a polarization mechanism, dispersive phenom-ena may arise from different physical processes occurring at electronic, atomic or ionic level. Since they involve interactions with quantum energy levels, the associated frequency response is character-ized by a resonant-like behaviour. On the other hand, if the material molecules already possess perman-ent dipole moments, say μ these individually interact with the field E through a potential energy U � � �μ E, which drives each dipole to orientate itself parallel to the field. Such orientational polar-izability represents the second important contribution to the global polarization P. Nevertheless, add-itional dispersive processes may originate from the limited mobility of the permanent dipoles, resulting in a frequency response typical of relaxation phenomena. Due to the very different time scales involved, resonant phenomena determine dispersive behaviours at infrared frequencies and above, while relax-ation phenomena show up at much lower frequencies; they are particularly evident in the case, for instance, of highly polar liquids (e.g. water), resins and polymers. In addition to such deformational and orientational contributions to polarization (whose associated properties in the following will be referred to as ‘ bulk ’ or ‘ intrinsic ’ ), also a limited displacement (diffusion) of possible space charges may give rise to a polarization; this, in turn, may be responsible for energy dissipation inside a hetero-geneous system. This is the case, for example, of the relaxation phenomena associated to the so-called Maxwell–Wagner (or interfacial) polarization. It takes place when surface charges accumulate at inter-faces between a dielectric matrix and other phases with different electrical properties (i.e. electrodes, inclusions, defects, fillers, impurities). Moreover, the dissipation of energy may be increased if the material, either homogeneous or heterogeneous, exhibits a finite DC electrical conductivity � DC , which may originate, for example, from diffusion of impurity ions. Differently from metals, electrical conduc-tion in dielectrics is an activated process, and thus � DC results to increase with temperature.

All these different contributions sum up to give an effective relative complex dielectric permittivity � * eff , which may be defined in a very general form as follows:

� � � � � ����

� � �

eff MWDC

MW

j* *,

*

,

( ) ( ) ( )

( )

� � �

� �

ii0

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

′ ′

∑

iii ii( ) ( ) ( ),� � � � �

��∑ ∑

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

′′ ′′⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟� � �j MW

DC

ε0⎟⎟

(6.4)

where each term � * MW, i accounts for an i th interfacial contribution. It is worth stressing that all the dis-persive phenomena associated to the intrinsic polarization are accounted for by � * ( � ) in Eq. (6.4). In particular, since the time scale of dielectric elastomer actuation is never shorter than the period associ-ated to radio waves, we are here mainly concerned with the dielectric properties of materials well below infrared frequencies, where any dispersive behaviour of the deformational polarization is absent. Thus, the bulk permittivity � * ( � ) can be thought as being composed by a constant real term representing the ‘ low frequency limit ’ (relaxed) value of the deformational permittivity, plus a frequency dependent component which accounts for the dispersive behaviour of the orientational polarization of the system. In presence of multiple intrinsic relaxations, � * ( � ) can be expressed as a superposition of individual contributions. Indeed, each relaxation process, either orientational or interfacial, can be analytically described by means of a proper relaxation function. In the simplest case of a material consisting of identical and non-interacting dipoles, whose relaxation is characterized by a unique time constant � , Debye derived the relaxation function for the complex permittivity in the associated dispersion region [2] . In the frequency domain, the Debye model brings to the well-known formula:

� � �� �

��*( ) � �

�

��

�s

j1 (6.5a)

where � s and � � , respectively, represent the static (relaxed) and the high frequency (unrelaxed) values of the permittivity, with respect to the considered process. For a material showing a unique dipolar relaxation in its whole spectrum, � � in turn coincides with the aforementioned relaxed value of the deforma-tional permittivity. Equation (6.5a) can be splitted in its real and imaginary parts and then equivalently

Ch06-I047488.indd 52 12/10/2007 8:20:57 PM

Enhancing the Dielectric Permittivity of Elastomers 53

expressed by the following pair of equations:

′

′′

⎧

⎨

⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪

� � �� �

� �

� �� � ��

� �

( )

( )( )

� ��

�

��

�

��

�

s

s

1

1

2 2

2 2

(6.5b)

Due to the very simplistic assumptions it is based on, it can appear obvious that the Debye model is found to fail in describing relaxation phenomena in complex systems. Thus, Havriliak et al. proposed a more general formula [3] . Though derived by a phenomenological approach, it has the merit of includ-ing the possibility of a distribution of different time constants through the introduction in Eq. (6.5a) of two shape parameters � and � :

� � �� �

��� �

� �*( )

( )

[ ( ) ]( , )� �

�

�

���s

j10 1 0 1

1 (6.5c)

For our purposes, the occurrence of a dispersive process of any nature in the frequency region of interest represents a drawback. In order to advantageously exploit a dielectric elastomer as an actuation material, the effective loss factor should be kept as low as possible. In fact, losses not only waste part of the input energy, but they also worsen the insulation properties of the material. In particular, for any dielectric material it is possible to identify a threshold electric field, which generates irreversible modi-fications in the medium accompanied by the onset of an intense and disruptive flow of charges. Such a sudden loss of insulation due to a very high electric field is named dielectric breakdown of the mater-ial. The minimum field responsible for such effect is called breakdown field or breakdown strength , E break . In most polymers, E break is included in the range 10 6 –10 8 V/m. It represents the analogous of the mechanical fracture threshold for a material subjected to an external load. Although dielectric break-down phenomena are object of intense studies since the first half of the last century [4] , physical models allowing reliable predictions of E break are still not available. In fact, several are the possible causes and processes related to dielectric breakdown; these include purity level, processing methods, working con-ditions, environmental conditions and mechanical solicitations [5] . However, it is generally accepted that mechanisms responsible for dielectric discharges can have both thermal and intrinsic (bulk) origin. In the first case, both dielectric polarization and conduction losses determine a temperature increase of the material. Indeed, the power density W dissipated into the dielectric medium, at expenses of the elec-tric field, is proportional to � � eff ( � ):

W E�� � �

� 2′′eff ( )

(6.6)

Such a heating, in turn, enhances the conductivity in a self-amplified process with catastrophic conse-quences; in fact, the amount of heat that the material is not able to dissipate drives it to the breakdown. As a second possibility, breakdown may be related to an avalanche discharge process that begins with the promotion of few valence electrons to the conduction band. These electrons, being accelerated by the applied electric field, strike against other valence electrons, driving them to the conduction band by a kinetic energy transfer; as this process of charge carriers multiplication goes on, the current flow grows rapidly in the dielectric and the material can locally melt and pierce.

Following the basic concepts about electrical properties of dielectrics just recalled, the next section proposes a summary of methods currently used for increasing the dielectric permittivity.

6.2 METHODS FOR INCREASING THE DIELECTRIC PERMITTIVITY: SUMMARY

In order to increase the dielectric permittivity of polymer materials, different methods are currently avail-able. They may be classified into three main groups: random composites, field-structured composites and new synthetic polymers. The first approach is based on the dispersion into the polymer matrix of a filler, either solid (e.g. powder) or liquid. The second method exploits a composite approach as well, although the material is now cured in the presence of an external electric field, in order to align dipoles. The third strategy deals with the synthesis of new materials with tailored characteristics.

Ch06-I047488.indd 53 12/10/2007 8:20:57 PM

Ta

ble

6.1

N

on-e

xhau

stiv

e sy

nopt

ic t

able

of

diffe

rent

met

hods

use

d fo

r im

prov

ing

the

diel

ectr

ic c

onst

ant

of p

olym

ers,

alo

ng w

ith r

elat

ed s

tate

-of-

the-

art

exam

ples

.

Pro

cess

Fill

er (

whe

re a

pplie

s)

M

atri

x

Ela

stom

ers

Ref

eren

ces

Non

-ela

stom

ers

Ref

eren

ces

Ran

dom

co

mposi

tes

Mix

ing w

ith

org

anic

and

in

org

anic

fill

ers

(p

arti

cles

)

Fer

roel

ectr

ic/

pie

zoel

ectr

ic c

eram

ics

PM

N–P

T

Sil

icone

[6, 7]

–

–

TiO

2 S

ilic

one

[7, 8]

–

–

BaT

iO 3

Sil

icone

[7]

PA

[9]

Conduct

ive

par

ticl

es

Fe

Sil

icone

[10]

UP

[1

0]

Epoxy r

esin

[1

1]

C

u

–

–

Epoxy r

esin

[1

1]

C

u-c

oat

ed

phosp

holi

pid

s S

ilic

one/

PU

[1

2]

–

–

C

B

PU

[1

3]

PE

[1

4, 15]

C

NT

–

–

Epoxy r

esin

[1

6]

PC

[1

7]

Org

anic

monom

ers

CuP

c S

ilic

one

[18]

P(V

DF

–T

rFE

) [1

9]

Org

anic

poly

mer

s

Poly

CuP

c P

U

[20]

EV

A

[7]

PAN

I P

U

[20, 21]

P(V

DF

–T

rFE

–C

FE

) [2

2, 23]

Fie

ld-s

truct

ure

d

co

mposi

tes

Cro

ss-l

inkin

g i

n

el

ectr

ic f

ield

of

el

asto

mer

s w

ith

in

org

anic

fill

ers

(par

ticl

es)

Fer

roel

ectr

ic/

pie

zoel

ectr

ic c

eram

ics

SiO

2 B

aTiO

3 , P

bT

iO 3

Sil

icone

Sil

icone

[24]

[24, 25]

–

Epoxy r

esin

–

[26]

Synth

esis

of

new

poly

mer

s

Funct

ional

izat

ion

–

S

-SB

S

[27]

P(V

DF

–T

rFE

–C

FE

) [2

2, 23]

Copoly

mer

izat

ion

(g

raft

ing a

nd/o

r

cross

-lin

kin

g)

–

F

LC

E

[28, 29]

–

–

NB

R

[30]

Poly

mer

ble

ndin

g

–

S

ilic

one/

PU

[1

2]

–

–

S

ilic

one/

PH

T

[63]

Not

es :

PM

N–P

T:

Lea

d m

agnes

ium

nio

bat

e-le

ad t

itan

ate

[Pb(M

g 1/

3 N

b 2/

3 )O

3 -P

bT

iO 3 ]

; P

U:

poly

ure

than

e; C

B:

carb

on b

lack

; C

NT

: ca

rbon n

anotu

bes

; C

uP

c: c

opper

phta

locy

a-

nin

e; P

oly

CuP

c: p

oly

(copper

phth

alocy

anin

e);

PAN

I: p

oly

anil

ine;

S-S

BS

: su

lfonat

ed p

oly

(sty

rene–

ethy

lene/

buty

lene

styre

ne)

; F

LC

E:

ferr

oel

ectr

ic l

iquid

-cry

stal

line

elas

tom

er;

NB

R:

acry

lonit

rile

-bu

tadie

ne

rubber

; P

HT

: poly

hex

ylt

hio

phen

e; P

(VD

F–T

rFE

): p

oly

(vin

yli

den

e fl

uori

de–

trif

luoro

ethy

lene)

; P

(VD

F–T

rFE

–C

FE

): p

oly

(vin

yli

den

e fl

uori

de–

trif

luoro

ethy

lene–

chlo

rofl

uoro

ethy

lene)

; PA

: poly

acry

late

s; U

P:

unsa

tura

ted p

oly

este

r; P

E:

poly

ethy

lene;

PC

: poly

carb

onat

e; E

VA

: poly

(eth

yle

ne-

co-v

inyl

acet

ate)

.

Ch06-I047488.indd 54 12/10/2007 8:20:57 PM

Enhancing the Dielectric Permittivity of Elastomers 55

Table 6.1 shows a list of such methods in terms of involved physical processes and adopted mater-ials, by mentioning specific state-of-the-art examples related to either elastomers or not. Some of the methods reported in this table have been already experimented for incrementing the dielectric constant of elastomers used for actuation. On the contrary, other examples relate to different types of materials (not elastomers) and/or different applications. These have been included as well for the sake of com-pleteness and because, in certain cases, they may suggest approaches that worth to be investigated for applications to actuation elastomers. The different considered techniques will be separately discussed in the following sections with reference to Table 6.2 , which reports the most significant results achieved by the studies mentioned in Table 6.1 .

6.3 RANDOM COMPOSITES

Since the last three decades, fabrication of composites has become a very common methodology in the field of materials engineering, aimed at achieving a set of specific properties superior with respect to those provided by the single constituents. Such an approach has also been extended to the development of dielectric elastomers with improved dielectric permittivity. For this purpose, fillers of high dielectric constant are usually introduced in the form of powder in the elastomeric matrix before vulcanization. In general, the resulting composite will have intermediate electric properties with respect to those of matrix and filler. However, a universal composition law capable of providing, given the electric proper-ties of both matrix and filler, reliable predictions of the composite response is still not available. Rather, several mixing rules have been proposed to account for the effective permittivity � c of a system consist-ing of two immiscible phases, as described in the following.

6.3.1 Dielectric mixing rules

Typically, mixing rules consider an isotropic medium of dielectric permittivity � m and volume frac-tion v m filled with spheroids of permittivity � f and volume fraction v f � 1 � v m . Both components are assumed to have null dielectric losses in the frequency region of interest. Moreover, they are usually derived in the form of composition equations for the effective permittivity at sufficiently high frequen-cies ( � � ) with respect to the arising Maxwell–Wagner relaxation process [31] . Among such models, those pertaining to continuous media filled with spherical particles are here specifically considered as a starting point for the following discussion.

It is possible, in general, to identify upper and lower bounds for � c such that [32]

� � �c c c,min ,max (6.7)

where � c,min and � c,max are solutions of equivalent series and parallel model circuits, respectively given by

�� �

� � cm f

m f f m,min �

� (6.8)

� � � c m m f f,max � � (6.9)

Beyond such rough limits, further steps in modelling the dielectric properties of a binary mixture have been accomplished in the frame of the so-called Wagner theoretical scheme [31, 33] . As reported by Van Beek [31] , under the hypothesis of sufficiently small filler concentrations, it is possible to select suit able intermediate regions surrounding the filler particles where two alternative points of view hold at the same time. The first considers the electric potential as arising from a distribution of spheres with dielec-tric constant � f , enclosed in an insulating medium of different dielectric constant � m ; the second fore-sees a larger heterogeneous sphere with overall dielectric constant � c embedded in the same insulating medium with dielectric constant � m [34] . By equating the two alternative expressions for the electric potential, the so-called Sillars [35, 36] or Landau–Lifshitz [34] mixing rules can be obtained:

� � � �

� �c mf f m

m f

� ��

�1

3

2

( )⎡

⎣⎢⎢

⎤

⎦⎥⎥

(6.10)

Ch06-I047488.indd 55 12/10/2007 8:20:58 PM

Table

6.2

Su

mm

ary

of th

e m

ain

resu

lts a

chie

ved

by th

e st

udie

s re

port

ed in

Tab

le 6

.1.

Syst

emL

oadi

ng (

%)

�� m�� c

� c�tg

δ cY

c (M

Pa)

Ebr

eak,

c (V

/μm

)S

m (

%)

Sc (

%)

Ref

eren

ces

Die

lect

rics

for

Max

wel

l-st

ress

ac

tuat

ion

Sil

icone/

TiO

270 w

t3 @

1 H

z10

––

10

30

––

[7]

Sil

icone/

PM

N–P

T70 w

t3 @

1 H

z8

––

10

34

––

[7]

Sil

icone/

PM

N–P

T30 v

ol

8 @

10 H

z32

32

10.1

3–

[6]

Sil

icone/

BaT

iO3

70 w

t3 @

1 H

z20

––

10

26

–0.4

tr@

25 V

/�m

[7]

Sil

icone/

TiO

230 w

t6 @

10

Hz

8~

0.8

0.1

0.0

16

–1 t

r@10 V

/�m

11 t

r@10 V

/�m

[8]

Sil

icone/

CuP

c20 w

t3 @

1 k

Hz

6–

––

25

6 t

r@26 V

/�m

12 t

r@26 V

/�m

[18]

PU

/CB

18.7

6 v

ol

6 @

1 H

z4400

~10

8~

10

528.7

0.8

~0 t

r@0.7

V/�

m0.0

35 t

r@0.7

V/�

m[1

3]

PU

/Poly

CuP

c/PA

NI

85/1

5/1

4 v

ol

8 @

1 H

z800

––

80

�20

–2 l

on@

20 V

/�m

–9 l

on@

20 V

/�m

[20]

EV

A/P

oly

CuP

c70 w

t3 @

1 H

z~

40

–~

10

2–

4.6

––

[7]

NB

R–

14 @

10 H

z–

––

––

–20 t

r@50 V

/�m

[30]

Sil

icone/

PH

T1–6 w

t4.4

@10 H

z5.6

–14

0.8

–3

0.1

–0.2

0.0

3–0.0

78–9

1 t

r@8 V

/�m

7.6

–2.3

tr@

8 V

/�m

[63]

Die

lect

rics

for

elec

trost

rict

ive

actu

atio

n

FL

CE

––

––

–3

––

–4 l

on@

1.5

V/�

m[2

8]

P(V

DF

–T

rFE

)/C

uP

c+ i

rrad

.40 w

t40 @

0.1

Hz

425

–0.7

~10

313

––2 l

on@

13 V

/�m

[19]

P(V

DF

–T

rFE

–C

FE

)/PA

NI

+ir

rad.

25 v

ol

60 @

1 k

Hz

5000

–0.6

530

3.8

5–0.2

lon@

16 V

/�m

–2.6

5 l

on@

16 V

/�m

[22]

P(V

DF

–T

rFE

–C

FE

)/g

raft

ed e

last

om

er–

––

––

3–

––0.1

3 l

on@

50 V

/�m

[29]

Die

lect

rics

fo

r dif

fere

nt

appli

cati

ons

S-S

BS

10 w

t H

2O

250 0

00

6.1

04

––

––

–[2

7]

10 w

t S

20 w

t H

2O

25 0

00

3.1

04

––

––

–20 w

t S

0 w

t H

2O

5–

––

––

–16 w

t S

Ch06-I047488.indd 56 12/10/2007 8:20:58 PM

Sil

icone/

PM

N–P

T30 v

ol

8 @

10

Hz

30

40

–0.1

35

––

–[6

]S

ilic

one/

Fe

50 v

ol

3 @

1 H

z60

20

––

–[1

0]

Sil

icone/

SiO

2 +

HV

str

.13 v

ol

2.3

@1

Hz

25

–18

0.0

61.5

[24]

PU

/PA

NI

17 w

t6 @

1 k

Hz

1120

––

80

––

–[2

1]

PU

/sil

icone/

Cu-c

oat

ed

phosp

holi

pid

s12 w

t–

30

2~

0.6

––

[12]

PE

/CB

5 w

t3 @

10

Hz

60.0

710

–2

––

––

[15]

2 v

ol

3 @

10 H

z20

––

–[1

4]

PE

GD

A/B

aTiO

330 v

ol

10 @

100 H

z40

––

––

––

[9]

TM

PT

A/B

aTiO

330 v

ol

3 @

10

0 H

z25

––

––

TD

DM

A/B

aTiO

330 v

ol

2 @

10

0 H

z20

––

––

Epoxy r

esin

/Fe

40 w

t5 @

10

0 H

z7.5

71

––

––

[11]

Epoxy r

esin

/Cu

40 w

t5 @

10

0 H

z12

60.5

––

[11]

Epoxy r

esin

/CN

T0.0

5 w

t3 @

10 H

z40

~10

325

––

[16]

Note

s: �

� m:

real

rel

ativ

e per

mit

tivit

y o

f th

e m

atri

x; �� c

, �� c

tg� c

: re

al a

nd i

mag

inar

y r

elat

ive

per

mit

tivit

y a

nd l

oss

tan

gen

t of

the

com

posi

te, re

spec

tivel

y;

Y c:

elas

tic

modulu

s of

the

com

posi

te;

Ebre

ak,c:

die

lect

ric

stre

ngth

of

the

com

posi

te;

S m, S c

: st

rain

of

the

mat

rix a

nd o

f th

e co

mposi

te, re

spec

tivel

y;

tr:

tran

sver

se;

lon:

longit

udin

al;

–:

not

avai

lable

/not

appli

cable

; ir

rad.:

irr

adia

tion;

str:

Str

uct

uri

ng;

PE

GD

A:

poly

-eth

yle

ne-

gly

col-

dia

cryla

te; T

MP

TA

: tr

imet

hylo

lpro

pan

e-tr

iacr

yla

te; T

DD

MA

: te

trad

ecan

edio

l-dim

ethac

ryla

te.

Ch06-I047488.indd 57 12/10/2007 8:20:58 PM

58 Chapter 6

However, Eq. (6.10) holds just at very low volume fractions of filler ( f 0.1) and only for fillers hav-ing a higher electrical resistivity than the matrix. More accurate predictions can be achieved with by one of the most popular equations, the so-called Maxwell-Garnett [36–40] formula:

� � � �

� � �c mf m

f f m m

� ��

� � �1

3

1 3

( )

( )( )

f⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

(6.11a)

which in principle should be valid without restrictions about resistivity. However, it is common to find in the literature the mixing rule of Eq. (6.11a) expressed in many other equivalent forms, such as:

� �� �

� �� �

c m

c mf

f m

f m

�

��

�

�2 2

( )

(6.11b)

so that it is sometimes referred to as Maxwell–Wagner [41–43] or Rayleigh [31, 33, 44, 45] or Lorentz–Lorenz [31, 46] or Kerner–Böttcher [33, 47] equation. Similarly to Eq. (6.10), these two equations can be derived within the Wagner approach, and indeed it is found that Eq. (6.10) is just an approxima-tion of Eqs. (6.11a–b) [31] . Both these results can also be obtained directly via the Clausius–Mossotti scheme for the polarizability of a medium [31, 46] .

By using a quite similar approach, Böttcher suggested to equate the electric field acting into each component of the mixture to the field which would settle in a sphere of the same material, embedded in a medium having the dielectric constant � c of the mixture [33] . Calculations lead to the following rela-tion, referred to as Böttcher [33, 45, 48] or Landauer [32, 47, 49] or Polder–Van Santen [50] equation:

� �� �

� �� �m

c m

c mf

c f

c f

( ) ( )�

��

�

��

2 20 (6.12a)

sometimes also written in the form:

� ��

� �� �

c m

cf

f m

c f

��

�

�3 2 (6.12b)

In case of diluted systems Eqs. (6.11a–b) and (6.12a–b) are equivalent. When the dispersed particles are not spherical in shape, the mixing formulas discussed so far must be

revised, in order to take account of their geometry. Typical is the case of particles with a spheroidal or cylindrical geometry, characterized by the ratio of their axes ( a / b ), which may even become pure rods or discs. The common way to include the information about such kinds of geometries of filler particles is to properly introduce a depolarization factor A , which contains the information about the particles shape in terms of their deviation from sphericity. Thus, for example, the widely used Maxwell-Garnett equation is modified into the form [31] :

� � � � � � �

c mf f m

f f m mffor � �

�

� � �1

10 1

( )

( )( ).

A

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

(6.13)

It is possible to determinate A by calculating it with specific formulas [31] or by referring to published tables [51] . In the case of spheres, A � 1/3 so that Eq. (6.13) turns back into Eq. (6.11a), as expected. Some other formulas, which come from exact solutions of the Wagner ’ s theory for very common cases, are (for a complete list see [31] ):

Wagner-Rayleigh for sc mm f f f m

m f f f m

� �� � � �� � � �

�� � �

� � �

2 2

2

( )

( )ppheres and fv 0 2.

(6.14)

Sillars

for spheroids with

c m ff m

m f m

� � � �

� � �� �

�

� �1

A( )

⎡

⎣⎢⎢

⎤

⎦⎥⎥

main axes parallel to the field and fv 0 1.

(6.15)

Bruggeman for lamellae and c fm f f m

f f f m

� �� � �� � �

�� �

� �

3 2

3

( )

( )ddiscs

(6.16)

Ch06-I047488.indd 58 12/10/2007 8:20:58 PM

Enhancing the Dielectric Permittivity of Elastomers 59

An improvement of these mixing rules was proposed by Bruggeman as an extension of the Wagner scheme, in which the initially low volume fraction of the filler is gradually increased by infinitesimal additions [31, 33] . The Bruggeman integration method leads to a distinct mixing rule, which permits to assess the overall electrical response at much higher content of (spherical) filler than for previous equations [31] . This is particularly attractive for a disordered system, where constituent particles may become very close to each other and even agglomerate, so that deviations from an ideally uniform and dilute system may be substantial even at low filler concentrations ( v f � 0.1). Thus, the solution of a dif-ferential equation obtained from either Eqs. (6.11a–b) or (6.12a–b) (they may be considered equivalent, as a starting point) leads to the Bruggeman ’ s formula [45, 48, 52] :

� ��

� ��

f c

c

f f m

c

��

� �1 3 1 3

1/ /

( )( )

(6.17)

which is expected to hold for v f values up to 0.5, with the constraint that the dispersed spheres do not form a percolative path throughout the medium.

With even larger filler contents, the electric field arising from the neat induced distribution of dipole moments is likely to become more and more important in determining the overall field locally experi-enced in the matrix. Accordingly, the need for more realistic assumptions in order to obtain a reliable mixing rule is evident. For this purpose, Jayasundere and Smith calculated the electric field within a dielectric sphere embedded in a continuous dielectric medium by also taking into account the polariza-tion of adjacent particles [47] . This approach led to the following equation:

�� �

�� �

� �� �

�

c

m m f fm

m ff

f m

m f

m fm

�

��

��

�

�

3

21 3

2

3

( )

( )

(

⎡

⎣⎢⎢

⎤

⎦⎥⎥

221 3

21� �

� �� �m f

ff m

m f��

�

�)

( )⎡

⎣⎢⎢

⎤

⎦⎥⎥

(6.18)

Interestingly, Vo and Shi proposed a dielectric constant modelling regarding the dependence of the effective dielectric constant of a composite material with respect to the interfacial phases generated between the polymer matrix and the filler particles [53] . Their results show that the composite dielec-tric constant mainly depends on the ratio between the filler and matrix dielectric constants, and on the degree of interaction between filler and matrix.

As mentioned at the beginning of this section, the mixing rules reported hold for the high frequency values of the permittivity. Nevertheless, an investigation of dielectric properties of an elastomer devoted to the enhancement of its electromechanical properties should focus mainly on the low frequency part of the spectrum. In fact, dielectric elastomer actuators are usually operated at relatively low frequency where, due to the limited bandwidth of elastomers, actuation strains are superior. According to Fricke, in case of spheroids it is possible to formulate a pair of mixing rules for both the relaxed and unrelaxed permittivity of the composite [31] :

� � � �

� � ��

� � � ��c,s m f

f m

m f mm

m f f m

m i

� ��

� ��

�

��

1

3 [ ( )] [ (, , A Aii a b c∑ �� �

� � � �

� � �

f m

c m ff m

m i f m

�

� ��

� �

�

�

)]

[ ( )]

, ,

,, ,

2

11

3

i a b c

i a b c A

∑

∑⎧

� ⎨⎨⎪⎪⎪

⎩⎪⎪⎪

⎫⎬⎪⎪⎪

⎭⎪⎪⎪

⎧

⎨

⎪⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪⎪

(6.19)

where A a , A b and A c are the depolarizing factors along three axes a , b and c (defined in [31] ) and � m and � f are the conductivities of the polymer matrix and filler, respectively. The presence of � m and � f in Eq. (6.19) should not be surprising, however, since the aforementioned mixing rules and their under-lying assumptions are still valid even if both matrix and filler possess finite electrical conductivities. In addition, it is exactly the mobility of some charge carriers which, although limited, gives rise to the interfacial polarization and the coupled relaxation processes.

All the above equations are based on different assumptions, even if they are derived within the same theoretical scheme. Thus, their predictions may considerably differ from one another. As an example, Fig. 6.1 shows a comparison among a set of experimental data from a composite dielectric elastomer and theoretical values expected from classical mixing rules [6] . The composite was a silicone elastomer matrix filled with particles of Pb(Mg 1/3 Nb 2/3 )O 3 –PbTiO 3 (PMN–PT) with an average size lower than

Ch06-I047488.indd 59 12/10/2007 8:20:58 PM

60 Chapter 6

50.00 0.05 0.10 0.15 0.20 0.25 0.30

(a) (b)

0.35 0.00

vf (PMN–PT)vf (PMN–PT)

0.05 0.10 0.15 0.20 0.25 0.30 0.35

10

15

20

25

30

35

5

10

15

20

25

30

BO

JS

BR

MW

LS

BO

JS

BR

MG

LS

BO

JSBR

MGLS Landau or Sillars – Eq. (6.10)

Maxwell–Garnett – Eq. (6.11)Bottcher – Eq. (6.12)Bruggeman – Eq. (6.17)Jayasundere–Smith – Eq. (6.18)

Experimental, 1 kHz

BO

JSBR

MGLS Landau or Sillars – Eq. (6.10)

Maxwell–Garnett – Eq. (6.11)Bottcher – Eq. (6.12)Bruggeman – Eq. (6.17)Jayasundere–Smith – Eq. (6.18)

Experimental, 100 kHz

ε c ε c Figure 6.1 Experimental � c data (dots) of silicone/PMN–PT composites at 100 Hz and 1 kHz for various filler contents v f compared with specified models (adapted from [6] ).

100 � m. This figure shows that at low filler contents (i.e. diluted systems with � f 0.1), predictions from Eqs. (6.10a–b), (6.11a–b), (6.12a–b), (6.17) and (6.18) are similar and in substantial agreement with experimental data. At higher filler contents (concentrated systems) differences among models become relevant. Notably, the Bruggeman model gave the best agreement with experimental data within the entire composition range and particularly at the higher frequency. This can be ascribed to the fact that, with respect to the occurring polarization processes, the dielectric permittivity at 1 kHz was closer to the unrelaxed value ( � � ) than at 100 Hz.

In order to compare models predictions with literature experimental data, it must be pointed out that a direct comparison is often not possible, due to a lack of information about the considered volume fractions. In fact, unfortunately, authors too frequently report compositions in terms of weight fractions (without any indication about density) rather than volume percentages, making any possible comparison very difficult.

6.3.2 Dielectric fillers

The use of high permittivity inorganic fillers is a well-established technique to improve the dielectric constant of a polymer matrix [54] . In particular, powders of ferroelectric/piezoelectric ceramics, show-ing the highest dielectric constants (e.g. � � f ~ 20 000 for lead magnesium niobate – PMN), can, in prin-ciple, allow significant increments of permittivity. For instance, a four-fold increase of the permittivity of a silicone elastomer was obtained at 10 Hz by loading the material with 30 vol% lead magnesium niobate–lead titanate (PMN–PT) [6] . Likewise, an increase of the dielectric constant of poly-ethylene–glycol–diacrylate (PEGDA) from � � m ~ 10 to � � c ~ 40 at 10 2 Hz by filling the material with 30 vol% bar-ium titanate (BaTiO 3 ) was described [9] . Other examples are reported in Table 6.2 .

Despite the considerable improvements of the material dielectric properties that can be achieved by using ceramic fillers, such a method is not always suitable for the sake of improving the actuation prop-erties. In fact, its use has brought so far limited results in this respect [7] . This is due to the fact that ferroelectric ceramics usually are highly stiff, which is likely to cause a loss of strain capabilities in the resulting composite. Nevertheless, taking such an assumption as a general rule can be misleading. In fact, also possible increases of the actuation strains within definite field ranges have been reported [8] . This usually happens for those systems whose mechanical properties can have specific benefits from the composite approach, at least in defined strain ranges. For instance, this is the case of small interactions between matrix and filler, as recognized in [7] and as it will be discussed in the following of this chapter. With respect to this, Fig. 6.2 shows an increase of the strain response achieved from a 100 %-pre-strained sample of silicone elastomer, loaded with 30 wt% (7.4 vol%) of a titanium dioxide (TiO 2 ) powder [8] .

More interesting results have been reported for organic dielectric fillers. As an example, Zhang et al. [18] mixed a silicone matrix ( � � m ~ 3) with a copper-phthalocyanine olygomer ( � � f ~ 10 000), obtaining increments of the dielectric constant up to about � � c � 6 for a filler concentration of 20 wt%, with a related electromechanical strain response of 12% at 26 V/µm. For this system the electromechanical

Ch06-I047488.indd 60 12/10/2007 8:20:58 PM

Enhancing the Dielectric Permittivity of Elastomers 61

response increased with the filler content. However, breakdown threshold was reduced, probably due to the formation of aggregates of copper-phthalocyanine particles.

Insulators are not the sole candidate materials as suitable fillers. In fact, dielectric improvements can be achieved with conductive (and semiconductive) fillers too, as described in the following.

6.3.3 Conductive and semiconductive fillers

The need for high permittivity fillers, as suggested by the mixing rules discussed above, has led to test also the effects of loading dielectric elastomers with conductive materials. The use of conductive fill-ers as a possible means to increase the dielectric permittivity is motivated by the fact that free charges not only contribute to conduction, but also they can give rise to Maxwell–Wagner polarization (see Eq. (6.4)). Nevertheless, as a drawback, such insulator–conductive composite systems are prone to show losses with percolative behaviour, which may result in a dramatic increase of their conductivity for filler concentrations exceeding a certain threshold v f , perc . The percolation threshold represents the filler concentration at which conducting paths between particles in contact with each other take place throughout the medium. Such a threshold strongly depends on the particle size and form factor [55] . Unfortunately, the maximum increase of the composite permittivity is achieved close to the percolation threshold, according to the following relation [56, 57] :

� �

� � �

� �

�

c mf,perc f

ff fwith 0.8 for

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

q

q 0 9. ,,perc

(6.20)

The parallel increases of both the dielectric constant and the overall losses are, of course, antag-onistic. This can seriously compromise the applicability of such types of systems as electromechanical transduction materials, due to their typically low dielectric strengths.

Some examples of systems adopting conductive and semiconductive fillers are reported below. Further details can be found in Table 6.2 .

As a specific type of conducting fillers, metals have been frequently tested. For instance, for mixtures of epoxy resins ( � � m � 5 at ~ 100 Hz) with 40 wt% copper particles or iron particles, values of � � c ~ 12 and � � c ~ 7.5, respectively, at 10 Hz with a rather limited loss factor (about 6–7) have been reported [11] . As a significant drawback, usually metallic fillers can dramatically increase the composite stiffness. Moreover, they can also show a lack of adhesion with the polymer matrix, with a further degradation of the mechanical properties of samples.

As an alternative to metals, graphitic conductors may provide advantages in terms of a superior sur-face compatibility with the polymer matrix. For instance, composites consisting of polymers loaded with carbon black particles are very common. The compatibility of carbon black with organic phases is demonstrated by its wide use with vulcanized rubbers for several types of common industrial applica-tions (tires, cables, etc.). As an example, for a carbon black-filled (18.76 vol%) polyurethane (PU) a

0 10 12 140

2

4

6

8

10

12

0

2

4

6

8

10

12

Tra

nsve

rse

stra

in (

%)

Electric field (V/µm)

Silicone � 30 wt% (7.4 vol%) TiO2

Silicone

2 4 6 8

0 10 12 142 4 6 8

Figure 6.2 Transverse strain versus electric field for samples made of a pure silicone elastomer (lower curve) and its composite with TiO 2 particles (higher curve), tested with a transverse pre-strain of 100% (adapted from [8] ).

Ch06-I047488.indd 61 12/10/2007 8:20:59 PM

62 Chapter 6

dielectric constant of 4400 has been described [13] . Likewise, carbon black-filled polyethylene (PE) samples showed large dielectric constants near the percolation threshold, varying from � � c ~ 20 for v f � 1.9 vol% up to � � c ~ 10 4 for v f � 2.5 vol% [14] .

In the light of reducing the stiffening introduced by an inorganic filler and simultaneously exploiting the drastic dielectric enhancement achievable near the percolation threshold (Eq. (6.20)), it is worth of note the work by Zucolotto et al. [58] ; they reported that, by loading a terpolymer styrene–ethylene–butylene with carbon black modified particles, the percolation threshold can be lowered down to 5 wt%, with evident advantages in terms of mechanical properties.

According to their amazing physical properties, and namely high electrical conductivity, carbon nano-tubes can also be used as electrically efficient fillers. Percolation threshold for carbon nanotube fillers can be considerably lower with respect to any other type of conducting filler. Accordingly, very small loading percentages (particularly advantageous in order to limit the elastic modulus) can offer interesting improve-ments of the dielectric permittivity. Nevertheless, attempts in this direction have so far produced compos-ites typically characterized by considerable losses, unsuitable for electromechanical applications. As an example, results concerning epoxy resin/carbon nanotubes composites (0.05 wt%) showing � � c � ~ 40 at ~ 10 Hz, but also losses of the order of 10 3 and elastic modulus increments of 20%, have been reported [16] .

In order to improve the compatibility with the polymer matrix, advantages can derive from the use of fillers consisting of organic conductors, in the form of either monomers or polymers. As an example, a work by Zhang et al. [19] reported for an electron-irradiated P(VDF–TrFE) copolymer (already stud-ied [33] ) filled with 40 wt% copper-phthalocyanine olygomer a composite dielectric constant of 425 at 0.1 Hz and a loss factor of about 0.7, starting from a matrix dielectric constant of 40.

Conducting and semiconducting polymers, such as polyanilines (PANIs), polythiophenes, polypyr-roles and polyphthalocyanines are frequently studied as possible fillers. For instance, by adding 70 wt% poly(copper phthalocyanine) ( � � f ~ 10 000) to a poly(ethylene-co-vinyl acetate) (EVA) matrix ( � � m � 3), an increase up to 40 at 1 Hz of the real dielectric permittivity was reported for the composite [7] . A work of Chwang et al. [21] describes a PU matrix filled with 17 wt% PANI and showing a composite dielectric constant of 1120; the authors underline the benefits of an ‘ in situ polymerization of PANI in PU matrix (ISP-blends) ’ with respect to a ‘ simple mixing of PANI and PU in aqueous solution (SM-blend) ’ . A more complex system, made of a bi-component matrix of PU and poly(copper phthalocya-nine) (poly(CuPc)) filled with 14 vol% PANI, showed a dielectric constant of about 800 at 1 Hz, along with an elastic modulus increase of about four times in comparison with the matrix [20] .

Concerning non-elastomeric matrices, all-polymer percolative electron-irradiated composites between poly(vinylidene fluoride–trifluoroethylene–chlorotrifluoroethylene) (P(VDF–TrFE–CTFE)) and PANI were described [22, 23] ; for a 25 vol% PANI loading, the composite showed a dielectric con-stant of about 5000 at 1 kHz, starting from a value of 60 for the pure matrix.

In general, conductive and semiconductive monomers and polymers can contribute to advantageously increase the orientational polarizability of the material. Nevertheless, they can give rise to percolation phenomena at high concentrations and bring great electric losses, due to their high electrons delocaliza-tion; such losses typically increase with the doping of the material.

6.3.4 Mechanical properties of random composites

Within an attempt of improving the electromechanical properties of a dielectric elastomer, the purely electrical analysis considered so far should always be parallel to an investigation of the effects on the mechanical properties of the material. In fact, any attempt of increasing the material dielectric constant should always preserve the mechanical compliance within an acceptable range. Approaches based on ran-dom composite can be particularly risky in this respect. The literature on composite systems is rich of models (not reported here) that propose possible composition rules of the elastic modulus. As a general property, it is worth mentioning that, as reasonably expected, such models foresee that the composite elastic modulus is intermediate between those of the constitutive phases. Accordingly, any advantageous increase of the dielectric constant can correspond to a disadvantageous mechanical stiffening. Such phe-nomena have, of course, antagonistic effects on the electromechanical strain response of the material.

Most of models for mechanical composition rules implicitly assume a perfect adhesion between the constitutive phases. This hypothesis is not always acceptable and it becomes quite unrealistic for specific types of systems, such as in the case of particle-loaded elastomers to be used for actuation, i.e. that have to sustain deformations. As a fact, the mechanical properties of composites can actually depend on

Ch06-I047488.indd 62 12/10/2007 8:20:59 PM

Enhancing the Dielectric Permittivity of Elastomers 63

several factors, such as filler type and geometry, its interaction with the host matrix, along with specific working conditions. Among the latter, eventual pre-strains (exerted by either external loads or internal parts of the device) play a relevant role; for instance, a decrease of the elastic modulus in elongated samples of a silicone elastomer loaded with PMN–PT or TiO 2 has been reported and interpreted as due to the formation of cavitations around the filler particles [6, 8] . An example is presented in Fig. 6.3 .

The cavitations, which are favoured by a lack of adhesion between the matrix and the particles, become progressively more and more important as the material elongation is increased. As previously introduced, this phenomenon can have a positive effect on the actual electromechanical properties of the composite material. The data reported in Fig. 6.2 offer an example of such a situation: the strain response of a sample of pure silicone is lower than that of a sample of the same material loaded with ceramic particles, when both samples are highly (100%) pre-strained; this evidence should be mainly attributed to the (significant) reduction of the elastic modulus, rather than to the (modest) increase of the dielectric constant [8] .

6.3.5 Dielectric strength of random composites

One of the typical drawbacks of the random composite approach consists of an observed substantial decrease of the material dielectric strength E break . More generally, it is straightforward to recognize that higher values of � � typically correspond to lower values of E break . This is a common experimental evi-dence, that can also be easily assessed from the large amount of literature data. This fact might be rea-sonably interpreted as mainly due to interfacial (Maxwell–Wagner) polarization phenomena [6, 8, 13] .

Although a general expression capable of reliably relating the dielectric strength and the dielectric constant of composites is currently not available, it is worth reporting at least a couple of simple models that can provide interesting estimates.

The first model deals with a very rough schematization: let us assume the elastomer as a homoge-neous material (that is not the case of random composites!) and a purely elastic body at low strains; for such conditions, it can be demonstrated [59] that in the case of Maxwell-stress actuation the nominal breakdown field of the material is given by the following expression:

EV

d

Y Ybreak

break

0

e� �� �

�1 2

0 020 6

2/ .

� � � �� (6.21)

where � � is the dielectric constant of the material, Y is its elastic modulus, V break is the breakdown volt-age of the sample and d 0 is its thickness at rest. This relation suggests that by increasing the dielectric constant of the material, its dielectric strength is expected to decrease as 1/ .�� Interestingly, such a trend has frequently been found to provide a satisfying fit of experimental data; as an example, see [60] .

0.00 100

0 30 60 90 120 150 180 210

200

Strain (%)

Str

ess

(MP

a)

300 400 500

0%

0%

10%

10%

20%

20%

30%

30%

600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.00

0.02

0.04

0.06

0.08

0.10

Figure 6.3 Stress–strain curves of silicone/PMN–PT composites for different volume fractions of the filler (adapted from [6] ).

Ch06-I047488.indd 63 12/10/2007 8:20:59 PM

64 Chapter 6

A subtler model is offered by the local field theory of dielectric media [61] . Let us consider a dielec-tric material subjected to an applied electric field E ; although the space-averaged electric field can be uniform, the actual internal electric field can locally vary from point to point, depending on interactions of local fields generated by dipoles. Accordingly, the local electric field E loc is defined as the field that actually acts on an individual polarizable unit (such as a molecule or an atom); it is also known as the Lorentz local field and it is given by the following expression [62] :

E Eloc �

��� 2

3 (6.22)

where, in this case, � � is the dielectric constant of the material surrounding the local polarizable unit (excluding the unit itself). Equation (6.22) can be used to obtain an expression that relates the dielectric constant and the dielectric strength of the matrix ( � � m , E break,m ) with those of the resulting composite ( � � c , E break,c ). In fact, let us assume that the value of the local breakdown field of the matrix is the same when the matrix is in its pure and in its composite form; in this case, by equating the right-hand mem-ber of Eq. (6.22) evaluated for both these situations, we obtain the desired expression:

� �� ��

� �mbreak,m

cbreak,c

2

3

2

3E E (6.23)

Moreover, Eq. (6.23) can be further developed by using for � � c one of the mixing rules previously described, according to different models. This can provide a useful tool in order to estimate the overall electrical behaviour of the composite system.

As a final remark, it is worth stressing that, despite the reduction of the dielectric strength typically observed in random composite systems, possible relative increases of the actuation performances at low electric fields demonstrated for some systems (as reported in the previous sections) encourage further investigations for possible uses at low voltages.

6.4 FIELD-STRUCTURED COMPOSITES

The dielectric constant of a random composite may result further increased by cross-linking the loaded elastomers under the action of a proper electric field. In fact, this may provide an alignment along a preferential direction of the intrinsic polar groups of both the material and the filler; this can happen especially if the latter exhibits ferroelectric properties. As a result, an increase of the global polarizabil-ity of the material may occur.

As an example, a silicone (polydimethyl-siloxane, PDMS) matrix loaded with 13 vol% SiO 2 cured under a field of 1 kV/mm showed a permittivity � � c � 25 in comparison with a dielectric constant � � m � 2.3 for the pure silicone [24] . Likewise, Khastgir and Adachi [25] described that filling a PDMS sample ( � � m � 5 at 100 Hz) with 13.7 vol% barium titanate (BaTiO 3 ) and curing the mixture under a DC electric field of 4 kV/cm, a permittivity � � c � 90 can be achieved.

Concerning non-elastomeric systems, a work of Wilson et al. [26] reported, for an epoxy resin loaded with 40 vol% lead titanate (PbTiO 3 ) and cured under a field of few hundreds V/mm, an increase of the die-lectric constant at 10 2 Hz from about 5 for the pure matrix, to about 16 for the field-structured composite.

As a general observation, it should be considered that field structuring provides a means to improve the material polarizability (and therefore its dielectric response) just along a definite direction, yielding a marked anisotropy in the material properties. This could not necessarily be a disadvantage for a mater-ial to be used for actuation; in fact, depending on the specific arrangement of the material within the actuator configuration, one could exploit this effect in order to increase the electromechanical coupling towards privileged directions, rather than others.

Nevertheless, it is worth of note that the actual electromechanical properties of field-structured sys-tems may result sensibly affected by possible decreases of the breakdown strength. In fact, depending on the nature and geometry of the filler, field structuring may introduce additional pathways for break-down currents.

According to these observations and given the inherent procedural complications of such a method of material processing, one can clearly recognize that it still poses many issues that need further basic investigations. Thus, deeper studies are currently necessary in order to assess the eventual suitability of such a technique for effectively enhancing the actuation performances of elastomers.

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Enhancing the Dielectric Permittivity of Elastomers 65

6.5 NEW SYNTHETIC POLYMERS

An ideal approach to obtain elastomers with specific improved dielectric properties is represented by a challenging synthesis of new molecular architectures. For instance, they might be obtained either as blends of known polymers or by copolymerization or by grafting of highly polarizable lateral chains to existing molecules ( Table 6.1 ). Some of the most significant examples of methods adopted so far in order to synthesize new polymers for actuation are briefly mentioned in the following. The related most important data are reported in Table 6.2 .

Butkewitsch and Scheinbeim described a thermoplastic elastomer consisting of a hydrated sul-phonated poly(styrene–ethylene/butylenes–styrene) triblock copolymer, whose dielectric constant was found to vary of four orders of magnitude (from 5 to 50 000), depending on both the amount of absorbed water and the sulphonation degree of the styrene groups ( Table 6.2 ) [27] . Nevertheless, the authors recognized also that this kind of material was too lossy for uses in Maxwell-stress actuators, due to a high hydrogen ions conductivity [27] .

Another interesting method to modify the dielectric properties of elastomers is the synthesis of liquid-crystalline elastomers, i.e. elastomer chains with grafted highly polarizable lateral groups [28] . In this type of materials the polarization phenomena can be enhanced by the rearrangement of the lateral group chains and the creation of crystalline regions [28] . Elastomers with grafted crystalline groups were also used by Su et al. [29] , in order to develop blends with the electrostrictive copolymer P(VDF–TrFE) ( Table 6.2 ).

As a different type of material, Jung et al. [30] reported the electromechanical properties of an acrylo–nitrile–butadiene rubber (NBR) used for dielectric elastomer actuation ( Table 6.2 ); this study compared the response of NBR with different state-of-the-art elastomers.

Chiou et al. [12] described a material consisting of immiscible silicone and PU that formed a system with two physically interpenetrating but chemically separated phases; the system was further modified, by introducing copper-coated phospholipidic tubules, which were found to be arranged along the mate-rial interfaces or in the component having the mayor affinity. For a 50–50 vol% PU-PDMS composite filled with 16 vol% tubules, a relative dielectric constant of about 40 at 10 GHz was measured [12] .

Blending of different polymers can result in new materials with potentially attractive properties. As an example, Huang et al. [20] proposed a blend of PU and phthalocyanine, which also included PANI, to obtain � � c ~ 800 at 1 Hz for a 14–15–85 vol% PANI-Pc-PU composition.

The blend approach was also used in a recent work, which described a silicone/polyhexylthiophene system [63] . Interestingly, very low percentages of polyhexylthiophene (1–6 wt%) yielded both an increase of the relative dielectric permittivity ( Fig. 6.4 ) and an unexpected reduction of the tensile elastic modulus ( Fig. 6.5 ). Both these factors synergically contributed to a remarkable increase of the electromechanical response, which reached a maximum at 1 wt% content of conjugated polymer as pre-sented in Fig. 6.6 (see also Table 6.2 ). We refer the reader to [63] for details and discussions.

3101 102 103 104 105 106 107 108

4

5

6

7

8

9

10

11

12

13

14

0 wt%Content of PHT:

1 wt%3 wt%5 wt%6 wt%

ε'

Frequency (Hz)

Figure 6.4 Frequency spectrum of the real part of the relative dielectric permittivity of a pure silicone rubber and its blends with different contents of polyhexylthiophene (adapted from [63] ).

Ch06-I047488.indd 65 12/10/2007 8:21:00 PM

66 Chapter 6

6.6 CONCLUSIONS

This chapter has presented the most followed techniques available at present in order to possibly enhance the dielectric permittivity of elastomers. The most significant state-of-the-art results have been reported. Random composites and field-structured composites represent readily applicable approaches suitable to actually increase the dielectric permittivity of elastomers. Nevertheless, such methods not always can guar-antee a real benefit in terms of resulting electromechanical properties. In fact, the possible material stiff-ening plays an antagonistic role, capable in some cases of exceeding any eventual electrical improvement. As a different approach, the most challenging synthesis of new highly polarizable polymers may offer, of course, superior opportunities, although at the price of considerably greater development times and costs. This represents one of the major future challenges for achieving new generations of more efficient dielec-tric elastomers suitable for more performing actuators, possibly requiring lower driving voltages.

References

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[2] Debye , P. ( 1912 ). The collected papers of Peter J. W. Debye (Interscience, New York, 1954) . Z. Physik , 13 , 97 .

8

00 1 2 3

Tra

nsve

rse

stra

in (

%)

4 5 6

Electric field (V/µm)

7 8 9 10 11 12 13 14 15

1

2

3

4

5

6

7Content of PHT:

0 wt%1 wt%3 wt%5 wt%6 wt%

Figure 6.6 Electromechanical strain response exhibited by the pure silicone rubber and its blends with different contents of polyhexylthiophene (adapted from [63] ).

140

Str

ess

(kP

a)

00 40 80 120 160 200 240 280

Strain (%)

320

20

40

60

80

100

120

Content of PHT:0 wt%1 wt%3 wt%5 wt%6 wt%

Figure 6.5 Stress–strain curves of both the pure silicone rubber and its blends with different contents of polyhexylthiophene (adapted from [63] ).

Ch06-I047488.indd 66 12/10/2007 8:21:00 PM

Enhancing the Dielectric Permittivity of Elastomers 67

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COMPLIANT ELECTRODES: SOLUTIONS, MATERIALS AND TECHNOLOGIES

Guggi Kofod 1 and Peter Sommer-Larsen 2

1 Applied Condensed-Matter Physics, Department of Physics, University of Potsdam, Potsdam, Germany

2 Polymer Department, Risø National laboratory, Roskilde, Denmark

Abstract

The role of the electrodes is to provide enough conductivity to let the dielectric elastomer actuator (DEA) charge

quickly, without impeding its mechanical motion, giving rise to the term ‘ compliant electrodes ’ . The approaches

can be split into two groups: those relying on thin metal film deposition and percolating networks of conducting

particles in an insulating matrix. The electrical and mechanical properties of either approach can be optimized for

the given actuator, to control the final actuation behaviour. Metal films can be structured through lithography or

other manufacturing processes, by which the actuation output can be forced into one preferred direction only. Metal

films of just 10–100 nm can be chosen, which endows the DEA with the added advantage of ‘ self-healing ’ capabil-

ities through localized breakdown sputtering of electrode material. The conduction and mechanical reinforcement of

percolating electrode systems must be understood in terms of complicated percolation theory; however, they permit

the use of very cheap materials like carbon black and a wealth of manufacturing procedures.

Keywords : Compliant electrodes, conducting particles, corrugation, electrical conductivity, insulating matrix,

lithography, mechanical stiffness, metal films, percolation, selective stiffening, self-healing.

7.1 SOFT CONDUCTING MATERIALS

The basic geometry of the dielectric elastomer actuator (DEA) is similar to that of a capacitor, con-sisting of an insulating film covered on both sides by compliant electrodes. In several of the preced-ing chapters, it has been described how the insulating material can be improved towards actuation, for instance, through optimization of network parameters or by inclusion of dielectric fillers. However, it is just as important that the compliant electrodes do not substantially impede the motion of the actuator. It is no surprise that a large number of approaches have already been suggested and tested, leading to a wealth of possibilities in the manufacture of compliant electrodes, drawing upon experience all the way from microelectromechanical systems (MEMS) to percolation physics.

Electrostriction in polymers was suggested as a means of actuation by Zhenyi et al. [1] , while Hirai et al. [2] presented the first actuator, a unimorph, based on electrostriction in elastomers. This type of actuator does not require compliant electrodes, since the electrodes experience strains of less than 1%. The first study to address the role and realization of compliant electrodes in detail was presented by Pelrine et al. [3] , which suggested a number of approaches: graphite powders and ionically conduct-ive water-based polymers used directly, as well as powders distributed in an elastomer binder material. Further, it was pointed out that metals would be highly preferable, but that they would have to be some-how structured, since simple thin metal films are not able to undergo large strains.

7.2 CONDUCTIVE FILLERS IN INSULATING MATRIX

The conductive fillers investigated are mainly carbon black particles in a soft polymeric matrix consist-ing of oil, gel or elastomer. The matrix provides the mechanical properties to the composite, while the

Chapter 7

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70 Chapter 7

conductive fillers provide conductivity. Since the DEAs usually demand the softest possible electrodes, the amount of filler should be as low as possible, to keep the elastic modulus of the composite low.

7.2.1 The percolation phenomenon for conducting composites

Composites of randomly mixed conducting and insulating parts display percolation, a critical phenom-enon resulting in an insulator–conductor transition when the volume percentage of the conductive filler rises above the percolation threshold [5] . Since the elastic modulus of the composite increases when filler is added [6] , it is often preferred to use filler particles with a low percolation threshold. In order to obtain high conductivity, the particles must be well dispersed in the insulating matrix.

The transition from insulator to conductor upon increasing the amount of the conductive phase (illus-trated in Fig. 7.1 ) is abrupt. Starting from the pure matrix, the addition of a small amount of conducting filler does not result in a conducting composite, since the particles are not close enough to form con-ducting pathways throughout the composite. When the concentration of conductive filler is increased (moving to the right in Fig. 7.1 ), the agglomerates begin to coalesce, and a continuous network forms, resulting in an increase of the conductivity of several orders of magnitude. Also other electrical proper-ties experience dramatic changes and near to the percolation threshold, many systems obey a general-ized formula: Q

x� � �� c , where Q denotes an electrical quantity, v is the volume fraction of the filler, v c is the percolation threshold and x is a universal exponent, which takes different values below and above the threshold [7] . For conductivity and permittivity, the exponent x is 0.87 below the percola-tion threshold and 2.0 above the threshold.

The effective-medium approximation (EMA) describes the conductivity of binary mixtures not too near to the percolation threshold. The EMA approximates the system with a fictitious homogeneous lattice of arbitrary dimensionality (a simple cubic lattice in the d = 3-dimensional case), where nodes are connected with bonds of different property, which could be either insulating ( � = 0), conducting ( � = � 1 ) or superconducting ( � = � ) [5, 8] . The bonds properties are randomly distributed, and in the conductor–insulator case (no superconducting bonds) the EMA conductivity becomes

� ��

�

��1

1

1

0

p p

pp pc

ccfor

otherwise

⎧⎨⎪⎪⎪

⎩⎪⎪⎪

where p is the relative number of conducting bonds (lattice occupancy). Here, the percolation thresh-old is located at an occupancy p c = (1 – d ). This corresponds to a percolation threshold of 1/2 in the 2-dimensional case and 1/3 in the 3-dimensional case. Through more rigorous simulations of the same system, it was found that the 2-dimensional result for the percolation threshold seems valid, while the 3-dimensional percolation threshold is lower than predicted by the effective-medium approach, and appears to be about 0.25 in the 3-dimensional bond percolation case [8] . The volume fraction of filler particles is given by the lattice occupancy and the packing factor of the filler (for instance 0.74 for a hexagonal close packing of spheres). The percolation threshold v c for spheres is approximately 16%.

The amount of filler required to obtain conductivity depends on the shape of the filler particle and on how well dispersed the filler is in the matrix. Filler particles with high aspect ratios or a shape far from spherical, or which form highly structured agglomerates, are all able to display percolation thresholds far below the limiting 16% volume fraction for spherical particles. As an extreme case could be men-tioned functionalized single wall carbon nanotubes, which form conducting composites in polystyrene

Figure 7.1 The composite becomes percolating when the volume percentage of filler material is high enough that conducting pathways form throughout the composite (adapted from [4]).

Ch07-I047488.indd 70 12/10/2007 8:21:41 PM

Compliant Electrodes: Solutions, Materials and Technologies 71

at a loading of just 0.1% weight fraction [14] . Table 7.1 summarizes some common carbon black types and their percolation thresholds.

7.2.2 Cured electrodes

Electrodes based on carbon black fillers in a curable elastomer can be produced either by mixing the rele-vant components or from ready-made commercial systems. Kofod [4] and Carpi et al. [15] both used a one-component silicone mixed with Ketchenblack EC and Vulcan XC-72, respectively. The mixture was dissolved in a volatile solvent and sprayed on the substrate elastomer using an air-brush. The electrode was then cured for hours typically. Kofod used a silicone (Wacker Elastosil ™ RT625) substrate elastomer and stretched it before applying the electrode. The elastomer was kept stretched while the electrode cured. After releasing the stress, the electrode formed regular buckles (see Fig. 7.2 ). The work demonstrated that the mechanical stiffness of the buckled electrode was negligible compared to that of the underlying elas-tomer. The next chapter discusses the compliance of buckled electrodes in more details.

7.2.3 Particulate electrodes without binding materials

Electrodes can be produced directly on top of an elastomer layer, without the inclusion of a binder material. Jungmann and Schlaak [16] describe the manufacture of a multi-layer structure. A two-component silicone elastomer layer is produced through spin coat, then a layer of graphite particles are brushed on top of the silicone layer through a mask. The resulting layer has a surface resistance of about 3 k � / sq. , and it is possible to directly spin coat another layer of silicone rubber directly on top of the brushed electrode. The approach was automated and structures with several hundred layers could be prepared.

7.3 METAL FILMS FOR COMPLIANT ELECTRODES

Metal coatings are commonly used in the plastics industry as gas and moisture barriers but also for electromagnetic interference, electrostatic discharge and electric circuitry applications. The processing methods are well established and used for high volume production. Vacuum coating – evaporation and sputtering, plating methods and conductive paints are generally used. Hence, metals are attractive as

Figure 7.2 Microscope images – at 20 � and 50 � magnification – of PDMS/Ketjenblack electrodes sprayed on a stretched elastomeric substrate. The buckles form when the ‘substrate’ silicone elastomer film is relaxed, by which the electrodes that are sprayed on top will suffer compressive strain, which is relieved by buckling (adapted from [4]).

Table 7.1 Percolation thresholds for common carbon blacks.

Carbon Black Percolation Threshold/Matrix Material/Method

Vulcan XC-72, Cabot Corp. 5 wt%/in HDPE/extrusion [9]6 vol%/in PP/torque mixing [10]

Ketjenblack EC300J, Akzo Nobel � 5 vol%/silicone oil/hesxane + ultrasound [4]

Raven 7000, Columbian Chem. Corp. 2.75 vol%/epoxy resin/‘mixing’, curing [11] � 4.5 vol%/diglycidyl ether of bisphenol F/propeller blade [12]

Shawinigan Acetylene Black P-1250 (VSP) � 15 wt%/EPDM rubber/mixing mill [13]

Ch07-I047488.indd 71 12/10/2007 8:21:42 PM

72 Chapter 7

electrode materials for actuators. However, a metal film coated onto an elastomer is not compliant. In order to show an appreciable conductivity the film must be sufficiently thick to be continuous and as metals elastic moduli are orders of magnitude times higher than elastomers, the coating layer also becomes much stiffer than the underlying elastomer. To overcome this limitation, metal electrodes must be structured on a scale comparable with the thickness of the elastomer film.

Recently, flexible metal electrodes have become a topic of interest for a growing number of research-ers dealing with electronics for flexible applications. See references below in the paragraph on buckling metal films.

Gold electrodes in forms of zig-zag strips on a dielectric elastomer was manufactured using photo-lithography by Pelrine et al. [3] . Benslimane and Gravesen [17] also used photolithography to manufac-ture the fully connected pattern illustrated in Fig. 7.3 . Both patterns utilize that the electrode lines bend when the elastomer is stretched. The pattern in Fig. 7.3 is furthermore compliant in one direction only.

Corrugated electrode patterns were demonstrated by Benslimane et al. [18] . Figure 7.4 shows the design. Typical dimensions for a sinusoidal corrugated profile are a period of 10 µm and an amplitude of 2 � m imprinted in a 20–40 � m thick polydimethylsiloxane (PDMS) film. A 50–100 nm thick silver layer is deposited on top of the corrugated profile. The compliance factor – the increase in compli-ance relative to a flat metal electrode of the same thickness – for a rectangular profile was estimated by Benslimane and Gravesen [17] in the limit of small deformations and large compliance factor to f C = 16( a / p )( a / h ) 2 . The thickness of the electrode is h , whereas p and a are period and amplitude of the profile, respectively. A smooth profile can be approximated by segments of a circular arc – at least for an aspect ratio less than ½. This profile is illustrated in Fig. 7.5 and its compliance factor is f C = 12( p / s )( a / h ) 2 . Here, s is the arc length along the full period. The effective Young ’ s modulus for a cor-rugated electrode is Y corr = Y metal / f C . The force constants of the compliant electrode and the rubber film are added in parallel resulting in an total modulus for the structure of Y total � Y corr ( h / d ) + Y rubber . The thickness of the rubber film is denoted d and its Young ’ s modulus is Y rubber . If one takes the dimensions of the structure given above � 50 nm Ag film, 20 � m PDMS, 2 � m amplitude and 10 � m period – and use a Young ’ s modulus of 83 GPa for bulk silver and 0.8 MPa for PDMS, one finds that the corrugated electrode contributes only a few per cent to the total modulus.

The effect may be even less. The effective Young ’ s modulus of thin silver films as function of their thickness was studied in [19] . The modulus coincides with that of bulk silver for thicknesses down to

15 �m

50 �m

Gold layercontact pad

Figure 7.3 Unidirectional compliant electrode manufactured by photolithography (Benslimane & Gravesen, Danfoss A/S, 2000 – adapted from [17]).

Actuation andcompliance direction

Stiffness direction

Contraction direction

Figure 7.4 Design of corrugated electrode.

Ch07-I047488.indd 72 12/10/2007 8:21:42 PM

Compliant Electrodes: Solutions, Materials and Technologies 73

50 nm. The modulus decreases for decreasing thicknesses below 50 nm. The decrease in modulus was interpreted as the effect of a relative increase in boundaries between crystalline grains and in surface area as film thickness decreases. The modulus was half the bulk value for a 6 nm film. That study dealt with films deposited on a silicon substrate. Metal films deposited on a soft rubber may be even more compliant. Bowden et al. [20] found that gold films evaporated on PDMS buckled as result of thermal contraction of the PDMS and that ordered buckling structures was formed. Lacour and coworkers in a series of papers showed how this effect could be utilized to construct electrode connections for stretch-able electronics [21–29] . Electrodes capable of 23% stretching were demonstrated in these studies.

Enhanced buckling is obtained when the elastomeric substrate is prestretched before deposition of the metal electrode. Watanabe [30–33] stretches the PDMS substrate 20% and deposits gold and even conducting polypyrrole on top. Corrugation amplitudes of 1 � m and periods varying from 7 to 41 � m were obtained depending on the thickness of the gold film. Many examples of microfabricated stretch-able patterns can be found in the literature. One beautiful example is a conductive wire made from sem-icircular arc segments imbedded in a silicone film [34] . Visual inspection demonstrates that stretching of this wire is possible almost to the theoretical limit and that the deformation is regular. Imperfections in shape are bound to cause failure because deformation becomes irregularly distributed along the elec-trode resulting in cracks or fracture. The wire in [34] is however perfectly shaped.

7.3.1 Deformation of corrugated electrodes

The corrugated electrodes described in [18] are produced by spin casting a solution of the substrate elastomer on a wafer. The corrugation profile is etched into the wafer using microtechnology methods. The elastomer film is removed from the wafer and silver is coated on the corrugated side. Two such films are assembled to form an actuator with corrugated electrodes on both sides. The corrugation pro-file was revealed by atomic force microscopy (AFM) and confocal laser scanning microscopy (CLSM) of a cross-section of the film (see Fig. 7.6 ). The AFM profile of a high aspect ratio structure is imprecise due to the finite size of the AFM tip. The laser microscope images reveal a less regular profile than obtained with AFM.

Shridhar et al. [35] studied the stiffness of actuators as function of the Ag film thickness. Figure 7.7 shows a representative set of results: stress versus strain curves that are reversible for extensions up to a critical value – the compliance limit. For larger extensions the curves show hysteresis. Subsequent resistance measurements show that the electrode fractures and looses conductivity when extended beyond the compliance limit. The compliance limits and the stress at these limits are shown in Fig. 7.8 . The effective moduli of the films at small deformations are likewise shown. The data show a def-inite increase in modulus with increasing thickness of the silver layer. The modulus, however, increases faster with Ag thickness than expected for a circular arc segment structure. The compliance limit does not show large variation, most likely due to imperfection in the profile. The compliance limit is also smaller than expected if the profile was composed of circular arc segments. Such a profile is compliant almost up to the theoretical strain at full extension of the profile. The strain at full extension is given in Table 7.2 for various ideal profiles. In case of the dimensions in this study, the limit is 38% for a circular arc segment profile and 28% for a triangular profile of the same amplitude and period. The conclusion is that the experimental profile is quite imperfect and more triangular like than circular arc segments.

The actual compliance limit may approach the strain at full extension for smooth profiles with con-tinuous derivatives. In the rectangular or triangular profile, the radius of curvature in the kinks is so

a

sp

Figure 7.5 Corrugated profile composed of circular arc segments. The amplitude, period and segment length are denoted by a, p and s, respectively.

Ch07-I047488.indd 73 12/10/2007 8:21:43 PM

74 Chapter 7

small that local stress beyond the ultimate strength of the metal film develops at these sites before full extension of the profile is reached.

7.4 UNCONVENTIONAL ELECTRODE MATERIALS

7.4.1 Self-assembled gold nanoparticle–rubber composites – Metal Rubber™

One approach to softer conducting materials is based on electrostatic self-assembly (ESA). A substrate is dipped alternately in polyanion and polycation solutions, with attached gold nano-clusters [36] .

10(a) (b)

210

�1�2

�m

20�m

30

Figure 7.6 Profile of corrugated electrode obtained with tapping mode (a) AFM and (b) a CLSM image of a cross-section of the film. The approximately 10 �m period and 2 �m amplitude are observed in both methods but the CLSM reveals a less regular profile than the AFM. The period measured with AFM is expected to be more accur ate than the CLSM measurements due to better calibration. The amplitude and profile are however influenced by the finite size of the AFM tip.

0.0 0.1 0.2 0.3 0.4 0.5

0.0

500.0 k

1.0 M

1.5 M

2.0 M

2.5 M

3.0 M

3.5 M

4.0 M

4.5 M

5.0 M

VI

V

IVIII

II

I

I 0.00 kÅII 0.50 kÅIII 0.75 kÅIV 1.00 kÅV 1.25 kÅVI 1.50 kÅ

Str

ess

(Pa)

Strain

Figure 7.7 Stress–strain behaviour of actuators with corrugated electrodes. Ag electrodes with thicknesses from 500 to 1500 Å were tested. An electrode can reversibly extend 25–30%. At higher extensions, the stress increases steeply. Afterwards, the electrode starts to fracture and the stress increases more slowly with strain. On subsequent contraction, the stress follows a smooth curve, but the electrode has lost conductivity. The compliance limit of an electrode is estimated from the crossing between two straight lines fitted to the initial part of the curve and the steeply increasing part of the curve (adapted from [35]).

0

Mod

ulus

(M

Pa)

Str

ess

(Pa)

0

1

2

3

450.30

0.240.250.26S

trai

n

0.270.280.29

1.3E�06

1.2E�06

1.1E�06

1.0E�06

9.0E�05

8.0E�05250 500 750

Ag thickness (AA)

1000 1250 1500500 750

Ag thickness (AA)

1000 1250 1500

Figure 7.8 Strain and stress at the compliance limit of actuators with corrugated Ag electrode. The effective Young’s modulus is shown to the right.

Ch07-I047488.indd 74 12/10/2007 8:21:43 PM

Compliant Electrodes: Solutions, Materials and Technologies 75

The multi-layered material thus prepared is capable of stretching more than 1000%, and can be pre-pared with a Young ’ s modulus from 1 to 100 MPa, while retaining its good conducting properties and a certain degree of transparency. The company NanoSonic has already shown many commercial applica-tions of this material.

7.4.2 Platinum salt reductions

Another approach forms the conducting particle network directly inside the matrix by chemical reduc-tion [37] . An elastomer pre-cursor is mixed with a platinum salt. The photo-initiated cross-linking of the elastomer prepares the electrode in the wanted shape. The material is then dipped in a reduction solution to precipitate the platinum particles inside the matrix. Particles of both spherical- and needle-like shapes appear. The materials become conducting when the platinum salt concentration is above 9%, and these materials can be stretched for about 40%. This preliminary work seems quite promising.

7.4.3 Ion implantation

Ion implantation is the process of bombarding the surface of the elastomer with metallic ions in order to make it conductive. Dubois [38] reports on the fabrication of microactuators based on ion implanted dielectric electroactive polymer (EAP) membranes. Ti-ions are implanted in the upper 10 nm of a PDMS elastomer. They find surface resistivities of the order 100 k � / sq . The authors report a ratio of out-of-plane displacement to diaphragm size of 13%, which was approximately eight times larger than the ratio previ-

ously reported for a microfabricated dielectric elastomer diaphragms having metal evaporated electrodes.

References

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elastomer-actuator . Angew. Makromol. Chem. , 240 , 221 .

[3] Pelrine , R. E. , Kornbluh , R. D. and Joseph , J. P. ( 1998 ). Electrostriction of polymer dielectrics with compliant

electrodes as a means of actuation . Sens. Act. A Phys. , 64 , 77 .

[4] Kofod, G. (2001). Dielectric elastomer actuators. Risø National Laboratory / Danish Technical University,

Pitney Bowes Management Services Denmark A/S. ISBN 87-550-2925-6, http://www.risoe.dk/rispubl/POL/

polpdf/ris-r-1286.pdf

[5] Clerc , J. P. , Giraud , G. , Laugier , J. M. and Luck , J. M. ( 1990 ). The electrical conductivity of binary disor-

dered systems, percolation clusters, fractals and related models . Adv. Phys. , 39 , 191 .

[6] Klüppel , M. , Schuster , R. H. and Heinrich , G. ( 1997 ). Structure and properties of reinforcing fractal filler

networks in elastomers . Rubber Chem. Technol. , 70 , 243 .

[7] Wu , J. and McLachlan , D. S. ( 1997 ). Percolation exponents and thresholds obtained from the nearly ideal

continuum percolation system graphite–boron nitride . Phys. Rev. B Condens. Matter Mat. Phys. , 56 , 1236 .

[8] Kirkpatr , S. ( 1973 ). Percolation and conduction . Rev. Mod. Phys. , 45 , 574 .

[9] Foulger , S. H. ( 1999 ). Electrical properties of composites in the vicinity of the percolation threshold . J. Appl. Polym. Sci. , 72 , 1573 .

Table 7.2 Strain at full extension of ideal corrugation profiles ordered after decreasing compliance.

Profile Strain at Full Extension – S max S max for a = 2 μm and p = 10 μm

Rectangular xa 0.8

Circular arc segment 1

2 1

2

2

�

���x

x

x

xsin 1 2

1⎛

⎝⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

0.38

Sinusoidal4

42

2

2�

���

��

22

2b1x E

x

x

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

0.32

Triangular1 2� �x 1

0.28

ax = 4a/p, where a and p are amplitude and period, respectively. bE is the complete elliptical integral of the second kind.

Ch07-I047488.indd 75 12/10/2007 8:21:44 PM

[10] Zhang , Q. H. and Chen , D. J. ( 2004 ). Percolation threshold and morphology of composites of conducting

carbon black/polypropylene/EVA . J. Mater. Sci. , 39 , 1751 .

[11] El Malhi , M. , Achour , M. E. , Lahjomri , F. and Bensalah , Y. ( 1999 ). Dielectric response in carbon black-

epoxy resin composites . J. Mater. Sci. Lett. , 18 , 613–616 .

[12] Brosseau , C. , Boulic , F. , Queffelec , P. , Bourbigot , C. , LeMest , Y. , Loaec , J. and Beroual , A. ( 1997 ). Dielectric

microstructure properties of polymer carbon black composites . J. Appl. Phys. , 81 , 882 .

[13] Sau , K. P. , Chaki , T. K. and Khastgir , D. ( 1997 ). Conductive rubber composites from different blends of

ethylene-propylene-diene rubber and nitrile rubber . J. Mater. Sci. , 32 , 5717 .

[14] Ramasubramaniam , R. , Chen , J. and Liu , H. ( 2003 ). Homogeneous carbon nanotube/polymer composites for

electrical applications . Appl. Phys. Lett. , 83 , 2928 .

[15] Carpi , F. , Migliore , A. , Serra , G. and De Rossi , D. ( 2005 ). Helical dielectric elastomer actuators . Smart Mater. Struct. , 14 , 1210 .

[16] Jungmann, M. and Schlaak, H. F. (2002). Miniaturised electrostatic tactile display with high structural com-

pliance, Eds. Wall, S. A., Riedel, B., Crossan, A. and McGee, M. R., EuroHaptics , Edinburgh.

[17] Benslimane, M. and Gravesen, P. (2000). ARTMUS Status Report 2000.

[18] Benslimane , M. , Gravesen , P. and Sommer-Larsen , P. ( 2002 ). Mechanical properties of dielectric elastomer

actuators with smart metallic compliant electrodes . Proc. SPIE Int. Soc. Opt. Eng. , 4695 , 150 .

[19] Mizubayashi , H. , Matsuno , J. and Tanimoto , H. ( 1999 ). Young ’ s modulus of silver films . Scripta Mater. , 41 , 443 .

[20] Bowden , N. , Brittain , S. , Evans , A. G. , Hutchinson , J. W. and Whitesides , G. M. ( 1998 ). Spontaneous forma-

tion of ordered structures in thin films of metals supported on an elastomeric polymer . Nature , 393 , 146 .

[21] Wagner , S. , Lacour , S. P. , Jones , J. , Hsu , P. H. I. , Sturm , J. C. , Li , T. and Suo , Z. ( 2004 ). Electronic skin:

architecture and components . Physica E Low-Dimens. Syst. Nanostruct. , 25 , 326 .

[22] Jones , J. , Lacour , S. P. , Wagner , S. and Suo , Z. ( 2004 ). Stretchable wavy metal interconnects . J. Vac. Sci. Technol. A , 22 , 1723 .

[23] Lacour , S. P. , Jones , J. , Wagner , S. , Li , T. and Suo , Z. ( 2006 ). Elastomeric interconnects . Int. J. High Speed Electr. Syst. , 16 , 397 .

[24] Lacour , S. P. , Wagner , S. , Prahlad , H. and Pelrine , R. ( 2004 ). High voltage photoconductive switches of

amorphous silicon for electroactive polymer actuators . J. Non-Cryst. Solids , 736 , 338 – 340 .

[25] Lacour , S. P. , Chan , D. , Wagner , S. , Li , T. and Suo , Z. ( 2006 ). Mechanisms of reversible stretchability of thin

metal films on elastomeric substrates . Appl. Phys. Lett. , 88 .

[26] Lacour , S. P. , Prahlad , H. , Pelrine , R. and Wagner , S. ( 2004 ). Mechatronic system of dielectric elastomer

actuators addressed by thin film photoconductors on plastic . Sens. Act. A Phys. , 111 , 288 .

[27] Lacour , S. P. , Wagner , S. , Huang , Z. and Suo , Z. ( 2003 ). Stretchable gold conductors on elastomeric sub-

strates . Appl. Phys. Lett. , 82 , 2404 .

[28] Li , T. , Suo , Z. , Lacour , S. P. and Wagner , S. ( 2005 ). Compliant thin film patterns of stiff materials as plat-

forms for stretchable electronics . J. Mater. Res. , 20 , 3274 .

[29] Li , T. , Huang , Z. , Suo , Z. , Lacour , S. P. and Wagner , S. ( 2004 ). Stretchability of thin metal films on elastomer

substrates . Appl. Phys. Lett. , 85 , 3435 .

[30] Watanabe , M. ( 2005 ). Wrinkles formed on a thin gold film deposited onto stretched elastic substrates . Polym. Adv. Technol. , 16 , 744 .

[31] Watanabe , M. ( 2005 ). Striped-pattern formation of a thin gold film deposited onto a stretched elastic silicone

substrate . J. Polym. Sci. B Polym. Phys. , 43 , 1532–1537 .

[32] Watanabe , M. ( 2006 ). Shrink-induced striped pattern on a thin gold film and switching of its orientation .

J. Appl. Polym. Sci. , 101 , 2040 .

[33] Watanabe , M. ( 2006 ). Preparation of polypyrrole film with well-ordered corrugation . Synt. Met. , 156 , 597 .

[34] Gray , D. S. , Tien , J. and Chen , C. S. ( 2004 ). High-conductivity elastomeric electronics . Adv. Mater. , 16 , 393 .

[35] Shridhar, M. H., Sommer-Larsen, P., Hillersborg, S., Kofod, G., Benslimane, M. and Gravesen, P. (2002).

Silicone elastomer as dielectric actuators. Proceedings of the ACTUATOR 2002 8th International Conference on New Actuators , Annex 10-6-2002.

[36] Claus , R. O. , Goff , R. M. , Homer , M. , Hill , A. B. and Lalli , J. H. ( 2006 ). Ultra-low modulus electrically con-

ducting electrode materials . Proc. SPIE Int. Soc. Opt. Eng. , 6168 , 460–464 .

[37] Delille , R. , Urdaneta , M. , Hsieh , K. and Smela , E. ( 2006 ). Novel compliant electrodes based on platinum salt

reduction . Proc. SPIE Int. Soc. Opt. Eng. , 6168 .

[38] Dubois , P. , Rosset , S. , Koster , S. , Stauffer , J. , Mikhaïlov , S. , Dadras , M. , De Rooij , N.-F. and Shea , H. ( 2006 ).

Microactuators based on ion implanted dielectric electroactive polymer (EAP) membranes . Sens. Act. A , 147 ,

130 – 131 .

76 Chapter 7

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Section III

Devices

Sec3-I047488.indd 77 12/11/2007 9:59:33 AM

Sec3-I047488.indd 78 12/11/2007 9:59:33 AM

FUNDAMENTAL CONFIGURATIONS FOR DIELECTRIC ELASTOMER ACTUATORS

Roy Kornbluh

SRI International, Menlo Park, CA, USA

Abstract

The functional element of dielectric elastomer actuators is a simple flat and flexible layered structure that may be

incorporated into a wide variety of possible configurations. This versatility allows the configuration to be tailored for

the desired output size scale, modality, and characteristics as well as conforming to the desired form factor. However,

the unique characteristics of dielectric elastomers also present some challenges when designing or selecting an actua-

tor configuration. In particular, the design must consider the high compliance of most dielectric elastomer materials in

order to effectively couple the actuator force and displacement to the output. Additionally, dielectric elastomer mate-

rials such as acrylics operate most effectively when there is a ‘ prestrain ’ applied to the elastomer film. The actuator

configuration must maintain this prestrain. A variety of actuator configurations have been developed to exploit the

capabilities of dielectric elastomers while addressing their unique challenges. These configurations range from simple

bending beam, diaphragm or stacked structures analogous to piezoelectric materials to muscle-like rolled actuators

to enhanced configurations such as entirely flexible thickness-mode actuators for haptic feedback, arrays of largely

transparent framed actuators for optical devices or large spherical balloon-like actuators for aerospace and acous-

tic applications. In addition to direct-drive actuators, dielectric elastomers can also be incorporated into a variety of

motor configurations as well as generators and sensors and active laminates for smart structures.

Keywords : Actuator, bending beam, configuration, design, diaphragm, generator sensor, haptic display, impedance

matching, motor, multifunctionality, roll, smart structures, thickness-mode, transducer.

8.1 INTRODUCTION

The preceding chapters have thus far discussed the phenomenon of dielectric elastomer actuation and the materials used to produce it. Here, we for the first time discuss how one would design a functional actuator that effectively uses the phenomenon of dielectric elastomer actuation. This chapter will show the large diversity of possible actuator configurations possible with dielectric elastomers.

Designing and building practical devices from dielectric elastomers is not fundamentally any more complex than designing and building devices from other actuator technologies. In fact, because of the simple basic structure, we can argue that a dielectric elastomer actuator is far simpler than an elec-tromagnetic actuator since there is no need to worry about bearings and high precision gap spacing. Further, since elastomers can be formed or deformed into virtually any shape desired and are far less temperamental than ceramics, we can argue that dielectric elastomer actuators are more versatile than piezoelectric actuators. Nonetheless, the unique characteristics of dielectric elastomers, particularly the high strain and compliance of the materials does present some technical challenges. In this chapter, we consider these design challenges and show a range of actuator configurations. Basic configurations are first presented followed by those that build upon the basic designs in order to offer better performance or exploit unique capabilities of dielectric elastomers.

Because of the great versatility of dielectric elastomers, it is not possible to comprehensively present all possible designs. Rather we offer the most basic designs and then describe how design principles have influenced the development of enhanced actuator configurations as a starting point. Subsequent chapters in this section of the book as well as subsequent chapters in the Applications sections of this book will explore other configurations unique to certain applications.

Chapter 8

Ch08-I047488.indd 79 12/10/2007 8:22:11 PM

80 Chapter 8

8.2 BASIC CONFIGURATIONS

The basic functional element of dielectric elastomer actuation consists of a thin elastomeric film sand-wiched between compliant electrodes (see Fig. 8.1 ). Although it is easy to understand how this element works, it does not really explain how we can make a practical actuator. Typically, we want to not only change the shape of the film but also actually move something with the film. There are many ways in which the basic functional element can be incorporated into an actuator. Figure 8.2 shows several basic actuator configurations.

These configurations are similar to those used for piezoelectric materials. This similarity is not sur-prising, since piezoelectric materials have the same basic functional element structure. However, there are important differences between actuator configurations for dielectric elastomers and piezoelectrics or other electric-field-activated materials. Most obviously, the magnitude of the strains is far greater with dielectric elastomers. This large strain allows the bending beam actuators to go from straight to tightly curled. The diaphragm can change from flat to hemispherical. Beyond the amount of strain, the following section describes the issues that make dielectric elastomers unique.

8.3 DIELECTRIC ELASTOMER ACTUATOR DESIGN ISSUES AND UNIQUE FEATURES

In contrast to many other electroactive materials such as piezoelectric ceramics and magnetostrictive ceramics, electroactive polymers are relatively compliant and capable of extremely large strains. For example, one type of dielectric elastomer, acrylic, is capable of actuating with more than 300% strain and has an effective elastic modulus of roughly 1–5 MPa when prestrained. PZT, a type of piezoelectric ceramic, can produce only 0.1% strain and has an elastic modulus of roughly 65 GPa. This high com-pliance and large strain capability present both opportunities and design challenges.

Figure 8.1 Basic functional element of a dielectric elastomer actuator.

Active electrodearea Direction of motion

V

V

V

V

V1

V2 V(a)

(d) (e)

(b)

(c)

Figure 8.2 Basic dielectric elastomer actuator configurations: (a) stack, (b) extender, (c) bimorph and unimorph bending beam actuators, (d) diaphragm and (e) tube.

Polymer film

Voltage on

Voltage off

Compliant electrodes(on top and bottomsurfaces)

V

zx

y

Ch08-I047488.indd 80 12/10/2007 8:22:11 PM

Fundamental Configurations for Dielectric Elastomer Actuators 81

Specifically, these design challenges include the following:

● Loading condition : Coupling the electrostatically induced actuation forces with forces imposed by the external load (if any).

● Maintaining tension or prevention of buckling : The basic operating element of the actuator is a thin and soft film. The actuator design and loading condition must ensure that the film does not undesir-ably buckle.

While the use of soft polymers presents many challenges, many properties of polymers can be exploited in actuator designs. Polymers in general, and the majority of the elastomeric polymers used in dielectric elastomer actuators, have many desirable features that can be exploited in actuators:

● Monolithic structure : Polymers can easily be formed into large area sheets or almost any desired shape. ● Flexibility and conformability : Since the polymers are soft, the actuators as a whole will be flexible

and can easily conform to different shapes or follow surface contours. ● Transparency : Many of the elastomers used for dielectric elastomers are transparent. This can be

exploited for optical applications or simply allow one to see through the actuators. ● Multifunctionality : Polymers can be easily incorporated into structures to serve not only as actuators

but also to serve structural or protective functions.

The following sections describe how these design challenges and unique properties have led to a variety of actuator configurations.

8.4 ENHANCED ACTUATOR CONFIGURATIONS

8.4.1 Configurations for coupling effectively to loads

The actuator configuration and geometry must ensure that the strains induced in directions orthogonal to the output direction do not adversely affect the desired stresses and strains in the output direction.

The importance of proper loading of the polymer material can be illustrated with a simple example. Imagine trying to push a heavy weight across a table by pumping water into a balloon that is in con-tact with the weight. The balloon would tend to bulge out at the sides rather than push the weight. To a lesser extent, the same thing happens when the electrostatic compression of a dielectric elastomer is poorly coupled to an actuator output. In our balloon analogy, proper loading would restrain the bulging in the undesirable lateral directions.

This restraint could be achieved several ways. Rings could be built into the balloon film that would restrain the lateral bulging while permitting the expansion in the desired direction. The balloon could be of a shape that is already flattened against the weight. Alternatively, an external mechanism could allow the lateral expansion to push the weight in parallel with the expansion of the balloon in the desired direction of the push. Such a mechanism could consist of a loosely woven tube that is narrower towards the centre than at the ends.

Like the water in the balloon, the dielectric elastomer material is essentially incompressible. In the most basic actuation configuration, such as that depicted in Fig. 8.1 , the electrodes uniformly impart an effective compressive stress in the z -direction, which tends to decrease the thickness of the polymer film. The incompressible polymer film expands in area so that the total volume of polymer between the electrodes is conserved. Depending on the loading, the area expansion can occur equally in both planar directions or in a single planar direction.

In many applications, motion is desired only in a single planar direction. As in the balloon example, we can restrain expansion in the undesirable direction or couple both directions of expansion into the desired output direction.

Undesirable deformation can be restrained by adding anisotropy into the material, or by changing the geometry, such as making the active area much wider than it is long. This latter approach is shown in Fig. 8.3 . Note that this basic design could also be rolled up.

In contrast to constraining one direction of deformation, both planar directions of deformation can also be coupled into a single desirable output direction. Two methods are shown in Fig. 8.4 . The spider configuration is similar to the moonie or cymbal actuators [1] .

Note that it is not always necessary to couple two directions of planar expansion into a single direction of output. For example, in diaphragm actuators that operate across a pressure gradient such as might be used

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82 Chapter 8

for a pump, the two directions of planar deformation are inherently coupled to the output. In this case, the planar deformations displace the diaphragm and thereby impart pressure to the fluid being pumped.

Note that the pressure that is produced in a dielectric elastomer film does not depend on the stiffness of the polymer (see e.g. Eq. (1.17)). If the elastomer is properly coupled to the load, then the pressure or forces that can be produced are determined by the strength of the electric field that can be produced in the material. Thus, while the dielectric elastomer materials themselves are usually relatively soft, the pressure or force need not be small. Returning to our balloon analogy, we note that even a balloon could lift a car if properly constrained (e.g. by placing it inside a hydraulic or pneumatic cylinder or bellows).

8.4.2 Configurations that exploit flexibility and conformability

The rolled actuator ( Fig. 8.5 ) takes advantage of the flexibility of dielectric elastomers. Rolled actuators are attractive because they have high force and stroke in a relatively compact package. Because, like mus-cle, this package is cylindrical, rolled actuators make good artificial muscles. Rolled actuators incorporate a large cross-sectional area of film and thus can produce a relatively large force. One of the more success-ful types of rolled actuators is the ‘ spring roll ’ [2] . This actuator is formed from a film that is stretched in tension and rolled around an internal spring. Spring rolls not only exploit flexibility but also use aniso-tropic prestrain to better couple to the load and also use the spring to maintain the actuator in tension and help prevent buckling. Chapter 9 describes rolled actuators in much more detail. The main disadvantage of the rolled actuator is that it is somewhat more difficult to fabricate, since it is no longer a flat structure.

In some cases, the flexibility is important not for packaging, but rather to conform to a surface. For example, Bolzmacher et al. [3] have developed an extender actuator (with transverse fibres to better couple the output to the load) that is designed to be wearable. The actuator is flexible so that is can con-form to the body.

Figure 8.3 Constraining the deformation of polymer film to a single output direction. (a) Long narrow shapes (with rigid edges on the long side) allow film deformation primarily in the short direction only; topology can be flat or rolled into a cylinder. (b) Stiffeners can also constrain the motion to one direction while allowing greater variety of shapes.

Trench

Trench

Active areaRigid edge

(a)

(b)

Roll

Roll

Compliantdirection

Compliantdirection

Stiffeners

Figure 8.4 Actuator configurations that couple both directions of planar deformation into the output. (a) Bowtie – uses a linkage formed by rigid spars about perimeter of the active area. (b) Spider – uses a radially symmetric mecha-nism attached to the edges of a circular active area.

Rigid apar

Hinge

Polymer film(a) (b)

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Fundamental Configurations for Dielectric Elastomer Actuators 83

8.4.3 Configurations that maintain tension and prevent buckling

Because the basic functional element is a thin film of a relatively soft material, it is clear that if it is desired to use the in-plane strains or stresses in the film then the film will buckle unless it is main-tained in tension. Further, in the case of acrylic elastomers and other dielectric polymers, a consider-able amount of tension is required to maintain the desirable state of prestrain. The need for maintaining tension is fairly obvious. ‘ You can ’ t push a rope ’ would be one way of describing the requirement. One way to deal with this issue is to simply use the actuator in tension. For example, the bowtie actuator above would be always loaded in tension and elongate when it is energized.

The most straightforward way to maintain a film in tension is to stretch it across a rigid frame. The basic diaphragm actuator is one such example. However, the approach of stretching the film on a plane is not limited to out-of-pane motions, despite the rigid frame. The framed actuator shown in Fig. 8.6 allows for linear motion to be extracted in the plane of the film. This particular configuration uses two ‘ phases ’ (individually addressable electroded areas of the film) so that the motion can be bidirectional. While the design of Fig. 8.6 produces simple linear motion from two active areas on the polymer film, almost any number and shape of active electrode regions could be patterned onto a film. Thus, it is pos-sible to get almost any desired motion output.

Framed actuators are well suited to optical applications. For example, the active area could also serve as a shutter for light. This configuration exploits the inherent transparency of many of the polymer materials (including the electrodes if desired). Note that the actuator of Fig. 8.6 is nearly transparent.

Figure 8.5 (a) Schematic of actuator structure and (b) photo of rolled actuator.

Rolledpolymer film

Inactive region(for electrical and

mechanicalconnections)

Active region(overlappingelectrodes)

V

(a) (b)

Figure 8.6 (a) Schematic of framed actuator and (b) still photo from video of a functional framed actuator (only one phase is active).

Rigid frameElectroactive polymerpatterned withtwo phases

Phase B

Phase A

Output shaft

Outputbar

(a) (b)

Artificial muscle stretched film actuatorSRI international

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84 Chapter 8

Recently, researchers have demonstrated the ability of framed actuators to be the basis of tunable opti-cal gratings [4] . The gratings are moulded into the surface of the polymer film.

Note that the frame that keeps the film in tension need not be rigid. The bowtie actuator ( Fig. 8.4 ) discussed above can be also thought of as a framed actuator in which the frame flexes. The ‘ bow ’ actua-tor of Fig. 8.7 shows another design in which the frame is a linkage comprised of rigid elements with flexible hinges. The expansion of the film during actuation causes the shape of the frame to change. The outer dimensions of such an actuator can change quite a large amount. The bow actuator can take advantage of another design principle, the exploitation of a negative spring constant. Normally, in dielectric elastomer actuators, as with any induced strain actuator, the actuator must perform work to deform its own material. In the case of the bow actuator, the linkage couples elastic forces from orthogonal directions in order to reduce the effective elastic energy needed to distort the linkage. Thus, large motions can be achieved with such designs. Pelrine et al. [5] discuss this basic ‘ negative spring constant ’ approach in more detail. This approach has been taken to an extreme by Dubowsky ’ s group at the Massachusetts Institute of Technology [6] (see also Chapter 26) where bistable actuators based on designs similar to the bow have been shown to be capable of very large deformations. The advantage of this approach is that no energy is needed to maintain the large deformation state (in the absence of large external loads). These bistable actuators are most often used in antagonistic pairs since an individual actuator cannot return to the inactive state.

Non-rigid frames can also take advantage of out-of-pane deformation. Kofod et al. [7] have demon-strated framed actuators in which the tension of the film causes a thin flexible frame to buckle out of plane until the elastic energy of the flexible frame balances the tension of the film. A square frame, for instance, would be net into a C-curve with the film forming a saddle shape across the film (see Fig. 8.8 ). When the film is energized, the tension is reduced and the curvature of the frame is also reduced. The advantage of such framed actuators is that it is easy to mechanically attach to a rigid frame as compared to the soft polymer. Such bending actuators are similar to unimorph or bimorph designs but they allow for greater forces to be imparted from the large deformation of the film (albeit with less bending).

The approach to using a frame to maintain an actuator in tension is not limited to flat films. Any linear actuator configuration can be stretched across a frame. While a single actuator would not be able to move in-plane if stretched across a rigid frame, if two actuators are connected in series (mechani-cally) and we make our output connection at the junction between the two actuators then we can move

Figure 8.7 (a) Schematic of bow actuator and (b) photo of bow actuator undergoing deformation from an applied voltage.

Articulatedframe

Active dielectricelastomer

Voltage off(a) (b) Voltage on

Figure 8.8 Flexible frame saddle actuator (Courtesy of Guggi Kofod, University of Potsdam).

Voltage off Voltage on

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Fundamental Configurations for Dielectric Elastomer Actuators 85

this connection in either direction by actuating one of the two actuators. Both actuator elements can be active at the same time. In ‘ push–pull ’ mode the voltage on one actuator is reduced as the voltage on the other is increased. While this approach can add complexity, compared to an actuator with a single active area, push–pull actuators are inherently bidirectional. Combined with other linearization tech-niques known in the literature, bidirectional push–pull actuators can be made to respond nearly propor-tionally to an input signal.

Another example of a compound actuator with a ‘ frame ’ is that of the ‘ Universal Muscle Actuator ’ developed by Artificial Muscle Inc. and discussed in Chapter 29. This actuator consists of two counter-opposed diaphragms that are joined at the centre with a rigid disc (see Fig. 8.9 ). More correctly these are more like the trench actuators of Fig. 8.3 where the trench is wrapped around a frustum to form the annular shape. Choi et al. at Sungkyunkwan University [8] describe another type of compound dia-phragm actuator in which the diaphragms are not joined in the centre but rather are deflected away from each other and joined by a rigid rod. These researchers also describe a variation on this type of actuator in which the individually addressable active regions of each of the two diaphragms is patterned into pie-shaped sections. Depending on which sections are activated, the centre rod can move up and down, side to side or tilt side to side.

In other cases, tensile loading can be imparted by how the actuator is attached to the load it is driv-ing. This design constraint is no different from most biological skeletal muscle which is also primarily used in tension. For example, just as biological muscle is often grouped into antagonistic pairs around a joint, linear dielectric elastomer actuators such as rolls or bowties can be attached to robotic joints in antagonistic pairs.

8.4.4 Thickness mode of operation

So far we have only discussed actuators that operate using the planar deformation of the film. Of the basic actuator configurations, only the stack actuator uses the thickness mode of operation. Stack actua-tors are attractive where a large amount of force is desired. Because each layer is thin, most stack actua-tors are limited to relatively flat form factors. Such flat, yet high force, actuators are well suited to haptic display applications. Researchers at the Technical University of Darmstadt have successfully developed an automated method of making stacked actuators with up to 200 layers [9] (see also Chapter 11).

Carpi et al. at the University of Pisa have made stacks by folding a large number of layers in an accor-dion configuration. These actuators are much taller than they are wide and so can be connected to rigid connections without constraining the expansion of the film. These types of actuator are being developed for a variety of linear motion applications including artificial muscles for robotics. Unlike most muscle-like actuators but more like natural muscle, these actuators contract upon the application of a voltage. In addition to making such actuators by folding many layers into a stack configuration, Carpi et al. have also made stack-like actuators using a helical configuration. One continuous electroded layer of film forms a spiral-staircase type of structure in which each subsequent layer of film falls on top of the pre-vious. These two types of contractile stack actuators are discussed in Chapter 12 and shown in Fig. 8.10 .

SRI International developed a new actuator configuration that is designed to enhance the thickness mode of operation. This configuration ( Fig. 8.11 ) is discussed in detail in Chapter 21. In this ‘ enhanced

Figure 8.9 Universal muscle actuator: (a) cut-away view showing internal structure of opposed diaphragms and (b) photo of a packaged actuator (Courtesy of Artificial Muscle Inc.).

(a) (b)

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86 Chapter 8

thickness-mode ’ type of actuator, a very soft gel layer is bonded to a stretched film with any desired electrode pattern. When the active regions defined by the electrodes expand the shear stresses cause the gel to move along with the film. Since the gel is largely incompressible, it thins as it expands and thickens as it contracts. Since the gel layer can be much thicker than the active dielectric elastomer film layers, the motion in the thickness direction can be as large as if many layers of active film were used (albeit at reduced force). Such actuators are well suited to haptic displays and conformal actuators with variable texture. As suggested by Fig. 8.11 , the active region can be subdivided into small individually addressable subregions to allow for a controllable surface profile.

8.5 MOTOR CONFIGURATIONS

Thus far, we have discussed only ‘ direct-drive ’ actuator configurations. That is, configurations in which the output is defined by a single cycle of deformation of the polymer film. However, it is possible to make linear, rotary or other actuators in which many cycles of operation can be used to produce the output. Any of the linear actuator configurations discussed above could be combined with clamping or latching mechanisms (which may themselves be actuated by dielectric elastomer or other means) in order to produce inchworm-like linear motors, for example. There is similarly a wide range of

Figure 8.10 High aspect ratio thickness-mode actuators: (a) basic stack, (b) helical and (c) folded (Courtesy of the University of Pisa).

Compliant electrodes

(a) (b) (c)

� ���

��

Figure 8.11 Example of an enhanced thickness-mode actuator.

Voltage off Voltage on

Cross-section of single elementTop view

Flexible foam backing(optional)

Passive polymer or gelcoating (typically sopt

elastomer)

Thickness changeof passive polymercoating

Bulges areenhanced aswellCompliant

electrodes

Directthickness

changePolymer

(e.g. acrytic)

�V

V

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Fundamental Configurations for Dielectric Elastomer Actuators 87

possibilities with rotary motors. For example, if we draw an analogy between an oscillating direct-drive linear actuator and a piston–cylinder assembly in an internal combustion engine, then one can readily see how linear actuation can be converted to rotary motion.

Countless rotary and linear motion devices based on piezoelectric ceramics have been developed. Many of these could be used with dielectric elastomers as well. Compared with piezoelectric motors, dielectric elastomers have the potential advantage that, because they undergo large strains, the precision of the motor components can be low.

Figure 8.12 shows an example of a very simple dielectric elastomer motor. This motor uses two counter-opposed bowtie linear actuators attached to a central axle. The bowties are actuated out of phase in order to make the axle oscillate. A wheel is attached to the axle via a one-way clutch. The oscillating motion of the axle is rectified by the clutch so that the wheel rotates in one direction. When operated at the resonant frequency of about 60 Hz, this motor was able to spin the wheel at about 600 rpm. This motor may not exhibit high performance nor be practical for many applications, but it does illustrate how a dielectric elastomer motor can be made very simply with off-the-shelf low precision components.

8.6 LARGE AREAS, ARRAYS AND MULTIFUNCTIONALITY

One of the inherent properties of polymers is that they can easily be manufactured into large area films. Figure 8.13 shows some examples of actuator configurations that take advantage of this.

Loudspeakers can be easily made from a simple diaphragm configuration with an air-filled plenum or soft foam behind it to bias the diaphragm. The largest loudspeaker in the figure measures 30 cm × 30 cm. Compared with conventional loudspeakers, the dielectric elastomer loudspeaker is much simpler, lighter and able to easily conform to surfaces. Chapter 30 describes dielectric elastomer loudspeakers.

Dielectric elastomers can be easily laminated to large flexible structures in order to impart shape con-trol. The basic actuation configuration is similar to a unimorph bending actuator but the shape change can be in two dimensions. While the flexible mirror shown in Fig. 8.13 is small, it does suggest how dielectric elastomers may be used for the shape control of very large flexible structures, such as space-based tel-escopes. Such approaches are described in Kornbluh et al. [10] .

The balloon actuator of Fig. 8.13 is a unique configuration that has so far not yet been introduced. This configuration includes unique features of dielectric elastomers in addition to the large size of the film. The tension is maintained in this actuator by means of the air pressure inside of it. No frame and almost no additional structure is needed. This configuration could be used for pumping or even a loud-speaker. This design also introduces the notion of multifunctionality – where the actuator itself serves an additional function, such as structure. In this case, the balloon can provide buoyancy, such as for an airship. Actuation can control the buoyancy or the shape of the aircraft.

8.7 BEYOND ACTUATORS: GENERATORS, SENSORS AND TUNABLE STRUCTURES

Thus far, we have discussed only actuator configurations. However, as has been described in Chapter 1, dielectric elastomers can also act in reverse as generators and sensors or even more generally modulate

Figure 8.12 Simple rotary motor based on bowtie actuators: (a) motor design and (b) video still of motor in operation.

Wheel with one-way clutch

Bowtie actuators(a) (b)

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88 Chapter 8

the electromechanical transduction to control stiffness or damping. In general, all the configurations presented so far could also operate as generators, sensors or variable impedance devices. However, it should be noted that the loading conditions and resulting deformation may differ considerably from those that led to many of the actuator configurations presented here. For example, in sensor or genera-tor mode, large motions may be imposed on the transducer, far exceeding those that could be produced by actuation. Figures 8.14 and 8.15 show some representative generator and sensor configurations, respectively.

8.8 SUMMARY AND DISCUSSION

This chapter has presented an overview of the variety of dielectric elastomer actuator configurations. The actuator configurations presented here are by no means exhaustive. Indeed, subsequent chapters

Figure 8.13 Examples of large area and multifunctional actuators.

Balloon actuator shown involtage-off (left) andvoltage-on (right) states.(Courtesy of Gabor Kovacs, EMPA)

Loudspeakersconsisting ofsquare-shapeddiaphragms.The largest is30 cm � 30 cm

A shape-controllable mirror:dielectric elastomer is laminated tothe back of a flexible mirror

Figure 8.14 Examples of generators.

Generatormodel

Rigid gridplate (plastic)

Rigid baseplate

Coupling medium

Dielectric elastomer layers

Schematic of generator operation

Generator configurations for power generation: bending (unimorph or bimorph) flags, stretchingtube or rolls (adapted from Prahlad et al., [11])

Mockup of generator installed in boot

Bellows (plasticor metal)

Floats provideextension motion

by riding on waves

Dielectricelastomer

located withinstretchable

tetherEnergy storageand accumulation

station

Fluttering wind generators can be located asdiscrete devices or strung from flexible wires

across large areas for wind energygeneration in urban or rural settings (across

a valley or on the top of tall buildings)

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Fundamental Configurations for Dielectric Elastomer Actuators 89

will introduce configurations that may not fit into the classification presented here. Undoubtedly new actuator configurations will be developed over time.

The configurations were introduced based on the particular unique feature of dielectric elastomers that were specifically addressed by that configuration. Subsequent chapters will discuss many of these and other actuator configurations as well as describe how certain configurations are suited for specific applications. Table 8.1 summarizes the actuator configurations discussed and shows the general classes of applications suited for each configuration. The applications are classified based on the desired out-put loading conditions and performance characteristics.

ACKNOWLEDGEMENTS

The author is grateful to Joseph Eckerle, Scott Stanford and Ronald Pelrine, whose inputs to this chapter were valuable. The author also wishes to thank those researchers who gave permission to use figures or photos of their actuators (as noted in the figures). Many of the actuator configurations in this chapter were developed at SRI International, where the author has performed his research. The author wishes to thank the many colleagues at SRI whose work is represented here as well as the commercial and gov-ernment sponsors whose generous funding allowed for the work to be performed. Many of the dielectric

Figure 8.15 Variety of sensor configurations including thin fibres and diaphragm arrays.

Table 8.1 Actuator configuration selection matrix.

Desired Output High Force Large Stroke Flat Form Factor Can Make Arrays, Skins or MEMS (2D Batch Fabrication)

Linear Roll, stack, trench extender

Spider, bow, unimorph, bimorph, flexible frame (saddle), diaphragm (with centre connection), motors (capable of any linear or rotary stroke depending on design)

Framed, bowtie, stack, extender, bow

Framed, stack, enhanced thickness mode, unimorph, bimorph, diaphragm spider (with microfabricated linkage), flexible frame (saddle), diaphragm (with centre connection)

Multi-DOF (single point of connection)

Roll (bending roll)

Bimorph, flexible frame (saddle), diaphragm (with centre connection)

Framed, bimorph, flexible frame (saddle)

Framed, bimorph, diaphragm (with sectored electrodes), flexible frame (saddle), diaphragm (with centre connection)

Distributed loading (e.g. fluid, skin (haptic))

Stack, enhanced thickness mode (multilayer)

Diaphragm, bimorph, unimorph

Diaphragm, enhanced thickness mode, unimorph

Diaphragm, enhanced thickness mode, unimorph

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90 Chapter 8

elastomer actuator configurations were developed under the management of the Micromachine Center of Japan under the Industrial Science and Technology Frontier Program, Research and Development of Micromachine Technology of MITI, Japan, supported by the New Energy and Industrial Technology Development Organization. Other SRI-based actuator configuration development described here was supported by the Defense Advanced Research Projects Agency (DARPA) and the Office of Naval Research (ONR). The Department of Education supported the development of the refreshable Braille display.

References

[1] Uchino , K. ( 1997 ). Piezoelectric Actuators and Ultrasonic Motors . Kluwer Academic Publishers , Norwell,

MA . pp. 142–143 .

[2] Pei, Q., Pelrine, R., Rosenthal, M. A., Stanford, S., Prahlad, H. and Kornbluh, R. D. (2004). Recent progress

on electroelastomer artificial muscles and their application for biomimetic robots. In Smart Structures and Materials 2004: Electroactive Polymer Actuators and Devices (EAPAD) , Ed. Bar-Cohen, Y., Proc. SPIE ,

5385 , 41–50.

[3] Bolzmacher, C., Biggs, J. and Srinivasan, M. (2006). Flexible dielectric elastomer actuators for wearable

human–machine interfaces. In Smart Structures and Materials 2006: Electroactive Polymer Actuators and Devices (EAPAD) , Ed. Bar-Cohen, Y., Proc. SPIE , 6168 , 27–38.

[4] Aschwanden , M. and Stemmer , A. ( 2006 ). Polymeric, electrically tunable diffraction grating based on artifi-

cial muscles . Opt. Lett. , 31 , 2610 – 2612 .

[5] Pelrine , R. , Kornbluh , R. , Joseph , J. , Heydt , R. , Pei , Q. and Chiba , S. ( 2000 ). High-field deformation of elas-

tomeric dielectrics for actuators . Mater. Sci. Eng. C , 11 , 89 – 100 .

[6] Wingert, A., Lichter, M., Dubowsky, S. and Hafez, M. (2002). Hyper-redundant robot manipulators actuated

by optimized binary dielectric polymers. In Smart Structures and Materials 2002: Electroactive Polymer Actuators and Devices (EAPAD) , Ed. Bar-Cohen, Y., Proc. SPIE , 4695 , 415–423.

[7] Kofod, G., Paajanen, M. and Bauer, S. (2006). New design concept for dielectric elastomer actuators. In

Smart Structures and Materials 2006: Electroactive Polymer Actuators and Devices (EAPAD ), Ed. Bar-

Cohen, Y., Proc. SPIE , 6168 , 689–697.

[8] Choi, H., Jung, K., Kwak, J., Lee, S., Kim, H., Jeon, J. and Nam, J. (2003). Multiple degree-of-freedom

digital soft actuator for robotic applications. In Smart Structures and Materials 2003: Electroactive Polymer Actuators and Devices (EAPAD) , Ed. Bar-Cohen, Y., Proc. SPIE , 5051 , 262–271.

[9] Schlaak, H., Jungmann, M., Matysek, M. and Lotz, P. (2005). Novel multilayer electrostatic solid-state actua-

tors with elastic dielectric (Invited Paper). In Smart Structures and Materials 2005: Electroactive Polymer Actuators and Devices (EAPAD) , Ed. Bar-Cohen, Y., Proc. SPIE , 5759 , 121–133.

[10] Kornbluh, R. D., Flamm, D. S., Prahlad, H., Nashold, K. M., Chhokar, S., Pelrine, R., Huestis, D. L., Simons, J.,

Cooper, T. and Watters, D.G. (2003). Shape control of large lightweight mirrors with dielectric elastomer

actuation. In Smart Structures and Materials 2003: Electroactive Polymer Actuators and Devices (EAPAD) , Ed. Bar-Cohen, Y., Proc. SPIE , 5051 , 143–158.

[11] Prahlad, H., Kornbluh, R., Pelrine, R., Stanford, S., Eckerle, J. and Oh, S. (2005). Polymer power: dielec-

tric elastomers and their applications in distributed actuation and power generation. Proceedings of the ISSS 2005 International Conference on Smart Materials Structures and Systems , 28–30 July, Bangalore, India,

pp. SA-100–SA-107.

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MULTIPLE-DEGREES-OF-FREEDOM ROLL ACTUATORS

Marcus Aaron Rosenthal 1 and Qibing Pei 2

1 Artificial Muscle, Inc., Menlo Park, CA, USA 2 Department of Materials Science and Engineering, University of California, Los Angeles, CA, USA

Abstract

By patterning the electrodes of dielectric elastomer actuators and having appropriate bias mechanisms, motion in

multiple-degrees-of-freedom (multi-DOF) can be achieved with a single actuator. Multi-DOF spring roll actuators

have been developed by pattering electrodes on dielectric film to have radial alignment on multiple spans that are

wrapped around a compression spring. The multi-DOF spring roll actuators are capable of linear actuation by actuat-

ing all spans at once and bending actuation by actuating separate spans. Mathematical equations have been derived

that correlate the stroke in a single electrode span with the bending angle and lateral force. Multiple biasing struc-

tures that have been developed are presented such as compression springs, pivot rolls and spine rolls. The novel func-

tionality of the multi-DOF roll actuators has been exploited in multiple applications. MERbot, a small walking robot

with one 2-DOF spring roll used for each of its six legs is described. Sushi rolls that have multiple 2-DOF spring

rolls connected in series can be driven to generate serpentine-like motion. By sealing the multi-DOF rolls using a

silicone coating, the rolls can be actuated underwater for potential use in aquatic robotic systems. The complexity of

multi-DOF roll actuators has made reliability a challenge which is being addressed by improved manufacturing tech-

nique and automation, improved design, and novel new materials.

Keywords : Artificial muscle, bending roll, dielectric elastomer actuators, electroactive polymer artificial muscle,

MERbot, multi-DOF spring roll.

9.1 INTRODUCTION

One of the most interesting characteristics of dielectric elastomer actuators is their ability to achieve motion in multiple-degrees-of-freedom (multi-DOF) within a single actuator. By patterning the electrodes and appropriately biasing the compliant dielectric elastomer, actuation with multi-DOF can be achieved in a single, elegant actuator component. The attractive characteristics of using a roll structure for 1-DOF motion, including easy fabrication, a compact structure, multifunctionality and mechanical robustness, naturally extend to multi-DOF motion as well [1, 2] . Multi-DOF rolls (multifunctional electroelastomer rolls or MERs) have been developed by patterning the electrodes such that they radially align on two, three or four circumferential spans of the rolls. Multi-DOF spring rolls, as shown in Fig. 9.1 , retain the linear actuation of 1-DOF spring rolls with the added functionality of bending actuation. Mathematical equations have been derived which correlate the actuated stroke in one of the electroded spans with the resulting bending angle and lateral force. While compression-spring-biased rolls continue to be a common architecture, alternative biasing structures, such as pivot rolls and spine rolls have also been developed.

Regardless of the configuration type, roll actuators represent a radically new actuation technology and are likely to be an enabling technology for a number of unique applications such as walking robots, steer-able catheters and endoscopes, manipulators, massagers, snake robots, and multi-axis motion cameras and lighting. A small walking robot, MERbot, with one 2-DOF spring roll used for each of its six legs has been demonstrated. ‘ Sushi rolls ’ have also been fabricated, which consist of multiple 2-DOF spring rolls, monolithic in structure, connected in series. The sushi rolls can be driven so as to generate wave-like or serpentine motion which may prove useful in the development of robotic snakes and snake-like manipulators. Multi-DOF rolls employing a silicone waterproof coating have also been

Chapter 9

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92 Chapter 9

operated underwater to demonstrate their potential for use in aquatic robotic systems. These are but a few examples of the wide applicability of multi-DOF roll actuators and the ways in which they are ena-bling a new generation of motion systems.

9.2 DESIGN

There are many possible designs for multi-DOF roll actuators, but they all have multiple features in common. In order to achieve multi-DOF motion, the patterning of multiple actuation segments is required (see Fig. 9.2 ). The central support structure of a multi-DOF roll can be either a compression spring or other structures such as that are used in pivot and spine rolls, described later in this section.

9.2.1 Multi-DOF spring rolls

Multi-DOF spring rolls are fabricated so that the compliant electrodes are radially aligned on two, three or four spans around the circumference of a compression spring. When one of the spans is actuated, the electroded EPAM film of the actuated span expands, releasing the spring ’ s potential energy and caus-ing the roll to bend towards the radially opposite span. When all spans are actuated at the same voltage, the roll expands in length similar to the 1-DOF rolls. As can be inferred from its name, the fabrication of a spring roll involves the use of a central compression spring. Figure 9.3 shows how the spring is compressed to its solid length on a bolt between two end caps with an outside diameter similar to that of the spring. Two films are prestrained and coated with compliant carbon-based electrodes [3] . The electrodes are patterned in rectangular areas separated by insulating gaps several millimetres wide. The films are then laminated together and rolled around the spring and end caps. Figure 9.3 illustrates the fabrication process. When the roll is released from the bolt to become freestanding, the compressed

Inactive film

Active film

Figure 9.2 Example of a patterned electrode for a 3-DOF, 4-phase, roll actuator.

Figure 9.1 A 2-DOF spring roll that can extend in axial length and bend under 3–6 kV of applied voltage: (a) at rest and (b) actuated on the right span at 5.5 kV.

(a) (b)

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Multiple-Degrees-of-Freedom Roll Actuators 93

spring holds the acrylic films in both circumferential and axial tension. When using pressure-sensitive adhesive (PSA) films, the adhesive force between the films and the surface of the end caps prevents the films from slipping. Additional techniques are often used to prevent slippage, such as pinning the film, or gluing the edge of the rolled films to the outside end or flanges of the end caps. After being rolled up, there are between 20 and 80 layers of film in cross section on a typical roll.

The theoretical model described in Section 9.3 indicates that the bending angle of a roll is inversely proportional to its diameter. Thus, by decreasing the diameter larger bending angles are possible. The fabrication of smaller-diameter multi-DOF spring rolls tends to present a significant challenge because electrodes coated on all layers of the films must be aligned radially on each circumferential span of a roll. As the diameter of the roll increases from the inner layers outwards, the circumferential distance of the electrodes also increases incrementally. In spring rolls with smaller diameters the percentage of an inactive, non-electroded span between two adjacent active spans increases because the active, elec-troded areas are narrower, whereas the inactive gap between electrodes must remain more or less the same size (about 2 mm) in order to electrically insulate adjacent electrodes. Currently, the inactive gap is a major limiting factor in scaling down the diameter of multi-DOF rolls. With improved processing techniques, such as coating thin insulating layers over the patterned film, the amount of inactive area can be decreased.

Both 2-DOF and 3-DOF spring roll actuators with outside diameter of 1.4 or 2.3 cm have been fab-ricated. The results are shown in Table 9.1 . Note that the maximum bending angle of the 2-DOF roll increases from 60 � to 90 � as the diameter is reduced from 2.3 to 1.4 cm [4] . The lateral force and stiff-ness of the smaller spring rolls are also less than those of the larger-diameter multi-DOF spring roll actuators, largely due to the reduced amount of film in the smaller rolls.

9.2.2 Multi-DOF pivot rolls

Another configuration of a multi-DOF roll actuator is the pivot roll, in which the patterned film is wrapped around a structure which contains pivoting sections, or discs, as shown in Fig. 9.4 . This con-figuration is inspired by biological systems that contain muscles configured in an antagonistic pair. Unlike compression-spring-biased rolls, in the pivot roll, the prestrain of the film on one side of the central structure serves to bias the dielectric elastomer film on the opposite side of the pivot structure.

Top electrodecontact

Bottom electrode contact

Rectangular electrodeareas, both on top andbottom of acrylic film

Compressionspring

End cap

Figure 9.3 Assembly drawing of multi-DOF spring roll.

Table 9.1 Experimental results of 2-DOF and 3-DOF spring rolls.

Attribute 2-DOF Roll 3-DOF Roll

Version 1 Version 2 Version 1 Version 2

Size (length, outside diameter) (cm) 9, 2.3 6.8, 1.4 9, 2.3 6.8, 1.4 Weight (g) 29 11 29 11 Maximum bending angle (deg) 60 90 35 20 Maximum lateral force (N) 1.68 0.7 1 0.2 Lateral stiffness (N/cm) 0.46 0.28 0.46 0.28

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94 Chapter 9

Since a pivot roll uses the internal structure as a pivoting lever, it is possible to achieve higher lateral forces with a pivot roll structure than a spring roll structure. The spring roll lateral force is limited to the lateral force of the spring/film structure. Additionally, while the pivot roll remains straight except for the final section or disc, multiple pivoting roll segments can be connected in series to increase the bending angle, effectively allowing a multi-segment system to achieve higher bending angles and DOF than any single segment could achieve, as shown in Fig. 9.5 .

The pivoting section geometry can take many forms, including forms which allow rotation along a single axis, such as a pinned joint, or forms which allow rotation along any axis, such as a ball and socket joint. To maximize motion, the aspect ratio of each pivoting segment must be designed so that the prestrained dielectric elastomer film does not come in contact with the rotation axis point in the internal structure of the pivot roll.

9.2.3 Multi-DOF spine rolls

The spine roll is another type of multi-DOF roll actuator. This actuator contains a linear array of discs along a flexible shaft or flexible flat spring, as shown in Fig. 9.6 . In this flexible structure, similarly to a compression-spring roll, the bending takes place between each disc as opposed to at the connection points of the roll, as in the pivot roll. This structure is much easier to manufacture than the pivot roll because each disc only needs a simple hole in order to be mounted onto the flexible centre shaft or flat spring, or the entire spine can be fabricated out of a single part using techniques such as injection moulding. The maximum performance of a spine roll is typically less than that of a pivot roll because the stiffness of the flexible shaft or flat spring opposes the force of the dielectric elastomer. There are many possible configurations of spine rolls where the structure composes a blend of materials that can

Figure 9.4 Pivot roll cross section drawings: (a) right span actuated and (b) at rest.

Figure 9.5 Pivot roll with multiple segments attached in series. Length approximately 8 ′ , 1.5 ″ diameter, 6 seg-ments; connected together electrically (i.e. not independent), bending to approximately 270 � (Courtesy of SRI International).

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Multiple-Degrees-of-Freedom Roll Actuators 95

include springs, rigid structural components, elastic components and compressible materials such as soft foam materials. It is also possible to integrate other functional components of a system into the structure of a spine roll. For example, in an endoscope, the wires to transmit an image back to a proces-sor can be used as the flexible shaft.

9.3 THEORETICAL DESIGN TOOLS

9.3.1 Longitudinal expansion and bending angle of a 2-DOF spring roll

The fabrication and structure of a 2-DOF spring roll is illustrated in Fig. 9.3 and described in Section 9.2.1. Figure 9.7 schematically shows the bending of a 2-DOF spring roll caused by a stroke, S , in the actuated circumferential span between points a and b [2] . It is assumed that the bending roll forms a curve with a constant curvature. The radial angle is � and the radius R . The stroke S , the unrestricted expansion caused by the applied electric field, would be equal to the stroke at the same voltage in a 1-DOF spring roll. The roll ’ s longitudinal length at the central (neutral) point is

h R� f (9.1)

The longitudinal length at a given angle, � , is

h R r t� �� �( )sin f (9.2)

rd

b

a

R

hCCh hCX

u

u

f

Figure 9.7 Schematic structure of a bending 2-DOF spring roll. The actuated circumferential span is between points a and b , with an angle � t .

Figure 9.6 Spine roll central structure.

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96 Chapter 9

If the linear spring constant of the spring roll is E , then the longitudinal force exerted by the actuated span between points b and a is

F E h S h

r

ra

b

cx

d� � �( )

( )0

2�

��∫ (9.3)

The longitudinal force exerted by the non-actuated span between points b and a is

F E h h

r

rb

a

cc

d� �( )

( )0

2�

��∫ (9.4)

At unblocked and equilibrium condition, the above two forces are balanced [5–9] ; i.e.,

F F E h S R r E h R r

a

b

b

a

cx cc sin d sin d� � � � � � � � �{ ( )} { ( )}0 0 0f f� � � �∫ ∫ (9.5)

Simplifying yields

h h St� �0

2

��

(9.6)

In addition to the longitudinal forces, bending momentums in the actuated span between points a and b and in the non-actuated span between points b and a are also balanced at equilibrium

M E h S h r

r

ra

b

cx sind

� � �( )( )

02

� ��

�∫ (9.7)

M E h h r

r

rb

a

cc sind

� �( )( )

02

� ��

�∫ (9.8)

M M E h S R r

h R r

a

b

cx cc sin sin d

sin sin d

� � � � �

� � �

{ ( )}

{ ( )}

0

0

f

f

� � �

� � �

∫+ 00

b

a

∫ (9.9)

Simplifying yields

f �

�2

2�� �S

rtcos (9.10)

In a 2-DOF spring roll, if the non-active, non-electroded span of the roll is negligible compared to the active spans, then � t = � . Equations (9.6) and (9.10) are reduced to

h h S� �0

1

2 (9.11)

and

f � 2S r/� (9.12)

Equation (9.12) indicates that one can increase the bending angle either by increasing the stroke or by reducing the roll diameter. The stroke is proportional to the length of the roll and the strain. The strain is determined by the electric field applied and the biasing of the active films. In practical spring rolls, at least one layer of non-electroded, non-active film is rolled inside and outside the active film layers in order to protect the active layers. The non-active layers negatively impact the longitudinal strain and bending angle.

According to Eq. (9.2), the longitudinal lengths of the roll at the convex and concave, where � = � /2 and � = 3 � /2, respectively, are

h h Scx cos� � �0

1

2

2

4��⎛

⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

(9.13)

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Multiple-Degrees-of-Freedom Roll Actuators 97

and

h h Scc cos� � �0

1

2

2

4��⎛

⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

(9.14)

The term 24��cos( ) equals 0.45, so h cx is less than ( h 0 + S ), meaning that the actuated span is actu-

ally compressed. On the other hand, h cc is greater than h 0 . The non-actuated span is under tension.

9.3.2 Longitudinal expansion and bending angle of a 3-DOF spring roll

Equations (9.6) and (9.10) can also be used to derive the longitudinal stroke and bending angle of a 3-DOF spring roll whose circumference is divided into four independently electroded spans [2] . Each span has a radial angle ( � t ) that is less than but close to � /4. When one electroded span is actuated, assuming that � t = � /4, the longitudinal length and bending angle of the roll are, respectively,

h h S� �0

1

4 (9.15)

and

f �

2

4��

cosS

r (9.16)

When two adjacent spans are actuated, the 3-DOF roll behaves like a 2-DOF roll. When three spans are actuated, the bending angle is the same as when only one span is actuated. However, the longitu-dinal length stroke is tripled:

h h S� �0

3

4 (9.17)

Note that in many cases the insulating non-electroded gap between two adjacent electroded spans is quite significant, particularly in the 3-DOF spring rolls. For instance, a spring roll has a diameter, r , of 12 mm and the gap is 2 mm wide. For a 2-DOF spring roll, � t is 0.89 � . For a 3-DOF roll, � t is only 0.40 � . The same non-electroded gap has a more profound impact on a 3-DOF roll than on a 2-DOF roll with the same diameter.

9.3.3 Bending force of a 2-DOF spring roll

When the roll is not allowed to deflect freely, it can be ‘ blocked ’ by a combination of axial force (which prevents extension) and radial force (which prevents bending). Let the net axial force along the neutral longitudinal axis of the roll be F a and the bending (radial) force be F r . The difference between the com-pression force in the actuated span between points a and b and the tension force in the non-actuated span between points b and a should be equal to the external blocking force F . If the spring constant of the 2-DOF roll is E , then the axial force is

F F F

Eh S R r h R r

a

b

b

a

a cx cc sin d sin d� � � � � � � �2

0 0�� � � �{ ( )} { ( )}f f∫ ∫+

⎡

⎣⎣⎢⎢

⎤

⎦⎥⎥ (9.18)

Simplifying yields

2

22 20

��

� � �F

E

Eh S ht

a � � �( ) (9.19)

From this equation, when h = h 0 (i.e. the roll is in a fully blocked condition),

F

ES ta �

2�� (9.20)

To increase the blocked force, one would increase the linear spring constant and stroke of the roll. These values are consistent with 1-DOF roll actuators where the blocked force is E � t .

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98 Chapter 9

An external radial (bending) force F r would cause imbalance between the bending momentums in the actuated span between points a and b ( Fig. 9.6 ) and in the non-actuated span between points b and a . Calling this moment imbalance or blocking moment M r from Eqs. (9.7) and (9.8)

M M ME

h S R r h R ra

b

r cx cc

sin sin d sin si

� �

� � � � � �

2

0 0

�

� � � �{ ( )} { ( )}f f∫ + nn d� �b

a

∫⎡

⎣⎢⎢

⎤

⎦⎥⎥

(9.21)

Simplifying yields

ME

S rtr cos�

��

22

2�� �

�f⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟ (9.22)

When the roll is in a ‘ blocked ’ condition, the bending angle � → 0, is

M

ES tr cos�

�

�� �

2 (9.23)

The blocking moment is equivalent to a radial force F r exerted at the tip of the actuator, such that

FM

R

M

h

E S r

h

t

rr r

sin sin

cos

sin� � �

��

f

f

f

f f

f

22

2

� ��

�

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

(9.24)

Therefore, the actual force exerted depends on the prestraining method. If a load cell at a certain angular distance from the end of a spring roll restrains both extension and bending, then Eq. (9.19) can be used to determine the neutral axial length h from the axial force F a ; the results can then be plugged into Eq. (9.24) to determine the bending angle � from the radial force F r .

Consider a special case where F a = 0 (i.e. the roll is free to extend), but F r is non-zero (the roll is restrained in bending). Then, as seen previously,

h h St� �0 2( /� �) .

In this case, the force F r is related to the bending angle � by the equation:

FE S r

h S

t

tr

cos

sin

�

��

�

22

22

0

� ��

���

f f

f

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

(9.25)

To simplify this equation, assume that the non-active, non-electroded part is minimal, that is, � t equals � (in a 2-DOF spring roll). The equation then becomes

FE S r

h S

ErS

hr

sin

��

�

�

�( )2

21

2

2

200

�

�

�

�

f f

f

f f

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟

SS�

1

2

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟ sin f

(9.26)

This equation is plotted at several radius ( r ) and strain ( S / h 0 ) values, as shown in Fig. 9.8 . Note that the plot assumes that the stiffness of the rolls is kept constant as the roll length is changed in order to compare the values. The equation and figure indicate that:

● The force is proportional to the roll stiffness. ● Increasing the strain substantially increases the bending force: the force increases in an approxi-

mately linear fashion with the strain. ● Reducing the roll radius without changing the roll ’ s stiffness does not affect the blocked bending

force. However, the intermittent force at a given angle is increased, due to the increased maximum bending angle.

● Longer rolls (at the same stiffness) also produce higher bending forces at a given intermittent angle. The blocked force remains unchanged.

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Multiple-Degrees-of-Freedom Roll Actuators 99

Please note that buckling has been ignored in the mathematical derivation. Buckling must be con-sidered when calculating the radial force of a roll with a high length/diameter aspect ratio [2] .

9.4 CHALLENGES

Reliability, patterning and the manufacturing of the centre structure are among several outstanding chal-lenges facing multi-DOF roll actuator designers. While achieving useful reliability levels for a given application is a goal for all dielectric elastomer actuators, the multi-DOF rolls present some additional challenges in the area of reliability engineering. Due to the large active area arising from the high effect-ive layer count in most multi-DOF rolls, given a certain probability of failure per unit active area, the probability of system failure is much greater than for smaller devices, such as the Universal Muscle Actuator (UMA) configuration which is described in Chapter 9. While simple in concept, the specific electrode pattern for multi-DOF roll actuators tends to be complex in practice and contains many geo-metrical features which have the unintended effect of being electrical stress concentrations. Additionally, since the roll actuator essentially consists of a 3D structure with multiple highly prestrained films wrapped around it, there are multiple mechanical stress concentrations on the dielectric film, including where the spring coils and/or discs contact the film, and at the interface with the end caps.

The patterning of the electrode and the electrical connections to each actuation phase also pose a significant challenge. For multi-layer rolls, the pattern needs to align accurately on each wrap to ensure that each successive layer adds to the performance as opposed to hindering motion in the intended direction and causing motion in unwanted directions. The electrode pattern needs to be carefully designed to account for the increase in thickness caused by each layer. Creating a mechanically stable and electrically reliable electrode connection to each layer of in a given actuation span without shorting to an adjacent layer or failing the entire device is another challenge.

A third challenge confronting the design and manufacture of multi-DOF roll actuators is the design and manufacturing of the centre structure. For the spring roll actuators, this is not as difficult as the pivot and spine rolls. While the spring rolls often need custom springs, multiple spring manufacturers are capable of supplying these parts. In contrast, the centre structure for pivot rolls is typically a com-plex 3D part or even an assembly of multiple parts. The centre structure for spine rolls is not as difficult

00

0.02

0.04

0.06

0.08

0.1

0.12

20 40 60 80 100 120 140Actuation angle (deg)

Act

uatio

n fo

rce/

roll

actu

atio

n st

iffne

ss (

F/E

) (c

m)

h0 � 5.5 cm, S/h0 � 0.1, r � 0.575 cm

h0 � 5.5 cm, S/h0 � 0.2, r � 0.575 cm

h0 � 5.5 cm, S/h0 � 0.4, r � 0.575 cm

h0 � 10 cm, S/h0 � 0.2, r � 0.575 cm

h0 � 5.5 cm, S/h0 � 0.2, r � 0.4 cm

Figure 9.8 Radial bending force ( F r ) as parameter of bending angle. The roll is assumed to have no restraint in the axial direction.

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100 Chapter 9

to manufacture, but assembly during prototyping can be tedious; in a final product, however, the spine structure would likely be a single flexible injection-moulded part.

9.5 APPLICATIONS

Multi-DOF roll actuators are capable of replacing existing actuators as well as enabling new types of motion in robotics, industrial, consumer and military applications. Multi-DOF roll actuators can be the legs of a walking robot, as in MERbot, they can be the fingers of a gripper or massager, they can be used to steer endoscopes and catheters, and multiple rolls can be connected in series to create snake-like motion or a multi-DOF manipulator. This section details three applications that have been demon-strated: MERbot, Sushi Rolls and a multi-DOF Roll Fish.

9.5.1 MERbot: biologically inspired robot based on 2-DOF spring rolls

The actuation behaviour of the 1-DOF spring rolls was found to be similar to that of natural muscles regarding strain, specific energy and power densities [10, 11] . However, such synthetic muscles do not duplicate the performance or characteristics of natural muscle in all respects. For instance, the stress–strain behaviour of natural muscles is highly nonlinear, whereas synthetic muscles have a largely lin-ear stress–strain response. Nevertheless, the spring rolls are well suited for applications in biologically inspired robots. Skitter, a small-legged robot, was designed with a 1-DOF spring roll as each of its six legs. Skitter is similar to the Sprawl robots built by Cutkosky et al. [12] , except that the pneumatic air-piston cylinder legs of the Sprawl robot are replaced by 1-DOF spring rolls. 2-DOF and 3-DOF spring rolls retain the linear longitudinal actuation strain of the 1-DOF rolls, but they further exhibit the func-tion of bending. Legged robots based on the bending 2-DOF and 3-DOF spring rolls are expected to provide much larger gait distances and allow higher clearances than Skitter.

To demonstrate the unique characteristics of 2-DOF spring rolls, a laboratory robot was fabricated. The robotic system shown in Fig. 9.9 , named MERbot, is a simple tethered robot that contains six spring rolls, a hexagonal frame and wires. The dimensions of the robot are 18 cm � 18 cm � 10 cm, and its weight is 292 g. The robot moves with a dual tripod gait which requires only four input signals: one to cause each of the two tripods to bend forward, and one to cause each tripod to bend backwards.

The speed of MERbot was measured as a function of driving voltage and frequency. The robot ’ s speed initially increases with frequency, peaks at around 7 Hz, and then declines. The decline is caused by two factors: (1) the low speed of response of the spring roll legs, which have a half-strain frequency

Figure 9.9 MERbot: six-legged robot with 2-DOF spring rolls as legs.

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Multiple-Degrees-of-Freedom Roll Actuators 101

of about 7–10 Hz and (2) the increasing drag from ground traction. The maximum speed of MERbot is 13.6 cm/s at 7 Hz and 5.5 V, which is equivalent to roughly two-thirds of its body length per second.

This proof-of-concept robot has not been optimized. In order to ensure that the spring rolls are oper-ated in a reliable voltage range, the robot was driven at not more than 5.5 kV. The bending angle at this voltage is roughly half of the angle at 7 kV, the typical breakdown voltage. The maximum achievable speed can be estimated from the current limitations of the spring rolls. At 4 Hz, with a maximum lat-eral stroke of 6.6 cm for each leg, the robot could theoretically obtain speeds of up to 53 cm/s. Further improvement could be achieved if the robot legs are driven at greater than 10 Hz, where dynamic effects may come into play.

9.5.2 Sushi rolls: spring rolls in series

Several spring rolls with a monolithic structure were fabricated in series. The one shown in Fig. 9.10 has four sections in series. Each segment of these ‘ sushi rolls ’ can be individually actuated like a single 2-DOF roll actuator. The entire sushi roll has 8-DOF in two groups, LRLRLR and RLRLRL, where L is a left circumferential span and R is a right span. The two groups can be actuated successively to gen-erate a wave-like motion. In an experiment in which a 6 kV voltage was applied successively from one segment to the next, the sushi roll moved in a serpentine fashion as expected. Sushi rolls can also be used for the low-cost mass production of 2-DOF spring rolls: each sushi roll could be cut into multiple spring rolls, yielding throughput improvements in roll manufacturing.

9.5.3 Multi-DOF roll fish

The motion of a multi-DOF roll is uniquely suited to the undulating motion of a fish or other aquatic crea-tures. A multi-DOF roll fish has been fabricated by attaching a fin and nose to the roll and encapsulating the structure in a silicone protective coating, as shown in Fig. 9.11 . The fish demonstrated the ability to reliably encapsulate the actuator and operate underwater.

Figure 9.10 Sushi roll with six 2-DOF spring rolls in series on monolithic structure – straight roll when voltage is off and bent roll when voltage is on. This roll has a total of 8-DOF.

Figure 9.11 Multi-DOF roll fish.

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102 Chapter 9

9.6 OUTLOOK FOR PRODUCTION OF MULTI-DOF ROLL ACTUATORS

To date, there has been limited production of multi-DOF roll actuators due to their complexity and less than optimal levels of reliability. The complexity issues can be addressed through development in several key areas including: (1) improved electrode printing techniques such as screen printing or other precision printing techniques that form well aligned and patterned electrodes in a simple process; (2) more special-ized design of the central structures and fixtures; (3) assembly of the multi-DOF actuators with specif-ically constructed machines and (4) using the new interpenetrating elastomer network films described in Chapter 5 which reduce the amount of internal stress due to prestrain (Soon Mok Ha et al.). Reliability is a critical issue that may be partially relieved with the use of the interpenetrating elastomer network films. The authors at Artificial Muscle, Inc. (AMI) and the University of California, Los Angeles (UCLA) are also addressing the reliability issue through other approaches, such as control of the quality of the dielec-tric film, the removal of stress concentrations, and control of electrode properties including formulation, thickness and quality of pattern alignment. Successful manufacturing and commercialization will depend in large part on the level to which the reliability can be improved.

ACKNOWLEDGEMENT

The authors wish to thank Dr Ronald Pelrine, Mr Roy Kornbluh, Mr Neville Bonwit, Mr Scott Stanford, Dr Hasha Prahlad and many other previous colleagues at SRI International who participated in the design and development of the multiple DOF roll actuators.

References

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roll actuators and their application for biomimetic walking robots. SPIE: Smart Materials and Structures ,

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[5] Timoshenko , S. ( 1925 ). An alternative method of solving multilayer bending problems . J. Opt. Soc. Am. , 11 ,

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[6] Otero , T. and Sansinena , J. ( 1998 ). Soft and wet conducting polymers for artificial muscles. Adv. Mater. , 10 ,

491 .

[7] Madden , J. D. W. , Madden , P. G. A. and Hunter , I. W. ( 2002 ). Conducting polymer actuators as engineering

materials . Smart Materials and Structures , Eds. Bar-Cohen , Y. , SPIE Press, Bellingham, Washington, DC ,

pp. 176 – 190 .

[8] Pei , Q. and Inganas , O. ( 1992 ). Electrochemical application of the bending beam method. 1. Mass transport

and volume changes in polypyrrole during redox . J. Phys. Chem. , 96 , 10507 – 10514 .

[9] Pei , Q. , Inganas , O. and Lundstrom , I. ( 1993 ). Bending bilayer strips built from polyaniline for artificial elec-

trochemical muscles . Smart Mater. Struct. , 2 , 1 – 6 .

[10] Meijer, K., Rosenthal, M. and Full, R. (2001). Muscle-like actuators? A comparison between three electroac-

tive polymers. SPIE: Smart Materials and Structures , Newport Beach, CA, Proc. SPIE , 4329 , 7–15.

[11] Kornbluh , R. , Pelrine , R. , Pei , Q. and Shastri , V. ( 2001 ). Application of dielectric EAP actuators . In

Electroactive Polymer (EAP) Actuators as Artificial Muscles – Reality, Potential and Challenges , Ed.

Bar-Cohen , Y. SPIE Press , Bellingham, Washington, DC , pp. 457 – 495 .

[12] Clark, J., Cham, J., Bailey, S., Froehlich, E., Nahata, P., Full, R. and Cutkosky, M. (2001). Biomimetic design

and fabrication of a hexapedal running robot. IEEE International Conference on Robotics and Automation, Seoul, Korea . May 21–26, 2001.

Ch09-I047488.indd 102 12/10/2007 8:22:56 PM

ACTUATORS AND SENSORS FROM DIELECTRIC ELASTOMER WITH SMART COMPLIANT ELECTRODES

Peter Sommer-Larsen 1 and Mohamed Benslimane 2

1 Polymer Department, Risø National Laboratory, The Technical University of Denmark, Roskilde, Denmark

2 Micro Technology Group (IS-TCR), Danfoss A/S, Nordborg, Denmark

Abstract

The compliant electrode is central for the dielectric elastomer actuator technology. The dielectric elastomer with

smart compliant electrodes (DESCE) actuator has a thin-film metallized electrode applied on a microstructured

elastomer film. The structured electrode constricts the movement of the actuator to given directions. DESCE allows

for both actuation and capacitive sensing, and they can be produced in a multitude of configurations: single sheet,

multilayer and roll actuators; extensional, shear and normal force sensors. The DESCE technology is apt for up

scaling production.

Keywords : Actuator, DESCE, dielectric elastomer, extensional sensor, multilayer, normal force sensor, roll, sensor,

shear sensor, smart compliant electrode.

10.1 INTRODUCTION

The compliant electrode is central for the dielectric actuator technology. Electrodes based on percolation of conductive particles are particularly simple to apply in form of dust or paste that is brushed, thick-film coated or sprayed on the elastomer film. A number of conductive paints, glues and curable rubber formulations are commercially available as described in Chapter 7. Such electrodes are easily applied after pre-stretching the actuator film; hence, the extremely high strains obtainable with dielectric elas-tomers are exclusive to percolated electrodes. The dielectric elastomer with smart compliant electrode (DESCE) actuator on the other hand has a thin-film metallized electrode applied on a microstructured elastomer film. The structured electrode constricts the movement of the actuator to given directions. The smart compliant electrode technology is described in details in Chapter 7 and reviewed in Fig. 10.1 . The DESCE was patented by Benslimane et al. in 2000 and the first results published in 2002 [1] .

10.2 ACTUATOR CONFIGURATIONS

An actuator consists of an elastomer sandwiched between two compliant electrodes. For DESCE actua-tors, two one-side corrugated films are assembled to an actuator sheet as illustrated in Fig. 10.2 . The conceptual steps in processing a DESCE actuator are: (1) casting of elastomer film on a microstruc-tured mould; (2) lift-off and metallization of electrode area and (3) assembly of sheet, frames and con-nectors. The elastomer used is a RTV two-component silicone: ELASTOSIL ® RT 625 from WACKER.

Multilayer actuators can be fabricated by stacking several sheets and making proper electrode con-nections. Each sheet has a side (electrode) of positive and negative polarity if the high-voltage supply is floating or a grounded and high-voltage side if the supply allows for grounding. A double layer actua-tor, for example, can be stacked such that the grounded electrodes face outwards and the high-voltage electrodes touch each other in the inside of the stack. A roll configuration can be made by rolling up such a double layer actuator.

Chapter 10

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104 Chapter 10

The corrugation pattern and the metallized electrodes constrict the movement of the actuator to the length direction. No change in width is observed under operation of the actuator. Circular patterns or other more elaborate patterns can allow for two-dimensional movements.

10.3 TESTING OF DESCE

In order to characterize the performance of a DESCE actuator, several properties need to be tested: (1) passive mechanical and electrical properties; (2) active equilibrium electromechanical properties and (3) dynamic electromechanical properties. These include the elastic properties (spring constant) of the actuators; the stroke as function of applied voltage and load; the capacitance of the sensor and actuator parts and how they change with extension; the resistance of electrical connections and the fre-quency dependent impedance. For vibration damping applications, the dynamic response to a step volt-age allows for determination of the impulse response function of the actuator.

10.3.1 Passive mechanical and electrical properties

Mechanical properties : To a good approximation, the DESCE behave as elastic springs under exten-sions in the range up to 10%. Stress–strain curves for DESCE are illustrated in Chapter 7. For 10–20%

Corrucated rubber 100 �stiffer

��

100 �compliant

Electrodes

Figure 10.1 The principle of the smart compliant electrode. Corrugation makes the sheet compliant in one direc-tion and stiff in the orthogonal direction. Sheet dimensions up to 320 mm � 320 mm and a thickness of 40 � m has been demonstrated. The corrugation pattern is 4–5 � m in amplitude and has a 10 � m period. A 50–100 nm thin metal layer is applied on both sides as electrodes.

Figure 10.2 Processing of actuator sheets. Hand-made sheets are fabricated on a laboratory scale. Step 1 : An elastomer film is cast on a microstructured mould – typically a wafer. After curing, the wave pattern is imprinted on one side of the film – the corrugated side. Step 2 : The sheet is released from the mould and the electrode area metallized on the corrugated side. Combining two films makes an actuator with corrugations facing outwards. Step 3 : The actuator is assembled; connectors and eventually frames are attached.

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Actuators and Sensors from Dielectric Elastomer with Smart Compliant Electrodes 105

strain, the stress follows finite strain models as discussed in Chapter 16. The compliance limit for the electrode is typically reached between 25% and 35% strains depending on the corrugation profile as detailed in Chapter 7. The response speed of dielectric elastomer actuators is coupled to the viscoelas-tic properties of the basic elastomer as discussed in Chapter 16, hence also stress relaxation or creep experiments yield important information.

Electrical properties : The capacitance of the actuator is important for the choice of high-voltage drive. The output power of small switch-mode amplifiers may set limits to the possible charging times of multilayer actuators with large capacitance. So far we have fabricated actuators with capacitance from 0.5 to 50 nF and the measured capacitance agree with the value found for a plate capacitor. The serial resistance in the electrodes is negligible – typically a few ohms – whereas electrode connections made from conducting rubber formulations or conductive tapes may show kilo ohms resistance. Nevertheless, RC charging times are typically negligible.

10.3.2 Active equilibrium electromechanical properties

Active equilibrium electromechanical properties are tested either isotonic or isometric. Isotonic tests measure elongation as function of applied voltage at constant load. Isometric tests measure stress as function of applied voltage at constant length. The actuator is tested in a setup depicted in Fig. 10.3 . The sheet is mounted in a rigid test stand with one end connected to a load cell and the other end to the sledge of a translation stage. The test stand and the high-voltage supply are controlled from a compu-ter. In an isotonic test, the high voltage is ramped and the position of the translation stage is controlled based on feedback of the load cell signal in order to keep the applied load constant. The movement of the translation stage is monitored.

Results from an isotonic test of a DESCE actuator are illustrated in Fig. 10.4 . The strain as function of applied electric field is proportional to the square of the electric field for strains less than 10% as expected for an actuator following simple Hookean behaviour (see Chapter 16). At higher strains, the strain response deviates due to influence from the electrodes and finite strains. The electrodes constrict the movement to extension in the length direction and with a proportional decrease of thickness (pure shear). The full Maxwell stress is transformed into elongational stress (see Chapter 16). The DESCE can be compared to an electrode that is compliant in two dimensions: the elongational stress doubles but the effective Young ’ s modulus is increased by a factor 4/3. In total, the DESCE is a factor 3/2 more efficient in transferring Maxwell stress into strain in one direction.

610 High-voltagepower supplyor amplifier

Force or displacementtransducer

Translationstage

Actuator

Figure 10.3 Computer controlled actuator electromechanical test stand. Sketch and actuator mounted in the test stand. Plastic frames connect the actuator to the load cell and moving sledge. Actuator dimensions: 90 mm � 70 mm � 40 � m (length � width � thickness). A stiff cage is mounted on a small damped optical table. A translation stage (Physik Instrumente, model M-410.DG) is fixed on one wall, with an L-piece mounted to form a small, movable horizontal sledge. Above the sledge a force gauge (load cell: Transducer Techniques model GS0-250) is mounted, such that an actuator may be fixed at one end to the gauge (using a stiff metal rod) and at the other end to the mov-able sledge. The analogue output of the force gauge amplifier is read into a computer via an I/O ADC (National Instruments, ATMIO-16E-10). The voltage is supplied by a tube amplifier (TREK ® model 610D) which receives its input from the NI card. The entire setup is controlled by a LabView ™ 8.0 (National Instruments) program.

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106 Chapter 10

10.3.3 Dynamic electromechanical properties

A transient test characterizes the actuators response to a voltage step. The translation stage is not suffi-ciently fast for this test so the lower end of the actuator is attached to an extended spring and the upper end to the load cell. The measured change in load is proportional to the change in extension of the spring. The moving mass is kept minimal in order to avoid mass oscillations. A result of such a test is showed in Fig. 10.5 . The measured response is faster than 60 ms. Most likely, it is even faster as the measured data is also limited by the data acquisition speed and response speed of load cell and high-voltage supply.

10.4 SENSOR CONFIGURATIONS

The capacitance of a DESCE sheet depends linearly on the extension of the sheet up to 20% strain, inde-pendently of the cause of extension: passive load or applied potential. Hence, the DESCE sheet can be used as position sensor through measuring its capacitance. The change in capacitance accurately follows �C C S/ ,0 2� where S is strain and C and C 0 are capacitances of the instant and unstretched actuator, respectively. Based on the constriction of deformation to pure shear, it should be expected that the change in capacitance is proportional to the square of the stretch ratio C C� 0

2� . The difference between the two predictions is however small for strains below 20%. Experimental results for stretching a DESCE sheet is presented in Fig. 10.6 . There is little hysteresis in the response and the reproducibility good.

A DESCE sheet can directly be used as a strain sensor. The sheet will typically be stretched by a load and the sensor works around an extended equilibrium position. The strain sensitivity depends upon the accuracy of the capacitance measurement. A typical setup based on a capacitance to frequency con-verter allows for measuring at least 0.1% strain.

The sensor read-out – measuring the capacitance – can be performed in several ways. A capaci-tance meter is a simple but bulky solution. Another solution is to use a capacitance to frequency con-verter (RC timer) to convert the capacity into a TTL signal. The TTL signal may either be counted by a data acquisition card or converted into an analogue or digital signal. An RC timer setup is shown in Fig. 10.7 . The capacity may also be measured directly for the actuator sheet by superimposing a high-frequency and low-voltage signal on the driving high-voltage signal [2] .

A sheet or roll – see Fig. 10.8 – of DESCE is used for strain measurements in extension and con-traction. In order to measure normal and shear stress, two sheets were imbedded in a silicone block as shown in Fig. 10.8 . Under a normal compressive stress on the silicone block, the two films are both extended and their capacitances changes with an equal amount proportional to the compressive strain. Under simple shear, one film is extended and the other contracted. The capacitance of one of the films

Data

Fit S � εε0

YE 2

0 20 40 60 80 1000.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Electric field (V/μm)

Str

ain

Figure 10.4 Strain as function of applied electric field for an actuator under constant load (isotonic test). The actuator of dimension 20 mm � 40 mm � 44 µm (length � width � thickness) was tested at a load of 0.14 N for applied voltages from 0 to 4000 V. Strain is measured relative to the loaded actuators length. The full line is a fit to a linear model for strains less than 10%.

Ch10-I047488.indd 106 12/10/2007 8:23:29 PM

Actuators and Sensors from Dielectric Elastomer with Smart Compliant Electrodes 107

0 5 10 15

Strain (%)

ElongationContraction

Act

uato

r ca

paci

tanc

e (n

F)

20 25 30

0 5 10 15 20 25 30

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

Figure 10.6 Capacitance as function of strain for a DESCE sheet of dimensions 31 mm � 44.5 mm � 42 � m (length � width � thickness). The data was measured under both extension and contraction of the actuator. The line is a linear fit to the extension data yielding �C C S/ 0 1.7� .

Figure 10.5 Transient test: sketch of test setup and results for a potential step of 2500 V applied and lowered again over a 5 s period. Potential and load is sampled every 30 ms. The measured high-voltage output potential (full circles) and the load (open circles) are shown. The actuator consists of four sheets of dimension 90 mm � 70 mm (length � width) and the total thickness is 148 � m. The top end of the actuator is rigidly connected to the load cell and the moving bottom end of the actuator is connected to an extended spring. In addition, mass can be added to the moving end. No mass was added in the reported experiment.

Loadcell

Pot

entia

l / k

v

Load

/ N

Time/s

0 1 2 3

0

2

4

6

8

10

�24 5 6

Actuator

Springor

mass

X

L

m

3.0

2.8

2.6

2.4

2.2

2.0

1.8

1.6

is increased and that of the other decreased with the same amount proportional to the shear strain. Hence, the sum of the two capacitances is proportional to the compressive strain and the difference to the shear strain. The sensor signals divide a given deformation into its shear and normal components.

The technology also opens for remote sensing by using the sensor sheet as the capacitive component in a RFID (radio frequency identification) oscillator.

10.5 CONCLUSION

The DESCE technology has several advantages both for actuator and sensor applications. Using a sili-cone elastomer material, sheets can be produced in a reproducible fashion. The choice of elastomer also secures a stable sensor or actuator which has little hysteresis or time delay in its response. The DESCE technology and principles are appropriate for large scale production.

Ch10-I047488.indd 107 12/10/2007 8:23:29 PM

108 Chapter 10

References

[1] Benslimane , M. , Gravesen , P. and Sommer-Larsen , P. ( 2002 ). Mechanical properties of dielectric elastomer

actuators with smart metallic compliant electrodes . Proc. SPIE Int. Soc. Opt. Eng. , 4695 , 150 .

[2] Toth , L.A. and Goldenberg , A.A. ( 2002 ). Control system design for a dielectric elastomer actuator: the sen-

sory subsystem . Proc. SPIE Int. Soc. Opt. Eng. , 4695 , 323 .

Csensor

10 kΩ

39 kΩ

Output

VDD

VDD

HARRISICM7555

1

2

3

4 5

6

7

8

Figure 10.7 Capacitance to frequency converter: an RC timer based on the HARRIS ICM7555 general pur-pose timer. The capacitor is the sensor under test. The frequency of the output TTL signal is f � 1/(2 1/2 RC ). With R � 39 k � and C � 2.5 nF (a typical value for a C -type sensor) the frequency becomes 7.3 kHz. The TTL signal is counted using the National Instrument ATMIO-16E-10 DAC card.

Figure 10.8 (a) Extensional sensor in form of a roll and (b) combined shear and normal force sensor).

l2

C1C2

Fig 3l2

6

l

f

15 � 15 mm prototype device(a) (b)

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MULTILAYER STACK CONTRACTILE ACTUATORS

Helmut F. Schlaak , Peter Lotz and Marc Matysek

Institute for Electromechanical Design, Darmstadt University of Technology, Darmstadt, Germany

Abstract

To increase the absolute deflection of dielectric elastomer actuators at limited driving voltage, thin dielectric

films and elastic electrodes are stacked on top of each other using a multilayer fabrication technology. The electro-

mechanical properties of these actuators with up to 200 layers have been evaluated theoretically using a viscoelas-

tic model. The static and dynamic electromechanical properties have been characterized experimentally. Maximum

strain values up to 20% for stacked films have been achieved. The multilayer fabrication technology provides stack

actuators with various electrode patterns like universal linear actuators, matrix arrays for a wide range of applica-

tions as tactile displays in telemanipulation or Braille displays and peristaltic pumps.

Keywords : Applications, Braille display, dielectric elastomer actuator, electroactive polymer, electrostatic actuator,

multilayer, peristaltic pump, tactile display.

11.1 INTRODUCTION

Solid-state actuators provide deformation and actuation forces mainly excited by electric fields. Piezoelectric actuators are well established providing high forces at low strain due to their material characteristic. In order to achieve large deformations electrostatic solid-state actuators consist of elastic dielectric layers between compliant electrodes.

Applying a voltage at the compliant electrodes the dielectric contracts due to electrostatic forces and expands in lateral direction ( Fig. 11.1 ).

Deriving the stored energy in a capacitor to the vertical coordinate under consideration of the lateral deformation the electrostatic pressure causing the deformation is

p T

V

zE� � �� � � �0

2

2 02

r r

(11.1)

where � 0 is the relative permittivity in air, � r the permittivity of the dielectric, z its thickness and V the applied voltage. The electrodes have to be highly compliant not to constrain the deformation, as the pressure in Eq. (11.1) is twice as large as compared to a capacitor with rigid electrodes.

Chapter 11

Elastic dielectricfilm

Compliant electrodes

p

V

p

Figure 11.1 Deformation of an elastic dielectric film under electrostatic pressure.

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110 Chapter 11

Pelrine et al. [1] have shown more than 30% relative strain in thickness and electrostatic pressures of more than 1 MPa on prestrained silicone elastomer dielectric films between carbon electrodes. These achievable values of strain are very high compared to other solid-state actuators. But, to realize a sufficient strain with reasonable voltages below 1000 V the thickness of the dielectric has to be less than 50 � m. Unfortunately, the absolute deflection remains rather small even for the large strains of dielectric elastomer actuators.

In order to increase the absolute deflection at limited voltages, certain configurations of the actuator are essential. Figure 11.2 shows two major assemblies.

Extending actuators use the strain perpendicular to the applied electric field. Hollow and solid cyl-inders (so called roll actuators – Fig. 11.2(a) ) are fabricated by a combination of only two dielectric layers and two electrodes. Before rolling the actuator the elastic film is prestrained. According to their dimensions they can perform comparatively high forces and deformations. However, this scheme deliv-ers single actuators.

In a contractile actuator ( Fig. 11.2(b) ) electrodes and dielectric films are stacked upon each other. To achieve both a limited driving voltage and a large deformation up to 1 mm actuators have to consist of a stack of multiple dielectric layers where the number of layers may reach several 100. They can be fab-ricated in different sizes and various arrangements with multiple actuators integrated in one foil where the density of actuator elements can become quite high. Commonly, the dielectric material of this type of actuator is not prestrained.

11.2 TECHNOLOGY

To fabricate elastomer stack actuators with up to 200 layers a multilayer process technology has been developed using high elastic silicone elastomers as dielectric and thin electrodes of graphite powder. The fabrication allows arbitrary configurations of multiple actuators on a common substrate retaining the high structural flexibility of the silicone material.

11.2.1 Material requirements

There is a huge variety of parameters to be kept in mind while choosing the ‘ right ’ elastomer for the special application of multilayer actuators. If we use an elastomer with a high hardness we can apply quite large forces causing a low prestrain before electrostatic excitation. The remaining displacement is close to its idle maximum. Therefore, a high electrostatic pressure is required. The high electric field may lead to a breakdown. On the other hand we may choose a very soft elastomer. The required voltage for maximum displacement is relatively low but the strain by the preload causes a high deformation and minimizes possible contraction.

Beside these considerations the elastomer material should have a low dynamic viscosity not to loose maximum displacement with increasing frequency. Furthermore, the mechanical parameters of the dielec-tric should have a high disruptive strength and due to Eq. (11.1) a high permittivity to maximize actuator performance.

Technological demands are a low viscosity to realize thin dielectric films by spin coating and an addition curing silicone to avoid fission products. Dilution of the components is possible but requires

(a)V V

(b)

1 mm

2 mm

50 mm

Figure 11.2 Configurations and function of electrostatic elastomer actuators.

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Multilayer Stack Contractile Actuators 111

a certain time to degasify, otherwise bubbles decrease the electrical breakdown strength. A low pot life leads to an acceptable production time – each dielectric layer has to cure before the electrode is put onto it. Often curing can be accelerated by thermal or optical radiation. Table 11.1 shows several sili-cones and their main parameters.

The electrical cut-off frequency is dominated by the series resistance of the feed lines (see Section 11.3.2). The resistance of the feed line and the electrode has to stay low during planar expansion other-wise the time constant would change immensely and the effective electrode surface might be reduced due to interceptions. Furthermore, the surface density of the electrode should stay high even under expansion to assure high effective electrostatic pressure.

The mechanical requirements are influenced by the deformation of the electrode layer. The ideal electrode has an infinite compliance, is thin compared to the dielectric layer and is patterned with high resolution [2] . A good adhesion onto the dielectric layer is needed to prevent partial wash-off effects reducing conductivity. The manufacturing process should not be too complex, to keep fabrication time as short as possible.

11.2.2 Realization

The automated fabrication process is controlled by a computer. A special LABVIEW © program is used to set and monitor the parameters and drive all process sequences. Figure 11.3 shows an overview of one cycle.

By spinning on silicone elastomeric dielectric films are realized. Spin coating is used to achieve homogeneous coating thickness of only a few microns. As mentioned above an addition curing silicone is used. The two components are stored in cartridges and are squeezed out by stepping motors. Flexible tubes lead the components into a static mixer where they get mixed homogeneously without embed-ding any bubbles. The volume of the mixer and the pot life have to be coordinated that way, that already

Table 11.1 Properties of applicable silicones.

Manufacturer Name Shore Hardness Viscosity, Uncured (Pa s)

Permittivity

Bayer IS 5663/20 15 8.5 3 Dow Corning 96-082 31 1.1 3.14 Wacker Elastosil RT 607 55 10 3.7 Wacker Elastosil RT 675 80 35 6.1

Component A Pressurized airGraphitepowder

Component B

Dosage, mixing andspinning-on elastomericcomponents

Thermal curing ofelastomeric layer

Masking elastomeric layer,spraying-on electrodes

TStatic mixerω

Figure 11.3 Process steps of one cycle of the automated fabrication for elastomeric actuators.

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112 Chapter 11

mixed elastomer within the mixer will not be cured before the start of the next process cycle. The spun on silicone ’ s curing is accelerated by thermal radiation. Enforced cooling of the rotary disc and hence the dielectric film reduces the time until the next process step can be started.

The electrodes are deposited onto the cooled elastomeric film. To contact the actuator to its supply voltage it is necessary to turn the leads of every second electrode. Figure 11.4 shows the schematic cross section of an actuator stack with a parallel interconnection of the stacked electrodes.

The fabrication tool for a structured spray coating of conductive powder on elastomeric layers has to realize three major functions:

1. masking the dielectric layer, 2. dosing the graphite powder, 3. spraying on the pressurized air-graphite powder mixture.

Masking is realized by a spray head carrying a shadow mask patterned by photolithography. The graphite powder is stored in a pressure vessel. By whirling up the particles the mixture is generated in the upper parts of the vessel. Out of a nozzle the air-graphite powder mixture is sprayed through the mask onto the dielectric film.

11.2.3 Results

Prototypes with up to 200 dielectric layers have been fabricated with the silicone elastomer Wacker Elastosil P7670. Various electrode patterns, e.g. for single actuator elements as well as for matrix assemblies, have been realized. The minimum thickness of dielectric layers is limited to approximately 25 � m due to the decreasing yield for thicknesses below 20 � m and the rotational speed of the spin coater drive. The electrode thickness is about 5 � m while the primary particle size of the graphite powder is 2 � m.

Figure 11.5 shows a micrograph of a 100-layer actuator stack. Comparing the realized actuator stack with the schematic assembly ( Fig. 11.4 ) it can be seen that the graphite particles of the electrodes do not immerse into the silicone layer nor a wash-off effect of the particles occurs. The reproducibility of the electrode edge from layer to layer is within a few microns ( Fig. 11.5(a) ).

The reproducibility of the thickness of the spun silicone layers has been investigated with a line width measuring system. The thickness of each dielectric layer has been measured from the cross section of a 50-layer stack ( Fig. 11.6 ). It can be seen that the firstly spun layers are thinner than the last ones: the mean value is slightly rising by the number of layers.

As mentioned before, the electrode and especially its conductivity are of high importance. Not only the material but also the way of deposition affects its quality. Two methods are analysed in Fig. 11.7 – spraying and brushing. Even if both types have low starting sheet resistances ( � 10 k � / sq. ), the sprayed elec-trode has a more than two times greater sheet resistance. This difference is rising as transverse strain is increased by a mechanical test device. Actuators with a high strain should carry brushed electrodes even if there are still difficulties by brushing graphite powder onto a micro-patterned shadow mask.

The two micrographs in Fig. 11.8 show the surface of a brushed ( Fig. 11.8(a) ) and a sprayed ( Fig. 11.8(b) ) electrode. The sprayed electrode shows an inhomogeneous surface that influences the conductivity obviously. The homogeneous layer of the brushed graphite may be the reason for a better conductivity for strained electrodes.

Supply region Active region

Vc

Supply region

Figure 11.4 Schematic cross section of an actuator stack.

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Multilayer Stack Contractile Actuators 113

00

20

40

60

80

100

120

140

160

5 10Transverse strain Sx,y (%)

15 20 25

y � 7.21x � 10

Graphite, sprayedGraphite, brushed

She

et r

esis

tanc

e (k

Ω /s

q.)

y � 3.28x � 7

Figure 11.7 Sheet resistance of graphite electrodes.

35

30

25

20

15

100 10 20

Film n

Film

thic

knes

s (�

m)

30 40 50

Measured valuesLinear fit

Figure 11.6 Measured absolute film thickness of a 50-layer stack actuator.

(a) (b)

Graphite

Active region

Silicone

Supply region Active region

Figure 11.5 Micrograph of a 100-layer stack (cross section): (a) boundary between supply region and active region (scaling bar: 50 � m) and (b) active region (scaling bar: 20 � m).

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114 Chapter 11

11.3 MODELLING

Due to high strained dielectric films of an actuator stack there is a nonlinearity of the stress–strain characteristic. Furthermore, viscoelastic behaviour is typical to elastomeric materials, hysteresis and damping effects are the consequence. In this section a model is presented characterizing the actuators behaviour under the mentioned restrictions [3] .

11.3.1 Geometrical nonlinearities

Geometrical nonlinearities are typical characteristics of elastomers, caused by a very low compress-ibility. Therefore, the volume Vol of a deformed elastomer stays nearly constant [4] . If we assume a constant volume, mechanical stress caused by the force F deforms the sample ( Fig. 11.9 ). The relation between vertical strain d z and area strain d A z is given by

Vol const d d� � � � �x y z A z A A z zz z z0 0 0 0 0 0 0( )( )− (11.2)

The transverse strain S x and the area strain S A of a uniaxial compressed elastomer volume are given by

Sx

x SS

A

A

S

Sxz

Az

z

z

z

� ��

� � ��

d d

0 0

1

11

1; (11.3)

Figure 11.10 shows the transverse and area strain as a function of the vertical compression. Exceeding 61.9% compressive strain the transverse strain is larger than the compressive strain. Regarding the achievable strains of up to 20% in vertical direction caused by the electrostatic field, it is recommended to use the actuators in a contractile manner, according to Fig. 11.2(a) .

At quasi-static deformation the stored mechanical energy W caused by the force F complies with the sum of the three expansion energies in each dimension:

d d d d dW F z F z F y F xz y x� � � � (11.4)

(a) (b)

Figure 11.8 SEM micrographs of (a) brushed and (b) sprayed graphite electrode.

dAz

dy

dzz0

y0

dx x0F

Figure 11.9 Geometrical proportions of a sample deformed by force F.

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Multilayer Stack Contractile Actuators 115

Here, F i � T i A i corresponds to the force acting onto the boundary face. Converting Eqs. (11.2) and (11.4) leads to

T T T Tz x y� � � (11.5)

T x and T y are negative because they are tensile stress assuming T z as compression. If we assume iso-tropic material properties and a constant, isotropic Young ’ s modulus Y � T i /S i we get the externally affecting stress T (using S x from Eq. (11.3)) causing the compression S z :

T Y S S Y SS

YSz x zz

n� � � ��

� �2 21

11( )

⎛

⎝

⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

(11.6)

11.3.2 Electrical model

The equivalent electrical circuit of an electrostatic multilayer actuator according to Fig. 11.4 is shown in Fig. 11.11 . R s represents the resistance of the feed line of each electrode, R p the resistance of the dielectric layer (leakage current) and C the strain dependent capacity ( C ( S z )).

The displacement current I f n in the feed line n splits up into I n and I n �1 to charge both adjacent dielectric layers, thus each single layer is connected to the driving voltage and ground by the effective resistance 2 R s , respectively ( Fig. 11.11(b) ). The first and last feed line and electrode have to charge only one dielectric layer, so the driving voltage changes slightly. In the following this edge effect has been neglected and Fig. 11(b) is assumed for all layers. Thus, the effective voltage drop across the dielectric layer is given by

V VZ

Z RV

R C S Rzc

p

p s s pj�

��

� �0 0

4

1

1 4 1� ( ) /( )

(11.7)

with Zp as impedance of one dielectric layer. The strain dependent capacity C ( S z ) is given by

C S

A

z

A A

z z

A S

z SzA

z

( )( )

( )� �

�

��

�

�� � � � � �0 0

00

0

0

1

1r r

0r

d

d

(11.8)

With Eq. (11.3) we can simplify the term, yielding

C S

A

z Szz

( )( )

��

� �00

02

1

1r

(11.9)

00

0.5

1

1.5

2

2.5

3

3.5

Str

ain

Sx,

SA

4

0.2

Transverse strain SxArea strain SASx � Sz

0.4Compressive strain Sz

0.6 0.8

Figure 11.10 Transverse and area strain depending on the compression strain.

Ch11-I047488.indd 115 12/10/2007 8:24:15 PM

116 Chapter 11

Combining Eqs. (11.7) and (11.9) we get

V V

RAz S R

z

c

s rp

j

�

��

�

0

00

02

1

1 41

1

1�� �

( )

⎛

⎝

⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟

(11.10)

By equating relation (11.1) for the electrostatic pressure and relation (11.6) for the mechanical stress we get the voltage Vc , needed to achieve the strain S z

V zT

z SYS

zn

cr r

� �� � � �0

00

1= ( )

(11.11)

where Y is the complex elastic modulus taking the viscoelastic behaviour into account [3] . The driving voltage Vc decreases with increasing frequency due to low pass filtering (Eq. (11.10)). The total imped-ance of the stack actuator is according to Fig. 11.11(b)

ZV

IN R C

R

nn

Nstackp

sj

� ��

�

�

0

1

1 1

14

∑

⎛

⎝

⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟/ �

(11.12)

Thus, the feed line resistance has to be kept as low as possible.

11.4 CHARACTERIZATION

To characterize the dynamic behaviour of stack actuators special prototypes have been realized. Figure 11.12 shows the prototype design and its dimensions. The thickness of the dielectric layer (silicone: Wacker Elastosil P7670) is 25 � m, electrodes are 5 � m thick. The permittivity of the elastomer is � r � 3. Stacks with 22 and 52 layers have been investigated – the two layers on the surfaces of the stack are to protect the electrodes. Material parameters are ascertained by cast cylindrical samples.

(a)

V0

Rs

Vc

Vc

Vc

Rp Rp RsRs

Rs

Ifn

In

In

In�1

Rp

Rp

Rp

2Rs

2Rs

C

C CCC

(b)

Figure 11.11 Equivalent circuit of (a) an electrostatic multilayer actuator and (b) a single layer inside the stack.

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Multilayer Stack Contractile Actuators 117

11.4.1 Quasi-static behaviour

The stress–strain characteristic is used to determine the quasi-static material parameters. Therefore, a cylindrical sample (Ø 10 mm; height 10 mm) has been compressed uniaxially and the force–deflection characteristic has been determined. The proceeding velocity is 10 � m/s. Figure 11.13 shows the stress–strain characteristic compared to the theoretical model (Eq. (11.6)). Stress values concern the face of the uncompressed sample ( A 0 ).

We can recognize the hysteresis in the measurement due to the complex elastic modulus Y and the friction on the contact surface. This friction is minimized by using Vaseline. Neglecting the hysteresis the Young ’ s modulus has been determined to Y � 123.7 kPa. This Young ’ s modulus can be used to cal-culate (using Eq. (11.11)) the strain of an actuator for an applied voltage.

The real strain as function of the supplied voltage is determined with a 20-layer actuator. To measure the deflection the actuator is put into a mechanical frame to prevent several sources of error (e.g. cam-bers). The deflection is measured by an optical surface profilometer. We obtain a similar characteristic between model and measurement data as shown in Fig. 11.14 .

11.4.2 Dynamic behaviour

The frequency response of a 50-layer actuator stack has been investigated in the frequency range from 10 Hz up to 1000 Hz. Figure 11.15 shows the measured frequency response � z / V and the qualitative comparison of the force–deflection–frequency � z / F response where � z is the measured stack thick-ness variation. The actuator is driven by a sinusoidal signal with DC bias to achieve a unipolar driving voltage [5].

Compared with the model data the actuator shows a lower resonant frequency and a higher resonance peak. This is obviously a result of the higher mass that results from the passive silicone surrounding

(a) (b)

Passive border area

40m

m

15m

m

Electrode

Supply

Figure 11.12 (a) Actuator design and (b) batch fabricated actuators.

0

0.5

0.4

0.3

0.2

Str

ess

T (

MP

a)

0.1

00.1

Model data

Measurement data

0.2 0.3 0.4Strain Sz

0.5 0.6 0.7

Figure 11.13 Stress–strain characteristic.

Ch11-I047488.indd 117 12/10/2007 8:24:15 PM

118 Chapter 11

of the electrodes. Assuming an actuator without a passive surrounding silicone ring the frequency response will be close to the model curve.

11.5 APPLICATIONS

As mentioned in Section 11.1 electrostatic solid-state actuators fabricated as multilayer stacks are pri-marily used for linear motion. They provide low forces at high deflection. This combination establishes new applications particularly in microelectromechanical systems (MEMS). As a result of the perpen-dicular effective motion direction actuators can easily be grouped close to each other. Multilayer elas-tomer stack actuators can meet a variety of applications in optics (micromirrors), switches, acoustics (micro-loudspeakers), mechanics (vibration damping) and microfluidics (valves, pumps) [6] .

11.5.1 Tactile display

A further field of application is the human tactile sense. The actuators performance is ideal to adapt actuators to the tactile sense of human skin. As an actuator for one Braille display element ( Fig. 11.16 ) there is only a 4 � 2 actuator matrix needed [7] .

But this is quite far away from the achievable potential of elastomer stack actuators. The high flexi-bility allows a tactile display to be integrated into a data glove. For stimulating the whole human hand there are some hundred actuators needed – due to the high selectivity and spatial resolution of the human sense.

00

500

0.05

Str

ain

Sz

0.1

0.15

0.2

1000

Voltage (V )

1500

Measured dataModel data

2000

Figure 11.14 Strain–voltage characteristic.

10

1E�1

1E�0

1E�1

1E�2

�z/

F �

z/V

1E�3

1E�4

1E�5

Model z/FMeasurement z/U

100Frequency (Hz)

1000

Figure 11.15 Frequency response of an actuator and force–strain ratio frequency response of the dielectric.

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Multilayer Stack Contractile Actuators 119

Figure 11.17 shows dielectric actuator matrices for tactile displays. The planar arrangement of the actuators into a hexagonal shape ( Fig. 11.17(b) ) assures equivalent distances between all adjacent actuators. To excite each actuator element independently insulated feed lines are required as demon-strated for a Braille cell ( Fig. 11.18 ). The electrodes of one layer are shown in Fig. 11.18(a) while in the whole stack the electrodes overlap within the actuator dots due to the transparent silicone films ( Fig. 11.18(b) ). Embedded bumps between actuator and human skin realize the force transmission: non-excited actuators are displacing the skin ( Fig. 11.18(c) ).

The excitation of a single actuator inside an actuator array is a challenge. If the actuators are arranged as a passive matrix every single line and column can be selected and the actuator gets charged or discharged. Figure 11.19 shows the principle with periodically switched column and row lines. Due to the slow discharging (through the non-ideal insulator between the electrodes) the display needs to be ‘ refreshed ’ at certain clearances. Such a passive matrix shows the principle disadvantage of crosstalk. If this crosstalk leads to noticeable displacements of the surrounding actuators an active-matrix arrange-ment has to be used (e.g. known from TFT displays).

Figure 11.16 Braille display as a possible application of multilayer actuators.

(a)

(c)

(b)

(d)

Figure 11.17 Matrix actuators for tactile displays: (a) 100 elements, rectangular shape; (b) 18 elements, hexagonal shape; magnifications (c) non-actuated elements and (d) actuated elements.

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120 Chapter 11

11.5.2 Peristaltic pump

The term ‘ peristaltic ’ denotes an actuation principle where mechanical energy is transferred to the fluid by periodic motion of the surrounding walls.

Compared with common rotary pumps, peristaltic pumps exhibit a number of advantages. First, the fluid that has to be transported only comes in contact with the smooth surface of the pump. Second, there are no rotating parts in the pump. Therefore, high relative velocities, which might cause cavita-tion, are not to be expected. This is a highly important feature if the transported fluid separates under influence of high flow velocities such as suspensions. Thus, peristaltic motion is an appropriate driving principle for dispersive fluids and fluids with living matter [9].

Figure 11.20(a) shows a schematic cross section of a silicone foil with integrated actuators. Driving the actuators with sinusoidal signals and delaying the signal between adjacent actuators by a phase shift � provides a travelling wave onto the pumping wall. For the application of a peristaltic pump two of these foils are bonded together, thereby doubling the volume of the pumping chambers. Irrespective of the connectors for the inlet and outlet, the whole pump consists of only two parts.

Passive

(a) (b) (c)0 V 1000 V

Active

Figure 11.18 Electrode layout for Braille display element: (a) electrode design; (b) top view of Braille cell stack actuator and (c) schematic cross section of Braille cell [8] .

Figure 11.19 Passive-matrix configuration with periodic refreshment.

Integrated stack actuator

d

L

l

Passive actuator

(a) (b)Activated actuator

Figure 11.20 Schematic (a) cross section and (b) top view of the peristaltic pump. Two single silicone foils with integrated dielectric actuators are bonded together.

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Multilayer Stack Contractile Actuators 121

Figure 11.20(b) shows the characteristic dimensions of the pump. For a functional model the length is set to L � 35 mm. There are two pumping waves to be expected along the pump creating a wave-length of l � 17.5 mm.

The performance of a peristaltic pump is described by several parameters, shown in Fig. 11.21 . The dominating parameter to influence the flow rate of the pump is the gap width g . Compared with well-defined chambers the moving walls of a polymeric peristaltic pump exhibit a relative large amount of leakage.

The pressure increase is proportional to the ratio of the length of the pump L and � which describes the wavelength of the wall ’ s motion. Therefore, a higher pressure increase can be achieved by a smaller wave-length � . The speed of the travelling wave is determined by the driving frequency f of the actuators.

Figure 11.22 shows the results of the fluid dynamic simulation [10]. The peristaltic pump exhibits a linear pressure-flow characteristic for several gap widths. For an open outlet the volume flow can be as high as 1.5 � l/s. Assuming an initial gap width of 50 � m, the pressure difference between the inlet and the outlet would reach 2 kPa per wavelength.

11.6 CONCLUSION

An automatic fabrication technology allows fabricating electrostatic multilayer stack actuators made of silicone. The electrodes consist of graphite powder deposited by spray coating through shadow masks.

Pump length X

Wall surface

b

a

k

z

c � lf

g

l

Figure 11.21 Parameters of two peristaltically moving walls.

00

500

Pre

ssur

e in

crea

se �

p (P

a)

1000

1500

2000

2500

50 �m

75 �m

100 �m

0.5 1Flow rate qv (�l/s)

1.5 2

Figure 11.22 Characteristic curve of the peristaltic pump for different gap widths g . Shown is the pressure increase per wavelength.

Ch11-I047488.indd 121 12/10/2007 8:24:18 PM

122 Chapter 11

Its function has been determined by several prototypes with different electrode designs and stacks with up to 200 layers.

The actuation frequency is limited due to low pass filtering caused by the high sheet resistance of the electrodes. Further developments will improve the material of the electrodes and their fabrication. To obtain a fabrication technology suited to different applications elastomers with different mechanical properties, e.g. compliance, have to be qualified.

References

[1] Pelrine , R. , Kornbluh , R. , Joseph , J. , Heydt , R. , Pei , Q. and Chiba , S. ( 2000 ). High-field deformation of elasto-

meric dielectrics for actuators . Mater. Sci. Eng. C , 11 , 89 – 100 .

[2] Pelrine, R., Kornbluh, R., Joseph, J. and Chiba, S. (1997). Electrostriction of polymer films for microactua-

tors. IEEE Proceedings of the 10th Annual International Workshop on Micro Electro Mechanical Systems ,

MEMS ’ 97, Nagoya, Japan, pp. 238–243.

[3] Schlaak, H. F., Jungmann, M., Matysek, M. and Lotz, P. (2005). Novel multilayer electrostatic solid-state

actuators with elastic dielectric (Invited Paper). 12th SPIE International Symposium on Electroactive Polymer Actuators and Devices (EAPAD) , 7–10 March, San Diego, CA, pp. 121–133.

[4] Carpi , F. , Chiarelli , P. , Mazzoldi , A. and De Rossi , D. ( 2003 ). Electromechanical characterisation of dielec-

tric elastomer planar actuators: comparative evaluation of different electrode materials and different counter-

loads . Sens. Act. A , 107 , 85 – 95 .

[5] Jungmann, M. (2004). Entwicklung elektrostatischer Festkörperaktoren mit elastischen Dielektrika für den

Einsatz in Taktilen Anzeigefeldern , Institut für Elektromechanische Konstruktionen, Darmstadt.

[6] Kornbluh, R. et al. (2004). Electroactive polymers: an emerging technology for MEMS. In MEMS/MOEMS Components and Their Applications , Proc. SPIE , 5344 , 13–27.

[7] Heydt, R. and Chhokar, S. (2003). Refreshable Braille display based on electroactive polymers. International Display Research Conference, IDRC ’ 03 , SID Society Information Display, P7.5.

[8] Matysek, M., Lotz, P. and Schlaak, H. F. (2006). Braille display with dielectric polymer actuator. ACTUATOR 2006, 10th International Conference on New Actuators , 14–16 June, Bremen, Germany, pp. 997–1000.

[9] Natarajan , S. and Mokhtarzadeh-Dehghan , M.R. ( 2000 ). Numerical prediction of flow in a model of a

(potential) soft acting peristaltic blood pump . Int. J. Numer. Meth. Fluids , 32 , 711 – 724 .

[10] Lotz, P., Matysek, M. and Schlaak, H. F. (2006). Integrated sensor-actuator-system based on dielectric poly-

mer actuators for peristaltic pumps. ACTUATOR 2006, 10th International Conference on New Actuators ,

14–16 June, Bremen, Germany, pp. 104–107.

Ch11-I047488.indd 122 12/10/2007 8:24:19 PM

CONTRACTILE MONOLITHIC LINEAR ACTUATORS

Federico Carpi and Danilo De Rossi

Interdepartmental Research Centre ‘ E. Piaggio ’ , University of Pisa, Pisa, Italy

Abstract

Contractile linear actuators are demanded for many fields of application. The design of efficient device architectures,

capable of taking the most from the material properties with practicable solutions, is not trivial. The state of the

art of contractile dielectric elastomer actuators offers device configurations resulting not always of easy fabrication.

According to the basic principle of operation of dielectric elastomer actuators, the most natural choice for assembling

a contractile unit is to stack several layers of elastomer alternated to layers of electrodes, as described in the previ-

ous chapter. Two alternative configurations, specifically conceived to obtain monolithic devices, are described in this

chapter. They consist of the so-called helical and folded actuators. Their specific features are discussed in the light of

a need of viable and simple architectures for contractile devices. Prototype devices based on both the configurations

are presented. The chapter describes the advantageous simplicity of the folded configuration, along with specific

applications that are currently being studied.

Keywords: Actuator, contractile, dielectric elastomer, folded, helical, linear, monolithic.

12.1 INTRODUCTION

A large number of different types of dielectric elastomer actuators have been demonstrated so far, as reported in the chapters of this book section ‘ Devices ’ . Most notable examples include planar devices, rolls, tubes, diaphragms, extenders, bimorph, unimorph benders, etc. [1–9] . Nevertheless, despite such a variety of structures and configurations, very few solutions are currently available to obtain actuators with linear contractile motion.

For such a purpose, a first type of approach that can be considered adopts auxiliary external mechanical components, to be used to transfer forces and motions towards preferred directions. Although mechani-cally effective solutions of this type can be implemented, such an approach is not always feasible, nor advantageous. In fact, auxiliary components (such as, for instance, flexible frames) can complicate the overall structure of the device and its fabrication; moreover, they may introduce additional sources of pos-sible failure, especially at the critical interfaces with the elastomer. In order to avoid such types of draw-backs, actuating configurations intrinsically capable of macroscopic linear contractions are needed.

According to the basic principle of operation of an elementary dielectric elastomer actuator, i.e. a sim-ple sheet of rubber with compliant electrodes, multi-layer stacks of such elementary components repre-sent the most natural choice for assembling a contractile unit. In fact, a stack-like actuator consists of several layers of elementary planar actuators connected in mechanical series and electrical parallel; the electrically activated thickness compression of each layer generates a resulting contraction of the device along its main axis [10] . Actuators of this type are described in detail in the previous chapter.

Despite the evident efficacy of the stack configuration, the fabrication of this kind of devices can present some specific delicate issues, which basically arise from the peculiarity of the structure itself. In particular, the structural discontinuity requires multi-step depositions of several layers of dielectric elas-tomer, alternated to layers of electrode material (see the previous chapter); additionally, each of the two resulting series of electrodes has to result electrically shorted, in order to establish the electrical parallel connection. These requirements can complicate the overall process of fabrication. In order to avoid such a disadvantage, different configurations consisting of intrinsically continuous elements and, preferably,

Chapter 12

Ch12-I047488.indd 123 12/10/2007 8:25:17 PM

124 Chapter 12

entirely monolithic structures represent a desired target, potentially enabling attractive simplifications. Aimed at reaching such an objective, a couple of alternative configurations were recently described: they consist of the so-called helical and folded actuators, separately described in the following sections.

12.2 HELICAL DIELECTRIC ELASTOMER ACTUATORS

A helical dielectric elastomer actuator consists of two helical layers of elastomer alternated to two helical compliant electrodes, as shown in Fig. 12.1 . An electrically activated squeezing of each helical elastomer causes an axial contraction and a related lateral expansion of the entire structure ( Fig. 12.1(a) ) [11] .

Actuators of this type were fabricated by adopting the following procedure [11] : a cylindrical hollow tube of dielectric elastomer (obtained by mould casting) was mounted onto a support and was cut with a blade having an automatic helicoidal motion, so as to obtain an elastomer helix; likewise, a second helix was also obtained; one of them was subjected to a masked coating in order to fabricate a couple of com-pliant electrodes; then it was intercalated to the other helix, so as to assemble the device; the final phase included also an external coating made of the same elastomeric material. Details about the specific fab-rication procedure can be found in [11] .

Prototype samples of helical actuators were fabricated with a silicone elastomer, owing to suitable mechanical and electrical properties, along with ease of processing, typically shown by this class of materials. In particular, a very soft and commercially available polydimethylsiloxane (TC-5005 A/B-C, BJB Enterprises Inc., USA) was selected. The extremely low elastic modulus (about 50 kPa) of this sili-cone enables high strains. The two main faces of one elastomer helix were coated with compliant elec-trodes consisting of a custom-made silicone/carbon black mixture (CAF 4, Rhodorsil, France/Vulcan XC 72 R, Carbocrom, Italy) [11] .

Figure 12.2 shows pictures of silicone-made helices having a thickness lower than 1 mm. An entirely assembled actuator is presented in Fig. 12.3 ; the translucency of the external coating permits to barely distinguish the underling helical arrangement of the electrodes. This sample presents the resulting shape of a soft hollow tube, having a length of about 60 mm, an inner diameter of 2 mm and an external diam-eter of 13 mm. The same figure shows a picture of a longitudinal section of a prototype actuator; this image shows the inclination of the helical electrodes, corresponding to an angle of about 83° with respect to the longitudinal axis.

Steady-state electromechanical axial strains of prototype helical actuators were measured for different step-wise driving electric fields, as reported in the example of Fig. 12.4 . These results demonstrate the feasibility of achieving linear contractile devices with a continuous structure.

A helical actuator potentially overcomes some of the fabrication problems characteristic of discontinu-ous stacks, owing to the structural continuity enabled by the helical solution. Nevertheless, the helical geometry itself can provide different kinds of fabrication problems. In particular, the custom prototype fabrication technique adopted so far still presents considerable drawbacks; they actually complicate the

Electrodes

Dielectric elastomer

(a) (b)

Figure 12.1 Schematic drawing of a helical actuator.

Ch12-I047488.indd 124 12/10/2007 8:25:17 PM

Contractile Monolithic Linear Actuators 125

manufacturing procedure and, in some cases, limit both the achievable performance and the reliability of samples [11] . The maximum contraction strain reported above (−5% for a field of 14 V/µm) is actu-ally rather poor. Such a relatively low value does not correspond to any intrinsic limitation of the helical configuration; it should be regarded as just due to the current ‘ state of the art ’ , according to the both adopted fabrication method, the quality of its specific implementation and the particular type of employed materials. Considerable improvements of course are still possible. Certainly, possible differ-ent processes and optimized solutions (some of them already identified but never tested [11] ) may offer advantages and higher performances. However, the peculiarity of the helical shape opens, as a matter of

8 mm

0.8 mm

Complaintelectrodes

(black area)

(a) (b)

Figure 12.2 (a) Elastomeric silicone helices as cut and (b) after coating with the electrode material.

�5

�4

�3

�2

�1

00 2 4 6 8 10 12 14 16

Electric field (V/µm)

Axi

al s

trai

n (%

)

Figure 12.4 Strain-field characteristic exhibited by a prototype sample of helical actuator.

(a) (b)

Figure 12.3 Helical actuator: (a) prototype sample and (b) portion of a longitudinal section.

Ch12-I047488.indd 125 12/10/2007 8:25:17 PM

126 Chapter 12

fact, certain challenging issues that any fabrication procedure has inevitably to face. For this reason, the availability of even simpler configurations may boost the short-term use of contractile actuators in prac-tical applications. Accordingly, a second alternative configuration was developed. It is described below.

12.3 FOLDED DIELECTRIC ELASTOMER ACTUATORS

Folded actuators were conceived to concentrate into a single device different attractive properties: (1) a functionality equivalent to that enabled by multi-layer stacks; (2) a continuity of the electrodes, as for heli-cal actuators and (3) a structure of easy fabrication. In order to satisfy such needs, the architecture of a folded actuator is rather simple: it consists of a single strip of an elastomer, that is first coated with compli-ant electrodes and then folded up, so as to form a monolithic compact body; the folded structure is finally ‘ sealed ’ with a thin coating made of the same elastomer used for the strip [12] . A high voltage difference applied between the electrodes causes a thickness squeezing of the entire elastomeric layer; this results in an axial contraction of the overall structure, along with related lateral expansions, as presented in Fig. 12.5 .

Of course the rectangular/square cross-sections considered in Fig. 12.5 are not the only possible; in fact, by opportunely shaping the strip that has to be folded, different implementations of the actuator can be achieved. As an example, Fig. 12.6 shows a device with a resulting cylindrical structure.

Prototype folded actuators with both rectangular and circular cross-sections were fabricated by using the same materials adopted for helical actuators. Details about the specific fabrication procedure can be found in [12] . Figure 12.7 presents actuator samples of both types. These prototypes are made of elas-tomeric strips having a typical thickness of 0.5–0.8 mm, while considerably different lengths and lateral dimensions have been tested, as shown in the figure.

A contraction of a folded actuator with rectangular cross-section is reported in Fig. 12.8 . As an obser-vation, one can clearly distinguish in this figure a peculiar deformation profile of the higher end of this sample: the contraction is maximum at the centre of the structure, since the particularly emphasized lat-eral inactive regions (i.e. not covered by the electrodes) provide a purely antagonist passive resistance.

Figure 12.5 Schematic drawing of a folded actuator with rectangular cross-section.

Electrode

Electrode

Dielectricelastomer

Figure 12.6 Schematic drawing of a folded actuator with circular cross-section.

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Contractile Monolithic Linear Actuators 127

Figure 12.9 reports steady-state values of the electromechanical axial strain and stress measured from a prototype actuator analogous to those presented in Fig. 12.7(a) , in response to step-wise electric fields of different strength. These data show that the specific silicone used as a dielectric elastomer for these actuators can enable a contraction strain of 10% at a relatively low electric field (10 V/ � m). However, such a strain corresponds to a low stress of 3.5 kPa, according to the considerably low elastic modu-lus of the material. Moreover, the low dielectric strength of the elastomer (of the order of 10 V/ � m) limits the maximum applicable electric field and, therefore, the maximum achievable performances. Accordingly, as an observation, it is worth stressing that the use of different types of elastomers could permit to address specific application needs. For instance, the adoption of stiffer elastomers, with increased dielectric strength as well, may provide actuators capable of delivering higher forces.

Data reported above show that the folded configuration provides a simple means to obtain contractile monolithic actuators. In particular, this configuration permits to reduce the complexity of fabrication of

Off On

Figure 12.8 Axial contraction of a folded actuator with rectangular cross-section.

(a) (b)

Figure 12.7 Prototype folded actuators: samples with (a) rectangular and (b) circular cross-section.

0�1�2�3�4�5�6�7�8�9

�10�11

0 1 2 3 4 5 6 7 8 9 10 11Electric field (V/µm)

0 1 2 3 4 5 6 7 8 9 10 11Electric field (V/µm)

Axi

al s

trai

n (%

)

Axi

al S

tres

s (k

Pa)

0.0

0.5

1.0

1.5

2.0

2.5

3.03.5

(a) (b)

Figure 12.9 (a) Strain-field and (b) stress-field characteristics exhibited by a prototype sample of folded actuator.

Ch12-I047488.indd 127 12/10/2007 8:25:19 PM

128 Chapter 12

both stack actuators (requiring layer-by-layer depositions of dielectric and conductive layers) and helical actuators (requiring two couples of helically shaped dielectric and conductive layers). Moreover, the final compact structure of a folded actuator is functionally equivalent to that of a multi-layer stack. In fact, both these configurations enable an alignment of the applied electric field with the axial working direc-tion. This feature is particularly attractive, since it guarantees the most efficient transduction of the input electrical energy into the output mechanical work. However, in comparison with a stack, a folded device advantageously provides the same functionality with a simpler structure. This can reduce the complexity of the fabrication procedures, with possible benefits at least in terms of production costs and times.

In order to further develop folded actuators, some particular issues require additional investigations. As a first point, a reduction of the thickness of the elastomer is definitely necessary in order to reduce the driving voltages. However, the effect of the structural folds with particularly thin elastomer strips is currently unknown. So far, no problems were experienced in terms, for instance, of premature dielectric breakdown of the material. Nevertheless, this may be reasonably due to the employed large values of thick-ness. Thinner layers may behave differently, even in consideration of the stress experienced by the material around the folds. Moreover, thinner strips imply more stringent constraints on material processing, in order to fabricate suitable elastomer films having a well-controlled thickness over considerable lengths. As an example, by assuming a thickness T = 100 � m, an actuator with a length H = 10 cm and a lateral dimen-sion W = 1 cm would require a strip having a length L that can be estimated (by neglecting the lateral folds) as follows: L = H / T � W = 10 � 1 /10 � 4 � 10 � 2 = 10 m. Such a huge length suggests that standard industrial processes for production of large thin films should be advantageously used. Finally, the adoption of thin strips introduces a further issue related to the fabrication technique; in fact, a large number of folds are required to reach macroscopic lengths of the device. For instance, according to the example mentioned above, an actuator of 10 cm would require approximately 1000 folds. This requires automatic (or at least semi-automatic) folding processes. In this respect, we are currently assembling a custom semi-automatic folding machine. It is expected to enable easier handlings of elastomers with reduced thickness and to pro-vide standard samples characterized by higher reliability and shorter production times.

12.4 EXAMPLES OF APPLICATIONS

Soft and lightweight electromechanical actuators capable of spring-like linear contractions may find short-term applications for different types of systems. In particular, we are currently studying some specific possible uses of the folded device, especially in contexts that require highly flexible and light-weight actuators. Some of them are briefly mentioned below.

12.4.1 Hand splints for rehabilitation

The major drawback that currently affects dielectric elastomer actuation consists of the high electric fields needed to drive the materials. This can be a disadvantage for certain types of applications and in the worst cases it can also completely prevent the possibility of use. For instance, this is the case of devices to be implanted in a human body. However, although the biomedical area could appear to be the most sensitive to this problem, it already offers possible fields of application. As an example, dielectric elastomer actuators may find valuable uses for wearable active orthoses for rehabilitation of body parts. With respect to this, we are currently developing a simple application of folded actuators for so-called hand splints: they consist of orthotic systems for hand rehabilitation. The dynamic versions of state-of-the-art hand splints typically include elastic bands, which exert a passive elastic resistance to vol-untary elongations of one or more fingers ( Fig. 12.10(a) ). In order to provide such splints with the possibility of electrically modulating the compliance of the resistive elements, we are working on the substitution of the passive elastic bands with contractile elastomer actuators. A prototype sample of such a type of system is reported in Fig. 12.10(b) . The electrical activation of the contractile actuators is used to vary the compliance of the system. This enables modulations of the force that acts as an antago-nist to voluntary finger movements, according to programmable rehabilitation tasks.

12.4.2 Bioinspired actuation mechanisms

Muscle-like actuation, aimed at mimicking some of the typical features of natural muscles, is a poten-tial area of application where new soft contractile actuators are needed. For instance, small robots with

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Contractile Monolithic Linear Actuators 129

bioinspired functions (e.g. locomotion, grasping, etc.) represent specific ambits of possible use. As an example of application of folded actuators, a simple bioinspired actuation mechanism for the eyeballs of an android robotic face has been considered. In particular, a couple of agonist–antagonist actuators was studied to mimic the actions of the lateral rectus-type human ocular muscles, in order to enable bi-directional rotations of an eyeball around an axis. Details can be found in [13] . Figure 12.11 reports an elementary prototype implementation of such a system and shows an active rotation of the eyeball.

12.4.3 Lightweight flexible space structures

Within the framework of a couple of projects financed by the European Space Agency (ESA), pos-sible applications of folded devices for lightweight and flexible space structures were identified and preliminarily studied. Such activities were driven by the recognized potential of dielectric elastomer devices to offer advantageous functions, such as reduction of launch loads, flexibility (compliance) and lightness of actuation devices, shape modulation of deformable structures, dynamic damping of ultra-lightweight structures, actuation of lightweight structures connected with joints, etc.

In particular, the actuation of lightweight deployable booms (i.e. flexible arm-like hollow tubes) was identified as one of the most useful potential fields of application of folded contractile actuators. Such booms consist of lightweight structures that can be stowed (during lunch and transportation) as a com-pacted assembly, to be successively deployed in space ( Fig. 12.12(a) ). They can be employed for several types of uses, such as deployable solar sails and solar arrays, deployable antenna systems, deployable arms used to position far away from the spacecraft different kinds of systems (such as cameras, sun-shields, antennas, measurement probes, etc.), structural links between satellite subsystems over large distances for position control, etc. Accordingly, deployable booms may have to be actively control-led for different reasons, such as to damp low-frequency vibrations (e.g. induced by orbital satellite ’ s manoeuvres), to maintain the shape of the structure, to provide deflections of the tip of the boom (e.g. for positioning of instruments), etc. Therefore, dielectric elastomer actuators could find possible useful

D

C

AA�

i

R

BA�

Figure 12.11 Prototype implementation of an elementary bioinspired actuation mechanism for robotic eyeballs.

(a) (b)

Figure 12.10 Dynamic hand splints: (a) a state-of-the-art sample and (b) prototype system equipped with folded actuators.

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130 Chapter 12

applications for the control of deployable booms, due to several attractive features: booms are light-weight structures, they need flexible and elastic actuators, high actuation accuracies are typically not required, actuators are not directly exposed to the external space environment.

Folded actuators may be attached inside the cross-section of a boom ( Fig. 12.12(b) ) and could be used for either shape modulation or local stiffening of the structure. A very simple prototype demon-strator of this concept was assembled and tested. The demonstrator is a scaled model of a lightweight boom: it consists of a plastic flexible tube with a length of a couple of metres, equipped with three cross-sectional actuators ( Fig. 12.13 ). The actuators permitted to locally deform the structure, providing contractions of the main cross-sectional dimension of approximately 2 mm.

12.4.4 Bi-directional tilters for pointing or positioning systems

Folded actuators were used to implement not only purely contractile units, but also bi-directional tilting devices. This can be easily achieved by considering a structure that conceptually results from coupling two folded actuators, as sketched in Fig. 12.14 ; an alternate activation of one of the two actuators ena-bles an alternate tilting of the overall structure. Of course, the concept can also be extended to four active parts, to be combined so as to enable bi-directional deflections within two possible orthogonal

Boom

Actuator

(a) (b)

Figure 12.13 Simple proof-of-concept demonstrator: (a) drawing of the cross section and (b) pictures of the prototype.

Deployableboom(portion)

Contractileactuator

(a) (b)

Figure 12.12 Considered space application of contractile actuators: (a) a small deployable boom and (b) schematic drawing of the proposed use.

(a) (b)

Figure 12.14 Schematic drawing of a bi-directional tilter made of a couple of folded actuators: (a) device at rest and (b) tilting due to an activation of the right-hand actuator.

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Contractile Monolithic Linear Actuators 131

planes (two degrees of freedom), instead of a single one. Figure 12.15 shows examples of activation of a prototype bi-directional tilter. In this case, the device was directly fabricated as a monolithic structure, by depositing two separate electrode tracks on the elastomer strip. As an example of application, these types of tilters may find uses as simple drivers for pointing or positioning systems.

12.5 CONCLUSIONS

This chapter has described two configurations suitable for implementing contractile monolithic linear actuators made of dielectric elastomers. The first configuration relies on a double helix of elastomers interposed to a double helix of compliant electrodes. The second type of actuator is obtained by folding several times a single strip of elastomer previously coated with electrodes. A folded device is function-ally equivalent to a multi-layer stack but offers an advantageously simpler structure. The simplicity of fabrication of folded actuators, as demonstrated by the silicone-made prototypes developed so far, may facilitate the short-term diffusion of contractile dielectric elastomer devices, to be readily employed for a broad range of potential applications.

References

[1] Pelrine , R. E. , Kornbluh , R. D. and Joseph , J. P. ( 1998 ). Electrostriction of polymer dielectrics with compliant

electrodes as a means of actuation . Sens. Act. A Phys. , 64 , 77 – 85 .

[2] Pelrine , R. , Kornbluh , R. and Pei , Q. et al. ( 2000 ). High-speed electrically actuated elastomers with strain

greater than 100% . Science , 287 , 836 – 839 .

[3] Pelrine , R. , Kornbluh , R. and Kofod , G. ( 2000 ). High-strain actuator materials based on dielectric elastomers .

Adv. Mater. , 12 ( 16 ), 1223 – 1225 .

[4] Pelrine , R. , Kornbluh , R. and Joseph , J. et al. ( 2000 ). High-field deformation of elastomeric dielectrics for

actuators . Mater. Sci. Eng. C , 11 , 89 – 100 .

[5] Pei , Q. , Pelrine , R. and Stanford , S. et al. ( 2003 ). Electroelastomer rolls and their application for biomimetic

walking robots . Synth. Met , 135–136 , 129 – 131 .

[6] Pei , Q. , Rosenthal , M. and Stanford , S. et al. ( 2004 ). Multiple-degrees-of-freedom electroelastomer roll actu-

ators . Smart Mater. Struct. , 13 , N86 – N92 .

[7] Benslimane, M., Gravesen, P. and Sommer-Larsen, P. (2002). Mechanical properties of dielectric elastomer

actuators with smart metallic compliant electrodes. In Smart Structures and Materials 2002: Electroactive Polymer Actuators and Devices (EAPAD) , Ed. Bar-Cohen, Y., Proc. SPIE , 4695 , 150–157.

[8] Ashley , S. ( 2003 ). Artificial muscles . Sci. Am. , 289 ( 4 ), 52 – 59 .

[9] Carpi , F. and De Rossi , D. ( 2004 ). Dielectric elastomer cylindrical actuators: electromechanical modelling

and experimental evaluation . Mater. Sci. Eng. C , 24 , 555 – 562 .

[10] Schlaak, H., Jungmann, M., Matysek, M., et al. (2005). Novel multilayer electrostatic solid-state actuators

with elastic dielectric. In Smart Structures and Materials 2005: Electroactive Polymer Actuators and Devices (EAPAD) , Ed. Bar-Cohen, Y., Proc. SPIE , 5759 , 121–133.

[11] Carpi , F. , Migliore , A. and Serra , G. et al. ( 2005 ). Helical dielectric elastomer actuators . Smart Mater. Struct. , 14 , 1210 – 1216 .

[12] Carpi , F. , Salaris , C. and De Rossi , D. ( 2007 ). Folded dielectric elastomer actuators . Smart Mater. Struct. , 16 ,

S300 – S305 .

[13] Carpi , F. and De Rossi , D. ( 2007 ). Bioinspired actuation of the eyeballs of an android robotic face: concept

and preliminary investigations . Bioinspir. Biomim. , 2 , S50 – S63 .

(a) (b) (c)

Figure 12.15 Prototype bi-directional tilter made of folded actuators: (a) and (c) tilting due to an activation of the left-hand and right-hand actuators, respectively and (b) device at rest.

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BUCKLING ACTUATORS WITH INTEGRATED DISPLACEMENT SENSOR

Federico Carpi 1 , Gualtiero Fantoni 2 , Gabriele Frediani 1 and Danilo De Rossi 1

1 Interdepartmental Research Centre ‘ E. Piaggio ’ , University of Pisa, Pisa, Italy 2 Department of Mechanical Engineering, University of Pisa, Pisa, Italy

Abstract

This chapter presents dielectric elastomer actuators specifically designed to operate with out-of-plane unidirectional

displacements of a rubbery membrane. The adopted configuration is very close to that of a typical diaphragm-type

actuator, although the necessary mechanical ‘ bias ’ of the membrane is enabled by purely passive means, consist-

ing of an underlying hemispheric stiff support. Moreover, the actuation function is integrated with a sensing one,

by equipping the device with either piezoresistive or piezocapacitive sensing elements for displacement monitor-

ing. Performances of silicone-made prototype devices demonstrate the feasibility of achieving significant relative

displacements.

Keywords : Actuator, buckling, dielectric elastomer, piezocapacitive, piezoresistive, sensor.

13.1 INTRODUCTION

Polymer-made membrane-like actuators capable of showing large displacements in response to applied electric fields are needed for different ambits of application. Diaphragm-type pumps, variable-curvature grippers or surfaces with controllable shape are just few examples. Devices suitable for such uses can be obtained by exploiting the basic electromechanical transduction principle of dielectric elastomer actuators. However, the achievement of the desired actuation behaviour requires, as for any device, an opportune design of components and driving conditions. When a flat sample of elastomer coated with compliant electrodes is considered, electrically induced deformations are not able to produce any curvature of the sample, unless specific ‘ tricks ’ are adopted. Basically, two main strategies can be recognized as effective for this purpose: they rely on the use of either electrodes with differential stiffness or specific boundary conditions. Solutions adopting either these approaches have been described.

In the first case, actuators based on a so-called unimorph bending configuration have been used. They typically consist of a layer of dielectric elastomer coated with two electrodes having a different stiffness. Following the application of a high voltage difference between the two electrodes, the induced expansion of the softer electrode is greater than that of the stiffer one. Accordingly, if the structure is not constrained at its boundaries, the free deformation can generate a bending of the actuator towards the stiffer side. This effect can be exploited to electrically induce and modulate the curvature of an elas-tomer sheet. Prototype demonstrators based on this concept and used for shape controls of lightweight mirrors have been described [1] .

A second means to achieve a variable curvature in dielectric elastomers can be obtained with con-strained boundaries. In this case, an elastomer membrane coated with electrodes having the same compli-ance can be used. The desired effect is enabled by the adoption of a pre-deformation of the membrane in its (electrically) inactive state. Then, a high voltage difference applied between the electrodes can trigger an actual buckling of the membrane: it moves in the direction identified by the pre-deformation, as a com-bined result of both the pre-deformation itself and the electrically sustained surface expansion. This effect has been exploited in the so-called diaphragm actuators, by typically stretching elastomer films on frames and applying below them pressurized/de-pressurized air, as a means to enable pre-curvatures. Several

Chapter 13

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Buckling Actuators with Integrated Displacement Sensor 133

examples of applications exploiting this principle have been presented, including high-performance loudspeakers, small pumps and variable-curvature mirrors [1–5] .

In this chapter, we report an alternative means to achieve unidirectional active variations of the cur-vature of a dielectric elastomer with constrained boundaries. The related devices, identified as ‘ buck-ling actuators ’ [6,7] , are described in the following.

13.2 DEVICE CONCEPT

A buckling actuator consists of a flat elastomeric membrane coated with compliant electrodes and arranged onto a rigid hemispheric support, which provides the necessary pre-deformation. The support offers a simple and purely passive means to enable unidirectional displacements. In these devices, the actuation function has been also combined with displacement sensing. For this purpose, two configu-rations for a buckling actuator have been considered. They differ for the adopted sensing strategy: the first configuration relies on a piezoresistive sensing, while the second on a piezocapacitive effect. The two implementations of the overall device are separately described below.

13.2.1 First configuration: piezoresistive sensing

A sketch of the constitutive components of a buckling actuator with an integrated piezoresistive sensor is presented in Fig. 13.1 . The actuation part of the device consists of a thin circular membrane of die-lectric elastomer coated with two compliant concentric circular electrodes. The membrane is arranged onto a rigid hemispheric support. A concentric ring-like frame provides boundary constraints for the actuator. In order to provide the device with a sensing function, a piezoresistive displacement sensor is coupled to the upper side of the actuator; it consists of a resistive compliant strip fabricated on a second thin layer of dielectric elastomer. The sensing strip can be made of the same material used for the actua-tion electrodes.

The resulting final shape of the constrained structure is sketched in Fig. 13.2 . When a high volt-age V is applied between the electrodes, the opposite charges on their surfaces generate an attractive

Ring (constraint)

Dielectric elastomerfor sensor insulation

Dielectric elastomerfor actuation

Sensor

Compliant electrodefor actuation

Compliant electrodefor actuation

Hemispheric support

Figure 13.1 Exploded view of a buckling actuator with integrated piezoresistive sensor.

Actuationelectrodes Sensor

Dielectricelastomerfor actuation

Dielectricelastomerfor actuation

Ring(constraint)

Ring(constraint)

V

R

Figure 13.2 Schematic drawing (lateral section) of a buckling actuator with integrated piezoresistive sensor.

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134 Chapter 13

force, which compresses at constant volume the intermediate dielectric membrane. Accordingly, its thickness tends to be reduced while its area tends to be increased. However, the membrane cannot radi-ally expand, owing to the boundary ring. Nevertheless, the initial out-of-plane arrangement enabled by the underlying hemisphere makes the membrane to lift up ( Fig. 13.2 ). Conversely, without any initial pre-deformation the activation would basically induce just an uncontrolled wrinkling of the elastomer surface. This simple solution allows a passive means for providing the appropriate boundary conditions for active buckling, without any additional component and instrumentation (e.g. any underlying pres-surized/de-pressurized chamber).

Following the actuation of the membrane, the overlaying sensing strip deforms and varies its resist-ance R accordingly. By monitoring the value of the resistance, the displacement of the device can be measured and followed.

A piezoresistive monitoring of the displacement is a solution particularly attractive, since measure-ments of resistances are easily practicable and reliable. Nevertheless, this methodology can be affected by potential sensing errors that, in some cases, can become significantly important. One of the most dangerous sources of potential error is due to possible time drifts of the sensing resistance; in fact, depending on the specific material used for the fabrication of the sensor, the rest value of its resistance can present variations due to different effects, including aging and contaminations with the surrounding environments, e.g. moisture (especially in the absence of appropriate encapsulations). Moreover, tem-perature-induced variations of the resistance may complicate the use of the device in specific domains of application characterized by relevant temperature variations; in such cases, appropriate compensa-tions of the recorded information should be made. In order to avoid such drawbacks, an alternative sensing scheme based on a piezocapacitive strategy has been implemented, as described below.

13.2.2 Second configuration: piezocapacitive sensing

A piezocapacitive sensing strategy has been considered according to the scheme sketched in Fig. 13.3 . The basic actuation part of the device consists again of a thin circular membrane of dielectric elastomer coated with compliant electrodes and arranged onto a rigid hemispheric support. However, for this sec-ond configuration a thin layer of dielectric elastomer is coupled to the lower side of the actuator. This insulating layer hosts a third compliant electrode, working as one of the two electrodes of the sensing capacitor. The second sensing electrode, that is rigid and fixed, is fabricated directly on the surface of the hemispheric support. For this purpose a thin metallized Mylar film is used, so as to easily have both the electrode and its insulation. According to such an arrangement, a variable capacitor between the lower side of the moving membrane and the fixed support is established. For the actuator in the rest position the device shows a rest capacitance C 0 . This value corresponds to a capacitor that has the shape of a hemispheric bowl, since the membrane at rest collapses onto the hemispheric support.

Ring (constraint)

Dielectric elastomerfor sensor insulation

Dielectric elastomerfor actuation

Compliant electrodefor sensing

Compliant electrodefor actuation

Compliant electrodefor actuation

Hemispheric insulator

Hemispheric supportand electrode for sensing

Figure 13.3 Exploded view of a buckling actuator with integrated piezocapacitive sensor.

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Buckling Actuators with Integrated Displacement Sensor 135

By applying a high voltage difference between the two electrodes of the actuator, the induced mem-brane displacement causes an increase of the separation between the electrodes of the sensing capacitor. In particular, the compliant sensing electrode lifts up with respect to the fixed sensing electrode ( Fig. 13.4 ); this generates a decrease of the measurable capacitance. It is worth noting that the geometry of the capacitor changes during actuation, as shown in Fig. 13.4 .

Prototype samples based on both the piezoresistive and the piezocapacitive configuration were fabri-cated and tested as reported in the next section.

13.3 PROTOTYPE DEVICES

For both the configurations, prototype devices were fabricated by using a silicone (polydimethylsi-loxane) rubber (TC-5005 A/B-C, BJB Enterprises Inc., USA) as a dielectric elastomer. This material is very soft (elastic modulus of about 50 kPa) and enables high displacements of the membrane. The same silicone was used for the thin layer that insulates the sensor from the actuator in both configurations. A custom-made silicone/carbon black mixture (CAF 4, Rhodorsil, France/Vulcan XC 72 R, Carbocrom, Italy) was adopted for the actuation electrodes and for either the sensing resistor (first configuration) or the compliant electrode of the sensing capacitor (second configuration). The hemispheric support was made of an insulating resin and had a height h 0 of approximately 3 mm. The actuation elastomer was shaped as a circular sample, with a thickness of about 0.8 mm. Circular electrodes with a diameter of 30 mm were fabricated on both of its sides. An analogous sensing electrode was fabricated on one side of the additional insulating layer used for the second configuration. This layer had a thickness of about 0.3–0.4 mm. A similar layer was employed for first configuration, although in this case it was covered with a rectangular sensing strip of approximately 30 � 6 mm.

Large displacements of such devices were observed in response to applied electric fields, up to a considered limit of about 10 V/ � m. This limit was used as a safety threshold in order to avoid dielec-tric breakdown of the actuators; it was identified following previous investigations on the electrome-chanical properties of the adopted silicone elastomer (see the previous chapter). Figures 13.5 and 13.6 present frames extracted from video sequences recorded during actuation tests.

The static displacement in response to increasing step-wise electric fields was measured by using an optical technique (not reported here). In particular, data were used to quantify the difference between

Figure 13.5 Buckling actuation for the first configuration: (a) device at rest and (b) device under an electrical activation. The piezoresistive sensing strip is visible on the surface of the structure.

Actuationelectrodes

Dielectricelastomerfor actuation

Dielectricelastomerfor actuation

Ring(constraint)

Ring(constraint)

Sensingelectrodes

V

C

Figure 13.4 Schematic drawing (lateral section) of a buckling actuator with integrated piezocapacitive sensor.

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136 Chapter 13

the electrically induced value h and the rest value h 0 (3 mm) of the membrane height with respect to the base of the hemispheric support; moreover, the difference h–h 0 was normalized by h 0 , in order to obtain the following relative displacement along the vertical direction:

Relative displacement ��h h

h0

0 (13.1)

At the same time as the displacement measurement, the variation of either the sensing resistance (for the first configuration) or the sensing capacitance (for the second configuration) was monitored. Accordingly, a correlation between the vertical displacement of the device and its sensing variable was achieved, as reported below.

Values of the relative displacement recorded from a prototype of the first configuration are plotted in Fig. 13.7 as a function of the driving electric field. In particular, the figure reports the percentage dis-placement for the device either equipped or not with the piezoresistive sensor (i.e. with and without the insulating layer coated with conductive elastomer).

These data were obtained by first measuring the response of a pure actuator (without any sensor) and, then, by repeating the test, following the deposition of a sensing layer onto the same sample. They show that, as easily expected, the addition of the sensing layer affects the electromechanical actuation response of the device. In particular, a decrease of the output displacement for each applied field is achieved. This is a direct consequence of the inevitable stiffening of the overall structure, with respect to the pure actuator, due to the overlaying sensor. This is the price to be paid to have an actuator with an integrated sensor. The steady-state response of the piezoresistive sensor for different displacements was

(a) (b)

Figure 13.6 Lateral view of a buckling actuator: (a) rest state and (b) an electrically activated state.

0

10

20

30

40

50

60

70

80

0 3 7 8 9 10 11

0

10

20

30

40

50

60

70

80

(h �

h0)

/h0

(%)

Electric field (V/µm)

ActuatorActuator�piezoresistive sensor

1 2 4 5 6

0 3 7 8 9 10 111 2 4 5 6

Figure 13.7 First configuration: relative displacement as a function of the applied electric field (fitting curves are inserted as a guide for the eye).

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Buckling Actuators with Integrated Displacement Sensor 137

evaluated by quantifying the percentage variation of the resistance R with respect to its rest value R 0 . A co-plot of the actuation and the sensing response is reported in Fig. 13.8 . The response of the pie-zoresistive sensor was found to be rather linear, as shown by the plot of the relative variation of the resistance as a function of the relative displacement, presented in Fig. 13.9 .

Analogous tests were performed for samples of the second configuration. The steady-state response of the piezocapacitive sensor for different displacements was evaluated by quantifying the percentage variation of the capacitance C with respect to its rest value C 0 . Results are reported in Fig. 13.10 . As expected, a progressive increase of the membrane displacement leads to a concomitant decrease of the

�10

0

10

20

30

40

50

60

70

3 4 5 6 10 11

Electric field (V/µm)

(h �

h0)

/h0

(%)

0

10

20

30

40

(R �

R0)

/R0

(%)

7 8 9

3 4 5 6 10 117 8 9

Figure 13.8 First configuration: actuation and sensing responses co-plotted as a function of the applied electric field (fitting curves are inserted as a guide for the eye).

0

5

10

15

20

25

300 10 20 30 40 50 60

0 10 20 30 40 50 600

5

10

15

20

25

30

(R �

R0)

/R0

(%)

(h � h0)/h0 (%)

Figure 13.9 First configuration: linearity of the piezoresistive sensor.

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138 Chapter 13

sensing capacitance (negative percentage variations). Figure 13.11 shows the plot of the relative vari-ation of the capacitance as a function of the relative displacement. It puts in evidence the fact that, as a difference with the piezoresistive technique, this alternative sensing strategy is not linear. Of course, such a behaviour is due to the geometrical peculiarity of the sensing capacitor ( Fig. 13.4 ): it clearly

0

5

10

15

20

25

30

35

40

450 2 4 5 8 9 10 11

Electric field (V/µm)

(h �

h0)

/h0

(%)

�12

�11

�10

�9

�8

�7

�6

�5

�4

�3

�2

�1

0

(C �

C0)

/C0

(%)

6 731

0 2 4 5 8 9 10 116 731

Figure 13.10 Second configuration: actuation and sensing responses co-plotted as a function of the applied elec-tric field (fitting curves are inserted as a guide for the eye).

0 5 10 15 20 25 30 35 40 45�12

�11

�10

�9

�8

�7

�6

�5

�4

�3

�2

�1

0

0 5 10 15 20 25 30 35 40 45

�12

�11

�10

�9

�8

�7

�6

�5

�4

�3

�2

�1

0

(C �

C0)

/C0

(%)

(h � h0)/h0 (%)

Figure 13.11 Second configuration: characteristic of the piezocapacitive sensor.

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Buckling Actuators with Integrated Displacement Sensor 139

suggests a non-linear relation between the displacement of the apex A of the membrane and the related variation of the overall sensing capacitance; in fact, the latter is geometrically determined by two vari-able parameters that are not linearly correlated with the displacement of the point A: these are the spa-tially uneven distance between the capacitor electrodes and the shape and extension of the compliant electrode of the capacitor.

As an example of application, arrays of such types of devices are being studied for controlling the shape of flexible surfaces. With respect to this, Fig. 13.12 shows a picture of a 4 � 4 matrix of buck-ling actuators with integrated piezocapacitive sensors. Each active element of this matrix has the same dimensions reported above and can be separately addressed, by activating both its actuation and sensing function. This type of array is currently being studied to modulate the shape of a flexible thin surface to be arranged on the top of it.

In order to investigate the performances achievable by bigger samples, actuators with larger diam-eters have been fabricated. As an example, Fig. 13.13 shows an actuation of a sample with a diameter of 10 cm. The electromechanical properties of prototypes of this type are currently being measured.

Besides any up (or down) scaling, the structure of a buckling actuator presented in this chapter is open to future optimizations that may improve the achievable performances. One of the most useful improvements that is expected to offer significant advantages consists in using pre-shaped elastomer membranes, instead of flat samples. In particular, the availability of membranes showing at rest a pre-curvature that follows the profile of the hemispheric support would be particularly attractive; in fact, it could permit to avoid the disadvantageous pre-stressed condition that arises in a flat membrane as it is arranged over the hemispheric support. A pre-shaped membrane would not experience, once adapted over the support, any pre-stress capable of limiting the subsequent electrically induced actuation.

Figure 13.12 Array of buckling actuators with integrated piezocapacitive sensors.

(a) (b)

Figure 13.13 Buckling actuator with a diameter of 10 cm, tested with an upside-down arrangement (in order to compensate for the antagonistic effect of gravity): (a) rest state and (b) an electrically activated state.

Ch13-I047488.indd 139 12/10/2007 8:30:27 PM

140 Chapter 13

In order to reach such a goal, different techniques for material processing can be used, depending on the type of employed dielectric elastomer. As an example, we are currently working to develop pre-shaped silicone samples by mould casting.

As a final observation, it is worth emphasizing that the configuration for a buckling actuator here described, though very simple, is useful to achieve unidirectional displacements only. However, some applications may require bidirectional motions. In order to obtain a device having such a feature, an elegant and effective solution is presented in Chapter 29.

13.4 CONCLUSIONS

This chapter has presented both the concept and silicone-made prototype implementations of simple actuators capable of producing large active bucklings of a dielectric elastomer membrane. The devices consist of elastomeric membranes arranged over hemispheric substrates that provide a mechanical ‘ bias ’ for unidirectional actuations. The actuation function is integrated with the sensing one, by equip-ping the structure with either piezoresistive or piezocapacitive sensing elements.

References

[1] Kornbluh, R. D., et al. (2003). Shape control of large lightweight mirrors with dielectric elastomer actuation.

In Smart Structures and Materials 2003: Electroactive Polymer Actuators and Devices , Ed. Bar-Cohen, Y.,

Proc. SPIE , 5051 , 143–158.

[2] Pelrine, R., Sommer-Larsen, P., Kornbluh, R., et al. (2001). Applications of dielectric elastomer actuators. In

Smart Structures and Materials 2001: Electroactive Polymer Actuators and Devices , Ed. Bar-Cohen, Y., Proc. SPIE , 4329 , 335–349.

[3] Pelrine , R. , Kornbluh , R., Joseph , J., et al. ( 2000 ). High-field deformation of elastomeric dielectrics for actua-

tors . Mater. Sci. Eng. C , 11 , 89 – 100 .

[4] Kornbluh, R., Pelrine, R., Pei, Q., et al. (2000). Ultrahigh strain response of field-actuated elastomeric poly-

mers. In Smart Structures and Materials 2000: Electroactive Polymer Actuators and Devices , Ed. Bar-Cohen, Y.,

Proc. SPIE , 3987 , 51–64.

[5] Heydt , R. , Kornbluh , R., Pelrine , R., et al. ( 1998 ). Design and performance of an electrostrictive-polymer-film

acoustic actuator . J. Sound Vibr. , 215 ( 2 ), 297 – 311 .

[6] Carpi, F., Fantoni, G., Guerrini, P., et al. (2006). Buckling dielectric elastomer actuators and their use as

motors for the eyeballs of an android face. In Smart Structures and Materials 2006: Electroactive Polymer Actuators and Devices , Ed. Bar-Cohen, Y., Proc. SPIE , 6168 , 61681A-1–61681A-6.

[7] Carpi, F., Fantoni, G. and De Rossi, D. (2006). Bubble-like dielectric elastomer actuator with integrated sen-

sor: device and applications. In Proceedings of the Actuator 2006 , Ed. Borgmann, H., Bremen, pp. 872–875.

Ch13-I047488.indd 140 12/10/2007 8:30:28 PM

VARIABLE STIFFNESS MODE: DEVICES AND APPLICATIONS

Ronald Pelrine

SRI International, Menlo Park, CA, USA

Abstract

Dielectric elastomers are fundamentally an electromechanical transduction technology. Converting between electrical

and mechanical energy is most commonly used for actuators and generators, but the technology can also be applied

to make variable stiffness and variable damping devices. Both variable stiffness and variable damping dielectric elas-

tomer technologies are in a relatively early stage of development compared with corresponding actuators. Nonetheless,

it is already clear that dielectric elastomers may offer significant advantages for a wide range of variable stiffness and

damping applications. Advantages include simplicity, low cost, wide range of stiffnesses and strains, and intrinsic soft-

ness for user comfort. This chapter describes basic features of variable stiffness and variable damping using dielectric

elastomers, as well as explores various general applications.

Keywords : Compliance, dielectric elastomers, resonance, tuning, variable damping, variable stiffness.

14.1 INTRODUCTION

In Chapter 1 on the fundamentals of dielectric elastomer operations, it was noted that dielectric elastom-ers can be operated in an actuator mode, a generator mode, or a mixed mode. In the actuator mode, the dielectric elastomer film is expanded in planar directions while charged, whereas in the generator mode the film is contracted in the planar directions while charged. Mixed modes occur when a dielectric elas-tomer film expands and contracts while in a charged state at different times in its normal operation.

Of course, such a mixed mode may occur to some extent in a device that is designed as an actuator or a generator. For example, one might bias an actuator with a DC voltage and apply an AC signal on top of the DC to drive the actuator. Or, one may leave some charge on a generator film during expansion simply because it is electrically inefficient with a particular circuit to try to remove all the charge during expansion.

Leaving some charge on the film of an actuator or generator during the return part of the cycle when it is ideally removed can have consequences for the device operation or electronics. Typically, the field pres-sure in these cases is negligible in the return direction (e.g. for an actuator the field pressure is designed to be much less during contraction than it is during expansion; for a generator the reverse is true). In such cases, the field pressure on the return part of the cycle can often be neglected in the mechanical analysis of forces. However, a more interesting situation occurs when a device is intentionally designed for mixed mode operation where the field pressures in both expanding and contracting motions are comparable [1] . Such devices are often called variable stiffness or variable damping devices depending on detailed design.

Note that we are describing variable stiffness and damping in terms of a mixed mode, dielectric elas-tomer device. Variable stiffness and damping can be achieved by other means, especially by geometry changes. For example, a flat sheet of paper is flexible in bending about an axis parallel to the width, but the same sheet would be stiff in the width axis if it is first actuated to a bent or folded state about a length axis. Many other cases of structures that change stiffness dramatically by changing geometry are well known, but, a priori, actuated geometries can be implemented as easily with alternate actuator technologies as with dielectric elastomers. 1 We also note that variable stiffness using variable geometry

Chapter 14

1 A good case can be made that dielectric elastomers may be advantageous because their large strains make geometric changes

easier, but this possible advantage is really an actuator characteristic, not based on an intrinsic material ability for variable stiffness.

Ch14-I047488.indd 141 12/10/2007 8:30:52 PM

142 Chapter 14

often has operational restrictions such as not being able to change stiffness in certain states. In the bending paper example, it is easy to bend the paper in the length axis to make it stiff in the width axis if one does the length-axis bending when the paper is flat, but difficult if the paper is already bent about a width axis. By contrast to variable stiffness using geometry changes, true variable stiffness and damp-ing are much less common as an intrinsic transducer capability, and will be the focus of this chapter.

14.2 GENERAL PRINCIPLES OF DIELECTRIC ELASTOMER VARIABLE STIFFNESS

As the name implies, the mechanical properties of electromechanical transducers depends not just on the passive mechanical properties, but also on the electrical boundary conditions. This behaviour is well known in piezoelectrics, where the stiffness and damping depends on electrical loading. The same is true of dielectric elastomers.

Dielectric elastomer variable stiffness and variable damping devices rely on the material ’ s electro-mechanical transduction properties. In particular, they benefit from good coupling between mechani-cal forces on the elastomer and electrical capacitance changes. Thus, although there may be special aspects to the design of variable stiffness and variable damping devices compared with dielectric elas-tomer actuators, many of the same basic configurations (such as described in Chapter 8) are applicable. Generally speaking, a good actuator or generator design is usually a good starting point for a good vari-able stiffness or variable damping device design, though some differences naturally arise.

Some of the basic equations for variable stiffness were developed in Chapter 1. Here we pursue a slightly different, though related, derivation. Figure 14.1 shows a dielectric elastomer fixed at one end. For simplicity we assume a constant width w and variable thickness t and length x . Ordinarily, a dielec-tric elastomer would vary in width when it is strained in other directions because of Poisson effects, but one can imagine spars or other structures that keep w fixed even if x and t are changing.

The core question for variable stiffness in this physical situation is how the stiffness in x changes depending on the electrical loading of the dielectric elastomer. First note that the constant volume assumption (see Chapter 1) for elastomers can be simplified in this case to

xt

w� �

Volconstant (14.1)

where Vol is the volume of the dielectric elastomer. We further simplify and assume the mechanical elastic energy U m can be described by

U x xm � �

1

22�( )0

(14.2)

where � is the spring constant for the passive material, and x 0 is the equilibrium length of the material. We can further express the stored electrical energy U e as

U CV

Q

Ce

2

� �0 5 0 52. .

(14.3)

EAP (dielectric elastomer)

X

Figure 14.1 Configuration for simplified analysis of variable stiffness.

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Variable Stiffness Mode: Devices and Applications 143

where V is the voltage, Q is the charge on the film, and C is the capacitance. The capacitance C can be expressed in terms of the length x as

C w

x

tb

x

tbx� � � ���0

2

(14.4)

where b� � � � 0 w and, using Eq. (14.1), b � � � 0 w 2 /Vol � constant. Using Eq. (14.4), Eq. (14.3) can now be rewritten as

U bx V

Q

bxe � �0 5 0 52 22

2. .

(14.5)

Now the force F applied at the end of the dielectric elastomer film (assumed perfectly elastic) is the rate of change of mechanical energy input into the film with x , and the stiffness of the film K is the rate of change of F with x . The system is lossless so the mechanical energy input to the film must result in a change in stored elastic energy U m , or a change in electrical energy. The change in electrical energy must, however, compensate for any energy that flows on or off the film electrically as a result of the change in x and the electrical loading. For example, we know increasing x will increase capacitance C , and if the film is connected to a constant voltage source, then electrical energy will flow onto the film if x , and therefore C , increases. Let U i be the electrical energy that flows from an external source onto the film as a result of a change in x. U e is the stored electrical energy on the film, so we can write

K

F x

x

U U U

x

U U

x� �

� �� �

�d

d

d

d

d

dm e i e i( ) ( ) ( )2

2

2

2� (14.6)

where we have used Eq. (14.2) to eliminate U m on the right-hand side of Eq. (14.6). Equation (14.6) can be used for two important cases where U i is known explicitly. If Q is fixed (con-

stant charge) so that U i � 0, then using the right-hand side of Eq. (14.5) for U e gives

K

Q bx

x

Q

bx� � � �� �

d /

d

2 2 2

2

2

4

0 53

( . ( ))

(14.7)

Equation (14.7) verifies the conclusion from Chapter 1 that a constant charge loading makes the film stiffer mechanically. Note that Eq. (14.7) does not describe the zero force or equilibrium value of x , just the change in stiffness. This is the source of some confusion when thinking about variable stiffness electroactive polymer artificial muscle (EPAM). When constant charge is applied, the equilibrium (zero force) value of x may change (increase) due to the electric field pressure. Thus, one has the somewhat non-intuitive result that a film may relax when charge is applied yet still be a stiffer film because the rate of change of force with displacement x is greater.

A constant voltage electrical loading can also be analysed using Eq. (14.6). The charge Q i that flows onto the film is Q i � V ( C � C o ), where C o is the initial capacitance and C � C ( x ) is the variable capac-itance. The energy going onto the film from an external source is therefore U i ( x ) � VQ i ( x ) � V 2 ( C ( x ) �C o ). Using Eq. (14.4) we have C ( x ) � bx 2 , so that combining Eq. (14.5) with Eq. (14.6) gives for constant voltage:

K

U U

xbV bV bV� �

�� � � � �� � �

d )

de i

2

22 2 22

( (14.8)

Equation (14.8) shows that a constant voltage boundary condition causes the film to be less stiff. Indeed, within this model one can make the stiffness zero by sufficiently high voltage. On a micro level one can understand the decrease in stiffness with applied voltage by noting that as the film gets thinner with a con-stant voltage, the field pressure increases, thus making the film easier to stretch further. For some voltages the increase in field pressure matches the intrinsic film stiffness ( � ) so that no force is required to stretch the film. Of course, in practice � is usually highly variable in x , so that exact matching over a broad range in x is difficult. Nonetheless, the trends are reasonably described by this model, and stiffness can be greatly reduced even with simple constant voltage loading over some range in x . The ability to change stiffness from a peak value to nearly zero over a significant range of motion is an advantage of dielectric elastom-ers because competitive technologies are often limited in their minimum stiffness or maximum strain.

As with constant charge loading, constant voltage loading will also cause a shift in the equilibrium or zero force position of the film in Fig. 14.1 . One way to remove this effect is to use counter-opposed

Ch14-I047488.indd 143 12/10/2007 8:30:53 PM

144 Chapter 14

films as shown in Fig. 14.2 . If both films are electrically loaded the same, counter-opposing films allows a pure change in stiffness without an equilibrium shift.

14.3 VARIABLE DAMPING

Variable damping can also be accomplished with suitable electrical loading. A simple example is using counter-opposed dielectric elastomers (EAP1 and EAP2) as shown in Fig. 14.3 [2] . However, with pas-sive components such as resistors, variable damping is typically more complex to analyse than the cases of variable stiffness described above. This is because variable damping using resistors generally requires one to consider the time or frequency domain rather than being able to just analyse the state of the dielectric elastomer.

One can electrically analyse circuits such as shown in Fig. 14.3 treating the dielectric elastomers as variable capacitances. The damping is calculated in this case as the electrical energy loss through the potentiometer R 1 . The resistor R 2 is envisioned to be sufficiently high resistance so that once the dielectric elastomers are charged up the power supply is effectively isolated from supplying significant energy to the dielectric elastomers during the timescales of mechanical displacement � m .

In addition to � m , one can see that another relevant timescale is the charging time for the dielec-tric elastomers, both from the power supply and for transfer of charge between EAP1 and EAP2. The capacitance of the dielectric elastomers is changing, but one can make a reasonable approximation if the deflections are not too great by assuming an average capacitance C a for EAP1 and similarly for EAP2. If � s is the time constant for charging from the supply, then � s � 2 R 2 C a and the supply will not provide significant charge during time t m provided � s � � � m . However, we want to dissipate significant energy in R 1 , so that transfer of charge between elements should take place in times � m . Thus, if t e is the time for electrical transfer of energy between EAP1 and EAP2 (as a result of a deflection in x that changes relative capacitances), then t e � R 1 C a , and we want t e comparable to � m .

The example above illustrates some of the features of dielectric elastomer variable damping. Many other configurations are possible, but essentially one is using the variable capacitance to resist mechan-ical motion by dissipating electrical energy. One does not need to use a counter-opposed design. For example, EAP2 in Fig. 14.3 might be replaced by a fixed capacitor, and motion of EAP1 drives charge back and forth through R 2 between EAP1 and the capacitor. Of course, one can also achieve varia-ble damping with a more active system, such as using a single chip controller and charging the film

X

EAP1 EAP2

Figure 14.2 Counter-opposed dielectric elastomers can achieve variable stiffness without shifting the equilibrium or zero force point.

Powersupply

R2

R1

EAP1 EAP2

X

Figure 14.3 A simple arrangement for variable damping.

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Variable Stiffness Mode: Devices and Applications 145

to resist motion. In essence, one is using the film as a generator to convert mechanical to electrical motion. Generator mode operation is described more fully in Chapter 15. However, one of the attrac-tive features of dielectric elastomer variable damping is that it can also be done using simple, adjustable passive components with no sensor feedback needed.

14.4 APPLICATIONS OF VARIABLE STIFFNESS AND DAMPING

Variable stiffness and damping dielectric elastomer devices may find applications in a wide variety of areas. Typically, the applications break down into performance enhancements of a system and comfort or customization enhancements for a user.

An example of a possible performance enhancement is in robotics. It has been shown that biologi-cal control systems employ stiffness and damping using natural muscles to allow creatures to better navigate rough terrain [3] . Hence, dielectric elastomer analogues may find use in autonomous robots. This application is related to the much larger commercial application of vehicle suspensions, where one would like to be able to control suspension characteristics depending on the terrain for a smoother ride. The variable stiffness and damping devices can be totally separate from the prime mover as in the case of an engine-driven vehicle, or they may be integrated into the prime movers such as designing a dielectric elastomer actuator in a robot to also provide variable stiffness and damping.

Just like robots, humans can also benefit from devices with variable stiffness in order to improve locomotion and dexterity. Chapter 21 discusses this need in more detail.

Vibration damping and control is a wide application area for dielectric elastomers beyond vehicles and robotics. Rubber already is commonly used to help control vibrations, so the notion of tunable rubber ele-ments is a natural extension of existing uses of elastomers. Many important vibration damping and control applications exist at both the high tech and mundane (but nonetheless important) parts of the application spectrum. For example, considerable effort and cost is needed to harden satellites for rocket vibrations during launch. A more common application might be suppression of washing machine or dryer noise. In many cases, the dominant noise or vibration frequencies are known or easily measured. For example, in the case of engine or motor mounts, one typically knows the rpm of the motor. If the mechanical driving frequencies are known, one can adjust the stiffness to avoid a resonance to prevent transmission of a vibration, or to tune to a resonance, if one wishes to damp the mechanical energy more effectively.

Other applications of variable stiffness and damping may occur because of a desire to customize for user comfort. Seats, beds, tactile interfaces, and wearable items are all examples where the ability to easily adjust stiffness or damping may be attractive. Dielectric elastomers may be particularly advanta-geous for human interfaces because, unlike competitive technologies such as piezoelectrics and electro-magnetics, they can be intrinsically soft.

14.5 SUMMARY

Variable stiffness and variable damping dielectric elastomer devices are in their infancy, even compared with dielectric elastomer actuators. Many potential applications have been identified, however, and some experimental results are beginning to become available. The chief advantages of dielectric elas-tomers compared with other ways to achieve variable stiffness and damping are its simplicity, low cost, the ability to address a wide range of parameters (stiffness, frequency, etc.) in a single device, and its intrinsic conformability and softness for users.

References

[1] Choi, H., Ryew, S., Jung, K., Jeon, J., Kim, H., Nam, J., Takanishi, A., Maeda, R., Kaneko, K. and Tanie, K.

(2002). Biomimetic actuator based on dielectric polymer. Smart Structures and Materials 2002: Electroactive Polymer Actuators and Devices (EAPAD) , Ed. Bar-Cohen, Y., July, Proc. SPIE , 4695 , 138–149.

[2] Kornbluh, R. and Pelrine, R. (2005). Variable stiffness electroactive polymer systems. US Patent #6,882,086,

19 April.

[3] Full , R. and Meijer , K. ( 2003 ). Natural muscles as an electromechanical system . In Electroactive Polymer (EAP) Actuators as Artificial Muscles – Reality, Potential and Challenges , Ed. Bar-Cohen , Y. SPIE Press ,

Bellingham, Washington, DC, pp. 67 – 83 .

Ch14-I047488.indd 145 12/10/2007 8:30:53 PM

GENERATOR MODE: DEVICES AND APPLICATIONS

Ronald Pelrine and Harsha Prahlad

SRI International, Menlo Park, CA, USA

Abstract

Dielectric elastomers can be run in reverse of their usual actuator operation to implement mechanical-to-electrical

transduction. In the generator mode of operation, charges are placed on the elastomer film in the stretched state.

Upon contraction, the increase in thickness of the elastomer increases the separation of opposite charges, and the

decrease in planar area compresses like charges. Both changes increase the voltage of the charge, and hence increase

the stored electrical energy. This chapter discusses fundamentals of dielectric elastomer generators as well as more

practical considerations such as optimal cycles and energy harvesting circuit topologies. Dielectric elastomer gen-

erator films have shown very good performance, such as up to 0.4 J/g generator energy density. More importantly,

dielectric elastomers have unique advantages compared with competitive electromagnetic generators. In particu-

lar, dielectric elastomers have excellent low and variable frequency response, and together with their high energy

density are well suited for direct drive designs that eliminate the need for costly and complicated transmissions.

Dielectric elastomer generators are promising for both point source applications such as heel-strike generators to

harvest energy from human walking, as well as distributed source applications such as wind and wave power.

Keywords : Dielectric elastomers, generators, generator mode, heel-strike, polymer engines, wave power, wind power.

15.1 INTRODUCTION

Chapter 1 discussed the principles of operation of dielectric elastomers. In the actuator mode, the electric field stresses (Maxwell stress) do mechanical work in contracting the film in thickness and stretching it in area. As with many actuator technologies, dielectric elastomers are reversible and can be operated in a generator mode. In this mode of operation, mechanical work is done against the electric field, and electrical energy is produced. Thus, the dielectric elastomer is acting as an electromechanical generator transducer in this mode of operation.

Technologically, the generator mode of dielectric elastomers is potentially as important as the actuator mode. Actuators are indeed pervasive in modern technology, yet the critical need for new energy sys-tems, such as generators, may be more important than the sheer number of possible actuator applications. New generator technology may enable economic exploitation of power sources that would otherwise be cost prohibitive. Wind, wave, and solar power are examples of distributed power sources that might bene-fit from new low-cost generator technology. Additionally, dielectric elastomer generators may be able to address more niche – though still important – power production needs such as micro-size generators or harvesting energy from ambient vibrations for remote sensing. These various applications, and why dielectric elastomers may be advantageous for them, are discussed in greater detail later in this chapter.

15.2 GENERAL PRINCIPLES OF THE DIELECTRIC ELASTOMER GENERATOR MODE

Figure 15.1 illustrates the generator mode of dielectric elastomers. In Fig. 15.1(a) , the dielectric elasto-mer is stretched in area by an outside mechanical force. In the stretched state, opposite charges are placed or induced on the opposing compliant electrodes using a voltage difference, just as they are in the actuator mode. The dielectric elastomer is now allowed to contract using elastic restoring forces.

Chapter 15

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Generator Mode: Devices and Applications 147

Note that in the contracted state, shown in Fig. 15.1(b) , the dielectric elastomer is thicker and has smaller area relative to the stretched state. Assuming charge is constant during the contraction process, the change in geometry has separated opposite charges by a greater distance (the increase in thick-ness from contraction), and has compressed like charges into a smaller area (the decrease in area from contraction). Both changes increase electrical energy, and hence the stored electrical energy in Fig. 15.1(b) , is greater than the stored electrical energy in Fig. 15.1(a) . Mechanical work has been converted to greater stored electrical energy, and the material has operated as a generator transducer.

The qualitative physics analysis of the generator mode described above can be analysed electrically in quantitative terms using conventional macroscopic lumped parameters. It is useful to keep the above qualitative physics analysis in mind, however. Although electrical lumped parameters such as capacitance are more easily manipulated in the engineering sense, the physics of the dielectric elastomer generator mode can provide greater insights into more complex phenomena, some of which are described below.

Lumped parameter models of dielectric elastomer generators typically start, as they do for the actu-ator mode, by considering the capacitance of the electroded film. The capacitance in the stretched or contracted (relaxed) states, can be written as

C

A

z�

� �0 (15.1)

where � 0 is the permittivity of free space, A is the stretched or contracted area where the opposite electrodes overlap (called the ‘ active area ’ ), and z is the polymer thickness. The electrical energy of a capacitor U e with charge Q can be written according to the well-known formula

U

Q

Cz A Qe 0� � �0 5 0 5

21 2. . ( )� �

(15.2)

We saw in Chapter 1 on electromechanical transduction that if the polymer can be described by the con-stant volume approximation typically used for elastomers; i.e.,

Az � �Vol constant (15.3)

where Vol is the volume of the elastomer, then the change in electrical energy d U e due to an incremen-tal change in state can be written as

d d d constant volume)e eU

Q

CQ U

AA� �

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟2

1(

(15.4)

or, equivalently,

d d d constant volume)e eU

Q

CQ U

zz� �

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟2

1( (15.5)

The term ( Q / C )d Q is just the incremental change in electrical energy due to charge flowing onto the film at voltage V � Q / C (see Eqs. (1.10) and (1.11) in Chapter 1). This term also includes any leakage of charge through the film. Equation (15.4) or (15.5) can be used to integrate finite changes in state provided the incremental geometric changes and incremental charge flows are known over the path through state space.

Equations (15.4) and (15.5) are very general given the constant volume assumption, but further insight into generator behaviour and the important parameters can be obtained by looking at simplified

Compliant electrodes (2)Elastomer

(a) (b)

� � � � � �

� � � � � �

� � � � � �

� � � � � �

Figure 15.1 Principle of dielectric elastomer generators: (a) dielectric elastomer stretched (charge at low volt-age) and (b) dielectric elastomer contracted (charge at high voltage).

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148 Chapter 15

cases. Consider a constant charge system with charge Q . Using Eq. (15.2) directly for the stored electri-cal energy on the film, the difference in electrical energy between stretched and contracted states, that is, the generated energy U g , can be written as

U U UQ

C

Q

CQ

C Cg ec esc s c s

� � � � �0 5 0 5

0 51 12 2

2. .. −

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟ (15.6)

where c and s subscripts are used to denote contracted and stretched parameters, respectively. Equation (15.6) can be rewritten as

UQ

C

C

CU

C

Cgs

s

ces

s

c

� �0 5

12.⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

−⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

⎛⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

−⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

1 (15.7)

From Eq. (15.4) it is apparent that if C c � C s , then U g � 0 and electrical energy has been generated. Other important parameters can be derived by extending this analysis. Experimentally, voltage is

more easily measured than charge. Using the fundamental equation Q � CV we can derive

Q V C V C� �s s c c (15.8)

V

V

C

C

A z

A zc

s

s

c

s c

c s

� � (15.9)

V

V

A

Ac

s

s

c

�⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

2

(15.10)

where Eq. (15.9) is derived using Eq. (15.1) for capacitance, and Eq. (15.10) uses the conservation of volume relation for elastomers described by Eq. (15.3).

The quantity V c / V s is referred to as the voltage gain of the system, and is a useful parameter to describe and evaluate dielectric elastomer generators. We see that with a constant charge assumption, the voltage gain is determined strictly from the geometric parameter ( A s / A c )

2 . Voltage gain is readily observed from contracting films, and Fig. 15.2 shows the voltage spike above the level V s illustrating the voltage gain phenomena. In a similar fashion, one can define the energy gain as U c / U s . The energy on any capacitor can be written as U � 0.5 VQ , and since we are assuming a constant charge on the sys-tem, it follows that the energy gain U c / U s � V c / V s � ( A s / A c )

2 is equal to the voltage gain. It is worth noting that the above basic description of the generator mode assumes the dielectric elas-

tomer film does in fact contract. It is known that if the applied voltage and charge are sufficiently large

Powersupply

DEelement

Drainresistor

R

Highimpedance

voltagemeasurement

Figure 15.2 Voltage increase from contraction of dielectric elastomer (shown from bias level).

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Generator Mode: Devices and Applications 149

so as to overcome internal elastic and external loading stresses, the film will expand in an actuator mode, not contract. If the field pressure just balances the internal and any externally applied elastic stresses, the film will not expand or contract and will remain essentially stationary. The electric field or voltage for this condition of balanced elastic and field pressure stresses might be referred to as the field-to-balance and the voltage-to-balance, respectively. To generate electrical energy, the electric field must always be below the field-to-balance, otherwise the film will not contract and no additional electric energy can be generated. This condition is more subtle than it might first appear, because both the voltage and field are typically increasing during the contraction cycle. The field may start out below the field-to-balance in the fully stretched state, but hit the field-to-balance point in some intermediate state before full contrac-tion. This phenomenon is easily observed, and an example is shown in reference [1] . Typically, when the field reaches near the field-to-balance condition, the natural elastic contraction slows appreciably and becomes governed by leakage losses and how fast charge is removed from the film by external circuitry.

In summary of the basics of the dielectric elastomer generator mode, an initial charge is placed on a dielectric elastomer film stretched in area. 1 The film is then allowed to contract, which in turn further separates opposite charges and compresses like charges to a smaller area. From a macroscopic lumped parameter perspective, contraction reduces the capacitance. Using either viewpoint, if charge is constant on the system, the contraction causes an increase in stored electrical energy by raising the voltage of the charge. This increase in electrical energy is due to the fact that mechanical forces work against the electric field pressure. Two convenient parameters for describing and measuring the increase in energy and voltage are the energy and voltage gain, which under constant charge conditions depends only on the change in film area. With suitable electrical circuitry, the increase in stored electrical energy can be harvested to produce a net generated electrical energy output from the system. Implicit in this descrip-tion is that the system typically cycles. That is, the film is again stretched by mechanical forces, an ini-tial charge and energy is placed on the film, followed again by contraction, and so forth.

15.3 MORE DETAILED ANALYSIS OF THE GENERATOR MODE

We noted from Eq. (15.4) that the term ( Q / C )d Q represents electrical energy flowing onto or off the film (including leakage losses) due to charge flow. The second term on the right-hand side of Eq. (15.4) is therefore the incremental generated energy d U g that has been converted from mechanical work to electrical energy:

d

1dg eU U

AA� �2

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

(15.11)

Not all generated energy from a contracting dielectric elastomer film as described by Eq. (15.11) may be harvested for useful output. Consideration of the net energy or power balance necessarily includes losses such as leakage, circuit losses, and so forth. Equations (15.4) and (15.11) can be divided by, for example, an increment in time d t , to form differential equations. System modelling can then be accom-plished by integrating additional equations of state describing mechanical inputs to the generator and electrical output or loading of the system.

Note also from Eq. (15.11) that negative electrical energy is generated when the film is expanding. This reflects the fact that when the film is expanding, it is operating in an actuator mode and convert-ing electrical energy to mechanical work. This observation is significant because it emphasizes that for optimal generator performance, voltage and charge on the film should ideally be zero during the film expansion part of the cycle. Otherwise energy is converted in the wrong direction, and suboptimal per-formance is obtained. In practice, however, it is sometimes electrically advantageous for overall system efficiency and cost to leave some voltage and charge on the film during expansion. The impact of such a design decision on net generated energy can often be estimated to first order by considering the relative magnitudes of 2U e = VQ during expansion compared with contraction at various points in the cycle.

1 An analogous derivation can be made assuming the film is initially compressed in thickness rather than stretched in area. The two

descriptions are very similar for elastomers because of the constant volume condition, which relates changes in area to changes in

thickness.

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150 Chapter 15

The notion of an optimal dielectric elastomer generator is described in [1] . Briefly, if it is assumed that the dielectric elastomer has a constant breakdown field E x (allowing for lifetime safety factors), then the optimal cycle for maximum energy generated per unit volume or per unit mass of dielectric elastomer consists of charging to E x when fully stretched, removing charge during contraction to hold the electric field constant at E x (maximizing the quantity 2U e in Eq. (15.11)) until the field pressure balances the elastic restoring stresses, then further removing charge to zero to reach the fully contracted part of the cycle. Figure 15.3 qualitatively illustrates this optimal cycle given the assumption of con-stant breakdown field. The film is cycled from states 1–2–3–4 and back again in the optimal cycle. In Fig. 15.3 , field pressure is proportional to the vertical axis and strain is on the horizontal axis. Field pressure time change in strain is proportional to energy output, so the area contained within the optimal cycle curve is indicative of energy output per unit volume. Figure 15.3 also qualitatively shows a more practical cycle that might be obtained using voltage limits on the stretched and contracted states. The practical cycle is shown as cycles 1 � –2 � –3 � –4 � and as expected produces less energy (encompasses less area) than the optimal cycle having the same maximum strain.

Note that some electrical energy U es must be placed on the film initially in the stretched state. This energy may be obtained from a secondary energy storage system such as a battery or counter-opposed dielectric elastomer. In practical terms, the need to supply and manipulate a finite energy U es means that the energy gain of the system should ideally be as large as possible. This is because electrical losses are inevitable in manipulating the initial energy U es , and if the energy gain is too low the net energy production may be zero or negative due to parasitic losses that are typically some fraction of U es .

15.4 PRACTICAL CONSIDERATIONS

There are many detailed designs for dielectric elastomer generators. An exhaustive description is beyond the scope of a single chapter, and, further, the technology is rapidly evolving. However, some general aspects can be considered based on the above analysis.

Figure 15.4 shows two general block diagrams of simplified dielectric elastomer generator circuits for discussion purposes. Other layouts can be considered and may be advantageous.

Dielectric elastomers typically operate at relatively high voltages. For power generation this can be an advantage, particularly for distributed power systems such as harvesting wind or wave energy and trans-mitting that energy to a central location. Higher voltage implies lower current and therefore thinner, lower cost wires, which is why conventional power transmission cables operate at high voltage. Nonetheless, for portable applications one typically wants lower voltages compatible with battery power, and to reach thesevoltages a step-down voltage converter is typically required to be part of the generator circuit as in Fig. 15.4 . Step-down converters are well known in electrical engineering. Typically, they use high-speed switching with inductors or transformers, though other methods such as piezoelectric converters are known.

If rechargeable low-voltage batteries are used, some designs put them inside the main generator loop as shown in Fig. 15.4(a) . However, one penalty for this type of design is that the initial charge for each cycle must be raised in voltage relative to the battery ’ s voltage. A step-up converter is needed in this

(Ele

ctric

fiel

d)2

Fieldsu

pport

Breakdown limited‘Optimal’ cycle

More practicalvoltage-limitingcycle

Strain1 2

2′1′

4′3′

4 3

Figure 15.3 Example energy cycles for dielectric elastomers.

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Generator Mode: Devices and Applications 151

case. Step-up converters add cost, but the important issue is not so much added cost but rather the added power loss from the conversion. Note that a step-down converter in the circuit in Fig. 15.4(b) only has to convert the generated energy. That is, it is stepping down only the net output energy. By con-trast, step-up or step-down converters in the main generator loop in Fig. 15.4(a) must convert not only the generated energy, but also the ‘ fixed ’ energy that is just recycled through the system to provide the initial charge in the stretched state. Converting the ‘ fixed ’ circulating energy on every cycle typically increases losses for the system as a whole. It is true that the high voltage management circuit in Fig. 15.4(b) may require some voltage conversion as part of its operation, such as a single step-up conver-sion to get started. But the voltage and charge manipulation in the high voltage management circuit in Fig. 15.4(b) is typically more efficient because it is converting between similar levels of voltage rather than converting the energy all the way from a high voltage to a low battery voltage for each cycle. The system layout of Fig. 15.4(a) using step-down for each cycle can still be attractive, however, if the energy gain per cycle is large. In this case, the penalty for stepping up the input on each cycle may be a small fraction of the generated energy per cycle, so the system efficiency can still be attractive.

Dielectric elastomer leakage is also a practical consideration in power generation. Leakage is a direct loss to the system. The importance of leakage phenomena depends very much on both the dielectric elastomer resistivity and the frequency of operation. Lower frequency operation requires lower leakage losses and higher polymer resistivities. This is because lower frequencies allow more time for leak-age losses to accumulate relative to the energy produced per cycle. Leakage losses may influence the choice of polymer, but good dielectric elastomers can be generally identified to address this issue for most applications. For example, some silicone elastomers have such outstanding resistivities that leak-age losses may be insignificant well below operating frequencies of 0.1 Hz.

Dielectric elastomer generator materials have demonstrated outstanding performance on mass or per volume basis. Acrylic elastomers, for example, have demonstrated generator output up to 0.4 J/g, a spe-cific energy that is possibly higher than any other generator material including piezoelectrics and elec-tromagnetics. High energy density reduces the amount of material needed for a generator application. This advantage can be used directly to make a light generator, but another way to exploit this advantage is to use it to enable a direct drive (no transmission) generator.

Dielectric elastomers are also outstanding as a generator material with regard to frequency dynamic range. Silicone has a dynamic range of at least 1000:1, and probably much higher, between highest and lowest frequency of efficient operation. Even acrylic elastomers, though more frequency limited than silicones because of leakage losses and viscoelasticity, has a dynamic range of at least 10 to 100:1. By contrast, electromagnetic generators have very limited dynamic range where even 5:1 would be con-sidered good. Electromagnetic generators have great difficulty adapting efficiently to variable speed

BatteryStep-downvoltage converter

Battery Step-upvoltage converter

Step-downvoltage converter

Polymerdevice

Polymerdevice

Initial chargesource

High voltagemanagement

circuit

(a)

(b)

Figure 15.4 Two conceptual circuit topologies for dielectric elastomer generators.

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152 Chapter 15

mechanical inputs because their transduction mechanism is fundamentally based on the rate of change of the magnetic flux through a coil. By contrast, the fundamental transduction of dielectric elastomer generators depends on changes in the strain state rather than the rate of change of the strain state, as shown by Eq. (15.11). Where variable speeds are unavoidable, electromagnetic generators must usually include variable transmissions, which add considerable cost and complexity to the system.

Perhaps the biggest advantage of dielectric elastomers is that, together with good dynamic range, they operate best at relative long strokes and modest forces. This is a difficult part of the design space to address using conventional ‘ smart ’ materials such as piezoelectrics. Yet, it is a very common mechanical input available from a number of sources in the environment such as human motion and wave power. These and other advantages are discussed more fully with respect to specific applications in the next section.

15.5 APPLICATIONS OF DIELECTRIC ELASTOMER GENERATORS

Virtually any application where there is a need for electrical energy is a potential application for dielec-tric elastomer generators. However, dielectric elastomer power generation is much more competitive for some applications compared with others, and it is important for a new technology to identify general and specific areas of application where it can be most competitive. The previous section described some general advantages or attractive features of dielectric elastomer power generation. These and other gen-eral advantages are summarized in Table 15.1 , and specific applications are discussed in greater detail in the following paragraphs.

Generator applications can be categorized into point generator applications, such as an alternator in an automobile, or distributed generator applications, such as harvesting wind power over a broad area.

15.5.1 Point generator applications

Dielectric elastomers can be used for traditional point generator applications as a direct replacement for electromagnetic generators. A dielectric elastomer generator can be coupled to an internal combustion

Table 15.1 General advantages of dielectric elastomer generators.

Technical Characteristic

Generator Implications Applications Where Characteristic May Be Important

Comments

High energy density Less material and mass required

Portable applications human power harvesting

Mass savings may be particularly important when fuel analysis is considered for vehicles

Direct drive capability

Transmissions not needed or simplified; lower cost and complexity

Many; human power harvesting, wave power, wind power, etc.

Feasibility of using direct drive is related to several other characteristics such as high energy density and dynamic range; also major potential advantage with regards to maintenance

Dynamic range Can efficiently use variable speed mechanical inputs

Wave and wind power Possible advantages for hybrid vehicles and other systems where harvesting energy at a large range of frequencies is desired

Large area films Can address distributed energy sources; enables batch fabrication of micro-devices

Wind power; batch fabrication of micro-generators

Very large area, high efficiency generator films are difficult using competitive technologies, so this may be an area for promising advanced research and development

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Generator Mode: Devices and Applications 153

engine to make a fuel-powered generator, for example. For these traditional point generator applica-tions, dielectric elastomers may offer advantages such as lower cost, lighter weight, or smaller size. However, for traditional high frequency, point generator applications, dielectric elastomer generators is a new technology competing against a mature technology (electromagnetics) that is well suited for the task. Hence, the competitiveness of the dielectric elastomers in these traditional high frequency applica-tions may depend a great deal on the specifics of the application.

Electromagnetic generators must use transmissions to operate efficiently at low speeds or when speed is highly variable. Transmissions can add significant cost, complexity, and size. Thus, dielec-tric elastomers are more competitive in the low or variable frequency domains. Similarly, dielectric elastomers are well suited for applications requiring relatively large, linear motions as compared with rotary motion.

Dielectric elastomers are well suited for harvesting energy from human motion. Natural muscle, the driving force for human motion, is typically low frequency and intrinsically linear, both characteristics where dielectric elastomers offer advantages. Human walking is a good example application of energy harvesting using human motion. Proof-of-principle heel-strike generators have been built using dielec-tric elastomers, as shown in Fig. 15.5(a) . Energy output from simulated steps have demonstrated 0.8 J per step using dielectric elastomer devices, with up to approximately 1–2 J per step probably feasible with more development. Heel-strike generators harvest energy from walking that would otherwise be wasted as heat. The upper limit for energy harvesting without causing discomfort to the walker is esti-mated at 2–4 W for two shoes, assuming a typical 1 Hz step frequency. Though not a large amount of power, 2–4 W is adequate for portable applications such as smart shoes, cell phone battery charging, and emergency locators for soldiers and hikers.

Another attractive point generator application is buoy generators. Batteries for buoys are expensive, and replacing or recharging buoy batteries is costly and often hazardous in high seas. Thus, onboard buoy power generation that eliminates or minimizes the need for batteries would be an attractive appli-cation. Existing commercial systems based on solar cells and small wind turbines cannot produce the desired power levels in certain environmental conditions. In particular, solar cells have difficulty in dark or clouded conditions, and salt spray and biofouling is a major problem. Wind turbines may also suffer from biofouling and bearing degradation in an ocean environment. Both wind and solar technolo-gies also rely on significant surface areas to produce power, and large surface areas are undesirable for buoy stability. In many cases, wave motion offers greater power levels and greater reliability.

Wave motion is typically low frequency in the 0.1–1.0 Hz range, but relatively high in amplitude (wave heights on the order of 1 m are common). Linear-type generators using dielectric elastomers are well

(a) (b)

(c) (d)

Electrical output

EPAM laminate(‘balloon’

configuration)

Fluttering EPAMwind generators,installed across

a valley

Floats provideextension motion

by riding on waves

Dielectricelastomer

locatedwithin

stretchabletether

Figure 15.5 Dielectric elastomer generator applications: (a) heel-strike generator, (b) polymer engine, (c) wind-power generator, and (d) wave-power generator (adapted from [4] ).

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154 Chapter 15

suited for this type of motion. Proof-of-principle dielectric elastomer buoy generators have been demon-strated in work to date [2] . Early buoy generators have produced over 5 J per stroke at 0.3 Hz using only about 40 g of dielectric elastomers. In wave tank tests using 10 cm waves, LED lights (such as might be used for navigation buoys) were flashed continuously using only energy harvested from the waves.

Many other interesting point generator applications exist for dielectric elastomers. Remote and/or wireless devices are growing in use, and these devices can ideally harvest their own energy to eliminate the need for battery replacement. Dielectric elastomers are well suited for these applications if mechan-ical energy is available such as from oscillatory or vibratory motions such as that might occur in port-able devices carried by people, animals, or automobiles. Many of these applications may be small or micro in nature. Limited work has been done on micro-dielectric elastomer generators, but work on micro-scale dielectric elastomer actuation [3] is encouraging for this area of application.

One of the most common sources of mechanical energy in modern technology is from chemical fuels. Applications of dielectric elastomer generators replacing electromagnetic generators in vehicles were mentioned previously, but even more revolutionary approaches are possible. Polymers themselves can be used to make engines, and if dielectric elastomers are used for the polymer, the device can gen-erate electrical energy directly from expanding hot gases. Figure 15.5(b) (adapted from [4] ) shows a simplified conceptual dielectric elastomer polymer engine. These devices use internal or external com-bustion to directly expand the dielectric elastomer, thus converting chemical energy into electrical energy. The dielectric elastomer power-generating structure replaces the piston and cylinder assembly of a conventional engine. Not only is the engine simpler and lighter weight with this approach, but there is no need for an additional generator element. Dielectric elastomer engines can also include mixed out-put, with part of the energy being made available mechanically as in a traditional engine, and part elec-trically from the dielectric elastomer materials. The ability to provide both electrical and mechanical outputs may have significant advantages at the system level, as different types of output usually require multiple subsystems using conventional technology.

Dielectric elastomer engines have been demonstrated at the proof-of-principle level. While initial lifetime testing has only been performed for up to 3 h to date, analysis indicates that the wall tem-perature of these engines can be maintained below 200 � C (as it is in many types of conventional metal engines), so that long-term lifetimes should be feasible. Dielectric elastomer engines are in the early stage of development, but they offer major potential advantages over traditional piston-cylinder engines including lighter weight, greater simplicity, lower tolerances, higher specific power densities, decreased noise, higher efficiency in smaller engines, and much lower cost (for some applications disposable engines would be practical).

15.5.2 Distributed generator applications

Dielectric elastomers can be made in large area sheets with high performance. Even when not pack-aged in sheet form, dielectric elastomers use potentially low-cost materials. These capabilities suggest that dielectric elastomers may be well suited for harvesting energy from large area, distributed power sources such as wind and wave energy.

Wind energy provided by conventional windmills is a competitive power source in many parts of the world. Yet, windmills have a number of known disadvantages, including the relatively high cost of towers and maintenance, noise, obstruction of natural views, and interference with birdlife. Many of these problems are particularly acute in heavily populated areas with the highest electrical demand.

Problems with conventional windmills might be addressed with dielectric elastomer generators. Many types of dielectric elastomer generators might be used for wind power. As with other applications, dielectric elastomer generators might directly replace electromagnetic generators, but more interest-ing system designs using dielectric elastomers may yield greater benefits. Fluttering dielectric elas-tomer flags, such as shown in Fig. 15.5(c) , is one approach [4] . These flags can be of any desired colour, including transparent, would not interfere with birdlife, and could present minimal obstruc-tion of views. Natural landscape features such as mountains and valleys might be used to eliminate the need for towers in some locations. Much greater loads can be supported in tension than in bending for the same amount of structural material, so by using tension cables much of the structural cost is further reduced. Even if towers are used, it is likely to be much less expensive to build two high load towers with a power-producing cable between them than to build multiple smaller towers with individual

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Generator Mode: Devices and Applications 155

windmills covering the same linear distance perpendicular to prevailing winds. Maintenance costs can also be reduced by a cable approach because the dielectric elastomer flags can be reeled in, rather than requiring workers to climb and disassemble very large windmill blades individually. Conceptual designs for dielectric elastomer flag generators have been developed, and early analysis supports the conclusion that flag generators can theoretically be efficient. This conclusion is perhaps not surprising because the waving motion of flags fundamentally has low losses [5] .

Wave power is another opportunity for dielectric elastomer distributed power generation [1] . An example design is shown in Fig. 15.5(d) . Wave power is a distributed power source, but has a fairly high power density per metre of length perpendicular to the direction of wave travel. Wave power is typically measured as the amount of power available (or harvested) per unit length perpendicular to the propagation direction of the wave. Power densities of 1–10 kW/m are typical for waves in many areas. Both coastal and offshore wave power can be considered, and the low cost of dielectric elastomer mate-rials suggests that large systems may be feasible. Figure 15.5(d) shows a conceptual distributed wave power generator system for coastal areas using floats. Many other designs are possible.

Polymer engines were discussed in the previous section as point generators. Polymer engines might also be used for distributed power sources because of their low cost and design flexibility. Polymer engines have been made as tubes and diaphragms, and fabricating sheets of such engines is an option. Sheets or large arrays of dielectric elastomer Stirling engines might be applicable as distributed gener-ators using, for example, solar power as a distributed heat source. Whether such an approach has advan-tages relative to centralized power generation (e.g. compared with a single large Stirling engine on a central tower surrounded by mirrors in the solar power case) remains to be shown, but the fact that sheets or large arrays of engines can be made inexpensively opens up novel approaches for consideration.

15.6 SUMMARY

Dielectric elastomer generators are potentially as important as dielectric elastomer actuators. In the gen-erator mode, when a dielectric elastomer film contracts in area the elastomer stress does work against the electric field pressure. Electrically, the generated electrical energy is manifest by an increase in voltage, and traditional electrical lumped parameters such as capacitance can be used to analyse the behaviour of the system.

Dielectric elastomers have demonstrated excellent performance using a number of metrics, such as 0.4 J/g demonstrated energy density. Many applications appear feasible, but challenges remain. Dielectric elastomers appear most advantageous for applications requiring low or variable frequencies, low cost, large areas, and/or direct drive. Dielectric elastomers might be used to directly replace exist-ing electromagnetic generators, but even more exciting potential applications exist in distributed power sources such as wave and wind power.

References

[1] Pelrine, R., Kornbluh, R., Eckerle, J., Jeuck, P., Oh, S., Pei, Q. and Stanford, S. (2001). Dielectric elasto-

mers: generator mode fundamentals and applications. In Smart Structures and Materials 2001: Electroactive Polymer Actuators and Devices , Ed. Bar-Cohen, Y., Proc. SPIE , 4329 , 148–156.

[2] Pelrine, R., Kornbluh, R., Prahlad, H., Stanford, S., Eckerle, J. and Chiba, S. (2006). New opportunities in

electric power generation using electroactive polymers. Jpn. Ins. Energy , November.

[3] Kornbluh, R. D., Pelrine, R. E., Pei, Q., Heydt, R., Stanford, S. E., Oh, S. and Eckerle. J. (2002).

Electroelastomers: applications of dielectric elastomer transducers for actuation, generation and smart struc-

tures. In Smart Structures and Materials 2002: Industrial and Commercial Applications of Smart Structures Technologies , Ed. McGowan, A., Proc. SPIE , 4698 , 254–270.

[4] Prahlad, H., Kornbluh, R., Pelrine, R., Stanford, S., Eckerle, J. and Oh, S. (2005). Polymer power: dielec-

tric elastomers and their applications in distributed actuation and power generation. Proceedings of ISSS 2005 International Conference on Smart Materials Structures and Systems , 28–30 July, Bangalore, India,

pp. SA-100–SA-107.

[5] Moretti, P.M. (2003). Tension in fluttering flags. 23rd Oklahoma AIAA/ASME Symposium, University of

Oklahoma, Norman, 8 March.

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Section IV

Models

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FINITE-ELASTICITY MODELS OF ACTUATION

Guggi Kofod 1 and Peter Sommer-Larsen 2

1 Applied Condensed-Matter Physics, Department of Physics, University of Potsdam, Potsdam, Germany

2 Polymer Department, Risø National laboratory, Roskilde, Denmark

Abstract

The high-strain actuation of dielectric elastomer actuators (DEAs) can be understood only in terms of specifically

non-linear elastic theory. In the ideal case, the static extension of a loaded and electrically activated actuator can be

modelled through the electrostatic and elastic stress with proper boundary conditions. Models that account for tem-

poral behaviour must include complications like viscoelastic properties of both insulating elastomer and compliant

electrodes. Further improvements can be achieved by including effects such as finite conductivity of the electrodes

and electrical losses in the insulating material. Quite complete models of actuators with complicated geometries

have already been suggested and compared to experimental realizations with good results, which is vital to the con-

trolling of DEA as reliably predictable biomimetic actuators.

Keywords: Boundary conditions, elasticity, geometry, high strain, hyperelasticity, loss, non-linear, strain, stress,

temporal behaviour, viscoelasticity.

16.1 INTRODUCTION

The description of dielectric elastomer actuators (DEAs) needs models that cover the very high strains often observed for such actuators. In fact, many actuators are already considerably stretched even before a voltage is applied. This condition is referred to as pre-stress, when the actuator is stretched because of loading and pre-strain, when the actuator is stretched during construction, e.g. stretched over a frame. Classically, the connection between force and extension in a material is described by Hooke ’ s law, which states that the force F on the ends of a spring is proportional to its extension from the equi-librium length l 0 ,

F k l l� �( )0

(16.1)

where k is the spring constant and l is the current length of the spring. Cast into a constitutive relation between stress and strain, Hooke ’ s law holds for all materials at infinitesimal strains and defines the Young ’ s modulus: T � YS.

If an elastomer is further stretched – the region of finite strains – a highly non-linear connection between force and strain is observed. The sketch in Fig. 16.1 illustrates the forces when strains up to

Chapter 16

F

Sa b

c

1 2 3 4 5

Figure 16.1 The force–strain curve of an elastomer string.

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160 Chapter 16

500% are applied. The curve only shows linear behaviour up to a few per cent strains. At low finite strains, in the initial a region, the material is ‘ hard ’ , while in the plateau b region it appears to be ‘ softer ’ , as judged by the slope of the stress–strain curve. As the constituent chains are stretched, more and more of them reach their elastic limit, and the material experiences strain-hardening ( c region). The lower-lying a and b regions can be modelled with the Neo-Hookean elasticity model, while the inclu-sion of the strain-hardening c region requires more sophisticated models, which can be based on either phenomenological or physical arguments, or more typically a combination of both.

In the following we will first illustrate actuation by a linear model using a simple sample geometry, an approach first suggested by Pelrine et al. [1] . We will then move to finite-strain modelling, first describ-ing a practical approach for static experiments, and then finally show how to include time-dependent behaviour. The sample geometry will always be kept the simplest possible, helping to view effects of material improvements directly.

16.2 INFINITESIMAL STRAIN MODEL

The infinitesimal strain approach is the most commonly employed model [2–4] . It is based on the assumption that the classical spring can be used as an approximation for the elastic material Eq. (16.1), in which case the usual form is

T YSz z� (16.2)

The positive direction is along the normal pointing outwards with respect to the surface of the dielectric. The pressure from the electrodes on the material is given by the Maxwell ’ s equation p � � � 0 E 2 � � � 0 V 2 / z 2 , such that the stress on the surface when a voltage is applied becomes ( S z � 0 in compression)

TV

z SYSz

zz� �

��

��02

02 21( )

(16.3)

Rearranging Eq. (16.3) results in

� � ���0

2

02

21V

YzS Sz z( ) (16.4)

The expression on the left-hand side represents stress normalization, such that the expression on the right-hand side is a normalized stress. This normalized stress is plotted in Fig. 16.2(a) , together with a line representing the value of the stress normalization at an arbitrary voltage. The crossing point of the curves at a designates the position at which the forces balance, and the corresponding strain S z is the current actuation strain. The crossing point at b is not stable since the curvature of the energy (stress integrated) is negative here, a situation which has been referred to as pull-in failure. Finally, when the voltage becomes high enough that the straight line does not intersect with the curve, the actuation strain becomes undefined. The last well-defined strain is

Sz � �1 3 . Figure 16.2(b) shows the calculated

�1 �0.8 �0.6 �0.4 �0.2

�0.14

�0.12

�0.1

�0.08

�0.06

�0.04

�0.02

Sz

Sz

Yz02

‘Norm

alized stress’ab0

(a) (b)

200 400 600 800 1000 1200 1400

�0.3

�0.2

�0.1

0.0

Voltage,V

z0�50 μm

Y�100 kPa 200 kPa

300 kPa

ε � 3

εε0V 2

�

Figure 16.2 The stability and actuation of a simple linear material.

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Finite-Elasticity Models of Actuation 161

strain for actuators with the parameters shown in the plot, and as expected the softest material shows the highest strain.

16.3 FINITE STRAIN MODEL

The infinitesimal model has a number of shortcomings, which all directly influence the results when leaving the infinitesimal strain range. The chosen representation of the stress–strain relation is not vol-ume conserving, and neither shows the strain-softening (region a in Fig. 16.1 ) nor the strain-hardening (region b ) of a real material. Finally, any realistic model should include effects of viscoelasticity, and the mechanical and electrical influence of the compliant electrodes. In the following, we will deal with some of these complications.

The geometry of the problem directly influences the structure of the resulting equations. For mater ials studies it is therefore advantageous to use simplest possible geometries to remove unnecessary compli-cations. This geometry should also lend itself to simple experiments. A practical choice is the planar flat film, with fixed edges, illustrated in Fig. 16.3 [2, 4–7] . The length direction of the actuator is along the x direction, the width along y and the thickness along z . The initial dimensions are denoted by x ′ , y ′ , z ′ . The fixed edges means that the width direction remains unchanged, y = y ′ always, and the stretch ratio is always � y � y / y ′ � 1. The volume conservation reduces the number of free dimensional variables to 1, since � x � y � z � 1 ⇔ � z � � x

�1 . The fixed edges geometry is approached by actuator, which is much wider than its length.

Before we continue with more elaborate expressions for the stress–strain relations, we first show how the simplicity of the geometry allows for inclusion of external forces. The stress in the film is given by

T T T pij ij ij ij� � �elec load � (16.5)

where the Lagrange multiplier ( � P � ij ) accounts for boundary conditions and Tijload represent an exter-

nal load of the actuator. With the standard geometry in Fig. 16.3 there will be no off-diagonal terms. In the length direction, an external force (load) results in a stress

T F yzxx x

load � / . The normal stress, found by eliminating � P � ij from Eq. (16.5), becomes

T T T T

F

yzxx zz xx zzx� � � �( )elec elec (16.6)

The electrical term can be estimated using T a E E a Eij i j ij

elec � � � � �( ) / ( ) /2 2 21 0 2 02� � � � � [8, 9] ,

where the electrostriction terms a 1 and a 2 are negligible for a amorphous isotropic elastomer. The electrical term then becomes the familiar

( )T T Ezz xx

elec elec� � ���02 . The resulting stress in Eq. (16.6)

is related to deformation of the actuator by the constitutive equation for the given material. Due to the chosen simple boundary conditions, and the incompressible nature of the isotropic elastomer, the stress–strain equation of the elastomer can be written as a function of just one variable, for practical reasons we will pick the stretch ratio in the length of the actuator, � x , as the variable.

x1

x3

x2′

F

F

Figure 16.3 Very simple geometry as basis for models that emphasize the effect of material properties on actuation performance ( x = x 1 , y = x 2 , z = x 3 ).

Ch16-I047488.indd 161 12/10/2007 8:32:01 PM

162 Chapter 16

The actual stress–strain relation can have many forms depending upon the assumptions made to derive it. A particularly simple set of constitutive equations is known as the Neo-Hookean model, in which the stress tensor is taken to be proportional to the Finger strain tensor, T ij � GB ij . The diagonal elements of the Finger tensor in the standard geometry are Bii i� �2 , such that

( )T T Gxx zz� � ��

�2

2

1⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

(16.7)

where � � � x . The Neo-Hookean expression typically holds for strains up to 30% [10] . Collecting terms, the total stress-balance equation becomes (all three parts are positive)

F

yzE Gx � � ��� �

�02 2

2

1⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟ (16.8)

This equation is fundamentally the static version of Newton ’ s second law, which can be illumin ated by an example: the top of the actuator film is fixed, while a mass is suspended from the bottom ( F x � mg ). On the bottom plane, three forces are acting: weight of the mass, Maxwell pressure of the electrodes and pull from the elastomer. The weight and the Maxwell pressure tend to increase length of the actua-tor and thus appear on the same side, while the elastomer tries to decrease the length of the actuator, and thus appears on the other side. The equation is especially practical, since each force originating from a separate source appears as a term independent of the others.

The stress-balance equation contains three variables: the external force, the voltage and the stretch ratio. Replacing y = y ′ , z � z ′ / � and E z � V � / z ′ , the equation can be rearranged to

� �

��� �1

1 2 02

22 2F

y z

V

zG

′ ′ ′� � � �( ) (16.9)

which is a fourth order polynomial in � . This equation should be able to model flat film actuators of fixed width under applied load and voltage, when the strain in the length direction is less than 30%.

The stress–strain relation on the right-hand side of Eq. (16.9) can be replaced with other constitutive models, such as presented in Chapters 3, 17 and 18.

The constitutive equation suggested by Ogden is

( ) ( )T Txx zz l

k kl

nl l� � � �

�� � �

1∑ (16.10)

where n is the total number of terms. Each term is characterized by the numbers � l and k l . Table 16.1 con-tains data for a three term expansion obtained by Ogden from data gathered by Treloar [11] . With three terms, Ogden was able to model Treloar ’ s data until elongations of 700%. The Young ’ s modulus of this material can be calculated as E kl l� 3 2 � , which for the Treloar rubber amounts to Y � 1.25 MPa, that is, a fairly stiff rubber. In Fig. 16.4(a) , the elongation in length due to an applied load and voltage has been plotted for a flat film with a fixed width of y ′ � 100 mm and an initial thickness of z ′ � 100 μ m.

It is difficult to make out the actuation behaviour directly; the effects of the voltage on the length are a bit obscured by the large variations due to applied load. Therefore, it is practical to introduce the actuation strain , � , where the length of the actuator at a given load and no applied voltage is taken as the initial length, which can be written as

�

� ��

( , )( , ) ( , )

( , )

( , ) ( , )

( , )m V

x m V x m

x m

m V m

m�

��

�0

0

0

0 (16.11)

The actuation strain has been plotted for several loads in Fig. 16.4(b) . It is seen that a pronounced optimum appears, for a load of approximately 500 g, and when going to higher loads, very little actua-tion is observed. Finally, in Fig. 16.4(c) , the electric field has been plotted instead of the applied voltage.

Table 16.1 Parameters in a three term Ogden equation ( ) ( )T Txx zz l

k kl

nl l� � � �

�� � �

1∑ for natural rubber.

� l 620 kPa 1.18 kPa –10 kPa k l 1.3 5.0 –2.0

Ch16-I047488.indd 162 12/10/2007 8:32:01 PM

Finite-Elasticity Models of Actuation 163

The highest electric field is 800 MV/m, which is quite high. For a different, softer elastomer material, lower electrical fields would be required.

The approach detailed in this section has a number of advantages, which were put to effect in [4–6, 13, 14] . The simplicity of the geometry elucidates the effect of material properties more directly. Inversely, this means that a new material can be more easily compared to known materials, based on measured elas-tic and dielectric properties. Further, the parameters of the constitutive models, as well as the geometric parameters, can be determined independently, thus there are no free parameters in this model.

Finally, if the length of the actuator film is kept constant, the only free variable is now the force on the end planes ( yz ) of the elastomer film. Consider the situation in which a film is pre-stretched to a given length x (0). The total force measured on the ends of the actuator at a given applied voltage is F x ( V ), the component of the force due to elasticity only is Fx

elast (equal at V: elast0 0F Fx x( ) )� , then it

can be calculated that

( ( ))( )

F F V

y zE Vx x

elast �

� �� �

��� �0

2 (16.12)

i.e. the Maxwell ’ s stress expression is retained. The left-hand side corresponds to the difference in stress measured on the end plane of the actuator, between the states with and without an applied voltage. Using this simple approach, the validity of the assumption that Maxwell ’ s stress is responsible for the actuation in a given dielectric elastomer actuator can be checked with a simple set of experiments. In [6] this approach was employed to show for the first time that the Maxwell stress was indeed responsible for the actuation stress in cases of high strain and high applied electric fields, that is, during all phases of actuation.

Elongation

Volta

ge V

(kV)

Mass m (g)

64200

10002000

3000

4000 0

2.5

5

7.5

10

λ1

(a)

Volta

ge V

(kV)

Mass m (g)

Actuationstrain

0.50

11.5

01000

20003000

40000

2.5

5

7.5

10

ε

(b)

Electric field E (MV/m)

Mass m

(g)

Actuationstrain

01000

2000

3000

4000

0

0.2

800600

400200

0

0.4

ε

(c)

Figure 16.4 Actuation of the Treloar rubber (adapted from [12] ).

Ch16-I047488.indd 163 12/10/2007 8:32:02 PM

164 Chapter 16

16.4 TEMPORAL DEPENDENCY

Elastomers in general display physical properties that changes with time and their response to external electrical or mechanical actions depends on how fast these actions are applied. For DEAs, the dielectric and viscoelastic properties directly influence the response of the actuator to an applied electric field. As explained in Chapter 3, the temporal dependence of both sets of properties reflects the relaxation of polymer chains in the elastomer. Typically, there exist at least two time domains: a fast change in proper-ties is related to the � -relaxations, which typically occurs faster than microseconds at temperature well above the glass transition of the polymer. A slow change is related to reptation of dangling ends attached to the elastomeric network as described in Chapter 3. Such changes can last seconds, hours or even days.

A significant fraction of the change in mechanical properties with time is governed by the slow relaxation. Dielectric properties on the other hand mainly changes by fast relaxations.

The description in the next subsections are based on the Boltzmann ’ s superposition principle: the dif-ferential response to an external action from all prior times may be added linearly (in time) to give the response at the present [15] .

The examples extend the description in [16] . The first subsection briefly discusses the possible time dependency of dielectric properties, whereas the second subsection introduces viscoelastic properties of the elastomer into time-dependent models for the actuator response. Within a purely elastic limit, Mockensturm [17] analysed the dynamic response of a spherical membrane used in their diaphragm pump. A non-linear viscoelastic model for finite deformations of dielectric elastomer membranes using Christensen ’ s theory of viscoelasticity was developed in [18] . Frequently, the influence of viscoelasticity on actuator performance is demonstrated for VHB ™ 4910 (or 4905). The viscoelastic properties – e.g. the loss tangent – of this elastomer depend on stretch ratio as demonstrated in [19] . This makes comparison between different experiments difficult, because all VHB based actuators are biaxially pre-strained to some degree. No thorough experimental investigation of actuation performance of viscoelastic rubbers has been performed.

16.4.1 Dielectric properties

An electric field induces a polarization in a material which depends linearly on the imposed field:

D

E( ) ( )

( )t t t t

t

t

t� � � �

�

���d � �

��0∫ (16.13)

where � ( t ) is a time-dependent relative dielectric constant tensor, E ( t ) is the imposed electric field, D ( t ) is the electric displacement ( D � P � � 0 E). P is the polarization, which equals the induced dipole moment per volume. Most rubbers are isotropic and the dielectric constant tensor reduces to the normal dielec-tric constant. If the dielectric constant depends on strain, the materials behave electrostrictively [8] . For most rubbers, electrostriction effects are small [20] although thermoplastic polyurethane elastomers is an exception [21] .

Materials analysis is commonly performed in Fourier space, where the frequency-dependent dielectric constant is measured for various temperatures. The relation between the time- and frequency-dependent dielectric constant is given by the one-side Fourier transforms:

� � � �

� �

�

*( ) ( ) ( ) ( )

( ) ( ) ( )cos(

� � � � �

� � � �

��

i t t

t

ti e di

0

02

∫tt)

d

0

�

∫

(16.14)

For a dielectric elastomer actuator, the electric field induced stress can be found simply by calculating the compressive and extending forces per area through differentiation of the electrostatic energy density, u , stored in the elastomer with respect to either thickness or length. The electric field is applied in the z direction and the elastomer is supposed to be isotropic. The electrostatic energy density is given by

u t E t D t E t t t t

E t

t

t( ) ( ) ( ) ( ) ( )

( )� � � � �

�

���

1

2

1

20d � �

��∫ (16.15)

Ch16-I047488.indd 164 12/10/2007 8:32:03 PM

Finite-Elasticity Models of Actuation 165

and the electric induced stress is similarly found to be

T T E t D t E t t t t

E t

txx zz

telec elec d� � � � � �

�

���( ) ( ) ( ) ( )

( )� �

��0∫

(16.16)

In case of constant applied potential, U , which is turned on at t � 0, the stress becomes

T T

U

z tt t t

z ttxx zz

telec elec d� � � � �

�

�

2

00

1

( )( )

( )� ��

�∫

(16.17)

The limit of Eq. (16.17) for large times ( t → � ) is the static value

T T

U

zxx zz� � � �0

2

( )( )

��

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

so for processes that are slower than any dielectric relaxation one can neglect the time dependency of the dielectric constant and use its static value. As stated above, dielectric relaxations in elastomers typi-cally occur faster than milliseconds, so they are faster than normal timescales for dielectric elastomer actuation. An influence of a time-dependent dielectric constant on the behaviour of actuators has never been experimentally demonstrated.

16.4.2 Mechanical properties

A slow relaxation of mechanical properties – take an example the elastic modulus – is observed for almost any elastomer. The relative change of elastic modulus varies considerably between different types of elastomers: for silicones with a Young ’ s modulus of the order 1 MPa, the modulus changes a few per cent within minutes whereas the modulus of the VHB acrylate tape changes 66% in an hour. Further more, this change depends on the pre-strain of the rubber.

We use the same configuration as in the static case to demonstrate the influence of viscoelasticity on the dynamic behaviour at finite strain. The system consists of an actuator hanging vertically from some rigid top plate and a moving mass attached to the end of the actuator. The mass of the moving part of the actuator is neglected because the actuators typically lift more than 100 times their own weight.

In the following, we neglect time dependence of the charging of the actuator (a possible RC time) and also any strain and time dependence of the dielectric constant. The dynamic equation governing the movement of the actuator is derived from Newton ’ s second law and Eq. (16.8). The elastic stress now depends on both finite strain and time:

mx

tF mg E

mxt

y zT T t mg

x

xx zz

d

d

d

d

elast2

2 02

2

2

� � �

� � � �

��

��

�

⇓

′′ ′

( )( , )���

�02′

′y V t

z

( )

(16.18)

where Fxelast is the total elastic restoring force of the actuator and the applied potential and stretch

ratio � depends on time. The normal stress in Eq. (16.18) is related to strain by some non-linear viscoelastic constitutive

equation. One such equation is the Rivlin–Sawyers equation [22] . In an approximation similar to the Mooney–Rivlin equation for the static stress–strain behaviour of a rubber in a pure shear geometry (constant width) a proper form, when the electric field is applied at t � 0, is

( )( , ) ( ) ( )( )

( )T T t G t

tt

G t t

txx zz� � � � �� �

�� �

��

�0

122

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

d ���

��

220

22

1

01

0

( )( )

( ) ( )( )

tt

G t

t� �

�

� �

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟

∫

⎟⎟+

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

G( ) ( )( )

���

22

01

0

(16.19)

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166 Chapter 16

The last two terms in the two equations take into account the possibility that the actuator is pre-stretched (e.g. by an external load) before actuation occurs.

G ( t ) is the shear modulus typically measured in a stress relaxation experiment. As example, the stress relaxation for VHB ™ 4910 was measured at 25% strain. The data shown in Fig. 16.5 fit a Maxwell model:

G t G git

i

i( ) ( )( )/� � �

�

� 11

4

e �∑ with constants given in Table 16.2 . The data shows a relaxation of the

Young ’ s modulus from 130 to 40 kPa over approximately 1 h. For a given applied potential, Eq. (16.18) can be solved numerically using the stress given in

Eq. (16.19) and either a measured relaxation modulus, G(t), or an analytic fit to G(t). The method can be illustrated for a step potential applied at t � 0. We use a relaxation modulus given

by a Maxwell model with a time constant of 2 seconds and a static term: G ( t ) = G 0 (1 + e � t /2 s ). The con-stants occurring in Eq. (16.18) is chosen such that

y z

mxG

y V

mx z

� �

��

�

� ��

�

�

0

02

1

0 9

s

s

2

2��.

The calculated extension ratio as a function of time is plotted in Fig. 16.6 together with the static

extension ratio obtained from Eq. (16.18) in the limit d

d

2

20

�t

� . The approach to the static extension

is considerably slower than the time constant in the Maxwell model. The solution can be compared to a mass suspended by a spring with an intrinsic damping – a damped harmonic oscillator. If the mass

15 000

0 2000 4000 6000 8000 10 000

20 000

25 000

30 000

35 000

40 000

Time (s)

For

ce/A

0(P

a)

Figure 16.5 Stress relaxation of VHB ™ 4910. Engineering stress versus time was measured in 10 000 s after quickly straining the sample 25%.

Table 16.2 Fit to relaxation modulus G t G git

i

i( ) ( )( )/� � �

�

� 11

4

e �∑

for VHB™ 4910.

G (� )/Pa 14 300 i 1 2 3 4 g i 0.94 0.55 0.32 0.22 � i /s 6.4 64 480 3870

Ch16-I047488.indd 166 12/10/2007 8:32:03 PM

Finite-Elasticity Models of Actuation 167

is dropped, it either starts to oscillate around its equilibrium position with amplitude that is damped in each oscillation, or if the mass is small; it monotonically approaches equilibrium. The solution illus-trated in Fig. 16.6 is different from both these limits because the applied electrical stress depends on extension and the spring constant depends on time. An often used configuration for testing dielectric elastomers is the expanding dot (or circle). Here the moving mass is the mass of the elastomer itself, and it is so low that only a monotonic approach to the equilibrium extension is observed. An example is shown in Fig. 16.7 . The dot made from VHB™ 4910 monotonically expanded and had clearly not reached equilibrium during the 30 seconds high voltage was applied. As mentioned, the relaxation mod-ulus of a biaxially pre-stretched film is expected to deviate from the uniaxial relaxation modulus deter-mined in Table 16.1 , and proper treatment of the biaxial case must follow the lines of [17, 18] .

0 20 40 60 80 100t (s )

1.2

1.4

1.6

1.8

2

λ

Figure 16.6 Stretch ratio as a function of time. The points are obtained by numerical solution of the integro-differential equations (16.18) and (16.19) with parameters given in the text. The dotted line is the static extension ratio when all acceleration has ceased. The solution corresponds to the mass bumping up and down while the actuator is approaching its static extension.

Figure 16.7 Snap shot from video of expanding dot made from VHB™ 4910 with graphite grease electrodes and extended over a circular frame. The overlaid graph show the area expansion ratio as function of time in seconds as measured from the video. High voltage (5 kV) was applied after 6 s and the dot immediately expanded. The dot con-tinued to expand while high voltage was applied, and it had not reached its maximum extension when the actuator was discharged after 30 s. Discharge was immediate and the subsequent slow contraction was solely due to viscoelasticity.

Ch16-I047488.indd 167 12/10/2007 8:32:03 PM

168 Chapter 16

References

[1] Pelrine , R. E. , Kornbluh , R. D. and Joseph , J. P. ( 1998 ). Electrostriction of polymer dielectrics with compliant

electrodes as a means of actuation . Sens. Act. A Phys. , 64 , 77 .

[2] Trujillo , R. , Mou , J. , Phelan , P. E. and Chau , D. S. ( 2004 ). Investigation of electrostrictive polymers as actu-

ators for mesoscale devices . Int. J. Adv. Manufact. Technol. , 23 , 176 .

[3] Pelrine , R. , Kornbluh , R. , Joseph , J. , Heydt , R. , Pei , Q. and Chiba , S. ( 2000 ). High-field deformation of elasto-

meric dielectrics for actuators . Mater. Sci. Eng. C , 11 , 89 .

[4] Carpi , F. , Chiarelli , P. , Mazzoldi , A. and De Rossi , D. ( 2003 ). Electromechanical characterisation of dielec-

tric elastomer planar actuators: comparative evaluation of different electrode materials and different counter-

loads . Sens. Act. A Phys. , 107 , 85 .

[5] Kofod, G. (2001). Dielectric elastomer actuators. Thesis, Risø National Laboratory, http://www.risoe.dk/

rispubl/POL/polpdf/ris-r-1286.pdf .

[6] Kofod , G. and Sommer-Larsen , P. ( 2005 ). Silicone dielectric elastomer actuators: finite-elasticity model of

actuation . Sens. Act. A Phys. , 122 , 273 .

[7] Hackl , C. M. , Tang , H. Y. , Lorenz , R. D. , Turng , L. S. and Schroder , D. ( 2005 ). A multidomain model of pla-

nar electro-active polymer actuators . IEEE Trans. Ind. Appl. , 41 , 1142 .

[8] Landau , L. D. , Lifshitz , E. M. and Pitaevskii , L. P. ( 1984 ). Electrodynamics of Continuous Media Landau and Lifshitz Course of Theoretical Physics , Vol. 8 . Butterworth-Heinemann , Oxford .

[9] Shkel , Y. M. and Klingenberg , D. J. ( 1998 ). Electrostriction of polarizable materials: comparison of models

with experimental data . J. Appl. Phys. , 83 , 7834 .

[10] Macosko , C. W. ( 1994 ). Rheology: principles, measurements, and applications . VCH Publishers, Inc ,

New York .

[11] Ogden , R. W. ( 1972 ). Large deformation isotropic elasticity – on the correlation of theory and experiment for

incompressible rubberlike solids . Proc. Roy. Soc. Lond. A , 326 , 565 .

[12] Kofod, G. (2006). High strain materials for electro-elastomer actuators. Proceeding of Actuator 2006 ,

Ed. Borgmann, H., Bremen, p. 885.

[13] Ma , W. and Cross , L. E. ( 2004 ). An experimental investigation of electromechanical response in a dielectric

acrylic elastomer . Appl. Phys. A Mater. , 78 , 1201 .

[14] Tanaka, T., Sato, M. and Kozako, M. (2004). High field Maxwell stress-strain characteristics of conventional

polymers as actuators. 2004 Annual Report Conference on Electrical Insulation and Dielectric Phenomena, CEIDP ’ 04 , 17 October, Boulder, CO.

[15] Bird , R. B. , Armstrong , R. C. and Hassageru , O. ( 1987 ). Dynamics of Polymeric Liquids, Vol. 2: Kinetic Theory . Wiley , New York .

[16] Sommer-Larsen , P. , Kofod , G. , Shridhar , M. H. , Benslimane , M. and Gravesen , P. ( 2002 ). Performance of

dielectric elastomer actuators and materials . Proc. SPIE Int. Soc. Opt. Eng. , 4695 , 158 .

[17] Mockensturm , E. M. and Goulbourne , N. ( 2006 ). Dynamic response of dielectric elastomers . Int. J. Non-Linear Mech. , 41 , 388 .

[18] Yang , E. , Frecker , M. and Mockensturm , E. ( 2005 ). Viscoelastic model of dielectric elastomer membranes .

Proc. SPIE Int. Soc. Opt. Eng. , 5759 , 82 .

[19] Palakodeti , R. and Kessler , M. R. ( 2006 ). Influence of frequency and prestrain on the mechanical efficiency

of dielectric electroactive polymer actuators . Mater. Lett. , 60 , 3437 .

[20] Yamwong , T. , Voice , A. M. and Davies , G. R. ( 2002 ). Electrostrictive response of an ideal polar rubber .

J. Appl. Phys. , 91 , 1472 .

[21] Zhenyi , M. , Scheinbeim , J. I. , Lee , J. W. and Newman , B. A. ( 1994 ). High field electrostrictive response of

polymers . J. Polym. Sci. B Polym. Phys. , 32 , 2721 .

[22] Bird , R. B. , Armstrong , R. C. and Hassager , O. ( 1987 ). Dynamics of Polymeric Liquids, Vol. 1: Fluid Dynamics . Wiley , New York .

Ch16-I047488.indd 168 12/10/2007 8:32:04 PM

MODELLING OF PRESTRAINED CIRCULAR ACTUATORS

Michael Wissler 1 ,2 and Edoardo Mazza 2 ,3

1 EMPA, Swiss Federal Laboratories for Materials Testing and Research, Laboratory for Materials and Engineering, Dübendorf, Switzerland

2 ETH, Swiss Federal Institute of Technology, Department of Mechanical Engineering, Zürich, Switzerland

3 EMPA, Swiss Federal Laboratories for Materials Testing and Research, Laboratory of Mechanics for Modelling and Simulation, Dübendorf, Switzerland

Abstract

This chapter reports on modelling and experimental characterization of a dielectric elastomer (DE) used as base

material for electroactive polymer (EAP) actuators. The mechanical behaviour of the acrylic elastomer VHB 4910

is characterized using large strain experiments (uniaxial and equibiaxial deformation) under force and displacement

controlled loading conditions. Next to tensile and relaxation tests, experiments were conducted also using so-called

circular actuators. Over 40 actuators were produced (with different in-plane prestrain levels) and activated with

voltages between 2000 and 3500 V. The experimental data are useful for determining constitutive model param-

eters as well as for validating models and simulation procedures for electromechanical coupling in EAP actuators.

A novel approach is proposed for finite element analysis of DE actuator, which has been used in the present work for

the evaluation of the experimental observations from circular actuators. Material parameters of a visco-hyperelastic

model have been determined from a subset of the experimental data and the predictive capabilities of the model

evaluated through comparisons with the remaining data. The prediction of the circular actuator behaviour was satis-

factory so that the proposed models might be useful for actuator design and optimization purposes.

Keywords : Actuator, dielectric elastomer, electroactive polymer, modelling, simulation.

17.1 INTRODUCTION

Modelling and simulation are key challenges in the development of the dielectric elastomer (DE) tech-nology for the design and optimization of actuators. Large strains, time dependency and the electrome-chanical coupling have to be included into the model formulation. In the last year, several papers have focused on the modelling of DE actuators [1–7] . In most cases, functioning of DE actuators is predicted by using uniaxial tensile test data for determining the material parameters for an actuator model. In-plane prestraining and out-of-plane electrostatical activation induce a three-axial stress and deformation state in DE actuators. Under such circumstances, hyperelastic–viscoelastic models derived from uniaxial tests are often inadequate for predicting the mechanical response: large strain biaxial and three-axial experiments have to be performed in order to determine the strain energy function that characterizes the non-dissipative component of the mechanical behaviour.

In the present work, a biaxially prestrained circular actuator is proposed as model system for the char-acterization of the electromechanical behaviour of a DE. A quasilinear viscoelastic constitutive model is applied and the corresponding material parameters are determined from experimental data of circular actuators. The mechanical model includes large strains and time dependence. Electrostrictive effects are neglected [8] and the electromechanical coupling is given by the electromechanical pressure p [9] :

pV

z� � �0

2

2r (17.1)

Chapter 17

Ch17-I047488.indd 169 12/10/2007 8:32:36 PM

170 Chapter 17

where � 0 is the free-space permittivity (8.85 � 10 � 12 As/Vm), � r is the relative dielectric constant, V is the electrical voltage applied to the electrodes and z is the thickness of the polymer film. For the simu-lation of the actuator behaviour a finite element approach is used. The material parameters are evaluated by optimization procedures. The material model is further validated with uniaxial tensile and relaxation tests.

17.2 EXPERIMENTAL DATA

For the formulation and validation of models and simulations experimental data are required. Several exper-iments have been performed for the acrylic elastomer VHB 4910 (from 3M), uniaxial (tensile and relaxa-tion) tests and experiments with circular actuators. Testing was performed at room temperature (23°C).

17.2.1 Uniaxial displacement controlled experiments

Uniaxial tensile tests were performed with a Zwick (Z010) machine and relaxation tests with a hand-operated setup under displacement control conditions (see Fig. 17.1 for the control profile). For the ten-sile test the probe dimensions in the undeformed state were 1 mm thickness, 10 mm width and 150 mm length in axial direction. The strain was monitored with an elongation sensor (Zwick multisens) in the middle of the sample, over an undeformed gauge length of 50 mm. For the relaxation test the undeformed sample geometry was set to a ratio between length and width of 10:1, in order to ensure uniaxial stress conditions, with thickness of 1 mm. Several experiments ( Fig. 17.1 ) were carried out: (i) relaxation tests (Rel50, Rel200 and Rel500); (ii) tensile tests at fixed deformation rate (Ten500) and (iii) tensile tests with a deformation history comprising a loading ramp, hold time and unloading (Ten300). The nominal stress history (force divided by the initial cross-section) is presented in Fig. 17.8 .

17.2.2 Experiments with circular actuators

Multiaxial electromechanical experiments were performed using biaxially prestrained circular actuators (in a so-called circular strain test [10] ) at room temperature (23°C) (see Fig. 17.2 ). The actuators consist of a VHB 4910 membrane radially prestrained and fixed on a circular frame with radius R � 75 mm. A circular area (radius r 0 = 7.5 mm) at the centre of the membrane is coated with a mixture of graphite powder (TIMREX SP30, 11 g) and silicone oil (DC 200/100 cs, 10 ml) for the electrodes.

Radial prestraining was realized by a special device developed at the DE laboratory of EMPA for biaxial stretching of elastomeric films. With this machine the prestretch ratio � p (for the circular actuator: the deformed radial length divided by the undeformed radial length of the membrane) can be arbitrarily prescribed. Three families of actuators were realized with prestretch ratios � p = 3, 4 and 5. After radial stretching, the film was fixed uniformly along a circular frame. The circular area at the centre of the film was coated with the graphite/silicone electrode on the upper and lower side (electrode thickness: approxi-mately 40 � m). The electrodes were connected to a high voltage supplier through a thin metal wire.

The experiment consisted of one single activation cycle in which a constant voltage of 2, 2.5, 3 or 3.5 kV was applied for 900 s. The nominal radial strain s r = r 1 / r 0 – 1 of the coated area was measured

0 1000 2000 3000

0

100

200

300

400

500

Ten300

Ten500Rel500

Rel200

Rel50

Nom

inal

str

ain

(%)

Time (s)

Figure 17.1 Nominal strain control profile for the uniaxial tests.

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Modelling of Prestrained Circular Actuators 171

with a video-extensometer (Ovex ME-46) connected to a PC LabView system for data acquisition and analysis.

A total number of about 40 actuators were used for the present experimental work, with identical con-ditions of prestrain and voltage applied to 3 or 4 actuators, in order to evaluate the repeatability of the test results. The experimental data (average curves of 3 or 4 identical experiments) are presented in Fig. 17.7 .

17.3 MATERIAL MODELLING

17.3.1 General aspects

The demands on a constitutive model describing the mechanical response of the elastomer are chal-lenging. Non-linear three-dimensional constitutive models have to be formulated and material param-eters determined in order to describe the time-dependent mechanical response over a wide deformation range: uniaxial stretch, biaxial deformation (from a kinematical point of view, a circular DE actuator is akin to a biaxial test) at different prestrain and voltage levels.

These challenges correspond to two classical problems of material modelling: (i) the model must be capable to describe the large strain response in uniaxial as well as multiaxial loading conditions and (ii) the time-dependent component of the model must be capable to describe the deformation history in force controlled experiments as well as the stress history under displacement controlled loading conditions.

Further challenges are related to the electromechanical coupling in DE: (i) prediction of the mechan-ical loading as function of the applied voltage; (ii) influence of the electrodes on the electromechanical performance and (iii) simulation of the active behaviour by numerical methods (finite elements).

17.3.2 Constitutive models

The quasilinear viscoelastic model proposed by Fung [11] and applied already for DE modelling in [5] is used here. It comprises hyperelastic equations (for the large strain elastic response) and a viscoelastic dissipative component (describing the time dependence of the mechanical response). For the hyperelas-tic part the strain energy potential of Yeoh [12] is used. Incompressible material behaviour is assumed.

The Yeoh form describes the strain energy function W as

W C C C� � � � � � � � � � � �10 1

222

32

20 12

22

32 2

30 12

22

323 3 3( ) ( ) (� � � � � � � � � ))3

(17.2)

where C 10 , C 20 and C 30 are material parameters and the principal stretch ratios � i are the eigenvalues of the deformation gradient tensor. The time dependence of the mechanical response is described by assuming time-dependent coefficients in the strain energy functions. The corresponding time functions are defined through the relaxation function g ( t ):

g t gt

tkk

K

k

( ) exp� � � ��

1 11

∑⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

⎛

⎝⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟ (17.3)

Circular frame

Active zone (coated area)

Voltage off Voltage on

r0

R

r1

Passive zone

M

X

Figure 17.2 Arrangement of the circular actuator for electromechanical measurements (r0 = 7.5 mm and R = 75 mm).

Ch17-I047488.indd 171 12/10/2007 8:32:36 PM

172 Chapter 17

where g k and t k characterize the relaxation behaviour. Here K is chosen as 4. For a specific material the quasilinear viscoelastic model is appropriate when the relaxation function g ( t ) is independent of the applied strain. Uniaxial relaxation tests were used to confirm the validity of this assumption for VHB 4910 [5] . The stress–deformation behaviour for arbitrary loading histories is calculated through so-called hereditary integrals. Further details on the quasilinear viscoelastic model are described in [5] .

17.4 FINITE ELEMENT SIMULATION

17.4.1 Circular actuator

The software ABAQUS 6.5.1 [13] has been used for the calculations. The axisymmetric model consists of 4-node elements (CAX4H: 4-node bilinear axisymmetric quadrilateral, hybrid, constant pressure). Subsequent mesh refinement was introduced (with higher mesh density at the extremity of the active zone) in order to avoid artefacts due to discretization errors. The model considers a symmetry plane in the horizontal direction ( Fig. 17.3 ). The axis of rotational symmetry is perpendicular to the membrane plane and passes through the centre of the coated area (see Fig. 17.3 ).

The electromechanical pressure p acts on the active zone and depends on the current membrane thickness and the activation voltage, according to Eq. (17.1).

In [5] a finite element calculation of the circular actuator behaviour was proposed in which the meas-ured radial displacement of the active zone is imposed as kinematic boundary condition (by prescribing the membrane thickness variation); in those simulations the corresponding ‘ required ’ activation volt-age represent the result of the calculation, to be compared with the experimental activation voltage. An alternative approach is described in which the activation voltage is the input and the time history of the radial strain the output of the calculation. Two procedures were implemented to this end:

(a) The straightforward approach consists of applying the electromechanical pressure p as a ‘ surface pres-sure ’ . Due to thickness reduction during the activation process, the amplitude of the pressure (for a given activation voltage) changes according to Eq. (17.1). The corresponding evolution of the ampli-tude of p is defined by a Fortran code (in a so-called user subroutine) which calculates the current pressure as a function of the current thickness z and the activation voltage V (which is constant for each experiment). The main disadvantage of this approach is that a large displacement analysis with kinetic (force) boundary conditions requires considerably larger number of iterations (and in certain cases does not converge) as compared with a calculation with kinematic (displacement) boundary conditions.

(b) This approach aims at realizing the same loading history by applying kinematic boundary conditions: the vertical displacement u v of the nodes at the upper border of the active zone is prescribed in order to achieve (at the upper face of the coated zone) a stress component in vertical direction equal to the current value of p (depending on the activation voltage and the current membrane thickness). The vertical displacement u v is controlled using a Fortran code (embedded in a user subroutine): the velocity change � v for the current calculation increment is defined as

�� ���

�0 2.

( )

V V

V Vpres calc

pres calcabs

(17.4)

Rotation axisPlane of vertical symmetry

pel Nodes constrained in radial direction

Figure 17.3 Finite element model of a circular DE actuator.

Ch17-I047488.indd 172 12/10/2007 8:32:36 PM

Modelling of Prestrained Circular Actuators 173

where v is the velocity in the previous increment, V pres is the prescribed activation voltage (e.g. 2 kV) and V calc is the calculated activation voltage of the previous increment, based on the values of vertical stress and thickness according to Eq. (17.1). In this way, the vertical displacement u v is continuously adjusted in order to minimize the discrepancy between the prescribed activation volt-age and the current voltage level.

Procedure (b) provides considerable advantages in terms of calculation times and convergence. However, this control procedure leads to an unstable behaviour when dealing with the sudden (stepwise) change of the activation voltage at the beginning of the test: for this reason procedure (a) was applied in the initial phase (20 s) and procedure (b) for the remaining duration of the active phase (880 s).

In Fig. 17.4 , an example is shown of the performance of the proposed procedure (Yeoh model, � p = 4). The applied voltage is compared with the constant prescribed activation voltage during the active phase. The discrepancy is larger for higher voltage level, but overall the agreement is satisfactory.

The simulation of one experiment consists of four steps: (i) radial prestrain; (ii) hold time of 1 h (with stress relaxation, corresponding to the experiments); (iii) application of the activation voltage step according to procedure (a) and (iv) control of the constant voltage level according to procedure (b).

17.4.2 Optimization procedure

The material parameters for the quasilinear visco-hyperelastic behaviour are determined using an opti-mization procedure (described schematically in Fig. 17.5 ) which is programmed to run automatically in Matlab [14] . Starting with initial material parameters as a vector X 0 Matlab writes an ABAQUS input file with these material parameters. The components of X 0 are the material parameters of the strain energy function ( C ij for Yeoh) and the relaxation function parameters ( t k and g k ). Matlab calls ABAQUS to run the simulation with the material parameters X 0 . When the simulation is completed the ABAQUS results (calculated strain history) are extracted and compared with the experimental strain history. Next, the error function f (Eq. (17.5)) is calculated:

f X f s si i( ) ( ( ) )� � �2 2

c eX∑∑ (17.5)

f depends on the material parameters (vector X ) and is defined as the sum of the squares of the dif-ferences f i between the calculated strains s c and the experimental strains s e . The optimization func-tion fminsearch (in Matlab) is based on the Nelder–Mead simplex algorithm and changes the material parameters (vector X ) in order to find a minimum of f . The whole procedure is repeated until the mini-mum of f is found.

The results of the combined optimization for the circular actuator tests at 2 kV, with � p = 3, 4 and 5 are given in Fig. 17.6 .

0 200 400 600 800 10000

1000

2000

3000

4000

Vol

tage

(V

)

Time (s)

Figure 17.4 Comparison of realized (symbols) and experimentally prescribed (horizontal line) activation voltages for the finite element calculation of the circular actuator (example with �p = 4).

Ch17-I047488.indd 173 12/10/2007 8:32:36 PM

174 Chapter 17

The material parameters obtained through the optimization procedure are reported in Table 17.1 . For the dielectric constant � r a value of 3.2 has been assumed [15] .

17.4.3 Uniaxial behaviour

The model used for simulation (in ABAQUS) of the tensile and relaxation tests consists of triangular plane stress elements. The time history of uniaxial displacement corresponded to the elongation control profile of Fig. 17.1 . True and nominal stresses were determined as a function of time for the material parameters reported in Table 17.1 and compared with the experimental results.

17.5 EXPERIMENTAL DATA VERSUS SIMULATION

The results for the circular actuators with prestrains 3, 4 and 5 are presented in Fig. 17.7 . Experimental data versus simulation for the uniaxial behaviour are reported in Fig. 17.8 . The model shows a reasonable agreement with respect to the actuator behaviour and a good agreement with respect to the uniaxial behaviour. The proposed quasilinear visco-hyperelastic model is able to describe the three-dimensional behaviour of the elastomer over a large range of deformation and loading conditions.

X0

f � fminsearch(X)

Run ABAQUS

Extract data

Interpolation

f � Σfi2

Minimum of f ?No Yes

X

fi

sc

seStr

ain

(%)

Time (s)

Figure 17.5 Optimization procedure for evaluation of the material parameters.

0 200 400 600 800 1000

0

5

10

Prestrain λp � 3 Prestrain λp � 4 Prestrain λp � 5

Rad

ial s

trai

n (%

)

Time (s)

Figure 17.6 Optimization of the mechanical model for 2 kV and �p = 3, 4 and 5. The filled symbols represent the experimental data and the open symbols the corresponding simulation.

Ch17-I047488.indd 174 12/10/2007 8:32:37 PM

Modelling of Prestrained Circular Actuators 175

17.6 CONCLUSION

The mechanical behaviour of the acrylic elastomer VHB 4910 used in DE actuators has been charac-terized. Next to force and displacement controlled uniaxial data, experimental observations from tests with 40 circular actuators are reported. The activation behaviour for different prestrain levels and at different activation voltages is presented.

The numerical procedure adopted for simulating the electromechanical behaviour of the circular actu-ator allowed determining material model parameters from the experimental data through an optimization algorithm. The novel approach proposed for electromechanical coupling might be generally useful for finite element simulations of DE actuators.

The quasilinear visco-hyperelastic model has been used to predict the actuator behaviour and further validated with uniaxial tensile and relaxation test data over a wide prestretch range (up to � = 6). Model parameters were determined from a subset of circular actuator tests and then applied for simulating the whole range of experiments performed. Since the circular actuator behaviour as well as the uniaxial elastomer response were well predicted, the proposed model is expected to provide useful results for actuator design and optimization purposes.

Table 17.1 Material parameters used for the present calculations.

C10 (MPa) 0.0538 g1 (−) 0.477 t1 (s) 0.153C20 (MPa) �4.857e–04 g2 (–) 0.205 t2 (s) 0.464C30 (MPa) 3.809e–06 g3 (–) 0.07265 t3 (s) 32.02

g4 (–) 0.0493 t4 (s) 215.9

0

10

5

20

15

25 2000 V 2500 V 3000 V 3500 V

Rad

ial s

trai

n (%

)

0 200 400 600 800 1000

0

20

40

60

80 2000 V 2500 V 3000 V 3500 V

Rad

ial s

trai

n (%

)

Time (s)

0 200 400 600 800 1000

Time (s)

0 200 400 600 800 1000Time (s)

0

10

20

30

40

2000 V 2500 V 3000 V

Rad

ial s

trai

n (%

)

(c)

(a) (b)

Figure 17.7 Comparison between experimental data and simulation for the actuator behaviour for prestrain (a) �p = 3, (b) �p = 4 and (c) �p = 5. The filled symbols represent the experimental data and the open symbols the corresponding simulation.

Ch17-I047488.indd 175 12/10/2007 8:32:37 PM

ACKNOWLEDGEMENT

Financial support from the Swiss National Science Foundation (Project 200021-107661/1) is gratefully acknowledged.

References

[1] Carpi , F. and De Rossi , D. ( 2004 ). Dielectric elastomer cylindrical actuators: electromechanical mod-elling and experimental evaluation. Mat. Sci. Eng. C , 24 , 555 – 562 .

[2] Goulbourne , N. , Mockensturm , E. and Frecker , M. ( 2005 ). A nonlinear model for dielectric elastomer membranes. J. Appl. Mech. , Vol. 72 , 899 – 906 .

[3] Kofod , G. and Sommer-Larsen , P. ( 2005 ). Silicone dielectric elastomer actuators: Finite-elasticity model of actuation. Sens. Actuators A , 122 , 273 – 283 .

[4] Plante, J. S. (2006). Dielectric elastomer actuators for binary robotics and mechatronics. PhD Thesis,

Massachusetts Institute of Technology, Cambridge, MA.

[5] Wissler , M. and Mazza , E. ( 2005). Modeling and simulation of dielectric elastomer actuators. Smart Materials Structures , 14 , 1396 – 1402 .

[6] Wissler , M. and Mazza , E. ( 2005 ) . Modeling of a prestrained circular actuator made of dielectric elastomers. Sens. Actuators A , 120 , 184 – 192 .

[7] Wissler, M. and Mazza, E. (2007). Mechanical behavior of an acrylic elastomer used in dielectric elastomer actuators. Sens. Actuators A , vol. 134(2), 494–504.

[8] Kofod , G. , Sommer-Larsen , P. , Kronbluh, R., Pelrine, R. ( 2003 ). Actuation response of polyacrylate dielec-

tric elastomers. J. Intel. Mat. Syst. Str. , 14 , 787 – 793 .

[9] Pelrine , R. , Kornbluh , R., Joseph , J. ( 1998 ). Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation. Sens. Actuators A , 64 , 77 – 85 .

[10] Pelrine , R., Kornbluh , R., pei Q. B., Joseph J. ( 2000 ). High-speed electrically actuated elastomers with strain greater than 100%, Science , 287 , 836 – 839 .

[11] Fung , Y. C. ( 1993 ). Biomechanics: Mechanical Properties of Living Tissues , 2nd edn . Springer-Verlag ,

New York , p. 277 .

[12] Yeoh , O. H. ( 1990 ). Characterization of elastic properties of carbon-black-filled rubber vulcani-zates, Rubber Chem. Technol. , vol. 63 , 792 – 805 .

[13] ABAQUS/Standard Manual (2003). Version 6.4.1, Hibbitt, Karlsson & Sorensen, Inc.

[14] Matlab (2004). Version 7.0, The MathWorks, Inc.

[15] Wissler, M. and Mazza, E. (2007). Electromechanical coupling in dielectric elastomer actuators. Sens. Actuators A , vol. 138, 384–393.

0 1000 2000 3000

0.0

0.1

0.2 Rel50 Rel200 Rel500 Ten300 Ten500

Nom

inal

str

ess

(MP

a)

Time (s)

Figure 17.8 Comparison between experimental data and simulation for the uniaxial behaviour. The filled symbols represent the experimental data and the open symbols the corresponding simulation.

176 Chapter 17

Ch17-I047488.indd 176 12/10/2007 8:32:37 PM

MODELLING DIELECTRIC ELASTOMER MEMBRANES

Nakhiah C. Goulbourne 1 , Eric M. Mockensturm 2 and Mary I. Frecker 2

1 Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, USA 2 Department of Mechanical Engineering, Pennsylvania State University, PA, USA

Abstract

Dielectric elastomers are of particular interest for many biomedical applications due to their fast actuation speeds

and very large strains, on the order of hundreds of percent strain. For example, the out-of-plane deformation response

of an edge-clamped dielectric elastomer membrane has been investigated as a potential replacement for the passive

diaphragm in a left ventricular assist device. Using a dielectric elastomer membrane eliminates the need for a sepa-

rate actuation source in the prosthetic pump, thus moving towards a simpler, lighter, and more compact device that

mimics the behaviour of the natural heart. The material and geometrical nonlinearities of dielectric elastomer actua-

tors make them more difficult to model than traditional linear actuators. In this chapter, a large deformation electro-

elastic model of dielectric elastomer membrane actuators is developed by combining Maxwell–Faraday electrostatics

and nonlinear elasticity theory. The dielectric is modelled as a continuum placed in an electric field subject to exter-

nal surface tractions. Taking a continuum mechanics approach, the stress in the dielectric medium is determined by

a superposition of the mechanical stress due to the local elastic state and the Maxwell stress due to the electrostatic

field. Based on the proposed expression for the electro-elastic stress, a large deformation model is derived using

membrane theory. Since the thickness of the membrane is much smaller than the radius, and given that bending

effects are negligible, it is reasonable to assume that membrane theory is applicable to active membrane inflation.

Using Green ’ s membrane theory as a starting point, various researchers have obtained solutions for the quasi-static

inflation of a planar elastic membrane (passive), the dynamic inflation of a planar membrane, and the inflation of

viscoelastic membranes. Here, solutions for the inflation of edge-clamped electro-elastic membranes are presented.

Specifically, this model has been derived by modifying Adkins and Rivlin ’ s theory of inflatable elastic membranes to

account for material stiffening at high strains (using an Ogden model) and electrical effects. The quasi-static inflation

of dielectric elastomer actuators by a uniform mechanical pressure and an applied voltage are presented. The model

is used to solve for the resultant membrane behaviour, subject to changes in various system parameters such as pre-

stretch, external pressure, applied voltage, and the percentage electroded area of the dielectric. A method for calcu-

lating the blocked pressure specific to inflatable active membranes is also introduced and for illustrative purposes a

hypothetical work-loop simulating cardiac diaphragm conditions is constructed and evaluated. This chapter outlines

a procedure for predicting the deformation response of axisymmetric dielectric elastomer membranes that can be tai-

lored accordingly for different electro-mechanical loadings and boundary conditions.

Keywords : Dielectric elastomer, large deformations, Maxwell stress, membrane.

18.1 INTRODUCTION

Large electro-elastic deformations of incompressible materials can be treated using a continuum mechan-ics approach. The theory of continuum mechanics presents a unified and consistent approach to determin-ing the overall macroscopic behaviour of continuous media subject to various external influences. This specialized treatment of deformable media employs three fundamental relations to determine a system ’ s response: (i) constitutive equations, (ii) kinematic equations, and (iii) equilibrium equations. Continuum mechanics is arguably one of the most well-developed theories; one of its most interesting applica-tions is the theory of elasticity. The theory of large elastic deformations was developed within a contin-uum mechanics framework; it is used to describe complex stress and strain states of deformable bodies.

Chapter 18

Ch18-I047488.indd 177Ch18-I047488.indd 177 12/5/2007 2:35:16 PM12/5/2007 2:35:16 PM

178 Chapter 18

Typically, dielectric elastomers configured for actuation undergo very large deformations due to combined electro-mechanical loadings. This chapter presents a theoretical approach to modelling the nonlinear elec-tro-mechanical response of dielectric elastomer membranes. Modelling the electro-elastomer as a mem-brane permits the use and subsequent modification of Green and Adkins ’ elastic membrane theory [1] . Specifically, special treatment of Rivlin and Adkins ’ continuum theory of elastic membranes accounts for the electro-mechanical effects occurring in dielectric elastomer actuators [2] . For a linear elastic solid sub-jected to a uniformly distributed load, a presumably uniform stress distribution in the solid is approximated using a Hookean relationship. For an elastic solid undergoing nonlinear large deformation, there comes a point when linear elastic assumptions break down and a special treatment is needed in order to determine the spatial distribution of stress and strain in the solid. Of course, the limit of a linear theory depends on the operating conditions of the material and hence is application dependent.

18.2 ELECTRICAL EFFECTS IN CONTINUOUS DIELECTRIC MEDIA

Consider an isotropic homogeneous dielectric medium subject to an electric field by virtue of the com-pliant dissimilarly charged surface electrodes separated by the elastomer thickness. The application of a voltage or electric field to a dielectric elastomer membrane causes a thickness reduction in the direction of the applied field and an in-plane accommodation or relaxation which causes an areal expansion if unconstrained. The total stress in the membrane has a quadratic dependence on the electric field; linear effects are ruled out by the isotropic nature of the solid. Physically speaking, there are two effects in dielectric media that exhibit a quadratic dependence on the electric field: (i) electrostriction and (ii) elec-trostatic effect (also referred to as the Maxwell stress effect). Dielectric solids that demonstrate macro-scopic electrostrictive effects are characterized by a significant spontaneous polarization. In Fig. 18.1 , an electroded dielectric element supporting a constant load P initially has a resting or spontaneous polariza-tion with a specific orientation illustrated by the horizontal arrow. The dielectric becomes polarized in response to an applied electric field; the dipoles will align themselves with the direction of the electric field. Locally, the centres of the dipole charges separate and move towards the oppositely charged elec-trode surfaces. This motion renders a macroscopically observable deformation commonly known as elec-trostriction. This effect occurs in both polarized and nonpolarized dielectrics but is oftentimes on such small scales for nonpolarized materials (10 –11 m) that it is ignored. Large strain electrostrictive effects have been observed (on the order of 5%) in PVDF TrFE copolymers [3] .

Figure 18.2 illustrates the electrostatic Maxwell stress effect, which is the major response mechanism in dielectric elastomer actuators. In this case, a nonpolarized dielectric medium, rubber, has no resting polar-ization associated with its unstressed state. When an electric field is applied the dielectric is in a state of electrical stress known as the Maxwell stress. Since the dielectric is mechanically soft the electrical forces of attraction between the dissimilar electrodes cause a thickness reduction and an accompanying areal expansion of the dielectric medium. The Maxwell stress is the electrical analogy of the mechanical stress

P P

0 V

V

Figure 18.1 Illustration of the electrostrictive effect in dielectric solids.

0 VV

Figure 18.2 Illustration of the Maxwell stress effect in dielectric solids.

Ch18-I047488.indd 178Ch18-I047488.indd 178 12/5/2007 2:35:16 PM12/5/2007 2:35:16 PM

Modelling Dielectric Elastomer Membranes 179

in a continuous solid. The application of a mechanical load to the solid ’ s surface causes the generation of a three-dimensional internal state of mechanical stress. Similarly, the application of an electrical surface traction induces a state of electrical stress known as the Maxwell stress.

Figure 18.3 shows experimental results for the uniaxial force versus strain behaviour for an acrylic elastomer (dotted line), also shown are two material model fits (solid lines) to the experimental data. This plot can be used to visualize the change in the material ’ s deformation profile when an electric field is applied. The electric field causes a forward shift of the initial operating point along the force–strain curve as depicted by the arrow in Fig. 18.3 . In certain materials like electrorheological and magnetorheo-logical fluids the force–strain curve itself is shifted; this is not the case for dielectric elastomer actuators.

18.3 THEORY OF ELECTRO-ELASTIC MEMBRANES

A body subject to a system of external influences will tend to be put in motion. This motion may be a rigid body motion or the body may deform. Consider a conservative system (no losses) where inertial effects and body forces are also neglected (no time dependence). A material point at P 0 of the undeformed body can be located by the Cartesian coordinates x i or x i referred to a rectangular Cartesian system. Under a system of forces or external influences, say, the same material point at P 0 is located by the coordinates y i or y i in the deformed state referred to the same rectangular system where Greek indi-ces take on the values 1,2 and Latin indices take on the values 1,2,3. The same material point can be located by a more convenient set of general curvilinear coordinates � i , which deform with the body. � i and x i are so-called convected or material coordinates; y i are spatial coordinates. The motion can then be expressed by the usual transformations

x x y y y x xy y x x x y y

i i i i

i i i i� �

� �

( , , ) ( , , )

( , , ) ( ,

1 2 3 1 2 3

1 2 3 1

or

or

� � �� �� �2 3, )

(18.1)

where Eq. (18.1) denotes single-valued mappings of the material points. In the � i coordinate system we can define the position vector R of the point at x i , and the position vector r of the point at y i . Therefore, the associated basis vectors and metric tensors are given by

gr

g g

GR

G G

i i i j ijir

rj ji

ij

i i i j iji

g g g g g

G G

� � � �

� �

���

�

���

, , ,

, ,

i

i

| |

rrrj j

iijG G G� �� , | |

(18.2)

where lower case variables refer to the deformed state and upper case variables refer to the undeformed state.

2 4 6 8

0.5

1

1.5

2

2.5

Strain (in/in)

Mooney–Rivlin

Ogden

For

ce (

lbf)

Figure 18.3 Fit of experimental simple tension data for a sample of 3M VHB polyacrylate film.

Ch18-I047488.indd 179Ch18-I047488.indd 179 12/5/2007 2:35:17 PM12/5/2007 2:35:17 PM

180 Chapter 18

In continuum mechanics, hyperelastic continua are described using the Cauchy method in which the stress is postulated to be a function of the deformation gradients only. If the system is conservative, there is a constitutive relationship between the stress and the displacement gradients that can be derived from a strain energy potential. Comparably, for deformable electro-elastics (elastic dielectrics), the approach that similarly postulates the form of the electro-elastic stress is called the ‘ analogous ’ Cauchy method (see [4] ). Since both mechanical and electrical fields are present in hyperelastic dielectrics, we assume that the state of stress at a point in the deformed medium is determined by (1) the local elastic state of the medium and (2) the electrostatic field [4] , where the electrical effects of the system are described by using Maxwell–Faraday electrostatics [4] . The well-known electrostatic Maxwell stress tensor T M for a homogeneous isotropic dielectric [5] is given by

T E E

E EIM � �

��

��

2 (18.3)

where I is the identity tensor and electrostrictive effects have been neglected. This expression is derived from the force of attraction or repulsion between charges (or conductive surfaces). A detailed treatment is given by Landau and Lifshitz, and Schwinger et al. [6–8] .

For an elastic dielectric, the total stress in the medium or the Cauchy stress tensor T is written as the sum of the local elastic stress tensor and the Maxwell stress tensor [5] we obtain

T T T� �E M (18.4)

where T E is the local elastic stress tensor given as a function of the displacement gradients. For the elastic portion of the constitutive relation, the dielectric elastomer actuator is modelled as a hyperelas-tic solid, that is to say, the mechanical stress is reversible – the natural state is recovered and there is zero dissipation when the external loads are released. Further, when the electric field is zero, the full elastic relations are recovered. In piezoelectric and electrostrictive materials, the stress T E is deriv-able from a single internal energy function � that depends on electrical variables such as the polariza-tion P or the electric displacement D in addition to the deformation gradients F [9] . For a hyperelastic isotropic dielectric that is electrically linear, the internal energy is ultimately reduced to a function of six independent scalar invariants ( I � ), where I � is not a unique combination of strain invariants and electrical invariants [9] . In the case of dielectric elastomer actuators there is no evidence of direct cou-pling between the polarization and the mechanical stress, where direct coupling implies that a change in the polarization yields a change in the deformation and vice versa. The internal energy is then a state function of only three scalar strain invariants; two independent scalar invariants if the material is incompressible. Consider a dielectric elastomer that is homogeneous, isotropic, incompressible, and hyperelastic, for such a system the elastic stress tensor is derived from a purely mechanical strain energy function � ( I 1 , I 2 ) as

T

FF T� �

��

��m

0

1 2( , )I I

∂ M (18.5)

where � 0 is the initial mass density and � m is the current mass density. The total stress tensor for an iso-tropic electrically linear elastic dielectric has both mechanical and electrical components.

18.4 DIELECTRIC ELASTOMER ACTUATORS: A DIAPHRAGM CONFIGURATION

In this section, an electro-elastic membrane model describing the deformation response of an axisym-metric dielectric elastomer actuator is derived [8] . We presume that the electro-elastomer can be modelled as an electro-elastic membrane. If this is the case, then Green and Adkins elastic membrane theory can be cast into an electro-elastic formulation for large deformation actuation materials [1, 10] . The actuator has a thickness to radius ratio that permits the use of Green and Adkins membrane theory to model the system response; that is to say, bending effects are negligible. Consider an incompress-ible insulating polymer subject to both mechanical forces in the form of an external pressure, and an

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Modelling Dielectric Elastomer Membranes 181

external electric field created by two parallel compliant conductors that exert an equal and opposite traction on the elastomer ’ s major surfaces. The insulating polymer is an elastomeric material, such as polyacrylate film or silicone rubber, and the soft conductors typically are made from carbon or silver grease.

Combining the theory of electrostatics and the theory of elasticity yields an electro-elastic theory. To demonstrate this approach, we will derive a model for the inflation of an axisymmetric diaphragm or membrane, clamped along the outer edge. Inflation and deflation of the membrane is achieved by increasing and decreasing the mechanical pressure thus creating a pumping motion. This problem was studied in detail by Adkins and Rivlin for purely elastic membranes. Here we consider the voltage con-trolled out-of-plane deflections of electro-elastic membranes. The treatment of large elastic deformations of inflatable elastic membranes is modified to account for material stiffening at high strains, prestretch, and electrical effects [2] . It is significantly less difficult to describe curved geometries using curvilinear coordinates rather than attempting to orchestrate a Cartesian network. In particular, it is most convenient to establish two curvilinear coordinates y on the middle surface and y 3 the perpendicular distance to the bounding surfaces of the shell.

In a membrane theory, all quantities are referred to the deformed middle surface M. Points on the middle surface of the deformed shell M are located by the position vector s . We denote the general curvilinear coordinates on this surface by � 1 , � 2 . The unit normal vector to the middle surface M is a 3 . Noting that � 3 = 0 is the surface M, the major bounding surfaces are given by � 3 � � h ( � 1 , � 2 )/2, where the coordinate � 3 is perpendicular to the surface M at all times, where h is the thickness of the shell. The augmented Cauchy equilibrium equations of a continuous medium for vanishing inertial forces and body forces are

Tij

i � 0 (18.6)

where T ij is the electro-elastic Cauchy stress (replacing the elastic Cauchy stress). In tensor form, the stress is referred to curvilinear material coordinates and a double line denotes covariant differentiation with respect to the curvilinear coordinates, where the metric tensors defined in the deformed medium are G ij , G ij . The Cauchy moment equations are satisfied by requiring the symmetry of the stress tensor. In membrane theory, the three-dimensional equilibrium equations can be expressed with respect to a set of orthogonal curvilinear coordinates ( � 1 , � 2 ) on the middle surface of a deformed surface [10] . A cylindrical coordinate system is employed such that ( � , � ) � ( � 1 , � 2 ). In the deformed state, the major surfaces of the membrane are given by � 3 � � 3 h/ 2, where 3 is the thickness extension ratio and h is the initial membrane thickness. The resultant equilibrium equations for an axisymmetric membrane

n�

� 0 (18.7)

n b p�� � �m 0 (18.8)

given the relation

n T

h

h� �

��

� d 3

2

2

3

3

/

/

∫ (18.9)

where n � are the stress resultants, 3 h is the deformed membrane thickness, b � is the curvature tensor, a i are basis vectors ( i � 1, 2, 3) referred to curvilinear coordinates, � � is the symmetrical stress tensor, and p m � p 1 – p 2 is the mechanical pressure differential across the membrane. Note that the electrical traction is equal and opposite on both sides of the elastomer and hence does not appear in p m .

For a dielectric elastomer actuator diaphragm subject to an external pressure differential p m , Eqs. (18.7) and (18.8) are reduced to

d

d

( )TT1

2

��

� (18.10)

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182 Chapter 18

1 1 2 2T T p� � (18.11)

where T 1 and T 2 are the stress resultants in the longitudinal and latitudinal directions respectively, defined by

n T n T n nb b b b

111

2 222

12 21

11

1 22

2 12 21

0

0

� � � �

� � � � � �

, ( ) ,

, ,

�

(18.12)

and 1,2 are the corresponding curvatures. Note that in Eqs. (18.10) and (18.11) the stress is defined in terms of (1) the principal extension ratios, (2) the elastic strain energy function, (3) the electric field, and (4) the material ’ s dielectric constant.

18.5 CONSTITUTIVE EQUATIONS

The constitutive stress–strain-field relationship that describes dielectric elastomers has two components derived from (1) an elastic strain energy function (the mechanical stress) and (2) the Maxwell stress. As we have previously emphasized, it is sufficient that the elastic portion of the stress is determined from a purely elastic strain energy function; the electrical portion is given by the Maxwell stress tensor [5] . Various mate-rial models have been developed to describe rubber elastic materials. Two such elastic strain energy func-tions are: (1) the Mooney–Rivlin model [2] and (2) the Ogden model [11] . Of course, the validation for any chosen strain energy function lies in its ability to capture the material ’ s physical response. Fitting the material models to experimental force–displacement data yields the model constants ( Fig. 18.3 ).

Assuming that the electric field E 3 is uniform in the thickness direction (geometrically characterized by non-varying field lines between the electrodes) and recalling Eq. (18.3), the surviving components of the Maxwell stress tensor are

TM �

�

�

�

� �

� �

� �

r

r

r

02

32

02

32

02

32

20 0

02

0

0 02

V

hV

hV

h

( )

( )

( )

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

(18.13)

where V is the dimensional applied voltage, h is the dimensional initial membrane thickness, � 0 is the vac-uum permittivity, and � r is the relative dielectric constant. Given the zero shear conditions of membrane theory, the principal stresses are written using the following notation: T 11 � t 1 , T 22 � t 2 , T 33 � t 3 are employed for the principal stresses. Employing the Ogden elastic strain energy function � , yields

� �

( , )( )

1 21 2 1 2 3

�� � �

���

� �

nn

q q q

n

n n n

q∑ (18.14)

where q n are dimensionless constants, and � n is the dimensional Ogden material constant. The number of terms needed in the summation is determined from experiments. The corresponding expressions for the principal stresses using the Ogden material model are

t pV

hii i

i

� � ���� �

� �h r

1 1

210

3

2⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

⎛

⎝

⎜⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟( �� 1 2, ) (18.15)

t pV

h3 33 1

03

21 1

2� � �

��� �

� �h r

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

⎛

⎝

⎜⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟ (18.16)

where i � (1, 2, 3), p h is the hydrostatic pressure enforcing the incompressibility constraint. Note that the electrical stress is subtracted for i = (1, 2) and is added for i = 3. For a given strain energy function,

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Modelling Dielectric Elastomer Membranes 183

Eqs. (18.15) and (18.16) explicitly give the total stress for the dielectric elastomer in a uniform electric field E 3 .

To solve the passive membrane inflation problem, the surface tractions on the major surfaces are set equal to zero, even though there is a nonzero external inflating pressure. Similarly, to solve the electro-elastic membrane inflation problem, we set the surface tractions to zero. Since the conductors on either side of the elastomer produce equal and opposite tractions on the elastomer surfaces, their contribution to the pressure differential across the membrane is zero. The approximation is therefore sufficiently accurate for the membrane because the actual surface traction produced from the external mechanical pressure is negligible compared to the meridional and latitudinal stresses t 1 and t 2 . Thus in this formula-tion, the external mechanical pressure contribution to the surface traction is neglected in accordance with the Rivlin–Adkins assumption and t 3 = 0 . This assumption is used to eliminate the arbitrary hydro-static pressure p h from t 1 and t 2 . Integrating the stresses over the deformed thickness 3 h yields the principal resultant stress components T 1 and T 2

T

V h q qq

1

20 1

222 2

1 1 11 2 1

21 1

1 2

1

� �

� � � �� � �

r

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

22

21 2 1

2

2

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

⎛

⎝

⎜⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟

q

h � (18.17)

T

V h q qq

2

20 1

222 2

1 2 21 2 1

21 1

1 2

1

� �

� � � � �� � �

r

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

�

2

21 2 1

2

2

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

⎛

⎝

⎜⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟

q

h (18.18)

where is the nondimensional ratio � 2 / � 1 .

18.6 NUMERICAL RESULTS: A QUALITATIVE ANALYSIS

Inflation and activation of the membrane leads to a deformed profile as illustrated in Fig. 18.4 . The pro-files depicted in the figure are for different inflation pressures applied to the membrane. The prestretch, 0 , is 2.5. The undeformed and deformed configurations of the clamped diaphragm can be described as surfaces of revolution. In this case, the independent variable of the analysis is the arc length, s , of the undeformed membrane. Assuming an incompressible material, the longitudinal, latitudinal, and trans-verse stretch ratios are given by

�

�

1 2 31 2

1� � �

d

ds R, , (18.19)

0.5 1 1.5 2

Radius (cm)

0.25

0.5

0.75

1

1.25

1.5

Hei

ght (

cm)

Figure 18.4 Inflation profiles of a dielectric elastomer membrane.

Ch18-I047488.indd 183Ch18-I047488.indd 183 12/5/2007 2:35:20 PM12/5/2007 2:35:20 PM

184 Chapter 18

and the curvatures by

1

12

2

1 1� �

R R, (18.20)

where � is the meridian curve length in the deformed state, R is the radius of the undeformed mem-brane, and R 1 and R 2 are the meridional and latitudinal radii of curvature, respectively. The perpendicu-lar distance of material points, y , from the symmetry axis of the inflated actuated membrane is given by

y s

s� � � �1

2 2

0d∫ (18.21)

The equilibrium equations together with the constitutive stress relationships and geometrical descrip-tions of the membrane surface yield four first order differential equations for � , 1 , y , and � that describe the deformation of the active membrane completely. This is a nonlinear boundary value problem that can be solved using a numerical integration approach – analytical solutions are not possible in this case.

Consider a circular axisymmetric membrane made from 3M VHB acrylic tape that is first pre-stretched and clamped at its outer edge and then subject to a mechanical inflation pressure and a voltage induced squeeze pressure. The membrane is radially prestretched to improve its dielectric per-formance and endure higher electric fields [12, 13] . Presume a dielectric constant of 4.7 for 3M VHB [12] . The diaphragm has a radius of 2.22 cm and thickness of 0.5 mm. A two term Ogden model is used to describe the elastic behaviour of the dielectric elastomer. In this first order analysis, the Ogden mate-rial constants are determined from simple tension tests – this is sufficient to qualitatively predict the response. For a more quantitative analysis, the constants are best determined under multi-axial loading conditions. Figure 18.5 shows the mechanical pressure versus swept volume (P–Vol) curves for a range of prestrain values. The applied voltage is 2040 V, and the Ogden material constant � 1 � 54.88 kPa. Each curve is initially fairly linear becoming nonlinear as the volume increases. Note that the P–Vol results are a nonlinear function of the prestrain itself in that equal increments in prestrain do not cor-respond to equally spaced downward shifts of the curves. Within a prestrain range of 62.5% and 265%, we observe that the pressure required to obtain a certain volume decreases with increasing prestretch of the material. This implies that, for the range considered, material softening occurs with increasing pre-strain. These calculated trends are in accordance with experimental data obtained by Tews et al. [13] for inflated dielectric elastomers subject to an applied voltage.

Applying a voltage causes the membrane to decrease in thickness and increase in overall surface area. In other words, activating the membrane causes tangential material relaxation and, hence, larger

Figure 18.5 Pressure–volume curves for various prestrain values.

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 5 10 15 20

Volume (cc)

Pre

ssur

e (P

a)

35%

62.5%

150%265%

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Modelling Dielectric Elastomer Membranes 185

transverse deformation for a prescribed inflation pressure. The result is an increase in volume for increasing voltage at a given pressure. Figure 18.6 shows the P–Vol results for applied voltages ranging from 0 to 3060 V, where the prestretch 0 � 2.65 (300% prestrain). The P–Vol curves are nonlinear for each applied voltage. At V � 1020 V there is only a slight increase in membrane compliance from 0 V. There is a much larger change between 1020 and 2040 V, the largest compliance change being observed between 2040 and 3060 V.

As it may not be practical or possible to electrode the entire surface area in an actual device, the per-formance of partially electroded configurations is investigated. Starting with electroding a small circle at the centre of the membrane, the electroded circular area is increased until the entire elastomer surface is covered. For a prescribed external pressure of 1194 Pa ( 0 � 2.3) and a voltage of 2500 V, the effect of having a partially electroded surface is illustrated in Fig. 18.7 , where % A means per cent of the entire prestretched membrane area that is electroded. In this figure, the quantitative measure � Vol/Vol 0 is the difference ( � Vol) between the volume calculated at a given % A and 0% A (unelectroded) divided by the 0% volume (Vol 0 ). The volume variance is particularly significant between electroded areas of approxi-mately 25% A and 70% A. Again, there is very little variance in the volume calculated if more than 80% of the elastomer is electroded. This S-pattern curve is preserved for different applied voltages although specific numerical values vary. A similar curve could be constructed by using the pressure as the meas-ure of variance. Figure 18.7 is representative of the observation that there is a threshold percentage elec-troded area beyond which very little volume variance is observed. It is interesting to note that the same cutoff threshold is consistently observed for different prestretch values. This occurs because electroding near the pole as opposed to electroding from the outer circumference is better for obtaining higher stroke volumes. Therefore, it follows that reversing the direction in which the electroded area is increased, that is to say starting with a ring at the clamped edge and electroding towards the centre of the elastomer, does not give the same behaviour observed in Fig. 18.7 – it is exactly reversed.

Although dielectric elastomers are capable of large strains (displacements), a tradeoff arises since the force output for a given configuration is low in comparison to other smart materials. To obtain a measure of what these low forces mean for an active pumping membrane we can calculate the blocked pressure of the active membrane due solely to the applied voltage. This is reminiscent of the blocked force used to characterize other active materials like piezoelectric ceramics and electrostrictive polymers. Here, we define the blocked pressure as the change in the pressure differential across the membrane during actua-tion such that the volume remains constant. A hypothetical work-loop, constructed between a zero volt-age curve and an applied voltage curve, is used to obtain the blocked pressure ( P blocked ). For V � 0 we can choose a point, A, having the coordinates (Vol A , P A ). While holding the external pressure constant, an increase in voltage ( V � 3.3e–5) leads to an increase in the volume from Vol A to Vol B . To return to

Figure 18.6 Pressure–volume curves for various applied voltages.

0

200

400

600

800

1000

1200

1400

1600

0 2 4 6 8 10 12 14 16

Volume (cc)

Pre

ssur

e (P

a)

0 V

1020 V

2040 V

3060 V

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186 Chapter 18

the starting volume Vol A , the pressure will drop to P C . The difference P A – P C is the blocked pressure; the area of ABC is the work. The blocked pressure for various initial volumes and applied voltages can be calculated. This relationship is shown in Fig. 18.8 . It is observed that the blocked pressure increases with increasing initial volume (pressure) and increasing applied voltage. Accordingly, for a given geometry, to generate large activation pressures both the initial volume and the applied voltage should be large. The highest blocked pressure in Fig. 18.8 for a diaphragm with dimensions: 0 � 2.45 and R o � 2.22 cm is 0.3 kPa. Short of using a different material with higher force output, one way that this pressure could be increased for any given geometry would be to make multi-layer actuators.

The work done in a pump cycle by the active membrane can be predicted using the electro-elastic model. Figure 18.9 depicts a work-loop constructed from the P–Vol curves for 0 and 3000 V. For illus-trative purposes, it is assumed that there are two one-way inlet and outlet valves that monitor fluid flow into and out of an open-faced chamber sealed with a dielectric elastomer membrane. The inlet pressure is set at P in � 1110 Pa and the outlet pressure is P out � 1240 Pa. At the point A, the activated membrane is in an inflated configuration and at the end of volumetric filling, Vol max � 11 cc. The diaphragm

Figure 18.7 The % variance in volume versus the % electroded area of the membrane.

00

5

10

15

20

25

20 40 60

% Area electroded

% V

olum

e va

rianc

e

80 100++ +++++++++++++++++++

+++++++++++++++++++++++++++++++++

Figure 18.8 The blocked pressure for various initial volumes and applied voltages.

0

50

100

150

200

250

300

0 2 4 6 8 10 12 14Initial volume (cc)

Blo

cked

pre

ssur

e (P

a)

1020 V

2040 V

3060 V

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Modelling Dielectric Elastomer Membranes 187

moves to point B when the voltage is turned off. Under elastic recoil the diaphragm will move until it is in equilibrium with the outlet pressure at point C where Vol � 8 cc. Upon re-activation, the diaphragm moves to point D and follows the active curve until volumetric filling is complete at point A. The area of the loop ABCD is the network done in a pump cycle. The upper triangular area is the kinetic energy added to the outlet fluid, the lower triangular area is the kinetic energy added to the inlet fluid. The centre box is the potential energy added to the fluid due to a pressure increase. The network during the ejection phase of the cycle can be maximized by increasing the area of the upper kinetic energy. For given design specifications, this is achieved by operating near the flattened region of the active curve, where there are large changes in the volume. In general, the work done can be increased by varying the design parameters such that the active P–Vol curve is shifted downwards (more compliant), and by increasing the voltage while being careful to avoid breakdown fields of the material. The fact that the pressures during volume output are very low is quite obvious. One way of addressing this is to increase the number of actuator layers of the membrane, where the same voltage is individually applied to each elastomer layer assuming the layers slide over one another. Comparing a single-layer actuator with a five-layer actuator, the network calculated is increased approximately by five-fold from 0.85 to 4.5 mJ.

In this chapter, an electro-elastic membrane theory was derived to describe the large deformation response of dielectric elastomers. A model for a clamped membrane was developed using this theory and numerical results calculated for the active inflation/deflation of the membrane. System effects due to changes in prestretch, voltage, electric field, and percent electroded area were discussed. Blocked pressures and pump work-loops were constructed using zero voltage and applied voltage curves to configure the membrane in pump mode.

References

[1] Green , A. E. and Adkins , J. E. ( 1970 ). Large Elastic Deformations . Oxford University Press , London .

[2] Adkins , J. E. and Rivlin , R. S. ( 1952 ). Large elastic deformations of isotropic materials. IX. The deformation

of thin shells . Philos. Trans. Roy. Soc. A , 244 , 505 .

[3] Zhang, Q. M., Cheng, Z. Y., Bharti, V., Xu, T. B., Xu, H., Mai, T. and Gross, S. J. (2000). Piezoelectric and

electrostrictive polymeric actuator materials. Proceedings of SPIE Smart Structures and Materials: Electroactive Polymer Actuators and Devices , 6–8 March, San Diego, CA, p. 34.

[4] Toupin , R. A. ( 1956 ). The elastic dielectric . J. Ration. Mech. Anal. , 5 , 850 .

[5] Maxwell , J. C. ( 1954 ). A Treatise on Electricity and Magnetism . Dover Publications Inc. , Oxford .

[6] Schwinger , J. , DeRaad , L. , Milton , K. and Tsai , W. ( 1998 ). Classical Electrodynamics . Perseus Books ,

Reading .

Figure 18.9 Hypothetical work-loop using numerical P–Vol curves for different voltages.

0

200

400

600

800

1000

1200

1400

1600

1800

0 5 10 15 20

Volume (cc)

Pre

ssur

e (P

a)

0 V3000 V

AD

B

CPout

Pin

Ch18-I047488.indd 187Ch18-I047488.indd 187 12/5/2007 2:35:22 PM12/5/2007 2:35:22 PM

188 Chapter 18

[7] Landau , L. D. and Lifshitz , E. M. ( 1984 ). Electrodynamics of Continuous Media . Butterworth-Heinemann ,

Oxford .

[8] Goulbourne , N. C. , Mockensturm , E. M. and Frecker , M. ( 2005 ). A nonlinear model for dielectric elastomer

membranes . ASME J. Appl. Mech. , 72 , 899 .

[9] Eringen , A. C. ( 1962 ). Nonlinear Theory of Continuous Media . McGraw-Hill Book Company , New York .

[10] Green , A. E. and Zerna , W. ( 1968 ). Theoretical Elasticity . Clarendon Press , Oxford .

[11] Ogden , R. W. ( 1972 ). Large deformation isotropic elasticity – on the correlation of theory and experiment for

incompressible rubberlike solids . Philos. Trans. Roy. Soc. A , 326 , 565 .

[12] Kofod , G. ( 2001 ). Dielectric Elastomer Actuators, Chemistry . The Technical University of Denmark ,

Denmark .

[13] Tews, A., Pope, K. and Snyder, A. (2003). Pressure–volume characteristics of dielectric elastomer dia-

phragms. Proceedings of SPIE Smart Structures and Materials: Electroactive Polymers and Devices , 3–6

March, San Diego, CA, p. 159.

Ch18-I047488.indd 188Ch18-I047488.indd 188 12/5/2007 2:35:23 PM12/5/2007 2:35:23 PM

V.I

Biomedical, Haptic and Micro-Scale Applications

Ch19-I047488.indd 191Ch19-I047488.indd 191 12/7/2007 3:06:22 PM12/7/2007 3:06:22 PM

Ch19-I047488.indd 192Ch19-I047488.indd 192 12/7/2007 3:06:22 PM12/7/2007 3:06:22 PM

A NEW FRONTIER FOR ORTHOTICS AND PROSTHETICS: APPLICATION OF DIELECTRIC ELASTOMER ACTUATORS TO BIONICS

Amit P. Mulgaonkar 1 , Roy Kornbluh 2 and Hugh Herr 3

1 Department of Materials Science and Engineering, University of California, Los Angeles, CA, USA 2 SRI International, Menlo Park, CA, USA 3 Biomechatronics group, MIT Media Laboratory, Cambridge, MA, USA

Abstract

Dielectric elastomer actuators (DEAs) whether used as artificial muscles or as replacements for traditional actua-

tors show great potential for use in modern active orthotic and prosthetic therapeutic applications. Such actuators

are roughly similar in function and biomechanics to natural muscle, including the ability to produce the high peak

power density needed for muscle-like actuation that can simplifying biomimetic and bio-inspired design. Further-

more, DEAs are also capable of multidirectional actuation, enabling novel external and implantable designs not

as suited to traditional actuation technology. Examples include artificial muscle-powered prosthetic arms, active

ankle-foot orthoses, and ventricular assist devices. While challenges currently exist in using dielectric elastomer-

based actuators for biomedical use, this technology shows great potential for the development of advanced orthoses

and prostheses, leading to a substantial benefit for those with physical impairments and disabilities.

Keywords : Artificial muscle, biomechatronics, biomedical electroactive polymer applications, biomimetics, bionics,

dielectric elastomer actuators, dielectric elastomer-powered ventricular assist devices, electroactive polymer bicep,

orthotics, powered ankle-foot orthosis, prosthetics.

19.1 INTRODUCTION

An ancient Egyptian stele slab 1 located in the Carlsberg Sculpture Museum in Copenhagen, Denmark dating from approximately 1500 BCE depicts a patient suffering from polio using a very long wooden stick as a mobility aid to vault over his non-functional limb. In many parts of the world, similar assistive aids are still used to treat the same disability, in a nearly identical manner. While this method ’ s longevity is a testament to the robustness of the ancient approach, current and emerging technology allows for the creation of more advanced and functional orthoses and prostheses. In this chapter, we explore the use of dielectric elastomer actuators (DEAs) for use in such external and implantable biomedical applications.

As defined in Chapter 1 of this book, DEAs are novel, muscle-like actuators that operate based on the electromechanical response of a polymeric material to the application of an electric field [1] . Commonly referred to as ‘ artificial muscles ’ , these actuators have demonstrated good performance over a wide range of parameters and configurations.

While no single, consensus definition for ‘ orthotics ’ and ‘ prosthetics ’ exists [2] , we chose to define a prosthesis as a device which replaces the function of a natural limb, while an orthosis serves by aug-menting the function of an existing natural-body system. 2 In other words, a prosthetic can be thought of as a series attachment to the body, as in for example a treatment for limb amputation, while an orthotic

Chapter 19

1 Stele slabs are traditional ancient Egyptian markers constructed in a variety of shapes, usually formed from stone or wood and usually

bearing inscriptions, reliefs, or paintings, generally used as boundary markers, tombstones, or for commemorative purposes.

2 Semantic note: ‘ Prosthetics ’ refers to the field of study, while ‘ prosthetic ’ is an adjective. The noun form is ‘ prosthesis ’ with

‘ prostheses ’ as plural. The same convention holds true when referring to orthoses.

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is attached in parallel to a body organ, such as in treatment of limb dysfunction [3] . For the purposes of this discussion, we will focus on three distinct bionic domains: active prosthetic limbs, external orthotic therapeutics, and implantable orthoses and prostheses.

To familiarize the reader, we begin with a concise background on orthotics and prosthetics, first reviewing the history of orthotic and prosthetic technology, then exploring general considerations for orthotic and prosthetic device design, and finally briefly discussing contemporary design paradigms and methodologies.

We then explore some of the competitive advantages over traditional actuation technologies of using DEAs as artificial muscles, and as regular actuators with respect to therapeutic orthotic and prosthetic applications. These advantages are illustrated by way of case study.

The first study takes the artificial muscle label literally and explores the use of DEAs in actuating an arm skeletal system in a biomimetic, agonist/antagonist manner. The second case study explores using DEAs to power an ankle-foot orthosis currently actuated by more traditional means. The final case study presents a situation where dielectric elastomer ’ s novel ability to actuate out-of-plane is har-nessed for cardiac ventricular assistance.

We conclude by considering limitations on the use of DEAs in orthotics and prosthetics, and implica-tions for near-term adoption.

19.1.1 Historical background

A need for orthoses and prostheses has existed as long as humankind has had to deal with the loss of limb utility through injury or dysfunction. Simple walking sticks must certainly have been used as basic canes since the earliest days of humanity and indeed, as demonstrated by the Egyptian stele slab previously mentioned, rudimentary walking aids are shown to have been used for much of recorded human history.

The art of orthotics can be traced back to the study of practical splint and brace making [4, 5] . Primitive orthoses and prostheses were generally simple devices constructed out of materials on hand, usually bone, wood, leather, and in time metals. Historically, the study of prosthetics has been closely associated with that of limb-amputation surgery performed as a critical-care measure in response to trauma and injury from warfare and battle [6] . While historical accounts exist attesting to ingenious artificial joints designed by armor-makers as early as the 15th or 16th century [7] , the development and invention of the prosthetic padded peg-leg served reliably as the gold standard of treatment for centuries [8] .

Credited with inventing ligatures, which replaced the contemporary method of searing the ends of residual limbs to stop blood loss, as well as pioneering the use of site selection to produce limbs that were as functional and useful as possible, French army surgeon Ambroise Paré (1510–1590) is con-sidered by many to be the father of amputation surgery and prosthetics.

In modern times, major periods of warfare, and the resulting numbers of grievously wounded sol-diers have had a catalytic effect on orthosis and prosthesis development [9] . The large number of ampu-tations resulting from the American Civil War established the prosthetics industry in the United States towards the end of the 19th century. Advances in the brutality of warfare in the 20th century required appropriate advances in orthotics and prosthetics technology to keep pace with the multitude of injured soldiers returning home.

While enormous progress has been made since the days of the peg-leg – using a modern prosthetic racing foot, the current world record for the 100 m sprint for a below-knee amputee is within 1.5 s of the mark set by an able-bodied sprinter [10] , frustration still exists within the disabled community as to the pace of prosthetic and orthotic development, relative to general, technical progress [11] .

19.1.2 General considerations for orthotic and prosthetic design

While the specific design criteria for orthoses and prosthesis vary based on the application, user, oper-ating environment, and exact disability being treated, several common considerations must be taken into account in designing such rehabilitative systems. The ultimate goal of such orthotic and prosthetic devices is, at a minimum, to match the performance of the natural limbs and body systems that are being replaced or augmented. Fundamentally, such devices must be functional, reliable, safe [12] , and ideally comfortable enough for routine, sustained use.

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From an engineering standpoint, such orthotic and prosthetic bionic devices must be capable of oper-ating in a highly constrained design space. One of the most important considerations faced in device design is weight. A therapeutic bionic system must ultimately be light enough to be used by the user – for example, an ambulatory foot orthoses must be light enough for the foot to be easily raised while walking. Furthermore, the biodynamic considerations of the additional weight on the body must be taken into account. A very heavy full-arm prostheses strapped far to one side of the body ’ s center of mass could create problems with balance.

In addition to functional concerns, issues of user comfort must be addressed. The noise signature and the heat produced by the device must be accounted for in a manner that does not cause undue discomfort to the user and those around them. With active or semi-active devices, the energy density of the active element must be high enough to power the device without undue penalty. Another approach is to minimize energy expenditure by maximizing energy recovery.

A final, yet equally vital consideration in the design of orthoses and prostheses is that of the physical appearance of the device (cosmesis) – in the case of external prosthetics, more natural-looking devices are preferred when possible.

All these factors must ultimately be balanced against the final cost of the resulting device to the end user. Ideally, the long-term costs of maintenance and ownership should also be economical, an especially important consideration considering the high level of use advanced orthoses and prostheses might see.

19.1.3 From passive to active: current directions in orthotic and prosthetic development

While entirely passive contemporary devices such as the Össur company ’ s Flex-Foot Cheetah ® pros-thetic sprint-foot can perform their single, chosen function remarkably well [13] , they do not possess the versatility and adaptability for everyday use in a multitude of real-world situations. In order to ena-ble increased functionality and more life-like behaviour, advances in orthotics and prosthetics must be towards active or semi-active devices. Active devices offer a level of control and adaptability not found in passive devices, yet are more complex, requiring sources of power and complicated control hardware and software.

Passive orthoses and prostheses are powered solely by passive elements, such as springs which are generally coupled in such a way that body motion provides them with the elastic deformation required to perform mechanical work in the device. In walking prostheses, springs are usually used to store elas-tic energy during one portion of the motive cycle, and return it later on in the cycle to aid in ambula-tion. However, dynamic tasks such as walking, running, or climbing stairs benefit from at minimum the ability to control the apparent stiffness of spring elements used. Such quasi-passive elements, defined as those which cannot apply a non-conservative force, include but are not limited to variable-dampers and clutches, including combinations of variable-dampers and clutches that function in conjunction with, or supplement other passive elements.

Active systems are capable of providing an even more robust functionality [14] . Currently, modern orthotics and prosthetics are in general powered through the use of a combination of springs, electric motors, pneumatics [15] , and, more recently, shape memory alloy (SMA) actuators [16–18] . The major-ity of these active devices are lab prototypes or developmental proof-of-concept test-beds, and have not yet been incorporated into commercially available orthotic and prosthetic therapeutics.

19.2 COMPETITIVE AND DEVELOPMENTAL ADVANTAGES OF DEA USE

DEAs have many inherent properties that make them well suited for use in orthotic and prosthetic applications, key among them being the similarity of DEAs in function to the body ’ s own actuation system – natural muscle, and the fundamental stand-alone technical benefits afforded by such polymer actuators.

Colloquially referred to as ‘ artificial muscles ’ , actuators based on dielectric elastomers are uniquely suited to orthotic and prosthetic development due to their rough similarity in function to natural muscle [19] . Fundamentally, both DEAs and natural muscle are compliant viscoelastic actuators that provide a linear contractile force and are capable of both isometric and eccentric actuation. The magnitude of the

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force and the displacement of the actuator can equal or exceed that of human skeletal muscle on a per mass basis as shown in Fig. 19.1 . As a result, elastomeric actuator ’ s similarity to natural muscle allows for more biomimetic and bio-inspired design and construction of orthoses and prostheses.

Like natural muscle, DEAs are force controllable (not strictly binary actuators), allowing for fine movement and position control. This allows for orthoses and prostheses that can potentially replicate precise, nuanced natural function.

Modelled in first order as an integrated spring-dashpot system, DEAs exhibit viscoelastic proper-ties similar to natural muscles, further simplifying orthotic and prosthetic design. This feature is useful because a separate damping element no longer has to be included to modulate the output of a mechan-ical actuator. The inherent compliance of DEAs could make orthotics and prosthetics designed using such actuators more comfortable to the end user. Furthermore, DEAs can be used to modulate the effec-tive viscoelastic behaviour of a joint, without the need for complex engineered structures or feedback loops. This property is explored in more detail in Chapter 14 of this book.

During level-ground running, energy is stored transiently in the elastic deformation of the stretched natural leg muscles – by being able to mimic this behaviour, dielectric elastomer–powered lower-extremity orthotics could allow for more energy-efficient ambulation [21] .

Furthermore, such actuator ’ s natural-muscle-like properties could lead to more anthropomorphic designs. If DEAs advance to the point where their physical form-factor becomes very similar to natural muscle, natural-looking orthoses and prostheses with superficially realistic-looking musculature could be created.

While DEAs are especially promising for orthotic and prosthetic applications due to such actuator ’ s similarity to natural muscle, their use simply as a replacement for traditional linear or angular actuation mechanisms also show great potential. The potential advantages of DEAs compared to traditional actu-ator technologies include:

● Lightweight : Elastomeric actuators capable of the same peak power weigh significantly less than competing electrical actuation technologies, allowing for more comfortable and natural bionics, as well as use of the actuators in orthotic systems augmenting body locations/limbs traditionally unable to support system weight.

● Out-of-plane (multidirectional) actuation : Flat-sheet polymer dielectric actuators are capable of taking on complex (curved) conformations and can expand in two planar directions or actuate out-of-plane relative to the sheet, generating force normal to the curve. This capability may be well-suited for implantable devices where, for example, it is desired to mimic the behaviour of non-planar muscula-ture, such as cardiac or respiratory diaphragm muscles.

Dielectric elastomers

Electromagnetic

Electrostatic

Shape memory

Acrylicelastomers

Naturalmuscle

Silicone

Soft silicone

Fluorosilicone

Polyurethanes

Piezoelectricand

magneto-strictive

Dielectric

Naturalmuscle

IPMC andconducting

Piezoelectric

Electromagnetic

105 W/kg

103 W/kg

106105104103102101100100

101

102

103

104

105

106

100

10

1

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Actuation pressure/density (kPa-m3/kg)

10

10 W/kgGels

Frequency (Hz)(a) (b)

Specificenergy(J/kg)

Str

ain

(%)

Figure 19.1 Comparison between natural muscle and direct-drive electric actuation technologies: (a) scale-invariant stroke and force comparison and (b) energy power and speed comparison and bandwidth for various actuators(adapted from [20] ).

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● Scaling and modularity : DEAs are relatively unique in that stacks of several actuators can practically be used in parallel to increase the output force while maintaining a given output displacement. (Force scales in parallel, displacement in series.)

● Low cost : Actuators are potentially cheap enough to be easily replaced and commoditized, moderat-ing reliability requirements .

● Noise : Elastomer actuator-powered devices can operate silently, an important concern for usability and quality of life on the part of the wearer .

● Biocompatibility : The similar physical properties of DEAs in comparison to the body ’ s natural soft tissues could help with biocompatibility in relation to implantable orthotics and prosthetics. Additionally, dielectric elastomer materials such as silicones have already been shown to be both bio-safe and biocompatible and have a proven track record for both internal and external use [22] .

19.3 CASE STUDIES: POSSIBLE APPLICATION OF DEA TECHNOLOGY TO ORTHOTICS AND PROSTHETICS

While there are a multitude of orthotic and prosthetic applications where electroactive polymer-based DEAs could make a substantial difference, we have chosen to highlight three specific applications which are uniquely, or most effectively enabled by dielectric elastomer actuation technology.

Used as artificial muscles, DEAs are especially fascinating with respect to bionics due to (a) their ability to provide power in a balanced agonist/antagonist manner, (b) the (visco)-elasticity that natural muscles exhibit which artificial muscles can mimic, and (c) the ability to physically actuate in ways that trad-itional linear actuators could never hope to. These three properties are illustrated by way of case study.

19.3.1 An electroactive polymer bicep: a dielectric elastomer-powered arm orthotic/prosthetic

Introduction

DEAs have been compared to natural muscles due to the similarity in their function, physical properties, and behaviour. In this case study, we extend that analogy and use DEAs in place of natural muscle in actuating a biomimetic skeletal arm system. Such a use highlights DEA ’ s suitability for use in balanced agonist/antagonist systems.

The human musculoskeletal system features a load-bearing skeletal system consisting of mineralized bone which is actuated by natural voluntary contractile muscles. Muscles are attached to their connec-tion points by tendons, tough yet flexible bands of collagen-based fibrous connective tissue that apply the tension of the muscle to the bone attachment point. The human arm consists of the humerus bone, which connects at the elbow joint to the paired radius and ulna bones, which continue on to attach the wrist. The humerus, the long bone of the arm runs from the shoulder to the elbow, fitting between the scapula (shoulder blade) and the ulna. The distal end of the humerus forms a hinge joint with the ulna at the elbow, allowing for flexion and extension. There also exists a pivot joint between the capitulum of the humerus and the head of the radius, which allows for pronation and supination motions.

In this example, we focus on the musculature and movement about the elbow. The elbow is bent and the forearm brought up (acute angle between ulna and the forearm) through the action of the bicep muscle. The origin, or fixed skeletal attachment of this muscle is at the scapula and the glenoid cavity (the inside hollow of the shoulder joint), and its insertion (tendon attachment to the bone that is to move) is near the elbow on the radius. When the bicep contracts, the arm is flexed at the elbow due to the tension applied by the bicep pulling the radius bone closer to the shoulder.

The elbow is straightened out by the action of the tricep muscle. The tricep originates in the shoulder and has its insertion on the ulna. The tricep functions by pulling its insertion point on the ulna closer to the shoulder, resulting in an increasingly obtuse angle between the humerus and forearm.

The bicep and tricep function as an antagonistic pair, with the antagonist tricep acting in opposition to the agonist, which in this case is the bicep, the prime mover responsible for generating the range of move-ment in the joint through contraction. The antagonist functions as an extensor, ‘ opening ’ the joint while the agonist functions as a flexor, ‘ closing ’ the joint. Another example of such a pair is the quadriceps and the hamstrings.

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Biomimetic application of dielectric elastomer artificial muscles

Biomechanically speaking, such antagonistic pairs are necessary in the body because natural muscles are only capable of contraction, and therefore can only exert a pulling force. This behaviour is similar to the functional mode of simple strained DEAs in their most basic configuration.

At first glance this might appear to be an area where traditional electromechanical linear actuators are of superior utility to natural or dielectric elastomer artificial muscles. Electromechanical linear actuators are generally capable of both pulling and pushing, providing an additional degree of freedom compared to their muscular competition. A single actuator capable of both pulling and pushing could functionally replace a system requiring antagonist actuators. While various dielectric elastomer con-figurations such as the spring roll are also capable of applying both a pushing and pulling force, not all applications are ideally suited to such function. Antagonist systems, especially as implemented with the specific physiology of the elbow allows for a level of very precise motor control not necessarily easily achieved by a single push–pull actuator. It is now understood that human motion control relies on not just the ability to apply a given force or move to a desired position, but to tune the impedance of the joint in order to achieve the desired behaviour for a given task [23] .

DEAs are well suited to such a biomimetic role. In order to function correctly, antagonistic systems must be fine-tuned in order to maintain the balance between the agonist and the antagonist. This bal-ance is potentially difficult to achieve with traditional electromechanical linear actuators. The elasticity inherent in DEAs simplifies antagonistic pairing by providing the ability to damp dynamic perturb-ations to the pairing, allowing for more robust and versatile actuated assemblies.

DEAs also show promise for such biomimetic applications since, like muscles, they are naturally lin-ear actuators. Electric motors typically generate linear motion by using gearing to translate the motors natural rotational output motion to linear form. Such gearing adds an unnecessary size, weight, and potentially a noise penalty to motors used as linear actuators. While linear electric motors can be used for position control, they require complex electric signalling, such as multiple phase trains and/or trans-lation steps.

As shown in Fig. 19.2 , Kornbluh et al. have demonstrated a model of a life-sized human skeletal arm powered by a dielectric elastomer artificial muscle [1] . The muscle consists of a rolled actuator con-nected between the humerus and the radius that takes the place of the bicep. While the resulting actu-ator is smaller than would be desired for true natural performance, proof-of-concept functionality has been demonstrated [24] .

Other researchers have begun to develop more practical DEA-powered arm prosthetics and orthotics. Recently, Carpi et al. have demonstrated a DEA-powered orthotic hand splint that is capable of modu-lating the joint impedance of the wrist for more effective rehabilitation [25] .

While practical DEAs presently have not been scaled up to match the force levels of larger natural muscles such as the bicep, these examples serve as a demonstration of possible bio-inspired applications

Figure 19.2 Mockup of a dielectric elastomer-rolled actuator on a full-size human skeletal arm model. Future prosthetic devices may use DEAs as muscles to closely mimic both the form and function of a natural arm.

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which could result in more natural and usable orthotics and prosthetics. Further, DEAs may find their first utility as the smaller muscles of the wrist or hand, where the ability to provide for fine motion con-trol is crit ical in producing a prosthetic with improved dexterity.

19.3.2 A powered ankle-foot orthosis to treat a drop-foot gait pathology

Introduction

In this case study, we explore the use of DEAs in an external, powered orthosis used as a treatment for the drop-foot gait pathology commonly associated with stroke, cerebral palsy, or multiple sclerosis.

Starting in the 1970s, Flowers et al. began research aimed at advancing the prosthetic knee joint from a passive non-adaptive mechanism to an active device with the ability to vary its damping [26–29] . The Flowers knee was capable of exhibiting a wide range of joint damping throughout the walking cycle. High knee joint damping during ground contact prevented buckling. Low damping during the leg-swing phase allowed the prosthetic to swing naturally and freely with damping smoothly increased to deceler-ate the prosthesis just prior to heel strike.

While the variable-damper Flowers knee was never released commercially, manufacturers have developed a knee orthosis system consisting of a computer-controlled variable-clutch. While only offer-ing locking and unlocking controllability, a variable-clutch design improves the metabolic economy of level-ground ambulation in comparison to more traditional fully locked-knee designs [30] .

In contrast to those available for the knee, commercially available ankle-foot orthotic and prosthetic devices are currently completely non-adaptive and passive while in contact with the ground surface. Such devices such as the Össur company ’ s recently released the Proprio Foot ™ are capable of actively changing their position during the swing phase, but remain passive during stance [31] . Such devices usually consist of carbon-composite leaf springs or elastomer bumper springs that function by storing and elastically releasing energy throughout the gait cycle. Compared to non-compliant or damping-only (dissipative) ankle-foot devices, passive elastic devices afford greater heel, toe, and vertical compliance to a below-knee amputee, which has been shown to increase the amputee ’ s comfort and ambulation speed [32] . While progress has been made, contemporary passive ankle-foot orthoses cannot match and do not perform as well as their biological counterparts in many key metrics, including balance and sta-bility, power generation, efficiency, and life cycle [3] .

Research has shown that powered ankle-foot orthoses that are capable of variable damping can over-come many of the existing shortcomings of contemporary ankle-foot orthoses [21] .

Current state of technology

To demonstrate the clinical and functional importance and efficacy of a powered ankle-foot orthosis, Herr et al. developed a powered orthosis ( Fig. 19.3 ) to treat the dominant complications of drop-foot, a gait pathology that results from a muscle impairment in the anterior compartment of the leg, as a result of which a patient is unable to dorsiflex the ankle or lift the foot. This leads to slapping of the forefoot after heel strike and dragging of the toes at the beginning of the leg-swing phase of walking.

The developed ankle-foot orthosis is comprised of a variable-force actuator controlled by algorithms tied into models of natural biomechanical ankle function. The actuation system consists of a spring placed in series with an electric motor, similar in concept to the series arrangement of natural tendon with muscle [33] . As a result, the series elasticity enables the modulation of force instead of position, with output force of this spring-electric motor system being proportional to the length-change across the series elasticity multiplied by the spring constant. Therefore, by controlling the position/length of the spring, force and torque can be controlled across the joint of the orthoses.

To counteract the gait complication of drop-foot, the controller commands the actuator to apply a torque proportional to joint position when needed. Therefore, the stiffness of the ankle is actively modu-lated to minimize forefoot collision after heel strike and the position of the foot is adjusted by dorsi-flexing the ankle, providing sufficient toe clearance during the late swing phase. Clinical data from a comparison of two drop-foot afflicted participants wearing both the described powered orthosis and a conventional, constant stiffness orthosis indicated that a powered orthosis that actively modulates both impedance and motive torque may present certain clinical benefits for the treatment of the drop-foot gait pathology in comparison to conventional constant joint stiffness ankle-foot orthoses [34] .

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However, this resulting powered orthosis is heavy enough to impede walking, unnatural in shape, and noisy. The use of DEA technology has the potential to overcome these present limitations, and by allow-ing for the integration of joint impedance and motive force controllability, the possibility of consider-able advantage to the challenged.

Application of DEAs to current technology

Field-activated polymer actuators such as those composed of dielectric elastomers show great potential for adoption in such an orthotic as described above. Since orthotic therapeutic approaches tend to draw inspiration from natural biomechanics, it would simplify the therapeutic approach to incorporate an actuation technology that best mimics natural muscle, the motive actuator for the natural body.

In such an application, a DEA would be used to replace the spring-electric motor system that is used to provide the active control of the ankle and foot during ambulation. A DEA would function as a lin-ear actuator with the ability to dynamically tune its stiffness and modulate its output force on demand. Such a system has the potential to be more functional, usable, and robust than one powered by a spring-electric motor assembly.

As noted, the viscoelastic behaviour of dielectric elastomer-based actuators is similar to that of nat-ural muscle [19] , allowing for inherently easier control and a more robust response to high-frequency shocks or disturbances. Considering the demonstrated impact that limb/orthotic stiffness has on ambu-lation, an actuator with the ability to dynamically modulate its stiffness is preferable. Since such poly-mer actuators are capable of fast, controllable responses, the force and strain of these actuators can be used to electronically modulate and control apparent stiffness [35] .

Motor and ball-screwactuator

Elasticcomponent

Angle sensor

Force sensor

Figure 19.3 Powered ankle-foot orthosis developed by Herr et al. The system is composed of a series-elastic actu-ator formed from a motor and ball screw in series with an elastic component, a potentiometric angle sensor, and a capacitive force sensor. The series-elastic actuator is used to modulate the stiffness of the ankle joint from step to step, controlling the movement of the foot during plantarflexion. Foot clearance is achieved during the swing phase by the motor dorsiflexing the foot (adapted from [21] ).

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Usability concerns are addressed by the low-weight and bulk of a dielectric elastomer-powered ortho-sis and the noise-free operation of such a system. Such considerations would make an orthosis powered by dielectric elastomers eminently more practical, and therefore usable.

As an added benefit, the high electromechanical coupling demonstrated by field-activated polymer actuators could allow for the dielectric elastomer powering the orthosis to be operated in reverse, as a generator, while at the same time providing integrated damping and energy absorption functionality. Such an operational mode could potentially be used to recapture some of the electrical energy applied to the muscle-actuator for actuation. This approach not only allows for a more natural model of muscle function, but could potentially be harnessed to extend battery life – a non-trivial concern.

The benefits and advantages of using DEAs in place of a spring-electric motor system that we have illustrated make such polymer-based actuators very promising for orthotic applications.

19.3.3 An orthotic dielectric elastomer-powered ventricular assist device

Introduction

In this third case study, we explore a potential use of DEAs for an implantable device which cannot be duplicated by more traditional actuation technology. We consider using a DEA as an out-of-plane actuator to actuate against the natural human heart, functioning as a ventricular assist device (VAD). In addition, we explore some of the considerations involved in using DEAs in orthotics or prosthetics implanted into the body.

Assisting a failing heart has been under consideration since the early 20th century. Early efforts focused primarily on replacing the entire heart or the technically simpler solution of supporting and augment-ing the function of the left ventricle. Limited progress was made till the development of reliable cardio-pulmonary bypass systems. Such a procedure allows for the circulation and oxygenation of the blood by diverting the blood from the heart and lungs through a heart–lung machine and returning the blood to the aorta. While effective in the short term, such a procedure ultimately resulted in high mortality rates for patients who did not regain normal natural cardiac function [36] .

The first attempts at implanting a ‘ modern ’ VAD in 1964 resulted in the deaths of most of the test patients within a few hours of implantation [37] . Another early attempt involving a left heart bypass through use of cannulation techniques resulted in the deaths of three out of four patients [38] . The most successful of the early assist attempts was the intra-aortic balloon pump. An inflatable balloon pump in the lumen of the thoracic aorta assists the heart by displacing blood volume from the inside of the chamber itself [39] . Vascular complications, particularly vascular trauma and aortic perforations resulted, causing this to ultimately be a less than ideal therapy [40] .

To date, there has already been substantial investigation in the cardiac assist device field. The cur-rent state of the art of implantable cardiac assist technology consists of either a cannula-coupled pump which bypasses the left ventricle entirely, or an implantable inter-aortic balloon.

Most therapeutic efforts focus on the left ventricle of the heart as it is required to produce considerably more pressure for the same volume of flow compared to the right ventricle of the heart [41] . As such, left ventricular assistance usually provides a more noticeable return to normal cardiac function. Most patients with heart failure do not undergo a course of right ventricle mechanical assistance, as such a procedure has not proven to be very clinically effective [42] .

A major problem facing pump-type VADs that makes contact with flowing blood is the formation of clots. Surface imperfections as small as 10 � m can induce platelet clumps to form. This problem was partially addressed by lining the inner part of the pump with a layer of biological cells [43] . Fibers that encouraged the growth of a cellular layer were attached by a procedure called flocking. To prevent these from breaking off, an over-coating was used in the flock process [44] ; however, coatings only proved effective for 2–3 months.

When a VAD is implanted in a patient with end stage heart failure it can restore blood pressure and cardiac output back to near normal levels. The VAD boosts the patient ’ s pumping power by feeding blood into a battery-powered pump and out through a tube connected to the main artery. Furthermore, the relief of pressure in the left ventricle appears to induce reverse structural remodel-ling [45] . Both the cells and the structure of the heart have been shown to recover after a VAD is put in place [46, 47] .

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While ongoing work has focused on VAD miniaturization [48] , the current generation of VAD devices unfortunately proves too bulky for implantation in small adults and some children. Smaller individuals just do not have the volume within their thoracic cavity for the placement of a pump and the associated electrical control hardware. Furthermore, many children have not physically developed to the point where their thoracic cavity can hold the weight of such devices [49] . This presents a major clinical limitation to the use and adoption of such devices.

Furthermore, current VADs require complicated surgical installation. Patients with VADs that rely on the cannulation of the heart face an increased risk of death due to complication from the surgery and infection [50] . In addition, most modern pump-based VADs simply replace the function of the entire ventricle. Current therapies do not allow the physician to selectively assist parts of the cardiac tissue.

Recent efforts have focused on providing a cardiac assist through direct compression of the heart. Such efforts have primarily relied on pneumatic methods of supplementing heart actuation [51] . Such efforts have proven to be effective [52] in laboratory animal studies [53] and show potential for use in humans. Furthermore, a VAD which directly contracts the heart could potentially provide the patient with improved recovery times and reduce damage to cardiac tissues.

Mechanical actuation of natural cardiac tissue

We postulate a novel left ventricular assist device (LVAD) that functions by mechanically actuating the heart ’ s own natural tissue in order to provide short term, localized relief for the heart muscle as it regen-erates and regains full cardiac function.

At the heart of this device will be a multi-layer DEA. The actuator alternately squeezes and relaxes against the natural ventricle, pumping blood through compression of the ventricle.

The VAD will consist of the DEA surrounded by a stiff ring for structural support ( Fig. 19.4 ). The entire device will be coated by a flexible, impermeable polymer membrane. This membrane will keep the electroded active region of the actuator free from fluid or moisture, while at the same time serving as insulation between the heart, the device, and the body at large. This membrane would be flexible and highly compliant.

Rigidstructuralframe

Coated dielectricelastomer actuator

Figure 19.4 Illustration of a possible dielectric elastomer-based VAD. Such a system could be composed of a DEA supported by a stiff structural frame sandwiched between biocompatible and impermeable polymer coating mem-branes. This would sit over the left ventricle of an ailing, semi-viable heart, actuating in sync with, and providing contractile assistance to the heart.

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The VAD would be affixed on and around the left ventricle of a semi-viable and functional heart. Regular diastolic filling [54] of the ventricle would coincide with dielectric elastomer electrode activation, deforming the diaphragm as the ventricle filled with blood. Systole would coincide with the cessation of electrode activation and the elastic return of the actuator to its natural state. This would serve to enhance and augment the natural contraction of the ventricle and provide contractile assistance to the ailing heart [55] .

Future iterations might feature an actuator that is segmented into several discrete, individually addressable and controllable sections, allowing for an overall expansion and contraction cycle that more closely mimics the path of the electric depolarization wave in the heart [56] .

This example is presented as a potential example of a novel use for DEAs, and does not take into account the many difficulties involved in such an endeavour from power, to tissue bruising, and the compliance of the organs against which this device will be actuating. Such a concept is not necessarily achievable with current technology, but is presented as an example of a unique actuation modality not easily or practically achieved by traditional actuation technologies in a biomedical context.

Specific issues pertaining to implantable orthotics and prosthetics

While many of the same engineering challenges that face designers of external orthotics and prosthet-ics are encountered in designing an implantable therapeutic, the task of designing an implant is com-plicated by the specific requirements posed by the body ’ s internal environment. At the very minimum, implants must be bio-safe and biocompatible, which includes being both non-toxic and also of such a construction that it will not trigger an immune reaction. Implants must, beyond almost all other consid-erations be highly reliable. Once implanted, it must be able to safely function without intervention for the entire life of the device, without servicing or outside intervention.

19.4 LIMITATIONS AND DESIGN CONSIDERATIONS OF ORTHOTIC AND PROSTHETIC USES OF DIELECTRIC ELASTOMER

While dielectric elastomer-based actuators have remarkable potential for use in orthotic and prosthetic applications, the technology as it stands at the time of this writing is not without its limitations. Some of these limitations can be alleviated, or even eliminated with more research, while others are funda-mental and inherent in this actuation technology. Limitations include:

● Performance : While the performance of practical DEAs has increased by several orders of magni-tude over the life of the technology and continues to show steady improvement, there is still room for growth as current performance with sufficient lifetime at large size scales is not enough for certain applications. Improvements in materials engineering will likely produce higher-performance dielec-trics, while advances in structures will better harness and turn those dielectrics into actuators.

● Reliability : An especially crucial aspect for biomedical/bionic applications. Again improving, but cur-rent DEAs are primarily hand-made laboratory devices, with rampant sample variation. The more integral the actuator becomes to the functioning of an orthotic or prosthetic, and the more crucial the orthotic and prosthetic becomes to a persons way of, or very life, the more reliable the actuator must be.

● Reverse operation compared to natural muscle : While not necessarily a shortcoming, it must be rec-ognized that dielectric elastomer artificial muscles have an opposite active state compared to natural muscle. Natural muscle contracts when energized, while dielectric elastomer artificial muscles con-tract when de-energized. However, research in this area is ongoing and Carpi et al. and others have demonstrated dielectric elastomer designs that are capable of operating in a contractile mode like natural muscle.

● Electrical safety : Dielectric elastomer-powered orthoses and prostheses must ultimately be safe for the user and those around them. While normally operating at low currents, dielectric elastomers require a high voltage to operate. Orthotics and prosthetics designed using dielectric elastomers must take this into account, ensuring adequate electrical safety conventions are followed. Chiefly, the device must be suitably shielded so that there is no risk of creating a pathway for potentially dangerous current leakage. Care must also be taken to ensure that the device limits the maximum leakage current and electric field that can occur under a worst case scenario. While many of the issues of high voltage

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can be addressed with proper packaging and intelligent electronic driver circuit design, public per-ception can still be a potential issue. Many might be uneasy with the thought of being, in the case of implantable devices, so intimately connected with and in such close proximity to a nominally ‘ high-voltage ’ device. External devices must be ruggedized to survive wear-and-tear, as well as changing environmental considerations while still maintaining electrical integrity and safety. Both devices tar-geted for internal and external use must be rigorously tested and proven.

19.5 CONCLUSION

Just as the digital revolution produced the computer as an updated analogue for the Egyptian stele slab discussed in the introduction, a similarly updated bionic analogue must be developed to replace the simple passive vaulting pole depicted on that stele slab. We stand at the threshold of an age in which current work in bioengineering and biomechatronics can be readily translated into potentially revolu-tionary orthotic and prosthetic devices that are capable of producing tangible and practical benefits for the physically challenged or those suffering from impairment.

The advanced limbs and engineered therapeutic devices of tomorrow will not necessarily be enabled by discoveries in a single field, but from the integration of advances in materials, mechanics, actuators, sensors, and control systems. While actuators based on dielectric elastomers are just one potential solu-tion to a particular subset of issues in such a broad domain, we strongly believe that the potential of dielectric elastomers with respect to such applications warrants further study, development, and explor-ation. While limitations do exist with the current state of the technology, DEA ’ s similarity to natural muscle, benefits as a traditional actuator and ability to actuate in non-traditional ways present a com-pelling case for their inclusion in the development of the next generation orthotics and prosthetics.

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dysfunction after repair of anomalous origin of the left coronary artery from the pulmonary artery . Ann. Thorac. Surg. , 67 ( 1 ), 169 – 172 .

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PORTABLE FORCE FEEDBACK DEVICE BASED ON MINIATURE ROLLED DIELECTRIC ELASTOMER ACTUATORS

Rui Zhang 1 , Patrick Lochmatter 1 , Gabor Kovacs 1 , Andreas Kunz 2 and François Conti 3

1 Laboratory for Mechanical Systems Engineering, Swiss Federal Laboratories for Materials Testing and Research (EMPA), Duebendorf, Switzerland

2 Institute of Machine Tools and Manufacturing, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland

3 Department of Computer Science, Artificial Intelligence Laboratory, Stanford University, Stanford, CA, USA

Abstract

In this chapter, we present the application of the miniature rolled dielectric elastomer (DE) actuators to a portable,

‘ hand-held ’ force feedback device (FFD). The miniature rolled DE actuators (diameter 12 mm, length 45 mm and

weight 8 g) were fabricated based on a machine-aided manufacturing process. The actuators were characterized by

isometric tests with driving voltages ranging from 0 to 3.5 kV and displacement levels between 0 and 8 mm. The

results showed a quasi-linear force–displacement behaviour. Furthermore, a quadratic decrease in axial force with

increasing voltage was observed, which agreed with the theoretical prediction. To ensure electrical safety to human

users of the FFD driven by the miniature rolled DE actuators, two failure cases were studied based on a device-user

configuration modelled in Simulink ® . Various protective measures were derived and implemented in the design of

the actuators and the force feedback system. Two demonstration devices were made to practically demonstrate func-

tions of the miniature rolled DE actuators in force feedback applications. Future work will address the issues such

as reproducibility and electromechanical durability of the rolled DE actuators, as well as the implementation of the

proposed ‘ hand-held ’ FFD in a force feedback control system.

Keywords : Electrical safety, electroactive polymers, force feedback, rolled dielectric elastomer actuators.

20.1 INTRODUCTION

Virtual reality (VR) can be traced back to about 50 years ago when Morton Heilig, a cinematographer, began designing the first multi-sensory virtual experiences. In order for spectators to be fully immersed in a film scene, he developed the ‘ Sensorama Simulator ’ which added to the projected film, sounds, vibrations, wind and even odours [1] . Nowadays, after a remarkable and complex history [2] , VR has lead to a wide range of multi-sensory applications for entertainment and professional purposes [3–6] .

While VR has strongly benefited from the important progresses in computer technology, there still remain limitations with the current techniques for including the stimulation of the sense of touch. Unlike graphical displays, which can render large photographic images at very high resolution, tactile displays can only generate limited forces within small punctual areas. With the appearance of new med-ical robotic tools to perform minimal invasive procedures in a more precise way in recent years, how-ever, there has been an increasing demand for more robust and efficient force feedback devices (FFDs) which allow users to intuitively grasp, feel and manipulate virtual or real objects [7] .

In respect of their location, current FFDs can generally be classified into the categories of ground-based and body-based devices. Ground-based devices are fixed to the environment such as a desk, a

Chapter 20

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208 Chapter 20

wall, the ceiling or the floor, while body-based devices are attached to the human body, for instance to the shoulders, arms, legs or hands.

Stylus apparatus such as the PHANTOM [8] and the Delta [9] provide continuous point contact forces in six degrees of freedom (DOF), and therefore, are leading ground-based solutions in gripper or end-effector designs. However, these devices are mainly actuated by electrical motors which convert a considerable amount of energy into heat when used in static configurations. Moreover, developing light-weight and portable structures with more than three active DOF has proven to be a very challeng-ing task given to the size and weight of such motors.

Body-based devices conventionally consist of a hand-exoskeleton structure [3, 10–13] . These devices are portable and thus provide access to large working space in a virtual environment. However, this portability is achieved at the cost of limited ergonomics since the user needs to carry the device as a whole or a part of it. In addition, the limited design space for the FFD, placed either on the palmar or on the dorsal side of the hand, makes the selection of an appropriate actuator technology quite challeng-ing, and requires complex design of the force transmission structure.

In this chapter, a FFD based on electroactive polymers (EAPs) is presented. As promising driving ele-ments for the FFD, rolled actuators from soft dielectric EAP are proposed. Theoretical considerations address the electromechanical behaviour of rolled dielectric elastomer (DE) actuators under activation. Experimental characterization results show the potential of the miniature rolled DE actuators for their application to FFDs. Given the high driving voltages in the range of several kilovolts needed for DE actua-tors, electrical safety issues are discussed. Finally, two force feedback demonstration devices are presented.

20.2 FORCE FEEDBACK SYSTEM

20.2.1 Components and principle of operation

Figure 20.1 illustrates the overall scheme of a force feedback system. The graphical interface displays a computer-generated virtual environment [14] via a computer screen or a head-mounted display to the user. Within this simulated environment, the hand of the user is represented through a cursor or a graphical avatar. During the force feedback simulation, the system runs through the following steps: the sensing system captures the flexion of the joints of the user ’ s fingers. This information is sent to the control

Graphical interface(e.g. 3D graphics)

Sensing system(e.g. CyberGlove®)

Visualfeedback

Forcefeedback

User

Fingerposition

Force feedback device

Actuatorcontrol

Controlcomputer

Figure 20.1 Schematic of a force feedback system. Pictures of the CyberGlove and the CyberGrasp [3] are included to give a comprehensive overview.

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Portable Force Feedback Device Based on Miniature Rolled Dielectric Elastomer Actuators 209

computer for updating the configuration of the avatar. The control computer checks for possible collisions between the user ’ s fingers represented by the avatar and the virtual object. In case of a collision, reac-tion forces are calculated and corresponding commands are sent to the controllers of the actuators. The specifically activated actuators exert thus forces to the contact areas of the user ’ s hand. At the same time, the graphical representation of the VR is updated and presented to the user via the graphical interface.

In general, a FFD has to cover the following requirements to achieve a realistic force feedback:

● Range of forces and directionality : The device should be able to generate forces at given contact points as soon as an interaction between the hand and a virtual object occurs.

● Backdriveability [15] : The device should exhibit low passive intrinsic mechanical impedance so that the free motion of the fingers is not disturbed. Extending this definition, a device is also considered to be backdriveable if it can actively follow the free motion of the fingers.

● Sensing bandwidth [7] : The sensing bandwidth refers to the frequency with which tactile (for texture) and kinaesthetic (for force) stimuli are sensed by the user. For a force feedback system, the interest is on the human kinaesthetic bandwidth of 20–30 Hz.

● Transparency [15] : The transparency determines the ability of a device to reproduce the exact contact force computed by the VR system when the user ’ s fingers collide with a virtual object. Ideally, a user should not notice the weight, inertia and internal friction of the device.

20.2.2 Conceptual approach

As schematically illustrated in Fig. 20.2(a) , the contact with an object during precision grasping con-centrates on the fingertips of the thumb, the index, the middle and the ring finger [16] . The fingers ’ flexion driven by the muscles and tendons in the hand and the forearm is blocked by the contact reac-tion forces, F object , of the grasped object. Neglecting the weight of the object, these reaction forces are opposed and of equal strength to satisfy the static force equilibrium.

In order to simulate precision grasping in VR, a FFD must provide equivalent contact reaction forces, F device , to the contact areas of the fingers as would arise from a real object ( F object � F device ).

Conventional portable FFDs on the dorsal side of the hand ( Fig. 20.2(b) ) need mechanically complex force transmission structures such as exoskeletons and cable-pulley structures [3, 10, 12, 13] , which makes them bulky and heavy. Due to the resulting internal friction and inertia such devices exhibit poor performance in mechanical transparency [15] and dynamics. Moreover, the attachment of the structure to the hand introduces undesired forces, which may bother the force feedback sensation.

One way to avoid force transmission structures is to directly attach the actuators to the contact areas of the user. Regarding grasping devices, the actuators may thus be located either on the palmar or on the dorsal side of the hand [7] . Following both approaches we evaluated various concepts for portable FFDs [17] . Due to minimum kinematics we finally selected the ‘ hand-held ’ approach, where the actua-tors are directly connected between the thumb and the opposing fingers ( Fig. 20.2(c) ).

20.2.3 Actuator evaluation

A ‘ hand-held ’ FFD was implemented earlier by Bouzit [11] based on pneumatic actuators (Rutgers Master II). The concept was proved to be simple, compact, portable and capable to provide a very realistic

Fobject

Realobject

Hand

Attachmentsto the wrist

Actuator

Actuator(a) (b) (c)

Forcetransmission

Actuator

Attachmentto the finger

Factuator

Contact area

Fdevice

Figure 20.2 (a) Reaction forces from a real object blocking the fingers ’ flexion during precision grasping. (b) Schematic of a conventional FFD. (c) Force feedback concept with minimal kinematics.

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210 Chapter 20

grasping feedback of soft and rigid objects to the user. However, for their application to FFDs pneumatic actuators have some distinct disadvantages such as their large weight, static friction, operation noise and compressibility of the air in the cylinders. Moreover, they require an elaborate supply system (compressor, pressure regulator, control valves, air-supply lines).

For force feedback applications, a set of lightweight actuators providing a wide range of forces and passive or actively tracked free motions are required. Furthermore, the actuators have to be safe, reli-able, energy-efficient and need to be supplied by a compact power source.

20.3 MINIATURE ROLLED DE ACTUATORS

According to preliminary investigations [18] , rolled actuators based on soft dielectric EAPs are likely to meet the challenging requirements for their application to a ‘ hand-held ’ FFD.

20.3.1 Design and manufacturing process

Rolled DE actuators consist of a stack of two biaxially pre-stretched DE films, which is wrapped around a fully compressed coil spring ( Fig. 20.3 ). By introducing a telescopic guidance in the core of the actuator, even axial compressive loads can be taken. Miniature rolled DE actuators were fabricated based on a machine-aided manufacturing process [18] .

20.3.2 Principle of operation

In the free-standing state, the coil spring is in force equilibrium with the pre-stretched DE film. In the axial direction, the elastomeric film is pre-stretched by the compressed coil spring, while in the radial direction the circumferentially pre-stretched film is supported by the coil spring core. Under activa-tion the actuator expands in its axial direction ( z -direction). The actuator reaches its maximum active elongation under free axial boundary condition, while the maximum active force is obtained when the actuator is blocked in the axial direction (see Chapter 27).

20.3.3 Theoretical consideration

The theoretical consideration focuses on two particular issues of the rolled actuator configuration. In addi-tion, an estimation of the axial force generation of rolled DE actuators as a function of voltage is given.

Non-uniform pressure distribution across the wrapped DE film

Wrapping of the biaxially pre-stretched film around the coil spring core causes the outer film layers to compress the inner ones. The resulting radial pressure on the inner film layers grows with increasing number of film wrappings as well as with stronger circumferential pre-stretching of the films. As a result, a strong gradient in axial stresses arises across the pre-strained film layers. While the outer film layers are still in the tensile domain the inner ones tend to expand in the axial direction (Chapter 27). In order to thus properly fix all film layers, both ends of the rolled actuators were sealed with polymer ( Fig. 20.3 ).

Aluminium foil

ϕSealed polymer end

Biaxially pre-stretchedDE film bilayer

Telescopicguidance

Working direction

Compressedcoil spring

Electric supply(high voltage)

Electric suppply(ground) Protective

elastomer film

z

r

Figure 20.3 Schematic of the design of rolled DE actuators.

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Portable Force Feedback Device Based on Miniature Rolled Dielectric Elastomer Actuators 211

Non-uniform thickness distribution of the DE film under elongation

For simplification, we assume that in the free-standing, deactivated state ( V � 0) N layers of pre-stretched DE film are concentrically stacked around the rigid spring core with radius R ( Fig. 20.4(a) ). The inner radius of the n th film layer is R n– 1 ( V � 0) and the corresponding outer radius is R n

( V � 0) . Hence, the thickness of the n th film layer is d n

( V � 0) � d ( i ) � R n ( V � 0) – R n– 1 ( V � 0) .

By applying the film ’ s incompressibility condition, the thickness, d n (V � 0 ) , of the biaxially pre-

stretched film (planar pre-stretch ratios � x ( i ) � � y

( i ) in the pre-stretch state (i)) can be calculated based on the original film thickness, d (o) , of the widely used acrylic film VHB 4910 (by 3M) by

d dd

nV i

o

xi

yi

( ) ( )( )

( ) ( ).� � �0

� �

(20.1)

Under free-strain activation ( V � 0), the electrostatic pressure squeezes the dielectric film in its thickness direction and thus the actuator elongates in its axial direction. When the actuator performs an axial strain of S z , all film layers are axially elongated to the same degree ( Fig. 20.4(b) ). Based on the volume conservation of each film layer n

� �R R L R Rn

VnV

nV

nV( ) ( ) ( ) ( )�

�� �

��� � �0

2

10

20

2

10( ) ( )⎛

⎝⎜⎜⎜

⎞⎠⎟⎟⎟ ( ) ( ))⎛

⎝⎜⎜⎜

⎞⎠⎟⎟⎟

21 1 2L S n Nz( ) , , ... ,� �

(20.2)

the normalized thickness of the film layers in the actively elongated state ( V � 0) is obtained by

d

d

d

d

R R

d

Rdn

V

nV

nV

inV

nV

i

i( )

( )

( )

( )

( ) ( )

( )

( )>

⎛⎝⎜

0

0

0 01

0 2

�

� ��

�

� ��

�⎜⎜⎜

⎞⎠⎟⎟⎟ ⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟⎟

� �

�� ��

��

�2 1

11

02

10n

S

R

d

R

dz

nV

inV

i

( )

( )

( )

( )), , ... ,

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟⎟

n N� 1 2

(20.3)

where the radius of the core is assumed to remain constant during elongation ( R o ( V � 0) � R o

( V � 0) � R ). The recursive relationship Eq. (20.3) is evaluated for the miniature rolled DE actuators, whereby R � 3.5 mm, d ( o ) � 1 mm and � x

( i ) � � y ( i ) � 3 � 6.5. The resulting normalized thickness distribution is

exemplarily plotted in Fig. 20.4(c) , for the film layers n � 1, 2, … , 60 and selected axial strain levels, S z , from 0% to 75%.

As can be seen, under axial elongation of rolled DE actuators the thickness of the inner film layers decreases significantly greater than that of the outer ones. This effect becomes more distinct for larger elongation in the axial direction. Under electrical activation of the actuator, this effect leads to an accu-mulation of electrical charges in the domain of the thinner film layers where thus the electrical field increases. Therefore, an electrical breakdown is estimated to occur primarily within the inner film layers of actively elongated, rolled DE actuators.

Film layer 1

Film layer nFilm layer N

Guidedspring core

DE film layer

(a) (b) (c)

R

Deactivated (V � 0)

L

Rn(V�0)

dn(V�0) �d (i)

0 10 20 30 40 50 600.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00Axial strain level

0% 25% 50% 75%

Nor

mal

ized

thic

knes

s, (

d n (V

�0

) /dn(V

�0

) ) (�

)

Film layer number n (�)

R

Activated (V � 0)

z

r

L(1�Sz)

R (V�0) dn(V �0)

Rn(V�0)

ϕ

n�1

R (V�0)n�1

Figure 20.4 (a) and (b) Idealized rolled DE actuator in the free-standing and axially elongated state. (c) Normalized thickness distribution of the film layers of the axially elongated actuator.

Ch20-I047488.indd 211Ch20-I047488.indd 211 12/7/2007 3:06:52 PM12/7/2007 3:06:52 PM

212 Chapter 20

Axial force under blocked strain activation

The compressive force, F com , needed to block the active elongation of a rolled DE actuator starting from the deactivated state ( V � 0) is derived as a function of the activation voltage, V . The stresses of the biaxially pre-stretched film (state (i)) are given by the Cauchy stresses, T j

( i ) , in the directions j � x, y, z ( Fig. 20.5(a) ) by

Tw

p j x y zji

ji

j

ihi( ) ( ) ( ) ( ) , ,� � ��

���

⏐ (20.4)

when introducing the proper boundary conditions (in x: T x � T x ( i ) , � x � � x

( i ) ; in y: T y � T y ( i ) , � y � � y

( i ) ; in z: T z � 0, � z � � z

( i ) ). Therein, w is the strain energy potential of the film, p h ( i ) is the hydrostatic pressure in

the film and � j ( i ) is the film ’ s pre-stretch ratio in the directions j � x, y, z .

The pre-stretched DE film is then wrapped around the coil spring core. We define that the x direction of the DE film points along the axis of the coil spring. Thus, the film ’ s coordinates change from the pla-nar to the cylindrical configuration according to x → z , y → � , z → r ( Fig. 20.5 ).

We assume that the stretch state (i) of the biaxially pre-stretched film equals the stretch state of the wrapped film of the free-standing, deactivated ( V � 0) rolled DE actuator. Furthermore, we take into account that the thickness of the pre-stretched film, d ( i ) , is by far smaller than the radius, R , of the coil spring core (( d ( i ) /R ) � 1). Thus, the equations for the Cauchy stresses in Cartesian coordinates accord-ing to Eq. (20.4) can be applied to all film layers n � 1, 2, … , N of the rolled DE actuator as well

r pw

p

Tw

r nV

zi

z

ih nV

nV

yi

:

:

,( ) ( ) ( )

,( )

,( ) ( )

� � �

�

� �

�

0 0

0

����

� �����

⏐

yy

ih nV

z nV

xi

x

ih nV

p

z Tw

p

⏐

⏐

( ),

( )

,( ) ( ) ( )

,( ):

�

� �

�

� �

0

0 0����

(20.5)

by adapting the boundary conditions (in r : T r � – p r,n ( V �0) , � r � � z

( i ) ; in � ; T � � T � , n ( V �0) , � � � � y ( i ) ; in z :

T z � T z,n ( V �0) , � z � � x

( i ) ). Under blocked strain activation ( S z � 0), the geometry of the incompressible DE film is maintained

since the actuator core is rigid and the actuator ’ s length is maintained. The Cauchy stresses in the acti-vated state ( V � 0) are obtained when the effective electrostatic pressure [19]

p

V

dr i� � �0

2

( )

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

(20.6)

Segment of thepre-stretched DE film

Segment of thewrapped DE film

Deactivated (V = 0) Activated (V > 0)

Layer n

(b)(a)

p

z

r

z

r

yx

z

R

Tx(i )

Tx(i )

d (i )λx(i )

λy(i )

Ty(i )Ty

(i ) Tϕ,n(V�0)

Tϕ,n(V�0) Tϕ,n

(V�0)

Tϕ,n(V�0)

Tz,n(V�0) Tz,n

(V�0)

Tz,n(V�0)Pr,n

(V�0)Pr,n

(V�0)Pr,n

(V�0)

ϕϕ

Figure 20.5 (a) Stretch state of a biaxially pre-stretched DE film. (b) Stretch state of a wrapped DE film layer in deactivated ( V � 0) and activated ( V � 0) condition.

Ch20-I047488.indd 212Ch20-I047488.indd 212 12/7/2007 3:06:52 PM12/7/2007 3:06:52 PM

Portable Force Feedback Device Based on Miniature Rolled Dielectric Elastomer Actuators 213

is superimposed in the radial direction ( T r � – p r,n ( V � 0) � –( p r,n

( V �0) � p ))

r pw

p

Tw

r nV

zi

z

ih nV

nV

yi

:

:

,( ) ( ) ( )

,( )

,( ) ( )

� � �

�

� �

�

0 0

0

����

� �����

⏐

yy

ih nV

z nV

xi

x

ih nV

p

z Tw

p

⏐

⏐

( ),

( )

,( ) ( ) ( )

,( ): .

�

� �

�

� �

0

0 0����

(20.7)

By combining Eqs. (20.4)–(20.7), the resulting compression force, F com , can be derived

F F F F FVz

V Vz

Vcom spring film spring film� � � �� � � �( )

,( ) ( )

,( )0 0 0 0( ) (( ) ( )∑� � �� � �

�

A T T Az nV

z nV

z nV

pn

N

z,( )

,( )

,( )

,(0 0 0

1 � ���� ���� filmVV

r i

V

d�0

0

2)

( ).� �

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

(20.8)

Therein, F Vspring( )�0 is the spring force and A V

film,z( )�0 is the overall axial cross-sectional area of the DE film

layers in the free-standing, deactivated state ( V � 0). As shown, under activation the effective electro-static pressure, p , is transmitted from the radial direction via the hydrostatic pressure into the axial direction of the rolled actuator. Thus, a quadratic increase in compressive force, F com , as a function of the activation voltage, V , is expected.

Taking into account the non-uniform thickness distribution of the wrapped film layers given by Eq. (20.3), the axial force, F z

( V � 0) , of an isometrically ( S z � constant � 0) activated rolled DE actuator is predicted to decrease from the deactivated tensile force, F z

( V � 0) , according to

F F p A F VzV

zV

nV

n

N

z nV

zV

r( ) ( ) ( )

,( ) ( )...� � �

�

� �� � � � �0 0 0

1

0 00

2 2∑ � � �RR

dnV

nV

n

N ( )

( ).

�

��

�0

01

1⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

∑ (20.9)

20.3.4 Experimental characterization of the rolled DE actuators

The actuators were mounted between a base frame and a pneumatic cylinder (Bramati by EMPA Duebendorf), which actively controlled the displacement of the actuators. To measure the forces along the principal axis of the actuator, a load cell was implemented (U2B by HBM). The measurement sig-nals were acquired via an adapter chassis (BNC 2090 by National Instruments) and a data acquisition card (PCI-6070e by National Instruments) and were processed by a LabVIEW program. Optoelectronic couplers (OK RB6200 by Relmatic) were used to isolate the high voltage from the low voltage circuit.

The actuators were characterized by isometric tests at different displacement levels from 0 to 8 mm for driving voltage levels from 0 to 3.5 kV.

From the tests, the force–displacement behaviour ( Fig. 20.6(a) ) and the force–voltage behaviour ( Fig. 20.6(b) ) were obtained. The force–displacement curves of the deactivated ( V � 0) as well as acti-vated ( V � 0) actuator are quasi-linear. As expected, the force–displacement curves gradually shift to lower force levels for increasing activation voltages.

An average compressive force of 5.5 N was found when blocking the actuator ’ s elongation in its free-standing state (blocking force). With free boundary condition in the axial direction an average displace-ment of 2.7 mm was reached (free displacement).

As shown in Fig. 20.6(a) , a wide range of material characteristics (from soft to hard) of both sticky and non-sticky objects can be simulated by the miniature rolled DE actuators in force feedback applications.

From the test results, it was observed that the blocking force decreases quadratically as the applied volt-age is increased ( Fig. 20.6(b) ). This behaviour is in qualitative agreement with the theoretical predictions according to Eqs. (20.8) and (20.9). However, for a quantitative agreement the theoretically estimated force development had to be reduced by a factor of 0.45 (dashed lines in Fig. 20.6(b) , � r � 3.12 [20] ). The undershooting of the experimental performance may have originated from inhomogeneities of the used materials and imperfections introduced during the manufacturing of the actuators. The wide variance in measurement results from the tested actuators (the blocking force ranged from 1.47 to 7.2 N and the free displacement from 1 to 5 mm) points out the issue of unsatisfying reproducibility.

Ch20-I047488.indd 213Ch20-I047488.indd 213 12/7/2007 3:06:53 PM12/7/2007 3:06:53 PM

214 Chapter 20

20.4 ELECTRICAL SAFETY ISSUES

The investigation of the electrical failure behaviour of the actuator-user system was based on an elec-trical model including the human user [21] , the DE actuator, a power supply and connecting electric cables ( Fig. 20.7 ). Possible failures of the system and thus endangerments to the user can occur mainly in two ways: the actuator is discharged through the human body (i) with or (ii) without being connected to the power supply ( Fig. 20.7 ).

In the failure case (i), the human operator is subjected to the supply circuit of the actuator. According to [22] , the current provided by the power supply has to be limited to 25 mA and is to be interrupted in failure case not later than 2 s. Beyond this limitation, disturbances of formation and conduction of impulses in the heart may occur. Practically, this limitation was accomplished by integrating a residual current circuit breaker between the actuator and the power supply.

In the failure case (ii), a maximum effective current of 22 mA over an impulse duration of 7 ms cor-responding to a discharge of 0.125 mC results for a driving voltage of 5 kV, resistances of R a � 90 k � and R s � 2.5 M � , a capacitance of C a � 25 nF, an impedance of Z i � 0.5 k � (current path hands to feet) and a copper cable length of 0.1 m (portable source). According to IEC 60479-2 [23] , this dis-charge through the human body may cause pain at the contact area, but does not have harmful physi-ological effects. Regarding the actuator design further protective measures were taken by insulating the rolled DE actuator and by connecting the outermost electrode to ground potential.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5�10

�5

0

5

10

15

Fitted theoretical estimation

Displacement

0 mm 1 mm 2 mm 3 mm 4 mm 5 mm 6 mm 7 mm 8 mm

Axi

al fo

rce

(N)

Activation voltage (kV)

Axial displacement

Blockingforce

0 1 2 3 4 5 6 7 8�6

�4

�2

0

2

4

6

8

10

12

14

16Activationvoltage

0 kV 0.4 kV 0.8 kV 1.2 kV 1.6 kV 2.0 kV 2.4 kV 2.8 kV 3.2 kV 3.5 kV

Axi

al fo

rce

(N)

Axial displacement (mm)

Working space fornon-sticky objects

Working spacefor sticky objects

Free-standingstate

Free displacement

Activation voltage

(a) (b)

Figure 20.6 (a) Force–displacement behaviour of the miniature rolled DE actuators at different activation voltage levels. (b) Experimental and fitted theoretical force–voltage behaviour of the miniature rolled DE actuators.

Power supply Electric cables DE actuator Human user

Zs2

Zi ZT

Rs

Ra

Ca

Zs1

Failure case (i)Failure case (ii)

Figure 20.7 Electrical model of the actuator-user system according to a FFD driven by the miniature rolled DE actuators.

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Portable Force Feedback Device Based on Miniature Rolled Dielectric Elastomer Actuators 215

20.5 DEMONSTRATION DEVICES

Two force feedback demonstration devices based on the miniature rolled DE actuators were built. The first device consisted of a rolled actuator, which was mounted inside a transparent Perspex cylinder ( Fig. 20.8(a) ). Holding both ends of the device, the user could feel the actively generated force and/or displacement of the actuator.

Secondly, a FFD according to the proposed ‘ hand-held ’ concept was implemented, where three rolled DE actuators were attached via spherical joints between the thumb and the index, the middle and the ring finger ( Fig. 20.8(b) ).

20.6 CONCLUSIONS

In this chapter, we presented a transmission-free, portable FFD driven by the miniature rolled DE actua-tors. The actuators exhibited a maximum blocking force (blocked boundary condition) of 7.2 N and a maximum elongation (free boundary condition) of 31% according to the active zone and 11% accord-ing to the overall length, respectively.

The implemented FFD operates noiseless and has a much lower mass (38 g) than existing devices such as the Rutgers Master II (185 g) and the CyberGrasp (340 g).

From the studies on the failure mechanisms of electrical safety, we found that discharging of the miniature rolled DE actuators alone does not have harmful physiological effects on a human user. To protect the user from the energy delivered by the power supply, the failure current in the circuit was limited to 25 mA by a circuit breaker.

In the next steps, the proposed FFD has to be implemented in a control environment and extensive psychophysical tests have to be conducted (preliminary results in [18] ). At the same time, the electro-mechanical reliability of the rolled DE actuators needs to be significantly improved. To overcome the viscous restrictions (frequency limitation, energy losses) of the DE actuators from widely used VHB 4910 (by 3M), appropriate dielectric films with purely elastic mechanical properties (e.g. silicone-based films) have to be developed [24] . A fully automated manufacturing process for the miniature rolled DE actuators is required to avoid poor reproducibility originating from manual production.

ACKNOWLEDGEMENTS

This study has been funded by the Swiss National Science Foundation (SNSF) and was greatly sup-ported by the Swiss Federal Laboratories for Materials Testing and Research (EMPA).

References

[1] Youngblut, C. (1996). Review of virtual environment interface technology. Technical Report IDA Paper

P-3186, Institute for Defense Analyses (IDA).

Figure 20.8 Two demonstration devices for the generation of a force feedback with the miniature rolled DE actuators.

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216 Chapter 20

[2] Hamit, F. (1993). Virtual Reality and the Exploration of Cyberspace . Sams Publishing, Carmel, IN, USA.

[3] www.immersion.com.

[4] Gausemeier, J. (2004). A virtual reality-based design environment for self-optimizing mechatronic systems,

In Mechatronics and Robotics , Eds. Drews, P. Eysoldt, Aachen, pp. 1333–1339.

[5] Spagno, C. (2003). Construction of a three-sided immersive telecollaboration system. Proceedings of the IEEE VR , March, Los Angeles, CA, pp. 22–26.

[6] Atkins , J. E. ( 2003 ). Experience-dependent visual cue recalibration based on discrepancies between visual

and haptic percepts . Vision Res. , 43 , 2603 – 2613 .

[7] Burdea , G. C. ( 1996 ). Force and Touch Feedback for Virtual Reality . John Wiley & Sons, Inc ., New York, USA.

[8] www.sensable.com.

[9] www.forcedimen sion.com.

[10] Stergiopoulos, P. (2003). Design of a 2-Finger Hand Exoskeleton for VR Grasping Simulation. Proceedings of Eurohaptics 2003 , July, Dublin, Ireland, pp. 80–93.

[11] Bouzit , M. ( 2002 ). The Rutgers Master II-new design force feedback glove . IEEE/ASME Trans. Mechatron. , 7 ( 2 ) , 256 – 263 .

[12] Bouzit, M. (1996). Design, implementation and testing of a data glove with force feedback for virtual and

real objects telemanipulation. PhD Thesis, University of Pierre et Marie Curie.

[13] Choi, B. (2000). SKK hand master-hand exoskeleton driven by ultrasonic motors. Proceedings of the 2000 IEEE/RS International Conference on Intelligent Robots and Systems , September, Taipei, pp. 1131–1136.

[14] Conti, F. (2005). CHAI 3D – an open-source library for the rapid development of haptic scenes. Proceedings of the IEEE World Haptics , March, Pisa, Italy.

[15] Barbagli, F. (2003). Enabling multi-finger, multi-hand virtualized grasping, Proceedings of the IEEE International Conference of Robotics and Automation , Taipei, pp. 1259–1263.

[16] Cutkovsky , M. ( 1990 ). Human grasp choice and robotic grasp analysis . In Dextrous Robot Hands , Eds.

Venkataraman , S. T. and Iberall , T. Springer , New York , pp. 5 – 31 .

[17] Zhang, R. (2006). Dielectric elastomer spring roll actuators for a portable force feedback device. Proceedings of the 14th Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems , March,

Arlington, Washington, DC, p. 53.

[18] Zhang, R. (2007). Development of dielectric elastomer actuators and their implementation in a force feed-

back interface. PhD Thesis, Diss. ETH No. 17584, ETH, Zurich.

[19] Pelrine , R. ( 1998 ). Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation .

Sens. Act. A Phys. , 64 ( 1 ) , 77 – 85 .

[20] Wissler, M. (2006). Electromechanical coupling in dielectric elastomer actuators. Sens. Act. A Phys. , 138(2), 384–393.

[21] Biegelmeier , G. ( 2003 ). Schutz in elektrischen Anlagen. Band one: Gefahren durch den elektrischen Strom . VDE Verlag GmbH , Berlin .

[22] IEC (1994). Effects of Current on Human Beings and Livestock. Part 1: General Aspects , IEC 60479-1 , 3rd

edn. International Electrotechnical Commission (IEC), Geneva.

[23] IEC (1987). Effects of Current Passing Through the Human Body , Part 2: Special Effect s , IEC 60479-2, 2nd edn. International Electrotechnical Commission (IEC), Geneva.

[24] Zhang, X. Q. (2004). Effects of crosslinking, prestrain, and dielectric filler on the electromechanical response

of a new silicone and comparison with acrylic elastomer. Proceedings of the Smart Structures and Materials 2004: Electroactive Polymer Actuators and Devices (EAPAD) , San Diego, CA, V5385, pp.78–86.

Ch20-I047488.indd 216Ch20-I047488.indd 216 12/7/2007 3:06:54 PM12/7/2007 3:06:54 PM

PROGRAMMABLE SURFACE DEFORMATION: THICKNESS-MODE DIELECTRIC ELASTOMERS AND THEIR APPLICATIONS

Harsha Prahlad

SRI International, Menlo Park, CA, USA

Abstract

The use of arrays of actuators or sensors to apply (or sense) arbitrary surface deformations without undue complex-

ity is critical for many applications. Some examples discussed in this chapter include Braille-type devices, vibrat-

ing actuators for tactile feedback in consumer devices, massagers, and other biomedical applications and in fluidic

systems. A configuration of dielectric elastomers (DE) called ‘ thickness mode ’ allows the creation of active surface

texture on a simple, monolithic structure in response to these needs. This configuration employs a thicker passive

layer bonded or coated onto the ‘ active ’ DE film. When the DE is actuated, changes in the polymer are at least par-

tially transferred to (and often amplified by) the passive layer. The result is a rugged, flexible, and conformal skin

fabricated using two-dimensional patterning that can be arbitrarily actuated in the out-of-plane direction. Thickness

changes of the order of 0.5–1 mm and out-of-plane blocked pressures exceeding 15 kPa (2.2 psi) on a 2–3 mm

thick device employing only one active DE layer have been demonstrated. Achieving similar deflections in the out-

of-plane direction would otherwise require a very large number of layers or a complex mechanism to convert the

fundamentally in-plane expansion of DEs into the out-of-plane direction.

Keywords : Adaptive topography, artificial muscle, Braille, dielectric elastomer, electroactive polymer, haptic

display, surface features, surface texture, tactile feedback.

21.1 INTRODUCTION

The ability to rapidly change the surface shape or texture of a monolithic material is desirable in numerous applications. Changing the surface texture on-demand requires a high density of actuators. Applying a large number of discrete actuators for many of these applications would be untenable in terms of cost and complexity. A thin, monolithic actuator with addressable patterns and the ability to actuate out-of-plane is more desirable for these applications. This chapter describes a configuration of DEs that allows relatively large out-of-plane actuation displacements on a thin, monolithic substrate.

The applications for such an actuator configuration are numerous and are discussed in more detail in Section 21.4. For example, programmable ‘ active ’ surface deformations are required in refreshable Braille displays. These refreshable displays can be used to convey changing information (such as read-ing web pages on the Internet, for example) for the blind [1] . Several other biomedical applications require the introduction of vibrotactile forces onto human skin. Perhaps the most common examples are commercially available massaging pads. Other biomedical devices employ mechanical vibrations for sensory augmentation or balance enhancement [2] .

Texture feedback is also desirable in teleoperated robots to allow the user to feel texture in addition to force. Currently, teleoperated robots being developed for remote surgery have force but not texture feedback [3, 4] . While discrete electromagnetic actuators are suitable for force feedback applications on fingers [5, 6] , they cannot be packaged into the spatial density required for real texture perception [7] . In addition to telesurgery, simulation of texture feedback is the subject of active research for a variety of other applications including textile and consumer product prototyping [8] .

Chapter 21

Ch021-I047488.indd 217Ch021-I047488.indd 217 12/7/2007 3:07:18 PM12/7/2007 3:07:18 PM

218 Chapter 21

The common need in these applications is an actuatable (or sensing) monolithic surface that is thin and can be finely patterned and individually addressed to produce (or sense) surface deformations and forces. Yet, assembling large arrays of discrete point actuators to achieve an active surface is prohibi-tive in cost, actuator density, package thickness, and fabrication complexity. Electromagnetic actuators as well as most traditional smart materials are rigid, and are not flexible enough to conform to human limbs or other uneven surfaces so as to form a smart ‘ skin. ’ They are also typically too big to be pack-aged with a high spatial density on a thin, flat substrate [1] . Assembling discrete actuators into a large array is also likely to be far more expensive than an approach involving patterning actuators onto a sin-gle substrate layer.

In response to these needs, a new configuration of DE actuator was developed. This configuration, called the thickness-mode actuation technique, greatly simplifies variable surface texture devices. Using this technique, one can create virtually any desired pattern of bumps and troughs on a single substrate by simply patterning the electrodes on one surface of the DE and addressing the appropriate electrode.

It is useful to note that DE films can be used to directly actuate surface texture and, indeed, these films intrinsically contract in thickness when actuated. The direct thickness contraction can directly change surface topography. However, in many if not most cases, the direct thickness contraction is much smaller than the desired topography changes. For example, a typical film might be 50 � m thick and contract 10 � m in thickness. If an application such as Braille requires, for example, a topogra-phy change of 500 � m, one would need to use 50 layers of DE film. DE actuators of more than 50 layers have been demonstrated [8] , but the large number of layers complicates fabrication, wastes power, and is unnecessarily costly if only the displacement, but not the full mechanical energy of 50 layers, is needed by the application. Thus, the thickness-mode configuration provides a way to amplify, in absolute terms, the out-of-plane motion of a DE actuator without increasing the number of layers.

21.2 THICKNESS-MODE ACTUATOR CONFIGURATION

The thickness-mode actuator forms a rubbery skin that can be quite rugged. It can be fabricated using only two-dimensional (2D) patterning. The result is a spatially distributed, thin, planar actuator or sen-sor that can be composed entirely of soft, rubbery materials and can provide patterned actuation (or sensing) in the out-of-plane direction wherever it is desired. In this way, a thin flexible skin that can cover large or small areas and contain finely patterned electrodes can be constructed. We note that although the basic principles and applications are discussed in this chapter with respect to DEs, many of the same techniques can be directly applied to other types of electroactive polymers (EAPs) and, in fact, even to some non-EAP smart materials. These characteristics make the thickness-mode configur-ation ideally suited for some of the applications described above, as well as for others that are described in Section 21.4.

Several different configurations are possible. In the primary configuration shown in Fig. 21.1 , the active DE polymer film is bonded or coated with a thicker passive layer, such that changes in the area and thickness during actuation of the DE are transferred to the passive layer. The passive layer in this case has no electric field applied across its thickness and is thus not electroactive. As the DE expands in area and decreases in thickness, it drags the passive layer with it. Thus, the passive layer also propor-tionately increases its area and decreases its thickness. Since the absolute thickness of the passive layer is larger than the DE layer, its absolute out-of-plane displacement is also larger. In this way, the change in thickness in the passive layer can be used to amplify, in absolute terms, the displacement produced by an increase in area or a change in thickness of the DE polymer layer.

A schematic diagram of this type of device and the results of thickness-mode actuation is shown in Fig. 21.1 . The grid pattern arises from the electrode configuration on top and bottom side of the active polymer film. Depressions indicate electroded regions and the raised lines indicate areas border-ing active regions, as shown in the figure.

Thickness-mode structures approximately 1 mm thick can show appreciable thickness change. In the case of prestrained acrylic films, laminating the passive layer onto the prestrained DE layer supports the prestrain in the film and can eliminate the need for a separate rigid frame to support the prestrain. It is possible to make the entire structure transparent or opaque as desired using appropriate electrodes and passive layers.

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Programmable Surface Deformation: Thickness-Mode Dielectric Elastomers 219

Any arbitrary shape can be produced by appropriate patterning of the electroded regions. For exam-ple, Fig. 21.2 demonstrates other shapes of surface deformation induced by different electrode pat-terns. If a fixed pattern of surface deformation is desired, the compliant electrodes can be deposited on the DE by a spray deposition process and actuated when required. One can also make a dense array consisting of pixels of electrodes and address the appropriate pixels to create an out-of-plane display. Alternatively, if a dynamic pattern is desired, it is best to deposit electrodes in a grid pattern based on ‘ pixels ’ of electroded area. Individual addressing of each electrode pattern can be accomplished by laminating the entire structure onto a printed circuit board. An alternative method of individually addressing individual EAP electrodes in a surface actuator array is to use a thin-film photoconductive high-voltage switch made of amorphous silicon fabricated on a plastic [9] . With this approach, one can simply use a light source with a mask to selectively allow light to hit only the photoconductive switches that address the appropriate actuators.

Passive polymer or gelcoating (typically soft

elastomer)

Thickness changeof passive polymercoating

Bulges areenhanced aswell

Compliantelectrodes

Flexible foam backing(optional)

Polymer(e.g. acrylic)

Directthickness

change

�V

V Top view(a)

(b) Voltage off Voltage on

Cross-section of single element

Figure 21.1 Thickness-mode actuation: (a) underlying electrode grid pattern and schematic of basic element and (b) resulting surface change of acrylic DE with electrodes in grid pattern.

Voltage off Voltage on

Voltage off Voltage on

Figure 21.2 Thickness-mode actuation using patterned electrodes can be used to display text or other patterns.

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220 Chapter 21

21.3 DESIGN PARAMETERS AND MODELLING

The forces and strokes of the actuator depend on a number of design parameters that are shown in Fig. 21.3 . The design parameters are as follows:

● Elastic modulus (Young ’ s modulus) of the DE material, Y d ● Elastic modulus of the passive layer, Y p ● Thickness of DE material, t d ● Thickness of passive layer, t p ● Width of electroded area, w ● Distance (spacing) between successive electrodes (not shown in Fig. 21.3 )

A preliminary analysis helps clarify the relationship between these design parameters and the thick-ness change (or blocked force). To simplify the analysis, we consider a DE device with a single elec-troded region with a width w and infinite length. The DE film and the passive layer are coated over the entire electroded area, as shown in Fig. 21.3 .

The normal actuation pressure for the DE layer is given by the pressure equations found in Chapter 1 of this book. In the absence of a passive layer, this actuation pressure p results in a free strain of the electroded area S f , given by (assuming small strains for analytical simplicity)

SP

Yfd

� �0 5. (21.1)

where the factor 0.5 is the Poisson ’ s ratio of the incompressible DE polymer. When an external constraining load is applied in the planar direction of the film (the compressive load

applied on the DE layer by the passive layer), the actuation strain in the planar direction [10] S x is given by

S

pFwt

Yx �

�0 5. load

d

d

(21.2)

The corresponding actuation thickness strain S z is given by

S

pF

wt

Yz �

� �0 5. load

d

d

(21.3)

The passive layer experiences a tensile load equal and opposite to the compressive load exerted on the DE film by the passive layer. This tensile load causes the passive layer to elongate and reduce in thickness. In addition, most thick passive materials undergo some shear deformation, which causes raised bumps bordering the electroded area as shown in Fig. 21.3 . For the sake of simplicity, we neglect the shear deformations and assume that the passive layer only undergoes homogenous planar (and thickness) strains. In this case, the planar strain on the passive layer is simply given by Hooke ’ s law:

F

wtY Sx

load

pp

2� (21.4)

Electroded areaActive (DE) layer

Passive layer

tp, Ep

td, Ed

Figure 21.3 Design parameters for thickness-mode DE.

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Programmable Surface Deformation: Thickness-Mode Dielectric Elastomers 221

The factor of 2 arises from the assumption that the passive layer is on both sides of the DE film. Similar structures, can, however, be built if the passive layer is coated on only one of the sides of the DE layer. Assuming perfect bonding between the DE layer and passive layers, the planar strain in the pas-sive layer is the same as that of the DE layer. The resulting thickness strain is related by Poisson ’ s ratio:

S SF

wt Yz x� � � �0 50 5

2.

. load

p p (21.5)

Rearranging Eq. (21.5) into Eq. (21.4), we get

S

pwt Y S

wt

Yz

z

�

� �2 p p

d

d

or

Sp

Yt Y

t Y

Vt

Ytz �

�

�

�

�dp d

d d

rd

dp

12

12

0

2

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

� �YY

t Yd

d d

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

(21.6)

where � r , � 0 , and V are defined in Chapter 1. The resulting thickness change in surface trough is given by

t t t

Vt

Yt Y

t Y

p p p rd

dp d

d d

� �

�

′

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

� �0

2

12

(21.7)

In the limiting case where if t p Y p � � t d Y d (i.e. the passive layer imposes a blocked force boundary con-dition on the DE layer), the thickness strain reduces to

′St p

Y tz � d

p p2 (21.8)

where p is the actuation pressure. The resulting blocked pressure that can be measured when actuation in this trough is switched off is

then given by

P Y

Vt

Yt Y

t Y

act p rd

dp d

d d

�

�

� �0

2

12

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

(21.9)

From Eq. (21.7), it is apparent that in order to obtain greatest height change, we want a thick layer of a very soft material as the passive layer. However, as seen from Eq. (21.9), this choice results in very small actuation pressures exerted by the tactile feedback device.

This trade-off is graphically illustrated in Fig. 21.4 . To illustrate the effect of the passive layer stiff-ness, we consider two different elastic moduli of 0.1 and 0.5 MPa for the passive layer. An elastic modu-lus of 1 MPa for the DE layer is assumed. The thickness of the unactuated DE layer in this example is 60 � m, and an electric field of 200 V/ � m is used for calculation. As seen from the figure, increasing the elastic modulus for a given thickness (or vice versa) increases the blocked actuation pressures that can be obtained, but decreases the thickness change that the material can undergo when there is no load.

The combination of thickness change and actuation pressure for a given configuration depends on the specific application needs. For example, in an application involving only surface topography change

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222 Chapter 21

such as adaptive three-dimensional (3D) displays, adaptive optics, and so on, obtaining a large thick-ness change may be of primary importance. However, in tactile applications such as haptic displays and tactile feedback devices, maximum possible actuation pressures may be the priority.

It is instructive to compare the surface height change of the thickness-mode DE to that of a single layer of active DE film. For example, from Fig. 21.5 , we see that a no-load thickness change of approximately 0.33 mm is obtained by actuating a DE film with a laminated passive layer of 0.1 MPa elastic modulus and a thickness of 1 mm. The DE film in this case is 60 � m in thickness. This configur ation corresponds to a thickness strain of nearly 33%. If the same thickness strain were observed in the DE film itself, the resulting change in thickness of the DE film would be 0.66 � 60 � 40 � m. Thus, a nine-layer stack of DE films, each 40 � m thick, would be needed to achieve the same thickness change of 0.33 mm that can be achieved with a single thickness-mode DE passive layer. Hence, it can be seen that the thickness-mode DE structure acts as a stroke amplification mechanism to increase the thickness of the DE film, or to dramatically reduce the number of stacked DE films that would be required to achieve a certain thick-ness change (assuming that the full energy of multiple layers is not required in the application).

To date, limited quantitative information is available on the performance parameters of the thickness-mode DE devices to validate this simple analytical model. Thickness changes of 0.5–2 mm have been measured using low-durometer elastomers as passive layers. As mentioned below, both the free stroke and the blocked pressure on the active area depend on several parameters not included in the prelimi-nary model. A measurement was made on a pattern comprising thick electroded lines as the active area.

Dielectric elastomer Ground electrode�Ve electrode

Travelling wavePassive elastomer

Substrate surface

Figure 21.5 Inducing a travelling wave through thickness-mode DE can result in gentle massaging. An alternative application is a vibrating conveyor that uses the travelling wave to move two surfaces relative to each other.

Displacement, Ep = 0.1 Mpa

Pressure, Ep = 0.5 Mpa

Pressure, Ep = 0.1 Mpa

Displacement, Ep = 0.5 Mpa

120.000.40

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.00

0.10 0.60 1.10 1.60 2.10Passive layer thickness (mm)

Blo

cked

pre

ssur

e (K

Pa)

Fre

e th

ickn

ess

chan

ge (

mm

)

2.60

100.00

80.00

60.00

40.00

20.00

0.00

Figure 21.4 Trade-off between thickness change and actuation pressures for a few different material and geomet-ric parameters of thickness-mode DE actuation.

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Programmable Surface Deformation: Thickness-Mode Dielectric Elastomers 223

The electroded lines were 5 mm in width, 5 cm in length, and 5 mm apart. The passive layers were 1 mm in thickness on each side. A force gage with a plastic tip 2.5 mm in diameter was used for the measure-ment. Measured force over the active area was 78 g or approximately 0.7 N with DC voltage actuation. This corresponds to a pressure of 16 kPa (2.3 psi) in a direction normal to the plane of the DE film. In this example, the actuation voltage was 3 kV and the DE device has two layers of 3 M VHB 4905 with a prestrained thickness of 30 � m in each layer. This results in an initial electric field of 100 V/ � m.

Estimating that the elastic modulus of the passive layer (not measured) was half that of the DE layer, and substituting the above information into Eq. (21.9), we obtain a predicted force of 0.83 N at an actuation field of 100 V/ � m. Even with some substantial unknowns and simplifications, the model pre-dictions are close to the measured data for this simplified blocked force comparison. A more compre-hensive evaluation of the model with experimental data has not yet been conducted.

It may also be noted that shear deformations in the passive layer cause raised bumps in regions neigh-bouring electroded regions, and these effects are not included in the simple model described above. In addition, interactions between successive electrodes in a grid pattern cause boundary forces that are not included in this simple analysis. When these factors are included, the surface deformation is expected to become a function of the electrode width w as well as electrode-to-electrode spacing.

The frequency characteristics of the thickness-mode actuator depend on the DE film material (acrylic or silicone), the passive layer material viscoelasticity, and the driving electronics. We have demonstrated a relatively flat force profile for thickness-mode devices with frequency. For example, using acrylic film, we have measured 60% of the DC forces at 100 Hz and 75% of DC forces at 50 Hz. Strong vibra-tions can be felt from such devices at frequencies of up to around 1 kHz. By adding chemical modifiers to the DE films, it is possible to further improve the bandwidth in acrylic films [11] .

21.4 APPLICATIONS OF THICKNESS-MODE ACTUATORS

There are several possible applications for thickness-mode DE actuation. These applications can be classified among the following categories.

21.4.1 Haptic displays

As mentioned in Section 21.1, haptic displays such as Braille and other force feedback input devices could benefit from arrays of thickness-mode DE actuators. Refreshable Braille displays that use piezo-electric bending beam, shape memory alloy (SMA) wires, and electrochemical-type EAP actuators to raise the Braille dots have been previously investigated. Some of the drawbacks of these methods include poor efficiency and excessive power consumption for SMAs and space and cost limitations of large array piezoelectric actuators. Electrochemical EAPs are also power-intensive, slow, and sensitive to temperature and humidity.

In contrast, a DE Braille display produces large displacement as well and can be low cost and effi-cient. A refreshable Braille prototype that has been previously demonstrated uses DE diaphragm actu-ators and pressurized air bias [12] . Replacing this device with the thickness-mode DE structure removes the need for an external bias mechanism and thus forms a thin compliant surface with addressable elec-trodes that can interface with human fingers. The all-polymer actuator can be moulded in the shape of a glove or in the form of a planar actuator pad. In addition to static surface deformation, the same device can be used to induce vibrotactile feedback by mixing a time-varying signal on top of a DC voltage.

Braille devices typically require a minimum blocked force of 5 gF on a 1.5 mm diameter area [13] . This corresponds to a blocked actuation pressure of around 27 kPa. This represents only a slightly higher actuation pressure than the 16 kPa measured to date with a thickness-mode DE device. We anticipate that with a thickness-mode device specifically designed and optimized for the Braille display, we will be able to come close to the requirement specifications with this configuration. Other significant issues such as the spacing of the electrodes and the lifetime of the device will also have to be investigated.

Force-feedback devices for other tactile applications (such as telesurgery or virtual manufacturing) typically convey force feedback by actuating kinaesthetic forces exerted by electromagnetic actuators on the user ’ s finger, hand, or body. Spatially distributed haptic texture information through the use of the thickness-mode actuators may be able to both increase the sense of realism of an object and convey vital information about the virtual object to the user [14] .

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224 Chapter 21

It is instructive to note the performance specifications required for tactile force feedback devices. These requirements vary greatly with the application. For example, commercially available electromag-netic actuators mounted on vibrotactile gloves provide 1.2 N of force on each finger [5] . In addition to the five fingers, these gloves typically also comprise one or two discrete actuators on the palm of the hand, making the total applied force applied by these actuators approximately 7.2 N. Estimating an available surface area of 120 cm 2 on a glove, this total force averages out to an actuation pressure of approximately 600 Pa over the entire glove surface. As discussed in Section 21.3, current thickness-mode DE devices deliver actuation pressures in excess of this average pressure. Although this is a first-order calculation, and it may not be desirable to have the vibration distributed everywhere in a glove, the preliminary calculation shows that the current levels of performance of thickness-mode actuators are likely to be viable, low cost, and simple alternatives to provide the required force for vibrotactile feedback in these types of haptic devices.

The elements of a thickness-mode DE pad can also be used as sensors to make a touch-sensitive skin for recording human interactions with the environment. The electrodes could be patterned or poled such that the capacitance of each individual element can be sensed, providing a tactile picture of an object. Sensing and actuation can be simultaneously accomplished with such devices. An example is a robot skin used to map contact or incorporated into a force plate for biomechanical studies. Another applica-tion for a soft, compliant sensor that can measure spatial distribution of pressures is a seat occupancy sensor in a car to help classify the passengers in an automobile.

There is an increasing demand for tactile feedback in user input devices for consumer electron-ics. For example, a conventional touch-screen display has no tactile or haptic component to it. These devices thus require the full visual attention of the user. Further, the user has no tactile feedback that indicates that the intended button(s) have been pressed successfully. The use of actuatable keyboards or buttons could offer tactile in addition to visual feedback in several consumer devices with shrinking user interfaces or keypads. It may also be possible to change the tactile buttons on the same device for various modes of operation (e.g. a mobile phone keypad that changes to a calculator layout, QWERTY keyboard, or game controller).

21.4.2 Biomedical devices

An all-elastomer thickness-mode DE pad conforms comfortably to the body and thus is ideally suited for external use in biomedical applications. For example, this pad can have a massaging function. One method to realize such a massager is to induce travelling wave patterns on a substrate, as shown in Fig. 21.5 . This design consists of two or more sets of electrodes that are actuated out-of-phase with each other to produce a travelling wave.

The requirements for massagers vary greatly with their intended use. Thickness-mode DEs are particu-larly suited for low-force, large-area massagers. For example, a large, thin, compliant, and lightweight elastomeric pad can be used as a portable massaging pad that can be draped over a chair or mattress. The material ’ s compliance and absence of hard points is also an advantage for massaging cuffs, braces, and the like, such as those used in sportswear and for physiotherapy. Flexible and wearable massaging cuffs or gloves may also aid surgeons during long procedures. The compliant and thin nature of these vibrating thickness-mode DE devices also enables them to be integrated into a variety of garments and textiles. In addition to massaging, compliant vibrating pads can form the basis of vibrating footwear products for sensory augmentation or balance enhancement functions [2] .

One attractive feature of the thickness-mode DE for the above applications is that mechanical load-ing (in a direction normal to the plane of the device) can result in even greater actuation pressures. The mechanical preload serves to decrease any viscoelastic or other losses in the passive layer, and in the transfer of the actuation pressures from the film more directly through the passive layer (at the cost of thickness change). This feature is attractive in footwear applications where human weight would serve as a preload to improve the vibrotactile forces that are felt through the thickness-mode DE.

If the thickness-mode structure is brought into close proximity with a rigid layer, the bumps and troughs could act as valves or pumping elements in a ‘ lab-on-a-chip ’ type of microfluidic system. Microfluidic devices promise to enable the rapid screening of pharmaceuticals or allow researchers to better understand the roles of proteins and genes by allowing fast, massively parallel testing. Recently, the need to rapidly screen for disease-causing agents has received much interest. Because the thickness-mode

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Programmable Surface Deformation: Thickness-Mode Dielectric Elastomers 225

DE device is based on very simple 2D fabrication procedures and uses low-cost materials, it can be made inexpensively enough to be disposable.

21.4.3 Mechanical devices

Several other applications of surface texture exist. These include applications in the field of consumer goods, fluid dynamics and aerospace (boundary layer control), automation (vibrating conveyors), adap-tive optics, and 3D signage. These applications are discussed below.

The current global marketplace puts a premium on the ability to design and test a product in a virtual form even before a physical prototype is constructed. Thus, there is an increased demand to perform virtual manufacturing and testing of products in the consumer marketplace. While force feedback and audio-visual cues are routinely part of this virtual environment, texture feedback is an important but largely missing component. In some cases, it is desirable to rapidly optimize the texture of a product through user feedback without manufacturing expensive prototypes for each type of texture. In such cases, having an actuatable surface that can simulate different surface textures rapidly can be part of an early user feedback survey. Several different prototypes can thus be simulated to obtain feedback before a manufacturing run. Depending on the spatial resolution and the specifications, thickness-mode DEs may offer a means to achieve this challenging goal.

In laboratory prototypes, it has been shown that the addition of polymers or micro-texture to the tur-bulent flow of water around flat plates can reduce friction drag by as much as 80% or more [15] . The foam-backed skin version of the device shown in Fig. 21.5 could be the basis of a smart skin that controls the fluid flow by actively inducing bubbles or surface deformations in the boundary layer on a boat or air-plane. Drag-reducing fixed ridges are also a regular feature in a variety of devices such as sailboats and golf balls. However, such ridges may not be desirable or beneficial under all flow conditions. An adaptive skin could help these ridges (or troughs) appear only when necessary, and only in desired spatial regions or in different patterns (such as depending on the speed of the object through the fluid). The skin could also modulate texture or appearance (at various electromagnetic or acoustic frequencies, depending on the size scale of the features). A vibrating smart skin based on thickness-mode DEs may also form the basis of anti-fouling skins that prevent debris or fouling agents from accumulating on an underwater surface.

A travelling wave structure such as the one shown in Fig. 21.5 might also form the basis for a vibrat-ing conveyor to transport lightweight materials across a flat surface by inducing vibrations. In this case, it is necessary to pattern additional electrodes and operate them with the appropriate phase lag to create such a travelling wave. SRI has recently experimentally demonstrated the use of thickness-mode trav-elling waves to convey a shaft on the surface of the actuator. Alternatively, the travelling waves could form the basis of energy-efficient locomotion of a lightweight robot, similar to pedal waves used by snails and slugs for locomotion. Travelling waves are also useful in transporting droplets of fluids from one point on a surface to another. Such devices could be used to prevent the accumulation of fluid drop-lets, or to enable lab-on-a-chip microfluidic devices, as mentioned above.

The complex surface changes produced by the thickness-mode DE can also serve as a flexible base for several applications. For example, as illustrated in Fig. 21.2 , adaptive logos or signs that appear on demand can be easily produced. A topographical 3D representation that can appear on a computer screen only when required might be used for secure visual communication. Adaptive 3D signage can be realized through this technique. The topographical actuation of the thickness-mode DE can also be used as a basis for adaptive optics. For example, the thickness-mode DE can be used to adjust the shape of a flexible mirror that is laminated over the passive layer. Such actuated mirrors with fine shape correction capabilities are required in large-area space-based adaptive optics . The bulging shapes produced on the surface of a thickness-mode DE can also form the basis of a shape-changing lens for adaptive optics. Such thin shape-changing (and thus focal-length-changing) lens could find a variety of applications in devices such as miniature cell phone cameras and optical switches.

21.5 SUMMARY

This chapter has discussed a configuration of DE that enables surface deformations to be induced on a compliant elastomeric substrate. In this configuration, the active polymer film is bonded or coated with a thicker passive layer, such that changes in the polymer thickness during actuation of the DE device

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226 Chapter 21

are at least partially transferred to (and often amplified by) the passive layer. Although the device pro-vides out-of-plane motion, it can be fabricated with only 2D patterning. The actuation characteristics of such structures are discussed.

Several possible applications of such devices discussed in the chapter can provide direction for future development. Although thickness-mode DEs are well suited for the applications described, the feasibil-ity of these applications depends on the system requirements for each. Some of these applications, such as haptic displays and vibrating biomedical devices, are being actively explored in current research at SRI International and at Artificial Muscle, Inc.

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[13] Heydt, R. and Chhokar, S. (2003). Refreshable Braille display based on electroactive polymers. Proceedings of the 23rd International Display Research Conference , 15–18 September, Phoenix, AZ.

[14] Jansson, G., Fanger, J., Konig, H. and Billberger, K. (1998), Visually impaired person ’ s use of the PHANToM

for information about texture and 3D form of virtual objects. Proceedings of the 3rd PHANToM Users Group Workshop , Massachusetts Institute of Technology, Cambridge, MA.

[15] Madavan , N. K. , Deutsch , S. and Merkle , C. L. ( 1984 ). Reduction of turbulent skin friction by microbubbles .

Phys. Fluids , 27 , 356 – 363 .

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APPLICATION TO VERY SMALL DEVICES: MICROACTUATORS, MICRO-OPTICS, MICROFLUIDICS, AND MORE

Roy Kornbluh , Ronald Pelrine and Joe Eckerle

SRI International, Menlo Park, CA, USA

Abstract

Dielectric elastomer transducers have many features that are desirable for microelectromechanical systems (MEMS)

and other very small-scale devices. These advantages include simple fabrication in a variety of size scales, and

ruggedness due to their inherent flexibility and environmental tolerance. The performance of dielectric elastomer

scale favourably at small sizes allowing dielectric elastomer transducers to produce high strain and energy density,

high efficiency and fast speed of response. A variety of proof-of-principle dielectric elastomer actuator configurations

have been demonstrated at the small size scales needed for MEMS devices, including ‘ artificial muscle ’ actu-

ators for insect-inspired climbing and jumping microrobots, framed and bending beam actuators for efficient opto-

mechanical switches and other devices, diaphragm and enhanced-thickness-mode actuators for microfluidic pumps,

and valves and arrays of diaphragm actuator and sensors for haptic displays and smart skins. Several challenges

remain for small-scale dielectric elastomers, including integration with driving electronics, and operational lifetime.

Keywords : Actuators, artificial muscle, energy harvesting, haptic displays, microelectromechanical systems, micro-

actuators, microfluidics, micro-optics, microrobots, smart skins, transducers.

22.1 INTRODUCTION

Very small devices offer opportunities to make actuators or other transducers that are significantly less obtrusive, faster acting, or less expensive, to name but a few potential advantages. Very small devices can also be incorporated into massively parallel arrays for new types of sensing or actuating arrays or smart skins. Very small devices, which include microelectromechanical systems (MEMS) as well as somewhat larger mesoscale devices, present both new opportunities and challenges to a new actuator technology. Dielectric elastomers have several potential advantages that arise both from the fundamen-tal physics as well as from practical considerations in materials and fabrication. At the same time many new challenges arise.

The following sections describe the fundamental benefits of dielectric elastomers at small size scales. Next, specific examples of dielectric elastomer devices applied to micro-optics, microswitches, micro-robots, microfluidics, and smart materials are described. The unique capabilities of dielectric elastomers compared with other MEMS and small-scale transducer technologies are highlighted. We conclude this chapter by discussing the challenges in realizing practical small devices and issues in scaling down even beyond the microscale.

22.1.1 Physics basis for dielectric elastomers: energy density

With regard to fundamental physics, while electromagnetics dominates transducers at the macroscale, MEMS and small-scale transducers are more typically electric-field operated (capacitive). These capaci-tive transducers include air-gap electrostatics and piezoelectric transducers. Many early MEMS papers touted the advantages of capacitive devices at small size scales. Interestingly, many of the early MEMS papers on microactuators relied on claims of enhanced dielectric breakdown due to the Paschen effect at

Chapter 22

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very small gap spacing in order to claim that electrostatics were fundamentally higher in energy dens-ity than electromagnetics (e.g. [1] ). In practice, it has been difficult for real MEMS devices to take full advantage of the Paschen effect due to almost unavoidable surface roughness, particulate contam-ination, or the impracticality of maintaining high-vacuum conditions. However, dielectric elastomers because they use a polymer dielectric rather than an air gap do not suffer from the practical limitations of air-gap electrostatic devices. As we have previously seen, dielectric elastomer actuators and gener-ators are capable of operating at electric fields of over 100 MV/m, with maximum values of more than 400 MV/m [2] (see also, for example, Chapter 4). In contrast, air-gap devices generally do not exceed 30 or 40 MV/m operating field [3] . Since the energy output density is proportional to the fourth power of the electric field [4] , the difference in operating field has a very significant effect. There are further benefits from polymer dielectrics. The polymer dielectric has a dielectric constant of 3–10 (depending on the polymer), compared with 1 for an air gap. The use of compliant electrodes, as opposed to the rigid electrodes required to maintain an air gap, also adds a factor of 2 to the energy coupled from the field to the deformation of the polymer.

The maximum strains and energy densities demonstrated in these dielectric elastomers exceed those of any field-activated material, including single-crystal piezoelectric ceramics and magnetostrictive ceramics [5] .

Also contributing to the advantages of dielectric elastomers at small size scales is the fact that it remains generally true that the energy density of electromagnetic devices is limited at small size scales due to unfavourable scaling laws for current density. High current density is needed to achieve high magnetic fields and therefore high energy density. While favourable heat transfer may allow for high current density, the efficiency of small electromagnetic devices would be low.

To be sure, capacitive devices are not the only ones finding application at small size scales. Actuators that convert electricity to heat, such as those based on shape-memory alloys, thermal expansion, and thermally induced phase change (e.g. microbubbles), have also found their niche in silicon microma-chined devices. However, these transducer technologies are not energy efficient and generally cannot be operated in reverse preventing their application to applications that demand efficiency and power generation or sensing.

22.1.2 Materials and fabrication basis

One of the great advantages of MEMS devices is that they can integrate electronics with the transducer in a very compact and simple package. For this reason, many MEMS devices are fabricated in silicon. MEMS transducers are traditionally those that are compatible with silicon micromachining. The basic functional element of dielectric elastomers is a simple laminate of three layers (two electrodes and one dielectric polymer): as such it is easily compatible with microscale batch fabrication techniques. Many of the dielectric polymers can be deposited by methods well known in the MEMS and microelectronics industries such as spin coating. The ability to integrate electroactive polymers with silicon microma-chined substrates as well as photolithographically patterned polyimide frame elements has been dem-onstrated, as will be discussed below.

The fact that the polymer itself maintains the electrode spacing is an important difference from air-gap electrostatic devices. Fabrication is simplified since electrodes can be deposited directly on the polymer without any additional structure. Since the polymer is not rigid, we can consider large-area devices without worrying about adding structures to maintain the electrode spacing. These large-area devices can be flexible.

While the small size and integrated nature of silicon-based MEMS is attractive for cost savings and simplicity of design, many applications can be better addressed by somewhat larger devices. Often the size of the MEMS device is driven by the need to minimize the amount of silicon used. In many cases, a smaller device must be packaged so that it is large and rugged enough to be incorporated into macroscopic devices. In other cases, it is desirable to directly incorporate the transducers into a mate-rial that provides structural support or protection. As we shall see, materials and packaging considera-tions are often what drive the size of the device rather than fundamental performance issues. Further, there is a growing trend to fabricate complete electronic circuits on low-cost, flexible substrates such as polyimide. The most versatile MEMS transducer technology would then be compatible with silicon micromachining yet not limited to the use of such techniques. Dielectric elastomers can be compatible

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Application to Very Small Devices: Microactuators, Micro-optics, Microfluidics, and More 229

with traditional MEMS as well as integration with ‘ macroelectronics ’ . Recently, dielectric elastomer actuation has been combined with electronic circuit components fabricated directly on polymer substra-tes [6] . In this work, photoconductive switches were fabricated in a thin layer of amorphous silicon that was deposited onto polyimide. The polyimide acted not only as the circuit substrate but also as a substrate for dielectric elastomer actuators.

In contrast to dielectric elastomers, electromagnetic devices are not easily fabricated using simple two-dimensional patterning. While electromagnetic rotary motors are ubiquitous, and have been made on the millimetre size scale, they would need to operate at extremely high speeds at small size scales in order to achieve high power density. This requirement in turn would require precise microbearings and rotary transmissions – both are exceedingly difficult to manufacture. The large motions of dielectric elastomers can achieve high peak power without the need for bearings or rotary transmissions.

22.2 REPRESENTATIVE APPLICATIONS

Table 22.1 lists a wide variety of MEMS and small-scale application areas and highlights the potential benefits of the dielectric elastomers, compared with existing transducer technologies. In this section we discuss some specific examples in more detail.

22.2.1 Microrobots

Microrobots, like larger robots, offer the promise of extending human presence to locations that are dan-gerous, dirty, or simply boring. However, microrobots can offer advantages that larger robots cannot. Small robots can access hard-to-reach places that larger robots simply cannot enter. They can be inex-pensive and unobtrusive enough to find much wider usage than larger robots. Small size and low cost confer several advantages over larger robots. Although each microrobot is small and weak, many small robots can act together in a swarm to accomplish a task. These swarms can cover an area faster and more reliably than individual larger robots. Small robots are also very light and can be transported in space probes to fan out and study the surfaces of planets or asteroids. To perform all these tasks, the microro-bots must have good mobility and dexterity. We can look to nature to provide inspiration: for example, insects and worms have excellent mobility and dexterity. A key to realizing such biologically inspired robots is the development of actuators that can effectively reproduce the behaviour of natural muscle.

Dielectric elastomers have been shown to be able to replicate several important features of natural muscle. A rolled actuator is a good way of making an artificial muscle with a shape factor similar to that of a natural muscle. Rolled actuators are described in Chapters 8 and 9. Rolled actuators have been made in a variety of sizes with both silicone and acrylic materials, including very small sizes. An example is a small silicone rolled actuator that weighs 0.25 g (including connectors), and has an active length of 15 mm and a diameter of 2 mm. Despite its small mass and size, the actuator can produce more than 15 g of force and has a 1.5 mm stroke. While not truly ‘ micro ’ in scale, this actuator is well suited for microrobot applications. Microrobots are not typically made smaller than insects because they must integrate power, locomotion and manipulation, sensing, communication, and information processing in a single structure, and must be able to travel significant distances. Thus, rolled actuators, whose size is limited only by our ability to devise a way to roll up small patches of dielectric elastomer film, are well suited to microrobots.

Robotic platforms using an inchworm-like propulsion system ( Fig. 22.1 ) could eventually be used to make small robots for tasks such as inspection in narrow pipes. This robotic platform is 16 mm in length. The body of the inchworm is also the rolled dielectric elastomer actuator that provides pro-pulsion. The rolled actuator has high strains and is flexible, to enable motion over rough surfaces or through convoluted pipes. This inchworm uses electrostatic clamps that enable it to travel over both vertical and horizontal surfaces.

Robots like those of Fig. 22.1 are resistant to shock and a large amount of abuse. They are mostly made of rubber. One could even step on such a robot and see it crawl away. This ruggedness is in sharp contrast to the brittle and delicate nature of micromachined silicon-based devices.

Microrobots can also be made from framed actuators (see Chapter 8). Framed actuators consist of a flat dielectric elastomer film stretched on a frame. Framed actuators are easily made at virtually any size scale since they can be made using essentially two-dimensional fabrication processes, including

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230 Chapter 22

many techniques already familiar to microelectronics. Since the strain of dielectric elastomers can be large, framed actuators can allow for large in-plane motions. Figure 22.2 shows examples of a framed actuator that uses the in-plane motion to allow the root of a robot leg to twist. This robot is capable of dynamic locomotion such as hopping or galloping.

Closely related to framed actuators are diaphragm actuators. Figure 22.2 also shows a simple robot based on a diaphragm actuator. Such robots can use the large out-of-plane motion of the diaphragm to hop many times their own height.

The robots of Fig. 22.2 are simple proof-of-principle platforms. They are more correctly mesoscale devices rather than micro. However, because of the simple two-dimensional structure, they could easily be fabricated at truly micro-size scales. Further, scaling laws related to the strength of the robot struc-ture versus its mass are advantageous as size is reduced.

Table 22.1 MEMS and small-scale applications for dielectric elastomers.

Application Common Existing Electrical Transducer Technology

Potential Advantages of Electroactive Polymers

Microrobotics Electrostatics, some electromagnetics Higher energy density, ruggedness and shock resistance, high peak power output, simpler structures and transmissions, higher efficiency than electromagnetics

Micro-optic devices Electrostatics, piezoelectrics Higher speeds, transparency, shock resistance, less sensitivity to dust, lower heat output

Microswitches (relays) Electrostatics Higher speeds, higher pressures, less sensitivity to dust

Micro- and nano-scale assembly automation

Electromagnetics, piezoelectrics, electrostatics

Higher speeds, better compatibility with direct drive approaches, low cost

Mini- and micro-loudspeakers

Electromagnetics, electrostatics Lighter weight, more flexibility in design shape (e.g. conformal, flat), higher power, lower-cost materials

Micronozzles and inkjets Piezoelectrics, thermal bubble jets Easier to control than bubble jets; better mechanical match to displacements and pres-sure than piezoelectrics

Microfluidics (pumps, valves)

Electrostatics (including electro-osmotic and other field-based drives), piezoelectrics, electromagnetics

Higher energy and power density; large strokes and good pressures for many micropump appli-cations such as ‘lab-on-a-chip’ devices

Haptic displays Few practical devices, some based on piezoelectrics, electromagnetics, shape memory alloys, etc.

High energy density, ability to fabricate large arrays on a single low-cost substrate, high flexibility and shock resistance, higher energy efficiency

Smart material (smart skin or large array)

None (some research with piezo-electrics, shape memory alloys)

New functionality in large area arrays; new applications including modulation of electro-magnetic properties, control of airflow or heat transfer, surface texture, etc.; large out-of-plane motions; greater ease of manufacture, greater ruggedness, lighter weight and lower cost than silicon- or piezoelectric-based alternatives

Generator (e.g. motion, vibration driven, human-motion driven)

Electromagnetics Higher specific power density, lower-speed operation; lower-cost materials; good imped-ance match to human and natural motion for high efficiency

Sensors Electromagnetic Greater simplicity, lower cost, greater range of sizes and shapes, ability to be integrated with many structures or textiles

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Application to Very Small Devices: Microactuators, Micro-optics, Microfluidics, and More 231

22.2.2 Framed and bending beam actuators for micro-optical and electrical devices

The amount of data transmitted over optical fiber is doubling every 9 months [7] . All-optical switches, in which there is no conversion of the information in the beam between light and electricity, are desir-able because they are faster, can carry more information, and require less power than approaches that must convert the received signals to electrical signals before switching can take place. With the increase in data rates and number of lines, the demands on switching technology become more severe. A technology that can rapidly switch between a large number of optical inputs and outputs in a reliable, cost-effective, low-power manner would have widespread application. Existing technologies have short-comings that can be addressed by dielectric elastomer actuation.

The most mature of the all-optical switches are those based on solid-state materials such as lithium niobate, a ferroelectric crystalline material whose refractive properties can be controlled by an electric field (typically at 20–30 V). Solid-state switches suffer from problems with inability to scale to large numbers of channels, crosstalk, thermal stability, excessive power attenuation, and speed of response.

Approaches based on opto-mechanical devices can address some of the problems of solid-state switches. These devices typically are silicon micromachined and use arrays of tilting mirrors [8] that

Electricaltether

16 mm

Rolled muscleactuator

Electrostatic clamps (2)

Metal surface (e.g. pipe, turbineblade, etc.)

Figure 22.1 Insect-inspired ‘inchworm’ rolled silicone actuator with electrostatic clamping feet.

Figure 22.2 Small robots based on flat actuators: framed-actuator legged robot (top left) and a framed-actuator inertial-drive robot (top right) (top row photos are courtesy of Anita Flynn, Micropropulsion Corp. based on work done with SRI International) and diaphragm hopping robot (right) (SRI International).

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232 Chapter 22

are electrostatically actuated. Such devices have been under investigation for several years [9] . The mir-rors are typically fabricated on silicon. Switching speeds of about 0.1–0.5 ms have been demonstrated. Other MEMS devices have been built that can steer an optical or other electromagnetic beam with vari-able beam deflection. One example is a variable blaze grating reported by Burns and Bright [10] . It should be noted that most existing MEMS devices based on electrostatic actuators have relatively small deflections because the stroke of the electrostatic actuator is generally limited.

While having the advantage of being compact, energy efficient, and low loss, opto-mechanical switches based on electrostatic micromachined devices do suffer from the drawbacks that we have discussed in Section 22.1. Physics-wise, air-gap electrostatic devices are limited by the electric breakdown strength of air and therefore have intrinsically low force-to-mass ratios. This lower force limits their speeds. For example, published response times are typically on the order of 0.2 ms for movements large enough to switch an optical beam. In contrast, response times are estimated at 0.01 ms for a 100- � m-wide dielectric elastomer. Already, response times of 0.01 ms have been shown on macroscaled elastomer actuators.

Fabrication-wise, air-gap electrostatic devices generally operate using submicron gaps that must be carefully patterned to prevent shorting. A high level of precision cannot be maintained over large areas, so that large-area devices are currently difficult to fabricate. By contrast, we have noted that the dielec-tric elastomer actuators themselves set the gap, so that the gap can be formed in only a single step, film deposition on a flat surface. By using monolithic polymer substrates, one should be able to make large-area arrays of dielectric elastomer actuators.

Other opto-mechanical MEMS devices use piezoelectric ceramics in place of electrostatics. Piezoelectrics have proven themselves in applications demanding high-speed, low-strain motion. The long-term reliability of piezoelectrics may be limited in the optical switching application since piezo-electric ceramics tend to crack under the repeated high strains. Piezoelectric devices require sol-gel or similar fabrication processes and may be relatively expensive to fabricate over large areas.

Many of the newer technologies such as bubble switches, thermo-optic switches, and liquid crystal switches have attractive features, but are still largely unproven. Many of these devices have larger attenu-ation of the optical signal than desired. In addition, many are N -squared; that is, they are simply binary switches, so that a number equal to the number of inputs multiplied by the number of outputs would be required. Some of these devices, such as the bubble switch and thermo-optic switch, require a signifi-cant amount of energy to operate and might not scale well to larger numbers of inputs and outputs.

Technologies that can successfully switch large arrays of light might also find use in new types of very bright or large-area displays that are a fraction of the cost of today ’ s large displays. Other unique photonic devices might also be possible. These devices would have a significant effect on consumer electronics as well as industrial automation and instrumentation.

Dielectric elastomers offer the low-cost fabrication, speed of response, low attenuation, efficiency, and scalability demanded for optical switches. While fully operational switches have not yet been fabricated, several small electro-optic devices have been made that offer some insight into their expected performance.

Figure 22.3 shows a simple small light scanner based on a ‘ unimorph ’ type of bending beam actu-ator. Compared with piezoelectric devices, dielectric elastomer benders can bend in much sharper angles because the strains they achieve are orders of magnitude larger. Bending angles as high as 270° have been observed. Position response bandwidths of 10–50 Hz were achieved. Smaller beams, because of there lower mass, could undoubtedly move much faster and so kilohertz bandwidths should be feasible.

Unimorphs can be used to change the angles of mirrors, and as such form the basis of an opto-mechanical switch. Arrays of 5–10 unimorphs were demonstrated [5] . Because the unimorphs are made by stacking and patterning flat films, they can easily be fabricated in batch processes to yield arrays with large numbers of elements.

The tunable radio frequency (RF) circuit is a related application that could also benefit from fast, reliable, and efficient switches. Many of the structures shown here in optical applications could also be adapted for use as electromechanical microswitches, relays, or tunable antennae or waveguides for microwave or RF applications.

Another feature of dielectric elastomers is their transparency, which can enable some unique opto-mechanical devices. Figure 22.4 shows a framed actuator (a film of elastomeric polymer stretched on a rigid frame) exhibiting an interesting optical effect: when the film is actuated, the optical density of the electrode changes because of the stretching expansion of the film, and the optical density changes from dark to semitransparent. Such a device could become an essentially solid-state shutter or optical modulator.

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Application to Very Small Devices: Microactuators, Micro-optics, Microfluidics, and More 233

Recently, researchers have demonstrated the ability of framed actuators to be the basis of tunable opti-cal gratings [11] . A thin elastomer film is cast using a conventional diffraction grating as a mould. This film is then bonded to a framed dielectric elastomer actuator. Actuator strain distorts the thin film (con-taining the imprint of the diffraction grating), thereby changing the grating spacing. The distorted grating will diffract light of a fixed wavelength by a variable angle (depending on the applied voltage). Deflection over a range of 118 mrad was achieved. Alternatively, the grating can be used to select a variable segment of a white light spectrum. The authors envision the later effect being used for a colour display.

22.2.3 Diaphragm and enhanced-thickness-mode actuators for microfluidics and haptics

Just as the ability to put large numbers of electrical switches on a chip enabled a revolution in informa-tion processing, the ability to put a large number of pumps, valves, or other fluidic devices in a small area can revolutionize fluid handling and allow great advancement in biotechnology, materials, and chemistry.

In biotechnology, microfluidic devices promise to enable the rapid screening of pharmaceuticals. Microfluidic devices can also allow researchers to better understand the roles of proteins and genes by allowing fast massively parallel testing. Recently, the need to rapidly screen for disease-causing agents and bioweapons has received much interest. In chemistry and materials science, microfluidic devices can allow combinatorial methods to be used to screen for virtually any desired feature of compounds or material. Improved magnets, conductors, and light-emitting polymers are but a few examples.

Diaphragm actuators can form the basis of simple micropumps. Figure 22.5 shows the structure of a diaphragm actuator.

We have demonstrated a wide range of diaphragm actuators as small as 50 � m on a side, including a 50 � m actuator fabricated by spin coating silicone onto a silicon wafer. The opening was created by anisotropic etching from the back side of the wafer. Pumping pressures as high as 20 kPa have been demonstrated in millimetre-scale diaphragms. We demonstrated the potential of the diaphragm actuator for micropump applications by building a simple proof-of-principle minipump. The 20 mm diaphragm could pump as much as 40 ml/min of air at pressures of about 1 kPa. Theoretical calculations indicate that much higher diaphragm pressures, around 1 MPa, should be feasible. We have also demonstrated the ability to use such small diaphragms for inkjet printing applications, where dielectric elastomers may provide a higher-performance or lower-cost alternative to piezoelectric driven diaphragms, for example.

Scanned beam forms arc or line

Muscleunimorph

Mylar reflector Unimorph

ScannedDirect

Figure 22.3 Unimorph type of bending beam actuator: linear array of silicone unimorphs approximately 10 mm long (left) and scanned laser beam trace from a unimorph (centre and right).

Voltage off Voltage on

Figure 22.4 Optical switch based on the change in transparency of the electrode of a dielectric elastomer caused by high strain during actuation. The electrodes are carbon fibrils and the elastomer is acrylic.

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234 Chapter 22

The primary advantage of dielectric elastomers is their high strain capability. Strokes are signifi-cantly larger than those produced with other types of diaphragms, such as piezoelectrically driven diaphragms. Dielectric elastomers can actuate from an essentially flat configuration to one that is hemi-spherical. The large volume displacements per stroke of electroactive polymer actuators make them tolerant of greater leakage and backflow losses in the valves. Passive flapper valves can be used, sim-plifying the pump design.

Haptic displays such as refreshable (computer controlled) Braille displays could also benefit from arrays of dielectric elastomer actuators. Present-day refreshable Braille displays typically use piezoelectric bending beam actuators to raise the Braille dots, although many actuation methods have been tried. These methods include shape-memory alloys that require excessive power consumption (the devices are typi-cally battery powered) and electrochemical-type electroactive polymers that are power intensive as well as slow, and sensitive to temperature and humidity. Space limitations associated with piezoelectric actuation, and the cost of manufacturing large actuator arrays, limit most displays to a single line of characters. The cost of such refreshable displays is too high for many visually disabled people. Dielectric elastomers can be used to make structures consisting of relatively large-area arrays of individually addressable actuator (or sensor) elements that can be fabricated by essentially two-dimensional techniques.

SRI International demonstrated a refreshable Braille display based on arrays of dielectric elastomer diaphragm actuators [12] . Individually addressable diaphragm actuators at the small scale of Braille dots (1.5 mm diameter and 2.3 mm centre-to-centre spacing) have been demonstrated. Such 2-mm-diameter diaphragm actuators built with acrylic films have produced pressures of up to 25 kPa (3.7 psi). These pressures can generate the 10–25 g of actuation force on the Braille dot that is needed for easy reading. Figure 22.6 shows a laboratory prototype actuator for a single cell (character) eight-dot Braille cell as well as a three-cell device. The design is based on the simple diaphragm actuator of Fig. 22.7 . The approach is scalable to large numbers of cells, and is expected to enable the building of refreshable displays with many lines of characters at an affordable price. Other work done on dielectric elastomers at the Technical University Darmstadt and Sungkyunkwan University for refreshable Braille or other haptic displays is discussed in detail in Chapters 11 and 25. Choi et al. [13] have also made a wormlike robot by stacking arrays of diaphragm actuators.

Another promising actuator configuration for microfluidics and haptics is the enhanced-thickness-mode actuator, as shown in Fig. 22.7 and discussed in Chapters 8 and 21. In the enhanced-thickness-mode actuator, a relatively thick passive layer is deposited on top of the active dielectric elastomer. This layer thins or thickens as the layer below it expands or contracts. Since the passive layer is much thicker than the dielectric layer, the absolute change in thickness is large. It is possible to create virtually any desired pattern of bumps and troughs on a single substrate by simply patterning the electrodes on one surface of the dielectric elastomer. The entire structure can be attached to a rigid frame. Alternatively, the structure can be laminated to a flexible foam backing. Although the device gives out-of-plane motion, it can be fabricated with only two-dimensional patterning.

There are several possible applications for enhanced-thickness-mode actuation. If an enhanced-thickness-mode structure is brought into close proximity with a rigid layer, the bumps and troughs could act as valves or pumping elements in a ‘ lab-on-a-chip ’ type of microfluidic system. The foam-backed-skin version of the device could be the basis of a smart skin that controls the fluid flow, such as in a boat or airplane. The skin could also modulate texture or appearance (at various electromagnetic or acoustic frequencies, depending on the size scale of the features). This type of actuation can also be used for haptic displays.

Diaphragm frame with hole(a) (b)

Elastomer with electrodes bonded to frame

Figure 22.5 Diaphragm actuator: (a) voltage off and (b) voltage on.

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Application to Very Small Devices: Microactuators, Micro-optics, Microfluidics, and More 235

Bias spring

Electrode

Raisedbraille dot

Raiseddiaphragm

actuator

Displaces upwardwhen activated

Display surfaceDielectric elastomerfilm

Dielectricelastomeractuator array

Sliding pin

Conductingtrace

passive ‘Spring’bias array

Figure 22.6 Refreshable Braille cells based on dielectric elastomer: structure of individual dot actuator (top left); structure of individual character cell (top right); single-cell device (bottom left); and three-cell device showing pro-grammability of character sets (bottom right) (adapted from [12]).

Passive polymer or gelcoating (typically soft

elastomer)Thickness changeof passtive polymercoating

Bulges areenhanced aswell

Compliantelectrodes

Flexible foam backing(optional)

Polymer(e.g. acrylic)

Directthickness

change

�V

V Top view

Voltage off Voltage on

Cross-section of single element

Figure 22.7 Enhanced-thickness-mode actuation: underlying electrode grid pattern and schematic of basic elem-ent (top); resulting surface change in silicone gel on top of acrylic dielectric elastomer, with electrodes in grid pattern (bottom).

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236 Chapter 22

22.2.4 Generators and sensors

Thus far we have considered only actuators as examples of potential dielectric elastomer applications. However, we have noted that dielectric elastomers also can offer good transduction as generators and sensors. The same transducer structures that we have already described for use in actuator applications can also offer advantages for generators or sensors.

Another type of pressure or force sensor could be made from the foam-backed, enhanced-thickness-mode skin discussed above. The electrodes could be patterned and poled such that the capacitance of each individual element could be sensed, providing a tactile picture of an object. Such a device could, for example, be a robot skin used to map contact, or could be incorporated into a force plate for biome-chanical studies.

Increasingly, MEMS technology is being used to eliminate the inconvenience of small batteries for electronic devices. Just as dielectric elastomer can act like natural muscle in actuation mode, in gener-ator mode dielectric elastomer is well matched to the relatively high-strain, low-force action of human muscle. SRI has demonstrated a device that is inserted in the heel of a shoe and uses the energy of a heel strike to deform diaphragm transducers and thereby generate electrical energy [14] . On a smaller scale, the dot array of the refreshable Braille device ( Fig. 22.6 ) can generate energy when the dot is depressed. In this way, we could power electronic devices with pushbuttons, such as remote controls for video or audio equipment or small touchpads for pagers, cellphones, or PDAs, simply by harvesting some of the energy used to press a button. Such generators must be efficient, low profile, and compat-ible with flexible circuit technology. Dielectric elastomers are well suited to these constraints. These microgenerators could also be used to power wireless networks of sensors that measure pressure or motion. The work done on the sensor can power the sensor and transmission of the information.

22.3 CHALLENGES

Most of the proof-of-principle devices to date have been made at the millimetre scale rather than the microscale. This size scale allows us to use simple electrode patterning techniques such as spraying or silk screening through masks. For many applications this size scale is actually desirable, since it can more easily interface with larger devices in a rugged package. However, in applications that require true microscopic-scale devices, we may need to explore the use of patterning and insulating electrodes with photolithographic or other techniques. These finely patterned electrodes cannot be based on formula-tions of conductive particles in a polymer binder that work well at larger scales. At very small scales, the particle size can be a significant fraction of the dielectric elastomer film thickness. While patterning thin metal is the logical choice, metals cannot maintain electrical conductivity when strained more than a few per cent, far less than that required for most dielectric elastomer applications. Fortunately, several researchers have developed methods of making patterned metal conductors that are compliant. These approaches, discussed in detail in Chapter 7, include in-plane patterns that allow for extension [15] (see also Fig. 22.8 ) and numerous out-of-plane corrugation or wrinkling techniques (e.g. [16, 17] ).

383 µm497 µm

(a) (b)

Figure 22.8 Photolithographically patterned gold zigzag traces allow for large strains without losing conductiv-ity: (a) relaxed and (b) stretched 30% (adapted from [15]).

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Application to Very Small Devices: Microactuators, Micro-optics, Microfluidics, and More 237

Aside from patterned metals, other emerging technologies can help address the compliant electrode challenge. Nanosonic Inc. (Blacksburg, Virginia, USA) has developed ‘ Metal Rubber ’ a nano-composite formed by self-assembly of metallic nano-particles in a polymer binder [18] . Such materials can be optically transparent or reflective. Similarly, Zhang et al. have formed largely transparent nanotube-based sheets of into stretchable electrodes [19] .

Dielectric elastomer actuators typically operate at voltages ranging from a few hundred volts to 10 kV. More generally, in practical applications silicones can sustain electric fields of up to 100 MV/m, while acrylics can sustain electric fields of up to 200 MV/m. Best performance is typically observed with lay-ers on the order of 50 � m thick. Operating voltages on the order of kilovolts may not be practical for very small devices since it may be difficult to adequately insulate the device without adding significant insulation. Further, it may be impractical to include voltage conversion circuitry in a very small device.

In theory, by making the elastomer layer thinner, we can use a lower operating voltage. Indeed dielec-tric elastomers have been actuated with voltages below 100 V, albeit at relatively small strains. However, if the layer is too thin, performance degrades because of the increased likelihood of small manufac-turing defects, and the stiffness and inhomogeneities in charge distribution imposed by the electrodes become critical. On the other hand, it is well known that thinner films, if they do not have defects, can actually have enhanced electrical breakdown strength [20] . Further, many MEMS and small-scale applications only need a very small area of film, so the probability of defects is further reduced com-pared with macroscopic applications. There are therefore intriguing possibilities with very thin films on the order of nanometres in thickness.

It should be pointed out that high voltage is not fundamentally bad at small sizes. High voltage can actually be safer because the current required for the same power is lower. It is actually the current that presents the danger. Low current also allows for thinner and smaller connectors and wires. At small sizes the cost of connectors and wires can sometimes dominate the entire device.

22.4 SUMMARY

Dielectric elastomers are an emerging transducer technology with many desirable features for small-scale transducers. These features include low-cost fabrication on a variety of substrates, inherent flexibility, ruggedness, and shock tolerance. While dielectric elastomers are compatible with silicon micromachining, dielectric elastomers can help extend the benefits of MEMS devices to larger and more rugged structures, such as smart skins, by enabling the transducer and circuitry to be integrated on low-cost polymer substrates. Dielectric elastomers have been integrated with both silicon and poly-mer substrates, demonstrating the variety of fabrication techniques.

Particular areas that can benefit include microrobots, micro-optical and electrical switches, micro-fluidic components, and smart skins for applications such as haptic displays. Application to these areas will require overcoming challenges in fabrication and electronics development.

ACKNOWLEDGEMENTS

The authors would like to thank the many individuals at SRI International who have contributed to the development of the dielectric elastomer actuation technology. Much of the basic dielectric elastomer technology was developed under the management of the Micromachine Center of Japan under the Industrial Science and Technology Frontier Program, Research and Development of Micromachine Technology of MITI, Japan, supported by the New Energy and Industrial Technology Development Organization. The development of dielectric elastomer artificial muscle actuators and the application of the technology to biologically inspired robots were later supported by the Defense Advanced Research Projects Agency (DARPA) and the Office of Naval Research (ONR). The Department of Education supported the development of the refreshable Braille display.

References

[1] Lang, J., Schlect, M. and Howe, R. (1987). Electric micromotors: electromechanical characteristics.

Proceedings of the IEEE Micro Robots and Teleoperators Workshop , Hyannis, MA, 9–11 November. Also

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238 Chapter 22

reprinted in Micromechanics and MEMS – Classic and Seminal Papers to 1990 , Ed. Trimmer, W., IEEE

Press, New York, pp. 286–293.

[2] Kornbluh , R. , Pelrine , R. , Pei , Q. , Stanford , S. and Heydt , R. ( 2004 ). Dielectric elastomer artificial muscle

for actuation sensing, generation, and intelligent structures . Mater. Tech. , 19 , 4 .

[3] Chen , C. , Yeh , J. A. and Wang , P. ( 2006 ). Electrical breakdown phenomena for devices with micron separ-

ations . J. Micromech. Microeng. , 16 , 1366 – 1373 .

[4] Pelrine , R. , Kornbluh , R. , Pei , Q. and Joseph , J. ( 2000 ). High-speed electrically actuated elastomers with over

100% strain . Science , 287 ( 5454 ), 836 – 839 .

[5] Kornbluh, R. D., Pelrine, R., Prahlad, H. and Heydt, R. (2004). Electroactive polymers: an emerging technol-

ogy for MEMS (invited). In MEMS/MOEMS Components and Their Applications , Eds. Janson, S. W. and

Henning, A. K., Proc. SPIE , 5344 , 13–27.

[6] Lacour, S., Pelrine, R., Wagner, S. and Prahlad, H. (2003). Photoconductive high-voltage switches of thin-

film amorphous silicon for EAP actuators. In Smart Structures and Materials 2003: Electroactive Polymer Actuators and Devices , Ed. Bar-Cohen, Y., Proc. SPIE , 5051 , 412–418.

[7] Walsh , S. ( 2001 ). Microsystems, micromachines and optical networks: the second wave . Microm. Dev. , 6 ( 1 ), 4 – 6 .

[8] Akimoto, K., Uenishil, Y., Honma, K. and Nagaoka, S. (1997). Evaluation of comb-drive nickel micromirror

for fiber optical communication. Proceedings of the 10th Annual International Workshop on Micro Electro Mechanical Systems , Nagoya, Japan, 26–30 January, pp. 66–71.

[9] Marxer, C., Gretillat, M.-A., de Rooij, N., Battig, R., Anthamatten, O., Valk, B. and Vogel, P. (1997). Vertical

mirrors fabricated by reactive ion etching for fiber optical switching applications. Proceedings of the 10th Annual International Workshop on Micro Electro Mechanical Systems , Nagoya, Japan, pp. 49–54.

[10] Burns, D. and Bright, V. (1997). Micro electro mechanical variable blaze gratings. Proceedings of the 10th Annual International Workshop on Micro Electro Mechanical Systems , Nagoya, Japan, pp. 55–60.

[11] Aschwanden , M. and Stemmer , A. ( 2006 ). Polymeric, electrically tunable diffraction grating based on artifi-

cial muscles . Opt. Lett. , 31 , 2610 – 2612 .

[12] Heydt, R. and Chhokar, S. (2003). Refreshable Braille display based on electroactive polymers. Proceedings of the 23rd International Display Research Conference (Sponsored by the Society for Information Display) , Phoenix, Arizona, 15–18 September, pp. 111–114.

[13] Choi, H. R., Koo, J. C., Nam, J. D., Lee, Y. K. and Jeon, J. W. (2004). Development of muscle actuator based

on dielectric elastomer without pretension and its applications, in WW-EAP Newsletter ( http://ndeaa.jpl.nasa.

gov/nasa-nde/newsltr/WW-EAP_Newsletter6-1.pdf ), 6 (1), June.

[14] Kornbluh, R., Pelrine, R., Pei, Q., Heydt, R., Stanford, S., Oh, S. and Eckerle, J. (2002). Electroelastomers:

applications of dielectric elastomer transducers for actuation, generation and smart structures. In Smart Structures and Materials 2002: Industrial and Commercial Applications of Smart Structures Technologies ,

Ed. McGowan, A., Proc. SPIE , 4698 , 254–270.

[15] Kornbluh, R., Pelrine, R., Joseph, J., Heydt, R., Pei, Q. and Chiba, S. (1999). High-field electrostriction of

elastomeric polymer dielectrics for actuation. In Smart Structures and Materials 1999: Electroactive Polymer Actuators and Devices , Ed. Bar-Cohen, Y., Proc. SPIE , 3669 , 149–161.

[16] Benslimane , M. , Gravesen , P. and Sommer-Larsen , P. ( 2002 ). Mechanical properties of dielectric elastomer

actuators with smart metallic compliant electrodes . Proc. SPIE Int. Soc. Opt. Eng. , 4695 , 150 .

[17] Lacour , S. P. , Wagner , S. , Huang , Z. and Suo , Z. ( 2003 ). Stretchable gold conductors on elastomeric sub-

strates . Appl. Phys. Lett. , 82 , 2404 .

[18] Hill, A. B., Claus, R. O., Lalli, J. H., Mecham, J. B., Davis, B. A., Goff, R. M. and Subrahmanayan, S. (2005).

Metal rubber electrodes for active polymer devices. In Smart Structures and Materials 2005: Electroactive Polymer Actuators and Devices (EAPAD) , 5759, Ed. Bar-Cohen, Y., Proc. SPIE , May, 246–251.

[19] Zhang , M. , Shaoli , F. , Zakhidov , A. A. , Lee , S. B. , Aliev , A. E. , Williams , C. D. , Atkinson , K. R. and

Baughman , R. H. ( 2005 ). Strong, transparent, multifunctional, carbon nanotube sheets . Science , 309 ( 19 ),

1215 – 1219 .

[20] Plessner , K. W. ( 1948 ). The electric strength of dielectric films . Proc. Phys. Soc. , 60 , 243 – 256 .

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A NEW BRAILLE DISPLAY SYSTEM DESIGN USING A POLYMER-BASED SOFT ACTUATOR TACTILE DISPLAY

Ja Choon Koo 1 , Hyouk Ryeol Choi 1 , Kwangmok Jung 1 , Jae-do Nam 2 , Youngkwan Lee 3 and Sangwon Lee 4

1 School of Mechanical Engineering, Sungkyunkwan University, Suwon, Korea 2 Department of Polymer Science and Engineering, Sungkyunkwan University, Suwon, Korea 3 Department of Chemical Engineering, Sungkyunkwan University, Suwon, Korea 4 Korea Institute of Industrial Technology (KAITECH), Chonan, Korea

Abstract

For the visually impaired, tactile sensation is one of the most important alternatives followed by auditory sense.

Braille displays therefore are a major information transfer kernel for those individuals. In this chapter, a new Braille

display design using a dielectric elastomer is presented. The proposed Braille device provides intrinsic softness, ease

of fabrication, low manufacturing cost, and ease of miniaturization. A development of high frequency bandwidth

control circuit that successfully drives multiple Braille tactile display units is also introduced. The simple operating

mechanism of the proposed display unit enables higher tactile cell resolution with reasonable cost. The new displays

are tested with visually impaired individuals and the psychophysical experimental results are provided.

Keywords : Actuator, Braille, dielectric elastomer, tactile display.

23.1 INTRODUCTION

Although optical display devices have been a dominant method for information interchange, the role of tactile sense becomes a critical means of modern information exchange in various technical fields such as robotics, virtual reality, remote manipulation, rehabilitation, and medical engineering [1–4] . For human-device interface applications, tactile displays transfer information through the controlled displacement or force that stimulates human skin. The more information that is created as technology advances, the more sophisticated tactile displays must become in order to generate a more realistic feel-ing. Communications relying only on graphical presentations are impossible for the visually impaired. For this reason, a large portion of the world population might be left out of internet access that may result in further isolation from educational resources and cultural activities. Advances in tactile display technology for higher sensitivity and higher resolution are of great benefit to the handicapped.

Braille is a tool for exchanging information among the visually disabled and has been extensively used to transfer textual information. It consists of a six pins arranged in pattern of a 3 � 2 matrix (a 4 � 2 matrix in the case of Chinese characters). Information is represented by stimulating human skin, usually finger tips, by vertical displacement of the pins. The tactile display device can be utilized as a refreshable dynamic Braille. In particular, application of the display can also be expanded to a tablet capable of displaying textural or graphical information [5] . With this capability, even an entire web page can be delivered in a single display step. However, it is very difficult to enable Braille to deliver graphical information mainly due to the limitation of arranging massive Braille dots for high spatial density. Complicated and bulky driving mechanisms of conventional tactile displays hamper the development of a high resolution Braille-type tablet.

Chapter 23

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240 Chapter 23

According to a physiological study for standardization of Braille devices, the pin-matrix density of a tactile display is typically up to 1 cell/mm 2 ; actuating speed should be faster than 50 Hz; and energy density should be about 10 W/cm 2 [6, 7] . Although the numbers are determined based on some experi-mental studies, the outcome of the display function is often deceptive since the sensitivity of the responses depends on the testing situation such as speed, depth, and strength of stimulation. Meanwhile, various mutated tactile display types are introduced in order to accommodate human sensitivity that normally varies from the finger tips to the palms. Many publications introduce several different types of tactile display devices that employ pneumatics, solenoids, voice coil, shape memory alloys, electro-statics, or electroactive polymers [6–13] . Although previous developments deserve attention, most of them commonly suffer from low actuation speed due to complex actuation mechanisms. Furthermore, a complicated actuator design limits expansion to the tablet type application due to high manufacturing costs and low integration density.

In this research, a new type of dynamic Braille display is presented. It employs a dielectric elastomer for the basis of the tactile display and is constructed with a notably simple mechanical and electrical architecture. The proposed device is organized with a dual-layered array of tactile cells that generates vertical motion used to push up or down the Braille pins. These electrically driven tactile cells can gen-erate either small scale vibratory motion or linear displacement. They differ from conventional devices in softness and controllable compliance, cost effectiveness, simple manufacturability, and high actuator density. Furthermore, the small size of the proposed concept enables the development of a high density display device.

23.2 DESIGN OF A CELL

23.2.1 Basic actuation principle

A tactile cell constructed with dielectric elastomer is presented here. The basic operational mechanism of a typical dielectric polymer actuator is introduced in various publications although they admit limi-tations in the formulation [14–18] . As shown in Fig. 23.1 , electromechanical transduction of a pair of parallel plates is at the core of the actuator ’ s operation. When an electric potential is applied across an elastomer film, the film is compressed along thickness direction while it expands along the lateral direction so that a mechanical actuation force is produced. The effective mechanical pressure in the thickness direction is derived as

� � �z E� � 0 r

2 (23.1)

E

V

t� (23.2)

where E is the applied electric field that is defined by Eq. (23.2) and V and t are the applied voltage and thickness of elastomer, respectively. � 0 and � r are the electric permittivity of free space and relative permittivity of the polymer, respectively. In other words, the stress � z along the thickness direction is proportional to the square of the applied electric field. Introduction of a high voltage across the thin

Dielectric elastomer

�

Compliantelectrode

V V

Figure 23.1 Basic operation of dielectric elastomer in transduction.

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A New Braille Display System Design Using a Polymer-Based Soft Actuator Tactile Display 241

polymer may result in a notable strain in the thickness direction. Let t be the thickness of the polymer then a relation between the initial thickness and the strain in the direction can be calculated as

t t z� �0 1( )� (23.3)

where t 0 and � z are the initial thickness and the strain in thickness direction, respectively. Substituting Eqs. (23.2) and (23.3) in Eq. (23.1) and dividing it with the elastic modulus Y yields the following:

�� �

�z

zY Y

V

t� �

�

1

10

0

2

r( )

⎡

⎣⎢⎢

⎤

⎦⎥⎥

(23.4)

�� �

�z

zY Y

V

t� �

�

1 1

10

0

2 2

r

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

(23.5)

using the assumption of the uniaxial stress and strain problem, a relation between input voltage V and strain in the thickness direction � z can be obtained by

� � � � �z z z Y

V

t3 2

00

2

21

� � � � r

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

(23.6)

Since the higher power of the strain � z might be negligible, the applied voltage V is approximately pro-portional to the square root of the strain � z .

Most elastomers are normally incompressible so that the volume of an elastomer cube can be assumed to be constant and it can be expressed as

( )( )( )1 1 1 1� � � �� � �x y z

(23.7)

For a disc shape, thin circular cylindrical block, it can be written as

( ) ( )1 1 12� � �� �r z

(23.8)

where the subscript r represents the radial direction of a cylindrical elastomer block. Therefore, � r can be written as

��

�rz

z��

� �1

11

1

2� (23.9)

It shows that the radial strain is only half of the axial strain. Recognizing a significant drawback, a small strain in the thickness direction even with a very high

electric potential input, a new actuator driving paradigm for the elastomer needs to be introduced before being applied to actual industrial problems. In the present work, a new actuator construction that can maximize the output is proposed and is one of the key contributions to this work. A schematic explana-tion of this new concept is provided in Fig. 23.2 . The proposed actuation mechanism can be detailed as follows: An incompressible elastomer block is attached between rigid boundaries. Application of

(b)

Expansion force

Reaction forceFrame

Compression forceDielectricelastomer

(a)

a

(c)

r

b � a(1�da)

a

h

θ

Figure 23.2 Schematic view of proposed actuation concept.

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242 Chapter 23

the electric voltage across the elastomer induces material compression in the thickness/axial direction while the elastomer expands in lateral/radial direction. The expansion along the lateral/axial direction causes the bent elastomer film to deform either concave or convex. For a generic actuator construction, a simple geometric relation for circumference of the convex b is defined by

b a ra� � �(1 )� � (23.10)

where r is the radius of curvature, � is the corresponding angle, a is the initial/undeformed block length, and � a is the induced strain in the direction. With a trivial identity

ra

sin�2 2

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟ � (23.11)

Substituting it into Eq. (23.11) into (23.10) yields

��

�sin( )

( )/2

2 1� � a (23.12)

Applying Taylor series expansion to the preceding result

sin( )

!

( )� � � � �2 2

2

3

24

48

3 2⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟ � � �

�/ (23.13)

and with the subsequent substitution of Eq. (23.13) into (23.12), an algebraic relation between � and � a can be determined by

��

� ��

24 11

1 a

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

(23.14)

Determination of the convex height is found through a straightforward trigonometric relation:

h r� �12

cos�⎛

⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎡

⎣⎢⎢

⎤

⎦⎥⎥ (23.15)

where r is to be determined by Eq. (23.11). The lateral strain � a is of course determined by the basic principle of the actuation delineated by Eqs. (23.1), (23.2) and (23.9).

23.3 BRAILLE DISPLAY DEVICES

Realizing the advantages of the presented tactile cell for potential use in high density actuator con-struction, a Braille display device has been developed using the proposed tactile cells. In this section, a detailed construction procedure of the device and its electronics are explained.

23.3.1 Arrayed pin actuator system

A typical Braille display unit is constructed with six stimulating pins that are arranged in 3 � 2 array format. An array normally represents a character as defined by the Braille alphabet. The standard Braille display unit is illustrated in Fig. 23.3 .

In the present work, a Braille display unit is constructed with the introduced tactile cells arranged in the format defined by the standard Braille display. The construction concept is depicted in Fig. 23.4 . Although the dielectric elastomer-based tactile cell is driven with high voltage electricity, users have no direct contact to the actuator surface. A Braille pin made from insulating material is the only contact to human finger tips.

In addition to the pre-deformed convex feature of a cell, note that the directional ball is placed under-neath each cell in order to guarantee unidirectional actuation. Packaging the six-pin actuators and corre-sponding electric wires in a constrained small space might require an expensive manufacturing process. For this reason, a dual layer construction is introduced in order to alleviate the fabrication problems caused by the high density small apparatuses. By allocating three pins in each layer with a staggered pattern, interferences caused by complicate wiring can be minimized. Each layer is shown in Fig. 23.5 .

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A New Braille Display System Design Using a Polymer-Based Soft Actuator Tactile Display 243

1

2

3

5

68

5.6

2.4φ1.6

2.4

2.4

12* unit: mm0.8

4

Figure 23.3 Standard Braille cell consisting of six dots.

Upper frame 1

Actuator 1Actuator 2

Actuator 3

SiliconeDirection ball

Lower frame 1

Upper frame 2

Actuator Actuator 5

Actuator 6

Direction ballSilicone

Lower frame 2

Vcc 1Vcc 2

Vcc 3

Gnd 1

Gnd 2

Braille pin

Figure 23.4 Exploded view of proposed Braille display.

Hole

Upper layer Lower layer

Actuatorcell

Figure 23.5 Top and bottom layers of a Braille cell.

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244 Chapter 23

As shown in Fig. 23.6 , the height of the fully assembled device is approximately 9 mm excluding the length of the terminals. Since each Braille cell is to be fully modularized for convenient installation, each unit can be plugged onto a circuit board with ease. With this simple drop-in feature a number of Braille cells can easily be combined so that a Braille tablet may be manufactured by arranging many Braille cells in a matrix format as illustrated in Fig. 23.7 . In Fig. 23.8 , a complete actuator system for a Braille display unit is shown. The unit is composed of an embedded controller, high voltage driving circuit, and a host PC.

23.3.2 Organization of embedded controller and driving circuit

All necessary electronic control parts are embedded and packaged on a PCB that communicates with a hosting PC through a universal serial bus. A micro-controller (AVR, Atmega 163) is used for the

(a) (b) (c)

Figure 23.6 Assembled Braille cell.

17m

m

18.8 mm

Figure 23.7 Braille tablet by assembling six modules Braille cells.

USB controller(PIDUSB12)

Host PCUser interface

Main controller(Atmel 163)

High voltageshort circuit

Control circuit Driving circuit Braille cell

USB

Figure 23.8 Schematic illustration of a complete Braille display unit.

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A New Braille Display System Design Using a Polymer-Based Soft Actuator Tactile Display 245

controller and a USB 1.1 (Philips, PDIUSBD12) is used for communication. A D/A converter (Texas Ins. TLV5614) and OP-Amp (Texas Ins. TLV4112) have been integrated in the controller for the modulation of high electric voltage. The complete circuit board architecture is shown in Fig. 23.9 . All required firmware source codes and controls are newly developed for the presented device.

Since the device is organized by packaging many small scale actuators in a tiny space, electrical wiring might be one of the key problems that need to be resolved. A control scheme called dynamic scanning actuation (DSA) is used for identifying constructional and functional analogies of the Braille device to a computer input keyboard. This strategy enables easy control of N 2 Braille cells with only 2 N electrical lines. The concept of this control is depicted in Fig. 23.10 . One of the lines (named data line) delivers a high voltage driving electric power to each cell and the other line (called scan line) functions as a ground. Therefore, each actuator cell can be driven using N lines of the data line and N lines of the scan line with alternating ‘ on–off ’ patterns on both lines.

For example (refer to Fig. 23.10 ), although the data lines D0, D1, D2 get ‘ high ’ / ‘ on ’ signals during three clocks, only one actuator located in the upper left corner, operates since only one scan line S0 maintains ‘ high ’ / ‘ on ’ during this time. In essence, an actuator cell moves only if those two lines are synchronized with the ‘ high/on ’ signal. The scan frequency is L � M when the number of actuators in a row is M and the desired driving frequency is L .

A dielectric elastomer actuator normally operates with a high electrical voltage of about 1–2 kV. However, introduction of the proposed control scheme DSA provides significant benefits for the reduc-tion in the number of required high voltage sources.

For example, a single Braille unit composed of six tactile cells can be actuated with only a single voltage source and the number of cells can be easily expanded.

USB controller

Microcontroller

D/A converterand

Op-amp

4-Channel output

Figure 23.9 Control and communication circuit board.

Data line

Scan line

D0D1

D2

S0S1S2

Vertical scan

Horizontal scan

Actuator arrayOn

On On

On

Figure 23.10 Concept of DSA.

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246 Chapter 23

23.4 EXPERIMENTAL EVALUATION

23.4.1 Experiments

In order to evaluate the performance of the proposed Braille display, psychophysical tests have been performed using visually impaired persons. Seven individuals participated in the test, six of them were males and one was a female with an overall average age of 32.6 years. All of them were employees of the Korean Association of the Visually Impaired. One of them had weak vision and the others were com-pletely blind. The software environment GUI used for the testing is shown in Fig. 23.11 in which output voltage, frequency, and duration time can be adjusted by a computer so that the Braille information can be encrypted and delivered to the display unit. Although only numeric characters were used for the testing as shown in Fig. 23.11 , nothing is precluded for the implementation of any characters defined by Braille.

As shown in Fig. 23.12 , two adjacent Braille cells were read by the subjects and the data for two types of recognition rates; hit recognition rate (HRR) and number recognition rate (NRR) were obtained. HRR denotes the rate at which a subject recognizes movement of the Braille dots and NRR represents whether a subject reads the character correctly as the Braille dots are activated. In the experiments, the HRR and NRR of each subject have been tested as the actuating frequency of the Braille pins was at 15 Hz, which is the normal-read out speed of Braille readers. Results of the tests are shown in Table 23.1 . In the experiment, the HRR reaches up to about 80% and the NRR shows a maximum of 41%.

23.4.2 Discussion

The test results of 80% for HRR and 40% for NRR are much better than originally expected. A main concern before conducting the experiment was the fact that the subjects did not have any experience on the proposed Braille display device. Realizing the sharp sensitivity of blind people the recognition rates are sure to improve provided that they have more exposure to the device. Also, it should be emphasized

Figure 23.11 User interface.

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A New Braille Display System Design Using a Polymer-Based Soft Actuator Tactile Display 247

that the recognition rates are greatly affected by two major factors such as the regularity of the Braille pin ’ s height and the activating frequencies. Note that the Braille unit used in this test is hand-crafted and the consistency was not tightly controlled. The higher driving frequency will of course aggravate the recognition rate. Although the maximum tactile sensitivity of a human finger tip is reported to be about 250 Hz according to a physiological study [20] , the subjects participated in the test complained about weakening tactile sensation when the tests were driven at high frequencies up to 60 Hz. Unlike a static Braille characters, the proposed dynamic Braille device might generate a small scale vibration from Braille pins and it confused the subjects and deteriorates the recognition rates. However, due to the intrinsic low-pass characteristics of polymeric materials such as dielectric elastomers, there is no situa-tion that a high frequency vibration caused by high frequency noise can be combined with the Braille signal. This problem should be further investigated with improved device fabrication and a larger subject size. Nonetheless, the presented device proves its industrial feasibility from the presented experiments. Furthermore, it is discovered from the experiment that the maintaining regularity of the Braille pin ’ s height might be one of the major factors for precise recognition. Even small variation of the height was easily detected by the subjects and had a tendency to confuse them. The problem could be eliminated if the fabrication was supported by sophisticated machines. Besides it is likely that the number of subjects should be increased for the precise evaluation of the proposed device.

Figure 23.12 Psychophysical experiment of the proposed Braille device.

Table 23.1 Psychophysical test results: HRR and NRR.

Subject Number HRR (%) NRR (%)

1 69 30 2 51 21 3 54 19 4 60 29 5 77 40 6 73 41 7 63 32

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ACKNOWLEDGEMENT

This research has been performed under the financial support by the Korea Ministry of Health and Welfare (Contract Number: 02-PJ3-PG10-30415-0001).

References

[1] Johansson, R. S. and Vallbo, A. B. (1983). Tactile sensory coding in the glabrous skin of the human hand.

Trends in Neurosciences (TINS) , Vol. 6, No. 1. Elsevier Biomedical Press, New York, pp. 27–32.

[2] Hannaford , B. , Wood , L. , McAfee , D. and Zak , H. ( 1991 ). Performance evaluation of a six-axis generalized

force reflecting teleoperator . IEEE Trans. Syst. Man Cybernet. , 21 , 620 – 633 .

[3] Yoshikawa , T. , Yokokohji , Y. , Matsumoto , T. and Zheng , X. ( 1995 ). Display of feel for the manipulation of

dynamic virtual objects . ASME J. Dyn. Syst. , 117 ( 4 ) , 554 – 558 .

[4] Moy, G., Wagner, C. and Fearing, R. S. (2000). A compliant tactile display for teletaction. Proceedings of the IEEE International Conference on Robotics and Automation , pp. 3409–3415.

[5] Shinohara , M. and Shimizu , Y. ( 1998 ). Three-dimensional tactile display for the blind . IEEE Trans. Rehabil. Eng. , 6 ( 3 ) , 249 – 256 .

[6] Jungmann, M. and Schlaak, H. F. (2002). Taktiles display mit elektrostatischen polymer aktoren. Proceedings of the Internationales Wissenschaftliches Kolloquium (in German).

[7] Asamura, N., Shinohara, T., Tojo, Y., Koshida, N. and Shinoda, H. (2001). Necessary spatial resolution

for realistic tactile feeling display. Proceedings of the IEEE International Conference on Robotics and Automation , pp. 1851–1856.

[8] Caldwell, D. G., Tsagarakis, N. and Giesler, C. (1999). An integrated tac-tile/shear feedback array for stim-

ulation of finger mechanoreceptor. Proceedings of the IEEE International Conference on Robotics and Automation , pp. 287–292.

[9] Debus, T., Jang, T. J., Dupont, P. and Howe R. (2002). Multi-channel vibrotactile display for teleoperated

assembly. Proceedings of the IEEE International Conference on Robotics and Automation , pp. 592–597.

[10] Tang , H. and Beebe , D. J. ( 1998 ). A microfabricated electrostatic haptic display for persons with visual

impairments . IEEE Trans. Rehabil. Eng. , 6 ( 5 ) , 241 – 248 .

[11] Spinks, G. M., Wallace, G. G., Ding, J., Zhou, D., Xi, B. and Gillespie, J. (2003). Ionic liquids and polypyr-

role helix tubes: bringing the electronic Braille screen closer to reality. Proceedings of the SPIE ’ s 10th Annual Symposium on Smart Structures and Materials: Electroactive Polymer Actuators and Devices (EAPAD) , pp. 372–380.

[12] Konyo , M. , Akazawa , K. , Tadokoro , S. and Takamori , T. ( 2003 ). Wearable haptic interface using ICPF actua-

tors for tactile feel display in response to hand movements . J. Rob. Mechatron. , 15 ( 2 ) , 219 – 226 .

[13] Taylor, P. M., Hosseini-Sianaki, A. and Varley, C. J. (1996). An electrorheological fluid-based tactile array

for virtual environments. Proceedings of the IEEE International Conference on Robotics and Automation ,

pp. 18–23.

[14] Bar-Cohen, Y. Ed. , ( 2001 ). Electroactive Polymer (EAP) Actuators as Artificial Muscles . SPIE press ,

Bellingham, Washington, DC .

[15] Pelrine , R. , Kornbluh , R. , Pei , Q. and Joseph , J. ( 2000 ). High-speed electrically actuated elastomers with over

300% strain . Science , 287 , 836 – 839 .

[16] Kornbluh, R., Pelrine, R., Eckerle, J. and Joseph, J. (1998). Electrostrictive polymer artificial actuators.

Proceedings of the IEEE International Conference on Robotics and Automation , pp. 2147–2154.

[17] Choi, H. R., Ryew, S. M., Jung, K. M., Kim, H. M., Jeon, J. W., Nam, J. D., Maeda, R. and Tanie, K. (2002).

Soft actuator for robot applications based on dielectric elastomer: quasi-static analysis. Proceedings of the IEEE International Conference on Robotics and Automation , pp. 3212–3217.

[18] Choi, H. R., Ryew, S. M., Jung, K. M., Kim, H. M., Jeon, J. W., Nam, J. D., Maeda, R. and Tanie, K. (2002).

Soft actuator for robot applications based on dielectric elastomer: dynamic analysis and applications.

Proceedings of the IEEE International Conference on Robotics and Automation , pp. 3218–3223.

[19] Mascaro, S., Cho, K. and Asada, H. (2003). Design and control of vast DOF wet SMA array actuators.

Proceedings of the IEEE International Conference on Robotics and Automation , pp. 1992–1997.

[20] Kaczmarek , K. A. ( 1991 ). Electrotactile and vibrotactile displays for sensory substitution systems . IEEE Trans. Biomed. Eng. , 38 ( 1 ) , 1 – 6 .

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V.II

Robotic and Biorobotic Applications

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BIOMIMETIC ROBOTS

Scott Stanford

SRI International, Menlo Park, CA, USA

Abstract

Traditional robots using wheels and geared joints have demonstrated utility on land, in the air, and under water.

However, the performance of even the best robots – in terms of mobility, manipulation, obstacle clearance, dexter-

ity, weight, and noise – is inferior to that of animals and other biological organisms. In this sense, nature provides an

existence proof of the possibility of robots with greatly improved performance, and the current trend towards biomi-

metic and biologically inspired robot design is well motivated. In order to exhibit biomimetic behaviour, however,

robots need high-performance biomimetic actuators – artificial muscles. Natural muscles are compliant, high energy

density, and high strain actuators. Animals make extensive use of these and other properties of natural muscle

for their mobility. Traditional actuator technologies such as electromagnetics and piezoelectrics cannot effect ively

function as artificial muscles because of limitations in energy density, strain, and compliance. By contrast, artificial

muscles made from dielectric elastomers have begun filling the role of artificial muscles and several biomimetic

robots have been built using these flexible actuators. Some of these robots are presented, as well as possible future

robots enabled by dielectric elastomers.

Keywords : Actuator, artificial muscle, AUV, biomimetic, dielectric elastomer, EPAM, robot, UAV, UGV, UUV.

24.1 INTRODUCTION

Traditional robots that use wheels, motors, gears, and discrete joints have demonstrated significant util-ity on land, in the air, and under water. However, the performance of even the best robots – in terms of mobility, manipulation, obstacle clearance, dexterity, weight, and noise – is greatly inferior to that of their biological counterparts, which can literally run, jump, fly, and swim circles around them. The development of biomimetic and biologically inspired robots is a logical step towards the performance available in nature.

In order to exhibit biomimetic behaviour, robots need high-performance biomimetic actuators – artificial muscles. These actuators should be quiet and efficient, with high power and energy densities to minimize mass. Animals make extensive use of dynamic effects in their movement, flapping wings at resonance and using muscles and tendons as springs to absorb shocks and store energy. Accord-ingly, actuators should also be compliant and flexible, like natural biological muscle. Traditional actuator technologies cannot meet these demands.

Artificial muscles made from dielectric elastomers have begun filling this roll and several biomimetic robots have been built using these flexible actuators.

24.2 ADVANTAGES OF BIOMIMETICS

An important question to answer is why to turn to nature for inspiration in robot design. We note that evolution of species occurs by random mutations; not by thought-out design. However, by pairing these mutations with millions of years of natural selection, nature has created specialized organisms that are optimized for their environments. One could say that Mother Nature is not a particularly good designer, but she iterates on her designs with a very thorough quality assurance programme. Human engineers, on the other hand, use purpose-driven design, and can therefore create many things not found in nature. For example, the rotary joint, the basis for wheeled movement, gears, pulleys, and the movement for the

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vast majority of mechanisms, is not at all prevalent in nature, despite its high efficiency. Yet, despite our advantage in design, nature is still able to outperform man-made machines in many areas.

24.2.1 Crawling robots

On the ground, traditional robots almost exclusively take after their larger brethren of cars and tanks for mobility, making use of wheels and treads and powered by electric motors. This can be very effective in certain circumstances, but not all. Motors can have high efficiency when operated at a certain speed on smooth ground, but deviation from this speed, or especially switching between forward and reverse, greatly reduces this efficiency. Wheels and treads themselves are limited in terms of their obstacle clearance. A wheel can only climb over a step less than half its diameter and, similarly, the top of a tread must be taller than an obstacle it wants to clear. Legged locomotion, on the other hand, can hurdle much larger obstacles than the legs themselves by storing elastic energy. Witness human motion in the high jump, or the vertical leap of a rabbit or grasshopper. Additional limbs provide the ability to pull oneself or climb over objects. We can also see nature ’ s answer in the opposite extreme where legless snakes can use multiple gaits to silently stalk prey, climb trees, and surpass almost all obstacles.

24.2.2 Flying robots

In the air, again we traditionally see rotary joints and motors as prevalent for rotors, propellers, and jet engines, with a separate lift mechanism (wings). Nature typically combines these two functions (lift and thrust), with some astounding results. For example, the Ruby-throated Hummingbird can nimbly hover from flower to flower and has no significant predators due to its high manoeuvrability, but it can also travel over 300 miles across the Gulf of Mexico as part of its annual migration. This high power (i.e. thrust), manoeuvrability, and efficiency provided by flapping wing flight is unparalleled by modern micro-air vehicles.

24.2.3 Swimming robots

In the water, current unmanned underwater vehicles (UUVs) overwhelmingly use traditional technolo-gies for movement and manoeuver: electric motors, propellers, and adjustable hydrodynamic surfaces. UUVs are typically autonomous hydrologic research vehicles with add-on sensors such as side- and front-mounted sonar for environment and bottom mapping, as well as mine hunting. While they have met with some degree of success in deep water, they have considerable shortcomings in very shallow water (VSW, under 40 ft depth) and the surf zone (SZ):

It is fair to say that limitations of the state-of-the-art in vehicles, sensors, computation, communica-tions and navigation preclude the effective use of UVs from the VSW to the SZ. No current or near-term UV capability for underwater communications and precise navigation exists for the SZ [1] .

Focusing on vehicular issues, there are shortcomings common to almost all traditional UUVs. These problems are exacerbated in VSW and the SZ:

● They have poor manoeuvrability in tight places, especially in the currents and surges associated with VSW and the SZ. Sleek torpedo-like designs with a rear-mounted propeller are limited in their abil-ity to execute small diameter turns. Designs with multiple thrusters are generally larger, limiting their ability to navigate through obstacles, using too much of the limited power in batteries, and becoming subject to wave surges.

● They are not particularly stealthy, thus limiting their survivability. Hard exteriors, motors, and pro-pellers provide a significant acoustic signature. Inorganic surfaces and wakes increase the chances of visual or radar detection. Ferrous components and motors provide a magnetic source for detection, possibly by the very mines a UUV may be hunting.

● Propulsion by propellers, fans, and hydrodynamic surfaces is easily fouled by sand, rocks, and oceanic vegetation, thus further limiting potential areas of effectiveness for these systems.

● Electric motors have poor efficiency when frequent speed changes are needed such as in the SZ. But even if speed is constant, the efficiency of electric motors is poor at slower speeds. While compli-cated gear shifting mechanisms can be used to keep the motor at high efficiency speeds while the propeller speed is low, such mechanisms add complexity, cost, and weight.

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Nature has developed numerous non-rotary solutions to underwater movement. It is hypothesized that because life forms have evolved in water, forms of locomotion are much more varied and complex in water than in air [2] . There certainly is no lack of inspiration: sea stars have hundreds of tiny feet (podia) on the bottom of each limb, and use their vascular system like hydraulics to fill them with sea water and move. Jellyfish, without hearts, brains, bones, or eyes still manage to use jet propulsion. Of course, most familiar is the movement of the true fishes, who use finned propulsion to move quickly and efficiently with high manoeuvrability.

24.3 DESIRED PROPERTIES OF NEW ROBOT ACTUATORS

Actuators suitable for biomimetic robotics require capabilities different from those used in manufacturing, consumer goods, or even non-biomimetic robotic systems. SRI ’ s dielectric elastomer electroactive poly-mer artificial muscle (EPAM™) technology addresses many of the key criteria found in actual muscle:

● Totally quiet operation reduces chances of its detection, and also decreases background noise for its own sensors. Stealth, useful in military or law enforcement applications, mimics the behaviour of natural predators.

● It has no metallic components, reducing its electromagnetic signature, as well as its susceptibility to corrosion.

● Dielectric elastomer actuators can be constructed in a variety of shapes and sizes, from cylindrical, like many skeletal muscles, to flat, as might be found in rays and skates that can bury their stream-lined bodies in the sand.

● Inherent spring-like compliance, to enable energy to be stored for efficient locomotion and adapta-tion to uneven terrain or cluttered workspaces. Natural creatures use the compliance of muscles and tendons to create oscillatory systems that locomote efficiently (consider the gait changes used for walking, trotting, and galloping). Creatures also use such energy storage in their leg muscles and tendons when they run or hop. The flight muscles of many insects operate at resonance in order to efficiently produce high-frequency oscillation. This compliance is also important in robot con-trol. Unlike highly geared motors, dielectric elastomer actuators are back drivable and have inherent damping. This allows them to more easily adapt to uneven terrain and easily recover from collisions.

● They have high power density, to enable explosive dynamic motions such as those used in hopping, jumping, or running to surmount obstacles or to track or avoid targets. Robots built with heavy motors and transmissions cannot produce the peak power needed for these dynamic motions.

● High efficiency in power conversion, also a key characteristic of biological actuators, enables animals to operate for long periods of time while consuming relatively small amounts of food. Since the theor-etical efficiency of EPAM can be as high as 90%, devices using EPAM actuators will be able to oper-ate for longer periods of time, on the same input energy, than robots using other actuator technologies.

● Several electrodes can be patterned on a single actuator, allowing many degrees of freedom (DOF) in a single structure. Multiple DOF afford manoeuvrability and dexterity without complex, heavy, and expensive mechanisms. The patterning of electrodes also allows biomimetic robots to contain arrays of smaller actuators in a distributed actuation system that is highly redundant and survivable. Long, thin cylindrical actuators can be patterned to enable snake-like motions or tentacle manipulation, for example. Flat actuators can create the type of wave-like motions that swimming skates or rays produce.

● High electromechanical coupling that provides multifunctionality – integrated sensing and power recovery. Inherent energy absorption during locomotion can be harnessed for sensing or generating power. For sensing, the same capacitive EPAM that propels a robot can be used to create a tactile sensor array that could help the robot localize itself in its environment or search for objects of inter-est such as buried mines. Natural muscle has such proprioceptive and sensor integration capabilities. For generation, one application could be a self-sustaining robotic system that, when energy reserves are low, anchors itself and uses wave or air-current motion to recharge its batteries.

24.4 FIRST GENERATION OF EPAM-ENABLED ROBOTS

In seeking to create robots that embody the advantages discussed above, SRI International (SRI) has built many first-generation prototypes. Some of the most striking examples are biologically inspired

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robots that use cylindrical ‘ spring roll ’ actuators made from dielectric elastomers. A spring roll actuator consists of electroded elastomer film wrapped around a spring. When an applied voltage actuates the film, the spring extends axially, creating a 1-DOF spring roll. By patterning multiple electrodes along separate quadrants of film, one can also make an actuator that can bend in multiple directions, creating 2- or 3-DOF spring rolls.

Flex [3] , the largest of the robots at 470 g mass and 36 cm length, was the first self-contained (i.e. battery-powered) walking robot powered by electroactive polymers ( Fig. 24.1 ). A second version of this robot used two 1-DOF spring rolls for each of its six legs, one actuator to lift and lower the leg, and the other actuator to move it forward and back [4] . Like the two robots described below (and most insects), Flex walks with a ‘ dual tripod ’ gait in which the left front, left rear, and centre right legs move up, down, forward, and back together. Flex can move at speeds greater than 12 cm/s, actuating its legs at over 10 Hz.

Skitter [5] was designed to demonstrate the ability of EPAM to act not only as an actuator but also as the structure of a robot as a first step in multifunctionality ( Fig. 24.2 ). Note how the actuator and the legs are not separate; the actuator is the leg, providing the equivalent of both the muscle and the skel-etal structure. This particular robot is based loosely on the Sprawlita robot [6] , which uses pneumatic actuators in a similar fashion. Each of the six legs points a single 1-DOF actuator down and slightly backward, and is attached to the body by a compliant joint. In spite of its simple design, Skitter has demonstrated a speed of 6.8 cm/s.

MERbot [7] , which gets its name from the multifunctional electroelastomer rolls (MERs) that form its legs, is the next logical step, using 2-DOF rolls as flexible legs in lieu of discrete hip or knee joints (see Fig. 24.3 ). The MERs yield a very light, simple robot that still has a high degree of dexterity. MERbot has travelled faster than 14 cm/s.

Figure 24.1 Flex, the first self-contained walking robot powered by electroactive polymers.

Figure 24.2 Skitter demonstrates EPAM as both an actuator and as structure (the leg).

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Biomimetic Robots 255

Jumping robots are also attractive with EPAM, and this application illustrates the advantages of high energy direct drive actuation. Fig. 24.4 shows an early jumping EPAM platform [7] . Note the potential simplicity of a jumping robot EPAM design. This design uses only three EPAM diaphragm actuators. Electric motors have difficulty in generating the high peak power density necessary for jumping start-ing from a stopped state, so electric motor jumping drives typically require gearboxes and energy stor-age in a spring with a sudden release mechanism.

24.5 FUTURE GENERATIONS OF EPAM-ENABLED ROBOTS

One design under consideration is a snake robot, which could be manufactured by concatenating several 3-DOF rolls (see Fig. 24.5 ) or by using pivot rolls (see Fig. 24.6 ). SRI has demonstrated a proof-of-concept snake segment. Snake robots are challenging from both a mechanical and a control perspective. Mechanically, snakes are highly articulated structures that are compact and lightweight and interact energetically with their environments, due to their friction, strength, and stiffness at many points on their bodies. Indeed, these interactions are their means of locomotion. From a control perspec-tive, snakes must be able to coordinate their large numbers of segments (biological snakes can possess more than 300 vertebral segments) and manage force interactions with their environments to produce useful and adaptive gaits and behaviours. Besides locomotion, EPAM bending rolls can be used for manipulators that can reach around objects in complex environments.

Snake robots based on conventional actuation technologies such as electric motors cannot meet these challenges. For example, electric motors must be used in conjunction with high-gear-ratio

Figure 24.4 A simple jumping robot made from EPAM diaphragms.

Figure 24.3 MERbot uses bending rolls as flexible legs instead of discrete hip or knee joints.

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transmissions that maximize the power output. Several researchers have developed snake robots with such motors [8, 9] . The specific power of the best electric motors does not generally exceed 0.5 W/g. When the mass of the gearbox and the mechanisms needed to produce the 2-DOF motion required at each joint are included, the effective specific power density of the actuation mechanism is less than 0.05 W/g. In contrast, natural muscle can produce a peak power of more than 0.2 W/g and dielectric elastomers have demonstrated 1 W/g. The high-ratio transmissions and stop-and-start motions typically used with electric motor drives in robot snakes result in relatively slow and inefficient motion. Electric motors can operate at high efficiencies when rotating at constant velocities and at high speeds. However, at slow speeds and with numerous accelerations and decelerations their efficiency is typically well below 25%. Other efforts to reproduce muscle-like actuation in snake-like robots have used shape-memory alloy actuation (e.g. [10] ). As thermal actuators, however, shape-memory alloys are energy inefficient (typically 2% or less) and have slow response speeds in air.

EPAM is also uniquely qualified to produce fin-like motion, and such a fin has been demonstrated in water ( Fig. 24.7 ). Particularly interesting is the rajiform motion used by skates and rays. A swim-ming ‘ Raybot ’ ( Fig. 24.8 ) would be highly manoeuvrable and able to rotate in place or travel backward. Its flat shape would be less susceptible to turbulence and would also afford more space for sensors or other payloads. Traditional actuation methods are clearly inadequate for such motion. A previous effort to reproduce muscle-like actuation in a rajiform robot (Robo-Ray, the product of a student project at the University of British Columbia) used a shape-memory alloy, but this material was found to be ‘ ineffi-cient and difficult to control ’ [11] .

EPAM could also enable other biomimetic propulsion technologies such as peristaltic movement, or jet propulsion such as that used by jellyfish and squid. The latter application would exploit the inherent compliance of EPAM and the fact that it matches the mechanical impedance and density of water.

Dielectric elastomers are also attractive for flapping wing flight (see Fig. 24.9 ); in fact, various EPAM-powered flapping mechanisms have been manufactured and tested in the laboratory [12] . These flapping

Figure 24.5 A conceptual design for a snake made by concatenating several EPAM rolls end to end.

Figure 24.6 Pivot rolls demonstrating over 240° of bending.

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mechanisms have not yet produced the continuous power necessary for self-contained sustained flight, because of excessive structural mass for the actuator (the EPAM fraction was only about 10% in tests to date) but they do show the ability for a very simple structure that can use resonance to achieve high flapping amplitudes at high power densities.

Electronics andpayload area

Unimorph EPAM tail toraise RF transmitterantenna above waterline

EPAM fins

Lateral sensor arrayFront sensor array

Figure 24.8 Conceptual design for Raybot, a rajiform robot enabled by EPAM.

Figure 24.7 A prototype EPAM fin being tested under water.

Figure 24.9 Conceptual design for a flapping wing robot.

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24.6 SUMMARY AND CONCLUSIONS

Electroactiv e polymer artificial muscles based on dielectric elastomers have been successfully used in a diverse array of robotic applications. Several proof-of-principle robots have been demonstrated. We anticipate continued advances in robots based on EPAM, as it enables high performance in simple, low-cost, multifunctional designs.

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[12] Kornbluh, R. D., Pelrine, R. E., Pei, Q., Heydt, R., Stanford, S. E., Oh, S. and Eckerle, J. (2002).

Electroelastomers: applications of dielectric elastomer transducers for actuation, generation and smart struc-

tures. In Smart Structures and Materials 2002 : Industrial and Commercial Applications of Smart Structures Technologies , Ed. McGowan, A., Proc. SPIE , 4698 , 254–270.

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MICRO-ANNELID-LIKE ROBOT ACTUATED BY ARTIFICIAL MUSCLES BASED ON DIELECTRIC ELASTOMERS

Hyouk Ryeol Choi 1 , Kwangmok Jung 1 , Ja Choon Koo 1 , Jae-do Nam 2 and Youngkwan Lee 3

1 School of Mechanical Engineering, Sungkyunkwan University, Suwon, Korea 2 Department of Polymer Science and Engineering, Sungkyunkwan University, Suwon, Korea 3 Department of Chemical Engineering, Sungkyunkwan University, Suwon, Korea

Abstract

The annelid provides a biological solution of effective locomotion adaptable to a large variety of unstructured

environmental conditions. The undulated locomotion of the segmented body in the annelid is characterized by the

combination of individual motion of the muscles distributed along the body, which has been of keen interest in bio-

mimetic investigation. In this chapter, we present an annelid-like robot driven by soft actuators based on dielectric

elastomer. To mimic the unique motion of the annelid, a novel actuation method employing dielectric elastomer

is developed. By using the actuator, a three-degree-of-freedom actuator module is presented, which can provide

up–down translational motion, and two rotational degree-of-freedom motion. The proposed actuation method pro-

vides advantageous features of reduction in size, fast response, and ruggedness in operation. By serially connect-

ing the actuator modules, a micro-robot mimicking the motion of the annelid is developed and its effectiveness is

experimentally demonstrated.

Keywords : Actuator, annelid, artificial, dielectric elastomer, inchworm, micro-robot, soft.

25.1 INTRODUCTION

Recently, the development trends of robots have been concentrated on mimicking human movements or animal functions. In this regard, there have been many reports on the development of annelid-like robots, such as inchworms or earthworms. The annelid is one of the most popular mechanisms in robotic fields and is employed in various areas such as pipe inspection robots, wall climbing robots, etc. [1] because the locomotion of an annelid is very simple and it is an effective way to move in any envir-onment. Unfortunately, the physical properties of traditional actuators such as electromagnetic motors and pneumatic actuators are truly different from that of biological muscles; therefore, the operation of a robot equipped with traditional actuators is confined only to a structured environment.

Shape memory alloys (SMAs) have been one of the active candidates used for the materials in artifi-cial muscles and are normally used to develop small-sized annelid-like robots [2–4] . A SMA is a good material to fabricate the micro-actuator and robot because it has both a simple deformation principle and structure. On the other hand, SMA actuators have a low bandwidth and efficiency because they accompany heating and cooling on working. Among the active candidate materials, electroactive poly-mers (EAP) seem to have a great potential to become a successful new alternative actuator [5] . In spite of the technical difficulties, their application areas are rapidly expanding by many frontier research-ers, especially in robotic research fields since the actuation mechanism of the polymers is similar to that of human muscles. Among the various kinds of EAPs, dielectric elastomers can be considered as a significant material used in artificial muscles. Dielectric elastomers are very soft and their deform-ation is much greater than that of any other existing electroactive material. The deformation of dielectric elastomers can be used in various ways to produce actuation [6, 7, 8–11] . Stretched film type, rolled,

Chapter 25

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260 Chapter 25

and bow tie actuators are the three major configurations of actuators employing dielectric elastomer [12] . Basically, dielectric elastomers have the advantages of low price, light weight, ease of fabrication, and adaptability to a variety of actuator configurations, factors that can provide the competitive edge over the other alternatives. In this study, a prototype annelid-like robot is developed that is constructed using artificial muscles based on a dielectric elastomer actuator. To mimic annelid motion, the actu-ator itself should have characteristics similar to the actuating scheme of annelid animals. Additionally, a new design for the dielectric elastomer actuator is proposed that has the advantages of reduced size, fast response, and ease and ruggedness of operation. The proposed earthworm robot is the result of a systematic study that takes these features into consideration. Also, demonstrations will be provided in order to confirm the effectiveness of the proposed robot.

25.2 LOCOMOTION OF EARTHWORM

As illustrated in Fig. 25.1 , an earthworm has two muscles that it uses for locomotion, both of which run the whole length of the worm ’ s body. These two muscles are circular and longitudinal. The circular muscles surround each segment and the longitudinal muscles run from segment to segment over the entire length of the earthworm. When the circular muscles are contracted, the diameter of the body is reduced making earthworm thin. When the longitudinal muscles contract the length of the body is reduced which makes the earthworm short. The contractions of an earthworm ’ s muscles resemble a wave contracting and relaxing a few segments at a time. Figure 25.2 shows the vermiculation of an earthworm. Traction is achieved through bristle hairs called setae that are distributed about the earth-worm ’ s segments. The setae are imbedded in the earthworm ’ s longitudinal muscles, therefore, when the longitudinal muscle contracts and relaxes the distance between the setae of different segments fluctu-ates. To move, an earthworm elongates its body and anchors its anterior with its setae and pulls the rest of its body forward. The locomotion of the earthworm is very simple and allows it to move effec-tively in its surroundings. The earthworm does not need its whole body to move because it only uses a small part of its body to give enough frictional resistance along the surface. Additionally, it can move on rough terrain and creep in thin tubes or across obstacles because it is very flexible. The detailed sectional view of an earthworm is shown in Fig. 25.3 .

Circular muscle

Septa

Longitudinal muscle

Figure 25.1 Earthworm [13] .

Direction of movementDirection of contractile wave

Figure 25.2 The vermiculation of an earthworm [14] .

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Micro-annelid-like Robot Actuated by Artificial Muscles Based on Dielectric Elastomers 261

25.3 NEW ACTUATION IDEAS FOR DIELECTRIC ELASTOMERS

Previously built dielectric elastomer actuators with pretension can generate quite a large amount of displacement through Maxwell stress as well as pretension, but the effect of pretension is dominant. However, pretensions give several negative aspects that are largely caused by the viscoelastic behav-iour of the polymer. Viscoelastic behaviour is a combination of elastic and viscous behaviour where the applied stress results in an instantaneous elastic strain followed by a viscous, time-dependent strain. The time-dependent behaviour of materials under a quasi-static state may be represented by three mecha-nisms: creep, stress relaxation, and constant rate stressing [15, 16] . The elastomer under pretension is subjected to a constant strain so that the stress due to stretching gradually decreases and thus the actua-tor shows a time-dependent behaviour. In particular, the output force decreases because the maximum actuation force is equal to the pretension of the elastomer film and the pretension decreases accord-ingly. Moreover, pretension requires a frame strong enough to sustain the tensile force, which makes the weight and size of the actuator increase. Recognizing the disadvantages of previous designs, the present work employs a new actuator concept that does not use pretension so that it can sustain its initial per-formance quality, although it may not generate a large deformation like the pre-stretched elastomer. To avoid the time-dependent behaviour of the dielectric elastomer actuator, a pure compression force by electric field, that is Maxwell stress, is used for actuation of the proposed actuator configuration.

25.3.1 Preview of direct compression

The actuator employing a dielectric elastomer is presented in the following. The basic operational mechanism of the polymeric material is introduced in various publications where they admit some of the limitations of the formulation [6, 12, 9, 10] . The electromechanical transduction of a pair of paral-lel plates is the main principle operation of the actuator. When an electric potential is applied across the elastomer film, the film is compressed along thickness direction while expanded along the lateral direction so that a mechanical actuation force is produced. The effective mechanical pressure in the thickness direction is derived as

� � � � �z EV

t� � � �0

20

2

r r

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

(25.1)

where E is an applied electric filed, t is thickness of elastomer, and � 0 and � r are electric permittivity of free space and relative permittivity of the polymer, respectively.

In order to avoid the time-dependent behaviour of the dielectric elastomer actuator, pretension should be removed and only a pure compressive force induced by the Maxwell stress should be used for actua-tion. For the first step of the non-prestrained actuator design, the deformation of the dielectric elastomer

Coelom

Circularmuscle

Cuticle

Longitudinalmuscle

Septa

Figure 25.3 Sectional view of earthworm [13] .

Ch25-I047488.indd 261Ch25-I047488.indd 261 12/7/2007 3:08:49 PM12/7/2007 3:08:49 PM

262 Chapter 25

caused by the Maxwell stress is calculated. The governing equation should be modified for the vertical strain � z according to the compression stress �z :

t t z� �0 1( )� (25.2)

�� � �

�� �z

zzY Y

V

t Y

V

t� � �

�� �

1

1

1 1

10

0

2

00

2

r r( )

⎡

⎣⎢⎢

⎤

⎦⎥⎥

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟ ���z

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

2

(25.3)

� � � � �z z z Y

V

t3 2

00

2

21

� � � � r

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

(25.4)

where Y denotes the elastic modulus, and t 0 is the initial thickness. Figure 25.4 shows the vertical strain � z curve according to the voltage increase about the silicone

KE441(ShinEtsu), the material properties of which are shown in Table 25.1 . As shown in Fig. 25.4 , the estimated compressive strain is about 1–3.5%, although that is dependent on the material properties and the applied input voltage. Since most dielectric elastomers are incompressible, that is if the actuator is assumed to be a thin circular disc, then the strain is derived as

( )( )( ) ( ) ( )1 1 1 1 1 12� � � � � � �� � � �x y z r zδ (25.5)

where

��r

z

��

�1

11 (25.6)

Approximation of Eq. (25.6) yields

� �r z� �

1

2 (25.7)

Table 25.1 Material properties of silicone KE441 by Shinetsu.

Elastic modulus (MPa) 2 Breakdown voltage (kV/mm) 20 Relative permittivity 2.8

0

�0.005

�0.01

�0.015

�0.02

�0.025

�0.03

�0.035

�0.040 500 1000 1500 2000 2500 3000

Voltage (V)

Str

ain

Figure 25.4 Simulated strain curve along thickness direction.

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Micro-annelid-like Robot Actuated by Artificial Muscles Based on Dielectric Elastomers 263

Equation (25.7) states that the usable strain is only half of the vertical strain. For this reason either a material with a high dielectric constant or a very high input voltage can be used to yield high actuator performance. However, neither seems to be very practical since the polymeric materials available com-mercially have limited dielectric characteristics and the electric circuit devices handling such high volt-ages are also limited. Therefore, a new actuating method needs to be developed for the non-prestrained actuator.

25.3.2 New design to amplify displacement

The basic operational concept of the non-prestrained dielectric actuator is illustrated in Fig. 25.5 . As shown in Fig. 25.5(a) , a thin dielectric elastomer sheet is confined by rigid boundaries. Once a com-pressive force is applied to the sheet it expands such that it induces a buckling situation on the sheet and causes it to become either convex or concave. This would create an efficient means of actuation without prestrain. The relation between the curvature r , the angle � , and the strain � a can be derived as follows:

b a ra� � �(1 )� � (25.8)

ra

sin�2 2

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟ � (25.9)

��

�sin( )

( )/2

2 1� � a (25.10)

From the Taylor series expansion

sin( )

!

( )� � � � �2 2

2

3

24

48

3 2⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟ � � �

�/ (25.11)

By substituting Eq. (23.11) into Eq. (23.10), the angle � can be derived through the following:

��

��

24 11

1−

⎡

⎣⎢⎢

⎤

⎦⎥⎥( )a

(25.12)

And the displacement h will be

h r� �12

cos�⎛

⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟

⎡

⎣⎢⎢

⎤

⎦⎥⎥ (25.13)

where

r

aa��[( ) ]1 �

� (25.14)

Compression force

Expansion force

Reaction force

b � a(1 � δa)

a

Frame

Dielectricelastomer

h

r

a

θ

(c)(b)(a)

Figure 25.5 Conceptual schematic view of the proposed actuator.

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264 Chapter 25

25.4 BUILDING THE PROPOSED ACTUATOR

In Fig. 25.6 , provides a schematic illustration of the non-prestrain actuator construction, its actual dimension is listed in Table 25.2 . The construction uses KE441 (ShinEtsu) silicone, which has a lower viscosity than VHB4905. The spin coated elastomer film was coated with carbon electrodes and stacked to make multiple layers. The total thickness of the membrane ( t ) is 0.75 mm and each dielectric elasto-mer has an approximate thickness of 50 � m. To create an insulating area between the electrodes, both sides of the dielectric elastomer have a non-electrode area. The diameter of the membrane ( d ) is slightly larger than the diameter of the fixed frame ( d f ) and might create either a concave or convex circular membrane that could provide more stable control over the deformation in the desired direction during actuation. Only expansion occurs in the area with electrodes d r , thus the actual strain � a should be cal-culated from � r . That can be derived as

� � �a r

rd

d� �i

(25.15)

where � a denotes a converted strain for total diameter and � i is the initial strain given by the initial condition � i = ( d / d f � 1). The � r is given by Eq. (25.6) and the vertical displacement is derived by Eq. (25.13). Figure 25.7 shows the actual fabricated prototype of a dielectric elastomer actuator.

Table 25.2 Specifications of the prototype actuator for experiments.

Item Specifications

Total diameter d (mm) 5.8

Effective actuation diameter d r (mm) 5.1 Total thickness t (mm) 0.75 Average thickness of each layer ( � m) 50 Stacked layers 12 Total weight of actuation unit (g) 0.02

d

dr

df

d

dr

df

Electrodes (Three-dimensional view)

Dielectricelastomer

Frame

Non-electric areafor isolation

(Sectional view)

(Top view)

Insert actuatorin frame

Figure 25.6 Construction of the proposed actuator.

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Micro-annelid-like Robot Actuated by Artificial Muscles Based on Dielectric Elastomers 265

25.5 SIMULATION AND EXPERIMENTAL RESULTS

To validate the mathematical modelling and evaluate the performance of the actuator proposed, several experiments were conducted. As shown in Fig. 25.8 , the displacements and forces of the actuator are measured with a laser displacement sensor (Keyence) and a strain gauge sensor.

A test and an analysis have been compared in Fig. 25.9 . The simulation and the experiments are in good agreement. There is small error between the calculated result and the experiment that might be caused by the disparity and difference in thickness of each layer, the externally coated shield layer, and the fabrication process. For complete measurements of the actuator performance, the frequency

Digital osiloscope

In/outputmonitoring

Function generator

Sinusoidalwave input

High voltage amplifier(Trek 10/10B)Driving circuit

Amplifier(KYOWA)

Load cell

Proposedactuator

Forcemeasuring

Displacementmeasuring

Laserdisplacement

(LK-81)

Figure 25.8 Experimental setup.

Frame5 mm

Actuator

Connectingelectrodes

Electrode

45–55 µm

Elastomer(KE441)

(a) (b)

Figure 25.7 Prototype of actuator.

0.2

0.160.18

25

20

15

10

5

0.140.120.1

0.080.060.040.02

00 500 1000 1500 2000 2500 3000

Voltage (V)(a)0 500 1000 1500 2000 2500 3000

Voltage (V)(b)

Dis

plac

emen

t (m

m)

For

ce (

mN

)

Experiments ExperimentsSimulation

Figure 25.9 Results of displacements for simulations and experiments.

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266 Chapter 25

2500 V2000 V

2500 V2000 V

0.6

0.5

0.4

0.3

0.2

0.1

0

16

14

12

10

8

6

2

4

0

10�1 100 102101

10�1 100 102101

Frequency (Hz)

Dis

plac

emen

t (m

m)

For

ce (

mN

)

(a)

Frequency (Hz)(b)

Figure 25.10 Frequency response of actuator proposed.

response of the actuator was also tested for both displacement and force. As shown in Fig. 25.10 , the soft-actuator generates a fairly large displacement and force. The weight of the actuator is only 0.02 g and the diameter is 6.5 mm (including frame) with a thickness of 0.75 mm. Furthermore, the actuator shows a fast response time for square wave form inputs as shown in Fig. 25.11 . This would indicate that the developed actuator can work for use in practical applications.

25.6 BUILDING AND OPERATING OF EARTHWORM ROBOT

To adapt the biological behaviour to artificial creations, modifications and simplifications of the motion are usually performed in order to minimize the actuators and the joints needed. The ultimate aim would be to develop robotic movers that fulfil the movement criterion using the simplest and fewest compon-ents. Therefore, according to the above observation of the locomotion of an earthworm, the major muscle involved in moving the earthworm is the longitudinal muscle. For mimicking the longitudinal muscle, the proposed actuator is adapted as shown in Fig. 25.12 . The module is connected in series, a multi-degree-of-freedom earthworm could be constructed. The actuator module consists of 12 actu-ators on both side of a printed circuit board, which is a patterned electric wire used to supply the electric voltage. This actuator module works as both a power plant for the movement and a body skeleton for the earthworm robot structure. In other words, the earthworm robot can be built by simply stacking actua-tor modules without any additional mechanical structures. The actuator module shown in Fig. 25.12 has 20 mm diameter, 3 mm thickness, and a weight of 0.4 g. In Fig. 25.13 , a fully assembled inchworm robot is shown. This robot has eight actuator modules (96 actuators). Four wires total are used to supply

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Micro-annelid-like Robot Actuated by Artificial Muscles Based on Dielectric Elastomers 267

electric power and are connected to each module. In order to connect each module, small silicone cylin-ders, which have a 1 mm diameter and a height between 0.2 and 0.4 mm, are used to make point–point connections between each modules and are bonded by silicone adhesives. The earthworm robot has front and rear sectors, each sector has four actuator modules. Each of the sectors is operated sequentially to create the motion of the earthworm. Specifications of the earthworm robot are shown in Table 25.3 . The speed of earthworm robot depends on the operating frequency of each actuator. Figure 25.14 shows 4-movie frames during a 3-s locomotion. The robot shows a speed of 1 mm/s with a 5 Hz actuation.

The earthworm robot is covered with artificial skin to protect the inner organs as shown in Fig. 25.15 . The skin is fabricated by a 3D molding method. The thickness of skin is only 100 � m. Additionally, it has wrinkles at the position of each septa to help the contraction and expansion of robot.

0.5

0.4

0.3

0.2

0.1

00 0.2

500

1000

1500

2000

2500

00.4 0.6 0.8 1 1.2

Time (S)

Dis

plac

emen

t (m

m)

Displacement

Vol

tage

(V

)

Voltage input

(a)

15

10

5

0

500

1000

1500

2000

2500

0

For

ce (

mN

)

Vol

tage

(V

)

Voltage input

0 0.05 0.1 0.15 0.2 0.25Time (S)(b)

Force responce

Figure 25.11 Response characteristic of the actuator.

Multi-layeractuator

Frame

Circuit pattern

PCB

Electric wire hole

Figure 25.12 Actuator module.

Stiff feather (setal hairs)

Modular PCB(septa)

Actuator unit(longitudinal muscle)

Figure 25.13 Earthworm robot.

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268 Chapter 25

25.7 CONCLUSION

This chapter presents an earthworm robot that uses a novel actuator. The robot consists of only polymer and plastic materials except for the electric wire, and shows the possibility of constructing robots in an inexpensive way. To construct the earthworm robot, a novel soft actuator based on a dielectric elastomer has been proposed. The soft actuator was built without prestrain so that the time-dependent behaviour can be dealt with. Also, the unnecessarily strong frame used to support a high pre-tension and the additional elastic body used to keep the balance of restoration force were removed. Therefore, we can construct an actuator with a relatively small size, light weight, and simple structure. To verify the per-formance of the proposed actuator, preliminary experiments were performed. According to the experi-ments, the actuator can generate a force almost 100 times the weight of itself. The major advantages

Table 25.3 Specifications of the earthworm robot developed.

Size ( D � L mm) 20 � 45 Speed (mm/s) at 10 Hz 2.5 Weight (g) 4.7 Load (g) >10

Time: 0 s

Time: 2 s

Time: 1 s

Time: 3 s

time : 0.0 time : 1.5

time : 4.5time : 3.0Over 4mm

(b) (a)

(c) (d)

Figure 25.14 Movie frame for locomotion: speed 1 mm/sec at 5 Hz.

Artificial skin

Quarter (USA)Earthworm robot

Figure 25.15 The earthworm robot covered with artificial skin.

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Micro-annelid-like Robot Actuated by Artificial Muscles Based on Dielectric Elastomers 269

of the proposed actuator can be summarized as follows: time-independent performance, high force-to-weight ratio, cost effectiveness, ease of fabrication, and intrinsic softness.

This not only enables efficient actuation but also makes it possible to manufacture a robot through a totally new fabrication method that enables mass production of a robot through processes such as injection molding or stamping. In addition, there exist the possibilities to easily mimic the natural and delicate motions such as animal skin motions, wrinkling, and eyebrow movement without using many actuators. The design of the segment addressed in this section illustrates a realization of embedding actuators in a robot without using complicated mechanisms or their substitutes.

ACKNOWLEDGEMENT

This research was performed for the Intelligent Robotics Development Program, one of the 21st Century Frontier R & D Programs funded by the Ministry of Science and Technology of Korea.

References

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BINARY ACTUATION

Jean-Sébastien Plante and Steven Dubowsky

Massachusetts Institute of Technology, Cambridge, MA, USA

Abstract

Binary actuation is a robotic and mechatronic system design paradigm that uses a large number (10 to 1000s) of

binary actuators. Each actuator typically has two stable states that do not need power to be maintained. Binary sys-

tem actuators need to be lightweight, low cost, and to have good performance, such as dielectric elastomer actuators

(DEAs). A key characteristic of DEAs is that their performance and reliability is highly dependent on stretch rate.

In particular, their maximum safe extension increases significantly when operated at high stretch rates. Binary actu-

ation exploits this property by using DEAs intermittently at high speeds for switching state. This chapter explains the

basics of binary actuation using DEAs. Two examples of the application of DEAs to binary devices are discussed: a

manipulator for intra-magnetic resonance imaging (MRI) medical interventions and a hopping robot for space explor-

ation. These examples suggest that binary actuation using DEAs is practical even with current actuator performance.

Keywords : Actuator, binary, bi-stable, dielectric, discrete, elastomer, hop, magnetic, manipulator, mechatronic,

medical, MR, resonance, robotic, space.

26.1 INTRODUCTION

Many robotic and mechatronic systems and devices would greatly benefit from a design paradigm called binary actuation [1–4] . Binary actuation can be thought of as the mechanical analogue of digital electronics where each actuator ‘ flips ’ between one of two discrete states. Such systems would be simple, robust, light-weight, inexpensive, and easy to control. Figure 26.1 illustrates a simple 3-degree-of-freedom (DOF) binary device in each of its 2 3 � 8 positions [5] . Systems design and control is greatly simplified since low-level feedback control is virtually eliminated, along with the associated sensors, wiring, and electronics [6] .

Simulations have shown that binary robotics devices are kinematically capable of executing practical tasks, such as instrument placement for planetary exploration, legged locomotion through rough terrain, and industrial and medical devices (see Fig. 26.2 ) [7, 8] . Studies suggest that less than 100 binary DOF will provide sufficient resolution for many practical tasks, and that the associated computing require-ments for solving their inverse kinematics are reasonable [5, 7] .

To date, the primary challenge to implementing practical large-DOF binary robotic systems has been the development of effective binary actuators. Conventional actuators are too expensive, heavy, and

Chapter 26

000 001 010 011

110 111101100

Figure 26.1 Eight discrete positions of a 3-DOF binary manipulator.

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Binary Actuation 271

complex to be used in large numbers. This chapter explores the strengths and limitations of bi-stable dielectric elastomer actuators (DEAs) technology as applied to robotic and mechatronic systems and devices. It is shown that these actuators are particularly well suited to binary actuation.

Under laboratory conditions, DEAs have shown substantial energy densities (actuator mechanical work per unit mass of actuator), significantly exceeding those of conventional technologies such as electromagnets [9–11] . DEAs are potentially a key enabling technology for large-DOF binary robotic devices with their linear extensions of more than 100% (see Fig. 26.3 ). They are lightweight and sim-ple compared to conventional actuators. They can be implemented in large numbers without complex motion amplification transmissions [8, 12] .

Reliability has been found to be an important problem of DEAs. For example, actuators based on VHB 4905/4910 have experienced high ‘ infant mortalities ’ and short shelf lives, particularly when high performance is required [13] . Most importantly, these actuators experienced erratic and misunderstood failures during operation [13, 14] .

Recent studies of DEAs failure modes have shown, by experimentally validated continuum mechan-ics models, that the failure modes of DEAs change dramatically with stretch rate (or actuator speed) due to their viscoelastic character [15] . A failure mode, called pull-in failure, significantly limits actuator extension at low stretch rates but not at high stretch rates. Thus DEAs can be reliable at high actua-tion rate, making them compatible with bi-stable binary actuation where they are only powered inter-mittently while changing positions between states. It is shown here that given these characteristics, prac tical robotic devices based on bi-stable DEAs can be developed. Two applications are discussed: a 7-DOF binary manipulator and a hopping robot for planetary exploration.

26.2 BINARY ACTUATORS

Since a relatively large number of actuators are generally required for binary systems, to be practical, these actuators must be simple and low cost. Furthermore, binary actuators should have relatively high forces and work outputs for their weight, acceptable energy conversion efficiencies, and be capable to operate at acceptable speeds. Conventional actuators, such as DC motors and pneumatic cylinders, while well suited for conventional systems, are too heavy and complex for binary actuation [16, 17] .

In recent years, new actuation technologies have been developed. However, these have limited use for binary systems [16] . Shape memory alloys (SMA) rely on volume contractions driven by alloy

(a) (b)

Figure 26.2 Examples of binary robotic applications: (a) manipulator on a conventional rover and (b) legs of a walking robot.

(a) (b)

41 mm19 mm

Voltage off Voltage on

Film

Structural frames

Interstitial frames

Figure 26.3 DEA with linear extensions greater than 100%: (a) exploded view and (b) prototype.

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272 Chapter 26

phase changes (see Fig. 26.4 ). They are relatively slow, limited to low efficiencies, and sensitive to environment temperature. Ionic polymers (conducting polymers) change volume when their polymer chains absorb or swell ions. Such systems must be kept in aqueous environments, are slow, and while have good force output, their extensions are very small. Piezoelectric materials are relatively heavy and also have very small extensions. Hence, both piezoelectric and ionic polymers require complex trans-missions for many practical applications such as binary actuation. Optimized linear electromagnetic systems (solenoids) can experience overheating issues and are heavy.

DEAs have been proposed to replace conventional actuators. They have good performance character-istics and are inherently inexpensive [19, 20] . However, as continuous actuators, their practical imple-mentation has been limited by their problematic reliability and efficiency. As discussed below, those limitations can be avoided in properly designed binary systems.

26.3 PROPERTIES OF DEAs

An experimentally validated analytical model of the failure modes of DEAs has recently been developed [15] . A brief summary of this model is presented in Section 26.6. The model considers three failure modes: material strength, dielectric strength, and pull in. Pull-in failure is an unstable condition that can occur when the Maxwell pressure becomes always greater than the film compressive stress. Model predictions are compared with experimental data of 10 identical diamond actuators (see Fig. 26.3 ) built with 3M ’ s VHB 4905/4910 elastomer. The actuators were all tested at the same pre-stretch area expan-sion of about 11 because this value was found to offer optimum performance [15] . The samples were first tested at a high stretch rate that is typical of many DEA applications ( � 10 s to reach 100% exten-sion). No failure was observed. The same samples were then tested at a low stretch rate where viscoelas-tic effects are negligible such as when an actuator holds its position for extended periods of time ( � 1 h to reach 100% extension). All 10 actuators failed. The data is presented in Fig. 26.5 where actuator area expansion, � 2 1,act , is plotted versus pre-stretch area expansion, � 2 1,pre . At high stretch rates, the actuators were pulled up to area expansion of 2.27 (150% linear extension) without failure, as predicted by the model. At low stretch rates, failure was caused by pull-in at an average area expansion of 1.28 (30% linear strain) with a lowest value of 1.05 (6% linear strain). As shown by Fig. 26.5 , the analytical predic-tions corroborate well with the experimental data.

The differences between the low and high stretch rate failure behaviour are explained by the fun-damental role of viscoelasticity on actuator failure. At high stretch rates, the viscous forces ‘ stiffen ’ the film and protect it from pull-in failures. In contrast, low stretch rates generate less viscous imped-ance and pull-in failures dominate. The conclusion of this study is that, to achieve long life and good reliability, DEAs must be used at high stretch rate where viscoelastic forces prevent pull-in failure.

It is fortuitous that reliable DEAs operation occurs at high speeds, precisely as required for bi-stable binary actuation where actuators are only used at high stretch rates during state switching and are other-wise unpowered. This strategy not only matches well with the reliability requirement but also signifi-cantly improve efficiency by minimizing current leakage losses [21] . Two examples of binary robotic devices are discussed below.

SMAactuators

Flexuredjoints

(a) (b)

Figure 26.4 The MIT SMA powered binary manipulator [18] : (a) single-stage and (b) five-stage devices.

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Binary Actuation 273

26.4 BINARY ROBOTIC SYSTEMS WITH DEAs

26.4.1 Binary manipulation

A proof of concept of a 7-DOF binary manipulator is shown in Fig. 26.6 [22] . This snake-like device demonstrates the large displacement capabilities of DEAs with a tip angle range of 55°, using only two and a half stages. Such all-polymer manipulators could be used for low-force ( � 5 N) medical interven-tions inside magnetic resonance imaging (MRI) environments since DEAs have been demonstrated to be MRI compatible [8] .

The simplest strategy to design a bi-stable module for binary manipulators is to use an antagonistic pair of actuators that ‘ flip ’ the state of a bi-stable element. An exploded view of a 1-DOF antagonistic module is shown in Fig. 26.7(a) . Figure 26.7(b) shows a prototype playing ‘ pool ’ with a plastic cylinder (the cylinder looks blurry because it is in motion) [12] . In the figure, DEA 1 is completing an opening cycle and is thus showed in an extended state. The bi-stable truss has been switched to the left, which set the plastic cylinder in motion. Firing DEA 2 would switch the bi-stable truss back to the right. The performance specifications of this prototype are shown in Table 26.1 .

A second strategy to implement bi-stable DEAs is to couple a single DEA with a compliant indexing transmission (see Fig. 26.8 ) [22] . The 16.4 g bi-stable module is shown switching a 25 g DC motor up and

20°35°

Figure 26.6 A 7-DOF binary manipulator prototype.

0(a)

(b)

5 10 15 20 25 30 350

1

2

3λ 1, a

ct2 λ 1,a

ct2

λ1,pre2 λ1,pre

2

4

5

6

7

0

1

2

3

4

5

6

7Experimental Experimental

0 5 10 15 20 25 30 35

Dielectricstrength

Material strength

Pull-in

Safe domain

(Meanfailure andscatter)

Dielectricstrength

Materialstrength

Pull-in

Safe domain

(No failure)

Figure 26.5 Failure analytical predictions for (a) low stretch rate ( ��uni s� � � �3 3 10 4 1. ) and (b) high stretch rate

( ��uni s� �0 0945 1. ) [15] .

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274 Chapter 26

down. These same modules were used for the 7-DOF manipulator of Fig. 26.6 . The performance specifi-cations are shown in Table 26.1 . The single actuator device is more compact, has better force-to-weight characteristics, but is more complex than the antagonistic pair actuator. Each of the binary modules discussed so far could be used in low-DOF binary applications such as, for example, automotive door locks and trunk release, general HVAC control, and industrial pick-and-place tasks.

26.4.2 Space exploration robots locomotion

A proposed mission concept for planetary exploration is based on the deployment of a large number of small hopping Microbots over vast areas of a planet ’ s surface and subsurface, including features such as caves and craters (see Fig. 26.9 ) [26]. This would allow extremely large-scale in situ analysis of the terrain.

A Microbot ’ s mobility concept consists in pumping mechanical energy generated by a DEA into a power spring via a ratcheting transmission (see Fig. 26.10 ). Each pumping cycle moves the power spring in a new stable state, each time raising the system ’ s potential energy. After a certain number of pump-ing cycles, the stored energy is quickly released to make the system hop. A 26 g Microbot prototype performed tethered hops of about 60 cm after cranking a carbon fiber leaf spring in 35 discrete actuator

(a) (b)Complianthooks

Complianttruss

Pins

DEA

Backplate

~8 mm

Figure 26.8 Bi-stable module using a single actuator: (a) exploded view and (b) prototype.

DEA 1

Casing

Casing

Bi-stable truss DEA 2

DEA 1

Bi-stable truss

(a) (b)

DEA 2

Rolling cylinder

Figure 26.7 Antagonistic bi-stable module: (a) exploded view and (b) prototype.

Table 26.1 Bi-stable modules specifications.

Performance Metrics Antagonistic Actuators (at 1.6 mm/s)

Single Actuator (at 0.8 mm/s)

Displacement 25 mm 13 mm Strain 30% 35% Force (min/max) 1–3 N 1–3.5 N Mass 220 g 16.4 g Force-to-weight 0.46 6 Work output 1.14 � 10 � 4 J/g 0.0015 J/g Switching time � 5 s � 5 s Size (closed) 135 � 81 � 48 mm 65 � 35 � 22 mm

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Binary Actuation 275

pumps (see Fig. 26.11 ). The discrete states are maintained by a ratcheting transmission using a pair of miniature needle clutch bearings. Such applications could be thought of as multi-stable actuation.

26.5 CONCLUSION

The simple, low cost, lightweight, and high performance DEAs are shown to be effective in binary robotic and mechatronic systems and devices. At the same time, bi-stable binary actuation allows DEAs to operate at high stretch rates where they show good performance and reliability. The marriage of DEAs and binary robotics is very harmonious.

Application examples of DEAs to binary manipulation have been discussed through a binary manipu-lator and a hopping robot using multi-stable energy pumping. The performance of bi-stable DEAs is superior to previous alternative technologies such as electromagnetics, SMAs, and ionic polymers. However, binary actuation using current DEAs still requires improvement, particularly in terms of actu-ator force-to-weight ratio. This is likely to happen in a near future with new material development and improved manufacturing methods. Also, improved binary manipulator design using elastically average actuators are currently under development. Such redundant parallel manipulators are likely to be stiffer and have larger forces than conventional serial chains.

Figure 26.9 Microbot mission concept (rendering by Gus Frederick).

φ110 mmshell

Powerspring

Transmission

DEA

Figure 26.10 Microbot mobility concept.

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276 Chapter 26

26.6 APPENDIX: SUMMARY OF DEA FAILURE MODES STUDY

Three failure modes are considered:

1. Material strength failure occurs when folded polymer chains are straightened beyond their unfolded length. Hence, it is primarily a function of stretch. Experiments have shown that a film area expan-sion of 36 is a reasonable limit [23] . Failure occurs when:

�1,tot

2 � 36 (26.1)

2. Dielectric strength failure is obtained from experimental breakdown voltage versus total stretch data. Failure occurs when the electric field is higher than the experimental dielectric strength:

E E� exp 1,tot( )� (26.2)

3. Pull-in failure instability appears when an equilibrium between the applied equivalent Maxwell pres-sure ( P ) and the film compressive stress ( � 3,act ) cannot be reached. The film collapses into highly complex 3D wrinkling patterns leading to failure from either dielectric or material breakdown.

An analytical model used to study the failure modes is developed by considering a small conduct-ive circle coated on both side of a large pre-stretched film fixed on rigid rings (see Fig. 26.12 ). Under Maxwell pressure resulting from voltage application, the circle ’ s radius increases from its pre-stretched value, r pre , to its actuated value, r act . The film deformation occurs largely away from the film ’ s rigid ring ( r rig � r act ) and local failure modes are minimized, putting emphasis on fundamental material fail-ure modes. The effect of external work is considered by imposing a radial load stress acting against the expanding circle and whose numerical value is estimated on diamond actuators.

The film is modelled as a hyperelastic material. Viscoelastic effects are included by defining differ-ent elastic material models at different, constant stretch rates.

The deformation of the active region (expanding circle) is illustrated in Fig. 26.13 . The deformation is decomposed into two consecutive deformations: the pre-stretch deformation and the actuation deform-ation. The dimensions in the reference configuration (prior to pre-stretch) are expressed in the R , � , Z system. The dimensions in the pre-stretched and actuated dimensions are expressed in the r , � , z coor-dinates. The pre-stretch deformation is due to the stretching of the film prior to actuation. It consists of imposed equibiaxial deformations that produce principal stresses in the pre-stretched configuration, � 1,pre , � 2,pre , � 3,pre . The pre-stretched configuration is then perturbed by the equivalent Maxwell pressure, P , resulting from voltage application. The film further deforms and the stresses in the actuated configu-ration reach a new equilibrium to � 1,act , � 2,act , � 3,act .

The Maxwell stresses are expressed by an equivalent Maxwell pressure, P , given in reference [24] :

PV

u� �� �d

act0

2⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

(26.3)

45 cm

11 cm

Figure 26.11 Microbot prototype performing hops of 60 cm.

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Binary Actuation 277

where � 0 is the free-space permittivity, � d is the material ’ s dielectric constant, V is the voltage applied across the electrodes, and u act is the actuated film thickness.

The objective of the model is to find the actuation stretches, � i ,act , for any given voltage, V , mechan-ical pre-stretch, � i ,pre , stretch rate of the uniaxial test used to define the elastomer constitutive model, ��uni , and load, � load :

� � � �i if V i, ,( , , , ) , ,act pre uni load � �� 1 2 3 (26.4)

The actuation stretch, � i ,act , is reached when the equivalent Maxwell pressure, P , of Eq. (26.1) is in equilibrium with the film ’ s axial stress:

P V( , , ) ( , , ), , , , ,� � � � � �1 1 3 1 1pre act act pre act load� (26.5)

The axial stress, � 3,act , is found from a stress/stretch model based on Ogden ’ s formulation [25] given by:

� � � � � � � � � �� � �

3 1 1 1 2 1 1 3 2 31 2 1

, , , , ,( ) ( ) ( ) (act act tot tot tot� � � � � ,, )tot�2 (26.6)

The film planar stress, � 1,act , includes the stress due to the deformation of the film ’ s passive region and the effect of a load stress estimated from experimental measurements taken on diamond actuators [15] .

ACKNOWLEDGEMENT

This work was sponsored by the Cambridge-MIT Institute (CMI) and the NASA Institute for Advanced Concepts (NIAC).

Pre-stretchdeformationλ1,pre λ2,pre λ3,pre

Actuationdeformationλ1,act λ2,act λ3,act

Actuatedconfiguration

Referenceconfiguration

Total deformationλ1,tot λ2,tot λ3,tot

Pre-stretchedconfiguration

σ1,pre

σ2pre

σ1,act

σ2,act

σ3,act � P

uactupre

rpre ractU

R

Z,z

R,r Θ,θ

Figure 26.13 The deformations and stresses of the active region.

(a) (b)

rpreract

rrig rrig

Figure 26.12 Expanding circle: (a) pre-stretched ( V � 0 kV) and (b) actuated ( V � 10 kV).

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278 Chapter 26

References

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[3] Chirikjian, G. (1994). A binary paradigm for robotic manipulators. Proceedings of the 1994 IEEE International Conference on Robotics and Automation , San Diego, CA, Vol. 4, pp. 3063–3069.

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digm in space robotics. International Symposium on Experimental Robotics (ISER ’ 00) , Honolulu, HI.

[6] Goldberg, K. (1992). Orienting polygonal parts without sensors. Algorithmica, Special Robotics Issue .

[7] Lichter, M., Sujan, V. and Dubowsky, S. (2002). Computational issues in the planning and kinematics of binary

robots. Proceedings of the 2002 IEEE International Conference on Robotics and Automation , Washington, DC.

[8] Vogan, J., Wingert, A., Hafez, M., Plante, J. S., Dubowsky, S., Kacher, D. and Jolesz, F. (2004). Manipulation in MRI

devices using electrostrictive polymer actuators: with an application to reconfigurable imaging coils. Proceedings of the 2004 IEEE International Conference on Robotics and Automation , New Orleans, LA, pp. 2498–2504.

[9] Kornbluh, R., Pelrine, R. and Joseph, J. (1995). Elastomeric dielectric artificial muscle actuators for small

robots. Proceedings of the 3rd IASTED International Conference , Cancun, Mexico.

[10] Kornbluh, R., Pelrine, R., Pei, Q., Oh, S. and Joseph, J. (2000). Ultrahigh strain response of field-actuated

elastomeric polymers. Smart Structures and Materials 2000 (EAPAD) , Proc. SPIE , 3987 , 51–64.

[11] Wingert, A., Lichter, M. D. and Dubowsky, S. (2006). On the design of large degree-of-freedom digital mechatronic

devices based on bistable dielectric elastomer actuators. IEEE/ASME Trans. Mechatron. , 11 , pp. 448–456.

[12] Plante, J. S., Dubowsky, S., Santer, M. and Pellegrino, S. (2005). Compliant bistable dielectric elastomer

actuators for binary mechatronic systems. Proceedings of the ASME International Design Engineering Technical Conference/29th Mechanisms and Robotics Conference , Long Beach, CA, Vol. 7A, pp. 121–126.

[13] Vogan, J. (2004). Development of dielectric elastomer actuators for MRI devices. M.S. Thesis, Department

of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA.

[14] Wingert, A. (2002). Development of a polymer-actuated binary manipulator. M.S. Thesis, Department of

Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA.

[15] Plante , P.S. and Dubowsky , S. ( 2006 ). Large-scale failure modes of dielectric elastomer actuators . Int. J. Solids Struct. , 143 , 7727 – 7751 .

[16] Hafez, M., Lichter, M. D. and Dubowsky, S. (2003). Optimized binary modular reconfigurable robotic

devices. IEEE/ASME Trans. Mechatron ., 8 , 18–25.

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etary exploration robots. Proceedings of IEEE/ASME International Conference on Advanced Intelligent Mechatronics , Como, Italy, Vol. 2, pp. 1273–1278.

[19] Pelrine, R., Sommer-Larsen, R., Kornbluh, R., Heydt, R., Kofod, G., Pei, Q. and Gravesen, P. (2001). Applications

of dielectric elastomer actuators. Smart Structures and Materials 2001 (EAPAD) , Proc. SPIE , 4329 , March 2001.

[20] Meijer, K., Rosenthal, M. and Full, R. J. (2001). Muscle-like actuators? A comparison between three elec-

troactive polymers. Smart Structures and Materials 2001 (EAPAD) , Proc. SPIE , 4329 , 7–15.

[21] Plante , J. S. and Dubowsky , S. ( 2007 ). On the properties of dielectric elastomer actuators and their design

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[22] Plante, J. S. (2006). Dielectric elastomer actuators for binary robotics and mechatronics. Ph.D. Dissertation,

Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA

[23] Kofod, G., Kornbluh, R., Pelrine, R. and Sommer-Larsen, P. (2001). Actuation response of polyacrylate die-

lectric elastomers. Smart Structures and Materials 2001 (EAPAD) , Proc. SPIE , 4329 , 141–147.

[24] Pelrine , R. , Kornbluh , R. and Joseph , J. ( 1998 ). Electrostriction of polymer dielectrics with compliant elec-

trodes as means of actuations . Sens. Act. A Phys. , 64 , 77 – 85 .

[25] Ogden, R. W. (1982). Elastic deformations of rubberlike solids. Mechanics of Solids . Pergamon Press,

Oxford, pp. 499–537.

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sion: microbots for large-scale planetary surface and subsurface exploration. Proceedings of the 2005 Space Technology and Applications International Forum (STAIF) , Albuquerque, NM.

Ch26-I047488.indd 278Ch26-I047488.indd 278 12/7/2007 3:09:55 PM12/7/2007 3:09:55 PM

ROBOTIC ARM

Gabor Kovacs , Patrick Lochmatter , Michael Wissler , Claudio Iseli and Lukas Kessler

EMPA, Swiss Federal Laboratories for Material Testing and Research, Dübendorf, Switzerland

Abstract

An arm wrestling robot was developed at the Swiss Federal Laboratories for Materials Testing and Research

(EMPA) in order to demonstrate the potential of the dielectric elastomer (DE) actuator technology in a humanoid

robotic system, where the unique properties of this material system come to a significant design parameter. The

EMPA was one of the three participating organizations in the first arm wrestling match of electroactive polymer

(EAP) robotic arm against human, which was held during the EAP-in-action session of the EAPAD conference in

San Diego, 7 March 2005.

Acrylic based elastomer was used as the dielectric layer in the DE actuators, due to its excellent mechanical and

electrical properties. More than 250 rolled actuators were arranged in two groups according to the human protagonist–

antagonist operating principle in order to achieve an arm-like rotation movement in both directions: The active

movement from the horizontal arm position to the upright starting position and the reverse ‘ arm wrestling motion ’

exhibiting maximal force. The robot was powered by a computer-controlled high voltage device. The rotary motion

of the arm was executed by electrically activating respectively deactivating the corresponding actuator group.

The focus of this chapter is on the main development and manufacturing technique of the rolled DE actuators

and on the engineering procedure for the robot design. The design of the DE actuators to produce a work against

an external force and to display a working loop by an adequate arrangement of a pre-stressed actuator system is of

primary interest.

Keywords : Artificial muscles, dielectric elastomer, electroactive polymers, robotics.

27.1 INTRODUCTION

In the field of robotics most actuators are supposed to perform mechanical work against external loads for displacement of elements and in some cases, for structural shape-changing. The principle of oper-ation of conventional actuators such as electric or piezoelectric motors, hydraulic or pneumatic cylin-ders is based on the active displacement of two stiff bodies in opposite directions (e.g. stator and rotor, cylinder and piston, etc.). These actuators can be up-scaled to exert large activation loads and can be designed to execute ‘ unlimited ’ displacements. Most conventional actuators and their supplies, however, make noise when activated and consist of complex, heavy and often expensive mechanical structures.

With actuators based on active materials on the other hand soft, lightweight structures with low-noise activation capability could be implemented. The major drawbacks of today ’ s active materials are their limited active deformation potential as well as the elongation-dependent active forces. Nevertheless, for many robotic systems used in human environment (e.g. prosthetic limbs) low-noise and soft actuators are preferred when taking into account the acceptance of the user. For many applications within this category actuators with muscle-like properties are required. So far, however, solely actuators made from electroactive polymers (EAP) exhibit an active performance which corresponds to natural muscles.

To demonstrate the potential of the EAP actuator technology in a humanoid robotic system, where the unique properties of this material system comes to a significant design parameter, the first arm wrestling match (AWC) between a human arm and a robotic arm driven by EAP was held at the EAPAD conference in 2005. Certain rules were specified to ensure the impartiality of the competition. As the most important requirements, the robotic arm had to be actuated by an EAP material and should emulate the wrestling action of a human arm. Aside from this, the shape and dimensions of the robotic

Chapter 27

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280 Chapter 27

arm should match the arm of an average human adult. In addition, the robot is required to execute a reversible motion: the arm had to be capable to return to its starting position after wrestling.

The AWC robot developed at the Empa was driven by a system of rolled dielectric elastomer (DE) actuators. Acrylic based elastomer was used as the dielectric layer in the DE actuators, due to its excellent mechanical and electrical properties. By stacking many actuator layers (rolled up structure), the generated activation force was multiplied. In addition, the passive mechanical stiffness of the stack was increased. When several actuators are combined in series, the activation displacement becomes larger. According to (1), the electrode pressure and thus the resulting active strain will increase for pre-stretched films under application of a persistent voltage. In addition, detailed investigations of the used acrylic films VHB 4910 (3M) have shown that pre-stretching increases the dielectric breakdown strength [10] of the film. As a consequence, higher electric fields can be applied to the DE actuator when pre-stretching the film.

More than 250 rolled actuators were arranged in two groups according to the human agonist–antagonist muscle configuration in order to achieve an arm-like bi-directional rotation movement. The rotary motion of the arm was activated and deactivated electrically by corresponding actuator groups.

The main development process of the robot is presented in this chapter where the design of the DE actuators to produce a work against an external force and to display a working loop by an adequate arrangement of a pre-stressed actuator system is of primary interest.

Although the robot has lost the arm wrestling contest against the human opponent, the DE actuators have demonstrated a very promising performance as artificial muscles.

27.2 ROLLED DE ACTUATORS

27.2.1 Actuator design

Outstanding actuator performances can be obtained when the acrylic film VHB 4910 is highly mechan-ically pre-stretched. Typically, the pre-stretching of DE films is characterized by the pre-stretch ratios � j

(i ) in directions j � x , y , z . The pre-stretch ratio is defined as the ratio of the pre-stretched film length in state ( i ) to its original length in state ( o ) ( � j

(i) � L j (i) /L j

(o) ). However, a support structure is necessary for maintaining the required pre-stretch in the dielectric film. When a high voltage is applied to the planar dielectric film, it expands bi-directionally in the plane. To emulate a natural muscle however, an expansion in only one direction is desired. For obtaining such deformation and in order to gain an elec-tromechanical work output, the support structure must have at least one degree of freedom in which the actuator can deform under activation and thus perform work against an external load.

A number of actuator configurations, such as the extender (planar), bimorph, tube, diaphragm, spider and bow-tie actuator, have been designed to support the reaction forces resulting from the pre-stretch-ing of the DE film [11, 12] . Nevertheless, the spring roll actuator [13] displays the most promising design for achieving uni-directional large activation forces and elongations.

This actuator is comprised of a bi-directionally pre-stretched and double-side coated dielectric film wrapped around an elastic coil spring ( Figs. 27.1 and 27.2 ). The interface for external fixation of the actuator is made from two threaded rods, which are screwed from both sides into the coil spring. In order to transmit the forces from the dielectric film to the spring, the rolled film is glued to the threaded rods. This actuator elongates in the axial direction when a voltage is applied and contracts back to its original length when deactivated. With rolled actuators, elongations of up to 26% and forces of up to 15 N were achieved [13] . For obtaining the needed wrestling power, rolled actuators consisting of acrylic elastomer VHB 4910 (3M) with elongations of up to 35% were used to drive the arm robot of Empa.

Rolledaluminium leaf Spring core Setscrew

ElectrodeShrinkdownplastic tubing

Uncoateddielectricum

Figure 27.1 Axial section of the rolled actuator used for the wrestling robot.

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Robotic Arm 281

(ii)

Free coil spring

Free DE film

Force

Displacement

Deactivated DE film (U � 0)

Activated DE film (U � 0)

Coil spring

(i)(iv)

Fullycompressedcoil spring

(i) Deactivated equilibrium (U � 0)

(ii) Activated under blocked-strain (U � 0)

(iii) Activated under free-strain (U � 0)

(iv) Deactivated under blocked-strain (U � 0)

(iii)

Ften

Fcom

Figure 27.3 Operating states of the DE spring roll actuator.

Coil spring core

Electrodes(a) (b)

Pre-stretched DE film

z

r

ϕ

Figure 27.2 (a) Schematic depiction of the rolled actuator and (b) different multilayer rolled actuators made for optimization tests.

27.2.2 Principle of operation

During the arm wrestling match, the robot must perform mechanical work against the arm of the opponent. Therefore, the electroactive actuators driving the robot must have the capability to exhibit mechanical work for the chosen activation loop. In order to explain the electromechanical principle of operation of the rolled actuators, the force–displacement characteristics of its interacting components namely the coil spring and the deactivated/activated DE film, are plotted qualitatively in Fig. 27.3 .

The following four states can be identified ( Fig. 27.3 ) from the activation/deactivation of the actuator under its set boundary conditions:

(i) Deactivated equilibrium : In the axial direction, the DE film is pre-stretched by the compressed coil spring. In radial direction, the circumferential loads of the pre-stretched DE film are sup-ported by the spring core.

(ii) Activated under blocked-strain : Starting from the deactivated force equilibrium state (i), the film relaxes and releases the compressed spring under electrical activation. In order to maintain the length of the actuator, an external compressive force F com is required to prevent the expansion of the spring.

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282 Chapter 27

(iii) Activated under free-strain : Starting from the deactivated force equilibrium state (i), the film relaxes under electrical activation and thus the spring expands until the loads from the spring and the DE film are balanced in a new axial force equilibrium.

(iv) Deactivated under blocked-strain : When fixing the length of the actuator in the activated state (iii) and subsequently deactivating the element, an external tensile blocking force F ten is required to prevent the actuator from contracting.

High activation performances can be achieved when the two pre-stretch ratios � x and � y are opti-mized. Isometric tests with DE spring roll actuators have shown that the best activation stresses are achieved when the pre-stretch ratios are � x � 3 and � y � 6.5 ( Fig. 27.4 ).

The length of the actuator plays a key role when the absolute displacement under activation is of primary interest. Based on the potential maximum strain of the material, the maximally achievable dis-placement can be adjusted by the initial length of the actuator. In regard to the actuator ’ s length, no relevant restrictions with respect to the actuation performance could be found, apart from some specific manufacturing difficulties.

27.2.3 Number of layers

The bi-directionally pre-stretched film which is wrapped around the coil spring core induces an initial compression of the inner film layers by the outer ones. The resulting radial pressure on the inner layers grows for an increasing number of wrappings as well as for stronger circumferentially pre-stretched films. Therefore, the internal stress conditions of rolled actuators have a major impact on the design of the actuators.

The following brief computational analysis of the internal stress–strain conditions quantitatively demonstrates the influence of the number of layers. The compressive force F com needed to block the elongation of a DE spring roll actuator in th e deactivated equilibrium state (state ( U � 0) in Fig. 27.3 ) is estimated as a function of the activation voltage U ( Fig. 27.5 ) . Due to the design of the DE spring roll actuator, the film is initially pre-stretched by planar stresses � x

(i) and � y (i) to planar pre-stretch ratios

� x (i) and � y

(i) ( Fig. 27.6(a) ). The inner film layers in a DE spring roll actuator are strongly compressed in the radial direction by

the outer layers. This leads to an increase of the hydrostatic pressure in the inner film layers. The result-ing axial stress state of the film is a superposition of the initial tensile stresses from the pre-stretching and the pressure stresses when wrapping the film around the core.

According to the radial component of (1), the hydrostatic pressure for the film layers is given by:

r pw

pnU

zi

z

ir nU: ( ) ( ) ( ),

( )� ��0 0����

⏐ + (27.1)

0 20 40 60 80 1000.00

0.05

0.10

0.15

0.20

Pre-stretch Ratios (λx � λy)

3.5 � 3.55.0 � 3.53.0 � 6.5

Str

ess

diffe

renc

e un

der

activ

atio

nΔ

σ z (M

Pa)

Electrical field E (MV/m)

Figure 27.4 Axial stress difference in the rolled DE actuator under activation for different pre-stretch ratios � x (axial direction) and � y (circumferential direction) of the wrapped film.

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Robotic Arm 283

Introducing this expression for the hydrostatic pressure of layer n into the axial ( z ) and circumferen-tial ( � ) components of (1), one obtains:

� � ����

�����: ,

( ) ( ) ( ) ( ) ( )

.

nU

yi

y

izi

z

i

const

w w�

�

� �0 ⏐ ⏐� ����� ������

� � �

� �

� �

�

p A p

zw

r nU

r nU

z nU

xi

x

izi

,( )

,( )

,( ) ( ) ( ) ( )

:

:

0 0

0� ����

��

⏐ww

p B pz

i

const

r nU

r nU

��⏐( )

.

,( )

,( ):

�

� �� � �

� ����� �����

0 0

(27.2)

Obviously, the terms for the strain energy derivations are equal for all layers and are thus defined as constants A and B. In the Yeoh form, the strain energy w depends on the first invariant of the so-called left Cauchy–Green deformation tensor I 1 :

w C C I C I� � � � �10 20 1 30 1

23 3( ) ( ) (27.3)

Thereby, C 10 , C 20 and C 30 are material parameters and the first invariant is given by

I x y z1

2 2 2� � �� � � (27.4)

With these equations, one can determine the constants A and B for an experimentally determined set of material parameters for VHB 4910 ( C 10 � 7.0 � 10 –2 MPa, C 20 � –9.0 � 10 –4 MPa and C 30 � 1.7 � 10 –5 MPa) and pre-stretch ratios of the wrapped film ( � x

(i) � � z (U � 0) � 3, � y

(i) � � � (U � 0) � 6.5 and � z

(i) � � r

(U � 0) � 1/19.5). By subsequent evaluation of Eq. (27.11), the radial pressure p r,n (U � 0) and the axial

stresses � z,n (U � 0) in each film layer n � 1, 2, … , N of the deactivated ( U � 0) and activated ( U � 0) DE

� rolled spring actuator can be calculated.

Load to axially pre-stretched the film

Load tocircumferentiallypre-stretched film

Load to compressthe spring

Supporting Load ofthe core

Figure 27.5 Passive equilibrium of axial/radial/circumferential loads in the spring roll DE actuator.

Segment of thepre-stretched film

Segment of the wrapped film

Deactivated (U � 0) Activated (U � 0)

σ(U � 0)

Layer n

pe

z

r

z

r

yx

zϕ,nσ(U � 0)

ϕ,nσ(U � 0)ϕ,n

ϕ ϕ

σ(U � 0)σ(i )

ϕ,n

σ(U � 0)z,n

σ(U � 0)z,n

P (U � 0)r,n

P (U � 0)r,n

yσ(i )

y

σ(i )x

(a) (b)

Figure 27.6 Theoretical considerations for the modelling of the DE spring roll actuator.

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284 Chapter 27

Figure 27.7 depicts the inner film layers in a DE spring roll actuator with large diameter (several hundreds of film layers) which are strongly compressed by the radial pressure of the outer layers. Under electrical activation, the electrostatic electrode pressure is superimposed on this radial pressure distri-bution. The dashed curves in Fig. 27.7 represent a blocked-strain activation with U � 3.8 kV (electric field of 74.1 MV/m in the dielectric film), which corresponds to an electrode pressure of 0.23 MPa ( � r � 4.7), according to (1).

As shown in Fig. 27.7 , this compression in the radial direction leads to a reduction of the axial tensile stresses in the inner film layers. The same effect can be observed in the circumferential tensile stresses.

When the number of layers N reaches a critical value, the innermost film is fully relaxed in the axial direction ( Fig. 27.7(b) ). When applying even more DE film layers to the core, the inner layers are no longer under tension but they exert pressure stresses in the axial direction. For certain numbers of film layers and pre-stretch ratios of the film, the axial contraction effect of the outer film layers may be bal-anced by the axial expansion of the inner layers. In this case, the core would not need to axially intro-duce any load, but simply has to circumferentially support the wrapped film. Generally, the electrode pressure will be uniformly superimposed to the axial stress distribution across the layers when activat-ing the DE spring roll configuration. Thus under blocked-strain activation, the tensile stresses of all film layers in axial direction will reduce (dashed lines in Fig. 27.7(b) ) and an external blocking force is needed to prevent the axial elongation of the actuator.

According to this theoretical considerations, DE spring roll actuators with only few film wrappings are especially promising since only weak squeezing of the inner film layers arises with such actuators. As a result, the ‘ thick ’ DE spring roll actuator with many film layers is not practically useful. Thus, for the activation of the arm wrestling robot, many ‘ thin ’ DE spring roll actuators switched in parallel were used in order to reach large forces.

27.3 ARM WRESTLING ROBOT

For the arm wrestling robot, the uni-directional deformation potential of the rolled actuators had to be transformed into a wrestling motion. In the following sections, the concept and development of the arm wrestling robot and the implementation of the rolled actuators are addressed.

27.3.1 Design

To accomplish the basic rules for the arm wrestling competition, a motion study of the human upper torso was performed. The translatory movement of the upper part of the body is mainly accomplished by the abdominal musculature (Obliquus externus/internus and Rectus abdominis). The upper right arm

DeactivatedActivated

N � 500

N � 500N � 200

N � 200

N � 20

N � 20

DeactivatedActivated

Tensile stress

Pressure stress

12

10

8

6

4

2

00 100 200 300 400 500 0 100 200 300 400 500

2

0

�2

�4

�6

�8

�10

Rad

ial p

ress

ure

P(U

�0)

(M

Pa)

Axi

al s

tres

s σ

(U�

0) (

MP

a)

r,n

z,n

Layer number n (�)Layer number n (�) (b)(a)

Figure 27.7 (a) Distribution of mechanical compressive radial pressure and (b) acting in axial direction on the layers in rolled DE actuators consisting of N film layers.

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Robotic Arm 285

of the wrestler has a static force transmission function and does not essentially contribute to the wrest-ling action. In order to compensate the resulting torsion moment of the wrestling action, the left arm of the wrestler holds on the handle bar of the table. As a result, all activated forces for the arm wrestling motion sequence are based on the superposition of a torsional moment of the upper arm and a lateral displacement force of the upper torso. The arm wrestling motion mainly consists of a single rotary motion of the upper human body, while holding the arm stiff. This observation allowed a considerably simplified functional design for the arm wrestling robot. Thus, the essential motions of the arm wrestler can be well simulated with a simple rotating box equipped with a stiff arm, which is driven by the DE actuators. The box, which carries the artificial muscles, is clamped to the table at the rotating axis.

Based on the set of rules and on the observations mentioned above, the Empa robot design specifica-tions are summarized in Table 27.1 .

Since all actuators are intended to be placed inside the robot body, the available space would be about the size of the upper torso of a human. Despite this limitation, the actuators have to be arranged in such that the needed wrestling force and motion can be produced. This limiting factor determines essentially the design and the arrangement of the driving actuators, which is discussed in detail in the next section.

To achieve the needed stiffness and strength of the lightweight robot body, carbon-fibre reinforced composites are used. Since high voltage devices are used, the black CFR box is enwrapped with glass-fibre composite material as the insulating layer for safety reasons ( Fig. 27.8 ). The torsion shaft of the robot is provided to fix the robot to the wrestling table and is designed to hold the robots weight and the arising torsion moment. The arm of the robot is made by a simple CFR rod, which is attached to the robot body.

Table 27.1 Specification for the arm wrestling robot.

Design Criteria Design Parameter

Design and principle of operation As human-like as possible (functionality, reversibility) Orbit of the robot hand Circular path perpendicular to the table Fixation Clamping at the table Rotation angle for the robot arm � 90° from the initial position Position of the rotation axis Elbow (upon the table surface) Material for the robot structure Polymer or composite-based Overall mass of the robot Maximally 15–20 kg Robustness Stiff design Bi-directional driving unit Electroactive polymers (dielectric elastomer actuators) Uni-directional force for wrestling motion About 200 N (measured from a female subject)

Figure 27.8 The structure of the arm wrestling robot is made of carbon-fibre composite and contains all actua-tors to execute the wrestling motion around the rotational axis upon the table. The arm of the wrestling robot is represented by a stiff CFC rod.

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286 Chapter 27

27.3.2 Principle of operation

In general, a human-like agonist–antagonist operating principle enables the reversible rotational move-ment of the robot arm ( Fig. 27.9 ).

When assembling the robot, the pre-stretch force in the two actuator groups Bloc I and Bloc II are in equilibrium ( Fig. 27.13 ). In the neutral position (position 0), all actuators are deactivated and the robot arm is rotated by 35° from horizontal. By activation of the actuator Bloc I, the robot arm rotates to the upright starting position (position 1) and is thus ready for the wrestling action. During the wrestling match, Bloc I is deactivated and Bloc II is activated simultaneously. Thus, the robot exhibits its maximal wrestling force F wrestling at position 1. The resulting motion depends on the reaction force of the human opponent. If the opponent produces less than 200 N, the robot arm performs the intended motion from the starting position to winning position 2.

27.3.3 Actuator system

The structure of the actuator system essentially depends on the active force–elongation behaviour of the actuators and the wrestling opponent. On the one hand, the length and the number of the actuators are limited by the size of the robot box. On the other hand, the force–elongation characteristic of the actu-ator must satisfy the requirements based on the estimated wrestling force.

27.3.4 Length of the actuators

According to the size of the natural human body, the maximum length of the pre-stretched and acti-vated actuator must not exceed 400 mm. With an actuator, an elongation of maximally 35% is expected and the length of the rigid end pieces including the length of the unstressed actuators must not exceed 250 mm.

27.3.5 Length of the wrapped dielectric film

The wrestling force of the opponent hand is assumed to be constant during the entire wrestling motion. In contrast to this trend, the activation force of the spring roll actuators decreases when they are elong-ated. Thus, the arm wrestling force of the robot would continuously slim down when rotating towards winning position 2 ( Fig. 27.9 ). For compensating the decreasing actuator force, we implemented a vari-able force transmission between the wrestling hand and actuator system. The transmission ratio was determined by the ratio of the actuator force and the force of the wrestler.

For the aimed maximal elongation of 80 mm, which corresponds to 35% strain, a maximal transmis-sion ratio of 12 is calculated and must be taken into account. Thus, based on the chosen robot design, a maximal force difference of 12 � 200 N � 2400 N between the agonistic and antagonistic actuator group had to be achieved. Assuming a maximal activation stress of 0.2 MPa for DE films, the needed material for the cross-sectional area for the DE spring roll actuators would amount to at least 1.25 � 10 –2 m 2 .

Force

Arm position02

Actuator Bloc I

Activated

Deactivated

Actuator Bloc II

Activated

Deactivated

Fwrestling

ActuatorBloc I

ActuatorBloc II

Wrestlingarm

01

2

1(b)(a)

Figure 27.9 Working principle of the actuator banks and the robot arm.

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Robotic Arm 287

Regarding an average thickness t of 50 � m for the pre-stretched film, this would lead to a considerable total length for the wrapped DE film of 250 m.

27.3.6 Actuator arrangement

Next, the number of required actuators and the corresponding diameter for each rolled actuator was determined in order to take the total required length of wrapped dielectric film. Based on the results of the theoretical considerations and on experiments with DE spring roll actuators, the number of wrappings per actuator must be as low as possible to obtain the best specific actuator performance. In addition, the robot ’ s reliability with many ‘ slim ’ actuators excels the variant with only few but ‘ thick ’ actuators ( Fig. 27.10 ).

Therefore, the final solution for the actuator system consists of banks equipped with many ‘ slim ’ DE spring roll actuators.

By filling the robot box with DE spring roll actuators, the best utilization of the available space is achieved for ‘ slim ’ actuators with outer radius of approximately 12 mm ( Fig. 27.11 ). As a result, up to 256 DE spring roll actuators are arranged in two agonist–antagonist groups ( Figs. 27.12 and 27.13 ). Around each actuator, a core of 2 m of pre-stretched acrylic film is wrapped, which results in 35 film wrappings. For practical reasons, both the agonist and the antagonist actuator groups are subdivided into two actuator banks, each equipped with up to 64 actuators.

The plates of the banks were dimensioned to distribute the external load to each actuator. The upper plates of the banks were fixated via long threaded rods at the top end of the box. Thus, an adjustment of the initial axial pre-stretch of the actuators was possible. At the lower plate, a chain connected the agon-ist and antagonist actuator blocs via the axis of rotation. The force transmission was implemented by a specially shaped cam disc, which was interconnected between the actuator banks and the fixing axle.

Cross

-sec

tiona

l are

a

Leng

th o

f wra

pped

film

t

Figure 27.10 Cross-sectional area and length of the wrapped DE film.

00

20

40

60

80

100

10 20 30 40 50 60 70

Outer actuator radius (mm)

Util

izat

ion

of c

ross

-sec

tiona

l are

a(%

) AxisAxis

(a) (b)

Figure 27.11 Utilization of the cross-sectional area of the robot box as a function of the actuator radius (diagram in the centre): (a) arranging many small actuators and (b) arranging a few large actuators.

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288 Chapter 27

Figure 27.12 Force transmission mechanism to achieve the required force characteristic from the arm wrestling robot: working principle on upper three pictures and implemented device on lower picture.

Top plate of robot box

Threaded rod

Upper plate

Bank of DE roll actuators

Lower plate

Figure 27.13 The four actuator banks, each equipped with 64 actuators, placed inside of the arm wrestling robot. The force distribution plates mounted on both ends of the actuator banks also served for the high voltage application.

Since a large number of actuators are used in the robot, the possibility of an electrical breakdown of some actuators must be considered when designing the electrical system. To supply all actuators of one actuator bank with the needed high voltage, they are connected in parallel. However, if one of the actu-ators electrically break down, all actuators in one bank will instantaneously discharge through the failed element. On one hand, this would lead to a considerable loss of arm wrestling force. On the other hand, an inflammation of the failed actuator caused by the concentrated heat dissipation from the high dis-charging current might occur. Both effects can be prevented by applying current limiters (fuses) in front of the DE spring roll actuators. However, due to the limited current, the charging time for the actuators of the arm wrestling robot increases distinctively.

27.4 CONCLUSIONS

For the most applications in the field of robotic or prosthetic limbs, the agonist–antagonist actuator arrangement is preferable since it can drive the system in a two way mode. By this robot, it has been shown that it is possible to work against an external force and to display a working loop by an adequate arrangement of a pre-stressed actuator system. Based on the general properties of DE actuators, the preferential fields of applications can be located where active structures with large and complex deform-ations are needed but only small driving forces are required. Such applications could be found in, for example, humanoid systems (artificial hands or mimic faces), where many small actuators could be

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Robotic Arm 289

applied and individually addressed. Furthermore, the actuators of Empa robot have impressively high-lighted the potential of the DE, where the unique properties of this material system, as they are noise free when actuated and very lightweight, come to a significant design parameter.

Although the Empa robot arm lost the competition, it was the only robot in the competition that could actively return to its upright starting position after the match, as required by the rules of the competition. This bi-directional motion of the robot arm became possible due to the agonist–antagonist actuator configuration. Nevertheless, the scientific experiences during the development process of the arm wrestling robot has pointed out the challenges, which need to be addressed for improving espe-cially the rolled DE actuator configuration.

ACKNOWLEDGEMENTS

We would like to thank Mr Claudio Iseli and Mr Lukas Kessler from the Swiss Federal Laboratories for Materials Testing and Research (EMPA) for their contributions to the present work.

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[15] http://armwrestling.com/rulesandregulations.html.

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STIFFNESS CONTROL OF BIOMIMETIC SYSTEMS THROUGH RECRUITMENT OF BUNDLE ELASTOMERIC ACTUATORS

Federico Lorussi 1 , Claudia Caudai 1 , Stefano Galatolo 2 and Danilo De Rossi 1

1 Interdepartmental Research Centre ‘ E. Piaggio ’ , University of Pisa, Pisa, Italy 2 Department of Applied Mathematics ‘ U. Dini ’ , University of Pisa, Pisa, Italy

Abstract

This chapter deals with the design and realization of bioinspired kinematic chains controllable both in position and

compliance (or stiffness) from a static and a dynamic point of view. In this work, the compliance idea explained

in the Feldman ’ s equilibrium point theory is provided with a mathematical architecture and the concepts of stiff-ness and compliance , according to the Feldman ’ s guidelines, are introduced and applied in a static case concerning

the perturbation of a motionless mechanical system. The muscle model developed by Feldman is provided by a

technique aimed at its artificial realization, supported by experimental data on electroactive elastomers. Dielectric

elastomer artificial motor unit bundles (corresponding to muscle fibres) are designed ad hoc and could be driven

by bioinspired control variables to implement pseudomuscular actuators devoted to the realization of biomimetic

movements. A strategy to control a kinematic chain actuated by these muscles, capable to solve the redundancy of

controls by imposing values for certain particular additional state variables, namely ‘ generalized stiffness or com-

pliance ’ , is provided. Finally, the idea of dynamical stiffness is introduced and active kinematic chains are studied

under this point of view. In particular the exploration of a meaningful simple example illustrates the potentialities

and limits of this control strategy.

Keywords : Biomimetic actuators, compliance, dielectric electroactive polymers, elastomers, Feldman ’ s muscle

model, stiffness.

28.1 INTRODUCTION

The recent development of a new generation of electroactive materials in the last 10 years endorses a possible approach to robotics problems which surpasses the classical topics related to industrial pro-duction. Historically, in this context, motor units are seen as elements capable to perform forces and displacements without taking particular care of their intrinsic mechanical properties. The main figures of merit considered in the choice of these actuators are often referred to maximum power or forces exerted, consumption, efficiency and lifetime. Scarcity in their performance is usually compensated by sensing devices and the use of heavy control algorithms, mainly based on feedback techniques, which consent motors to be continuously corrected during their work. This approach, in addition to massive sensing apparatus devoted to acquire data, needs a large information flow to one or more control units, which elaborate corrections needed by the motor system. Nowadays, computational resources furnished by machines are rapidly growing up to consent the simultaneous control of more complexion actuator systems, this approach admits possible alternatives based on further requirements that elastomeric actuators can perform. In fact, recent progresses of electroactive based actuators consent the implementa-tion of additional features in the design of more efficient control algorithms. In particular, the realization of stiffness controllable actuators opens new ways to drive systems by lighter decisional control units. The feed-forward control strategy, generally discarded for its inefficiency, can be improved by tak-ing particular care to several related concepts, in particular its robustness, and mixed to a closed-loop control strategy, to decrease the number of iterations in receiving elaborations and transmitting data.

Chapter 28

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On the other hand, biological mechanical systems widely use this paradigm by the so-called hierarchi-cal control. In few words, several control levels deputed to implement movements, synergically work with their own scope. According to physiological principles, while the central nervous system (CNS) plans and periodically checks the execution of movements, it demands the details of the computation to the segmental and peripheral nervous system, even if several theories attribute different tasks to the involved nervous parts. Some of these interpretations are based on certain mechanical properties of muscles and infer the work mode of the nervous system by them. In particular Bizzi and Feldman developed two muscle models and based on them the Equilibrium Point Theory of the human motor control [1] . This theory, which gathers feed-forward and closed-loop controls, is based on the concept of stiffness of a kinematic chain. Feldman solved the problem of redundancy of muscle groups, which at a certain movement, by enriching the concept of movement with a further property, that is stiffness. This idea, very close to the concept of robustness in robotics, ensures error limitation during the open-loop phase.

In the present work the concepts of stiffness and compliance according to the Feldman ’ s guidelines are summarized and applied in a static case concerning the perturbation of a motionless mechanical system. The muscle model developed by Feldman is provided by a technique aimed at its artificial real-ization, supported by experimental data on electroactive elastomers. A strategy to control a kinematic chain actuated by these muscles, capable to solve the redundancy of controls by imposing values for certain particular additional state variables, namely ‘ generalized stiffness or compliance ’ , is provided. Finally, the problem of the generalization of a stiffness or compliance control strategy in dynamical case is preliminarily analysed. The main concepts to implement it, both from a theoretical and compu-tational point of view, are summarized to provide the reader with a complete overview on the problem and its solution. In particular the exploration of a meaningful simple example illustrates the potential-ities and limits of this control strategy.

28.2 FELDMAN ’ S MUSCLE MODEL

The activity and the forces exerted by a muscle in a biological system are regulated by the central and the peripheral (and segmental, in biological language) nervous systems through a twofold mechanism: by means of variations of the electrical activity of motoneurons and by means of an increment of the number of active motoneurons (the motoneuronal recruitment ). During his in vivo experimental trials, by stimulating subcortical nervous centres with electrical signals, Feldman [1] proved that muscles can exert different forces according to the stimuli by maintaining the same length. Feldman proposed a muscle model based on the equation:

F x x

xp

� � ��

� � ��

( )0{ (28.1)

where p is a positive integer, x represents the actual length of the considered muscle, � the rest length (i.e. the maximum length a muscle assumes without exerting any contractile force) and � is a mechan-ical parameter. Historical reasons led researchers to approach the problem by using a linear model (i.e. p � 1) where � , which coincides with the stiffness of the muscle, was thought as a parameter controlled by the CNS. Unfortunately, a simple explicit relation among the electrical signals, which stimulated the muscle, and � was not found, and so Bizzi ’ s model is more rarely used. On the other hand, by main-taining unchanged the electrical stimulus and by varying the length of the muscle, he verified that the forces performed increased proportionally with the square of the muscle length (see Fig. 28.1 ).

This case is described by Eq. (28.1) by assuming p � 2 if � (which is replaced by k ) does not prac-tically depend on the stimulus and on the muscle length. In this case Feldman ’ s muscle model becomes

F k x x

x� � ��

( )0

2� ��{ (28.2)

Since each curve in Eq. (28.2) intersects the abscissa axes in a unique point � , this value can be used to label each mechanical characteristic. On the other hand, since each characteristic is obtained by unchanging the electrical stimulus (i.e. the central control), � uniquely characterizes it. In this sense Feldman formulated one of his main results, i.e. the CNS directly controls the rest length of a muscle .

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292 Chapter 28

According to this hypothesis, the force exerted by a muscle is given by the CNS and the external loads which produce the actual length x � � .

A classical mechanical implementation of a device with these characteristics can be realized by using tapered compression springs having variable section, which work with packed wires. One end of the spring is connected to the load while the other one is linked to an inextensible cable pulled by the motor and whose length is directly related to the parameter � . However, this device presents as disadvantage a fixed and un-programmable elastic characteristic and the weight and encumbrance of the classical mechanic components.

Let us consider a two-actuator system ( Fig. 28.2 ), where the active elements, represented by nonlin-ear springs controlled by motors, can be seen as agonist and antagonist muscles which act together with an external force F 1 on a mass, in an established position for the system.

The equilibrium of the forces is expressed by

k x k x F( ) ( ) 01 1

22 2

21� � � � �� � (28.3)

where x 1 and x 2 are the distances between the ends of the springs and the motors. If we assume that x 1 � x 2 � l � const and by replacing x 1 by x , Eq. (28.3) is clearly satisfied by infinite couples ( � 1 , � 2 ). But if we consider a perturbation P of the force which acts on the system, we have

k x k l x F P( ) ( ) 012

22

1� � � � � � �� � (28.4)

and if we define the following quantity:

Cx

P�

d

d (28.5)

The system described by Eqs. (28.3) and (28.5) with an assigned C � C 0 is verified by a unique couple ( � 1 , � 2 ), for x 1 � � 1 and x 2 � � 2 . It is easy to show that, if springs had linear characteristics, C value would not be a consequence of the choice of � s and the map ( � 1 , � 2 ) � ( x , C ) would not be surjec-tive, i.e. infinity couples ( � 1 , � 2 ) would produce the same x and an uncontrollable value of C . Let us

5 10 15 20 5

0

20

40

0

20

40

10 15 20

NN

mm mm(a) (b)

ND ND

9

7

6

5

3 3

6

7

1313

Figure 28.1 Comparison for shape of the various mechanical characteristics of the gastric muscle of decerebrated cat.

X1 X2

F1

Figure 28.2 A mechanical system with pseudomuscular actuators.

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Stiffness Control of Biomimetic Systems Through Recruitment of Bundle Elastomeric Actuators 293

consider a more general case of a kinematic chain with n degrees of freedom collected in a geometric state vector q ([ q ] � n ). The chain is actuated by a functional group controlled by a vector � (whose length m is greater than n ). By introducing functions y i ( q ) (accounting the geometry of the system and the pur-pose of the problem) of the state q , it is possible to define a ‘ supplementary ’ state vector c (or s having length p of generalized compliances C i (or stiffness S i )

Cy q

PS

y q

Pi pi

ii

i� � ���

���

( ) ( )1

1⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟⎟ …, , (28.6)

so that p � n � m . Hence, the redundancy of controls can be solved by defining a global state vector z � ( q | c ) (respectively z � ( q | s )), obtained by appending the supplementary vector c (or s ) to the geo-metric vector q . Let us consider, as an example, the two systems represented in Fig. 28.3 where the same bi-phalangeal finger architecture is actuated by three (on the left) or four (on the right) muscles, respectively.

While in the left case only three controls are available, in order to complete the state vector, just one generalized compliance can be defined:

C

P�

���

(28.7)

where � is the vector ( � 1 , � 2 ) containing the two joint angles which characterize the state of the system and P � ( P 1 , P 2 ) is the bidirectional perturbation which can affect the system contained in its plane, in the right case four different controls can be used to define two different (and concentrated) compli-ances by choosing y 1 :( � 1 , � 2 ) � � 1 and y 2 :( � 1 , � 2 ) � � 2 . The two canonical projections generate the two additional state variables:

C

PC

P11

22� �

���

���

(28.8)

In a general static case, i.e. when the system is motionless and the geometrical state variables do not change, Eq. (28.6) can be easily computed by using the implicit function theorem.

In fact, let us suppose F ( q , P ) � 0 is the complete set of equations which describe the equilibrium of a system in a state q 0 (i.e. a generalization of Eq. (28.4)) and let us suppose that

det

��F

qq P( , ) 00 0

⎡

⎣⎢⎢

⎤

⎦⎥⎥ �

(i.e. trivially verified by the consistence of the mechanical system). By differentiating F ( q , P ) � 0 and solving with respect to ( � q )/( � P ), we have

��

��

��

q

P

F

q

F

P� �

�⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

1

(28.9)

�2

�1

�2

�1

Figure 28.3 Bi-phalangeal finger with two degrees of freedom actuated by three and four pseudomuscular actuator, respectively.

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294 Chapter 28

By pre-multiplying ( � y i ( q ))/( � q ), i � 1, …, p and extracting the norm operators, we explicitly obtain the expressions (28.6):

Cy q

q

F

q

F

Pi pi

i� � �

��

���

��

( )1

1⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

…, , (28.10)

which represent all the compliances defined according to the y i ( q ) choice.

28.3 DIELECTRIC ELASTOMERS, ARTIFICIAL MOTOR UNIT FIBRES AND PSEUDOMUSCULAR AC TUATORS

One of the aims of this chapter is to propose a feasible technical solution able to implement the Feldman ’ s mechanical characteristic in a lighter way than the simple example described in the previous section. In addition to the requirements on the nonlinearity of the mechanical (force versus strain) characteristic, we would satisfy properties such as space saving, lightness and programmability of the device to mime sev-eral different muscle actions [9, 10] . To obtain these results, dielectric elastomer actuators, able to convert directly electrical energy into mechanical energy, have been considered. Cylindrical actuators having form of a roll, previously introduced in this book, have been built by this technology [2, 3] . These actuators show good elastic properties and modify their rest length when they receive electrical stimuli. Unfortu-nately, since they change dimensions without changing volume, the desired quadratic law in Eq. (28.2) cannot be directly obtained but only approximately by combining the effects of many fibres. In this way, it is possible to gain the desired force-lengthening characteristic in a deformation range where the Young ’ s modulus Y of the material can be considered constant. In fact, the stress–strain relation for a linearly elastic, isotropic and homogeneous element, subjected to axial stress (according z ), is given by

d

df YA z

z

zb � ( ) (28.11)

If a cylindrical fiber is considered, the area of a section, related to the length z , is A ( z ) � Vol 0 / z , where Vol 0 represents the volume of the fiber. Thus, due to the iso-volumetric hypothesis, the infinitesi-mal force exerted by a portion of the fiber is d f b � ( Y Vol 0 / z 2 )d z .

In order to obtain f b , by integrating on the interval [ � , x ] we have

f Y

z

zz Y

xu x

x

b � � � �� �

�∫⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

Vold

d Vol0 2 0

1 1( ) (28.12)

where u ( t ) represents the Heaviside function. In Fig. 28.4 , the length–force curves for an acrylic elasto-meric motor unit driven by different electric fields are plotted. Dotted lines represent the experimental data, while solid lines represent the theoretical data derived by Eq. (28.12).

When many collinear fibres, a set I , having actual length x , are grouped in a bundle B , the resultant force is

F f Yx

u xBi I

ii I i

i� � � �� �∗ ∗∑ ∑

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟b Vol0

1 1( )

�� (28.13)

where I * is the set of active fibres, the ones for which x � � i holds. It is worth noting that the global behaviour of the bundle can be modified by selecting a particular activation order for the artificial motor units I * . Hence, it is also possible to approximate Feldman ’ s muscle model in Eq. (28.2) by using a fiber bundle ( F B ). In other terms it is possible, for a chosen tolerance � , to define an activation order that sat-isfies the following relation

F F F FF

x

F

x

k x Y

B Cx

Bx

B

x i I

� � � � �

� � �

1

2( )

� �

� �

� �

�

��

��

�

sup sup

sup∗

∑ Vol00

0 2

1 1( )

2 ( )1

��

��

ii

x i I

xu x

k x Yx

� �

� � �

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

⎛⎝⎜

∗∑

� �

sup Vol ⎜⎜⎜⎞⎠⎟⎟⎟⎟u x i( )� �� �

(28.14)

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Stiffness Control of Biomimetic Systems Through Recruitment of Bundle Elastomeric Actuators 295

( x � � i , i � I * ), where � is a union of open intervals where F B is differentiable. The choice of the C 1 ( � ) norm, which is not defined only in the points x where a single fiber of the bundle starts to be activated, ensures the possibility of obtaining a position and stiffness control since it accounts the nonlinearity of the muscle mechanical characteristic, fundamental for this purpose.

Figure 28.5 shows the combination of 21 fibres to join a single pseudomuscular actuator. By simul-taneously exciting all the fibres, the characteristic shifts and the global rest length changes, as for bio-logical muscles.

As already stressed, a complete control of a kinematic chain (i.e. including generalized compliance) can be reached when the active bundle is included in a context of other actuators. By completing the set of state variables z � ( q | c ), we have obtained a full rank local function Z � h ( L ) from control space L to state space Z . This function stands at the basis of the feed-forward control of the kinematic chain linked

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

00.07 0.075 0.08 0.085 0.09 0.095

m

N

0.1

Figure 28.5 Feldman ’ s muscle model approximation obtained for 21 fibres with effective Young ’ s modulus Y = 0.07 MPa. The solid lines represent the sum reported in Eq. (28.13), while dotted lines represent experimental data.

0.2

0.18

0.16

0.14

0.12

0.1

0.08

0.06

0.04

0.02

00.02 0.025 0.03 0.035

m

Vol0

Increasing voltageN

Figure 28.4 Length–force curves for an acrylic elastomeric fiber, ( Y = 0.07 MPa, Vol 0 = 1.3800 10 � 7 m 3 , � = 0.023 m (unstretched) driven by different electric fields ( E ). Dotted lines represent the experimental data, while solid lines represent the theoretical data (Eq. (28.12)).

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296 Chapter 28

to the actuators. Chosen a class of mechanical characteristics (spanned by � , Fig. 28.5 ) for a certain muscle to be mimed, and given the electroactive bundle compatible with the mechanical requirements, a peripheral control unit (PCU) which realizes the recruitment has to be designed. In order to comply with the Feldman ’ s theory, this unit has � (provided by a central control unit, CCU) and x (provided by a suitable sensing system) as inputs. Given these two variables, the PCU has to compute the exact configuration of the bundle (the set of fiber which have to be activated, i.e. the ones whose rest lengths have to be smaller than x ) according to performance required for the controlled muscle. The central unit, which computes all the global variable � for each muscle involved in the kinematic chain to set position and compliance, keeps enough computational resources since the computation of the ‘ details ’ on the fiber status is demanded to PCUs. This is the basis of the control for a biomimetic robot based on the Feldman ’ s equilibrium point theory. This architecture can be completed by a central memory unit which can store the � s evolution during certain fundamental movements of the mechanical chain. This unit partially replicates the role of the biological cerebellum in managing habitual movements, i.e. the movements that a subject performs without keeping particular attention on what he is doing. Without going into the specific details of this argument, we cite the most accredited theories [4, 5] which demand the choice of these habitual trajectories to the minimization of variational functionals, such as the minimum jerk and the minimum torque change hypotheses, respectively:

Jt q

tt T

t

ttk

nk

tk

nk� �

� �0

1

3

3

2

01

3

3∑∫ ∑∫⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

⎛

⎝⎜⎜⎜⎜

⎞d

dd

d

d

⎠⎠⎟⎟⎟⎟

2

dt (28.15)

where q k are the geometrical state variables and k the torques at the joints of the controlled chain. What we will propose in our future studies is a characterization of movements (including compliances) in terms of � s, with particular care to the ones which satisfy properties (Eq. (28.15)).

28.4 COMPLIANCE CONTROL: INTRODUCTION TO THE DYNAMIC CASE

In this section we provide the idea of stiffness in the dynamical case as a generalization of the concept treated in the previous parts of this work. The definition of dynamic stiffness has to coincide with the correspondent static concept when the system is motionless and shall provide an idea of the robustness of a trajectory in terms of muscular co-activation. In the static case, stiffness is represented by the norm of a matrix which relates position variations and load perturbations. In the dynamic case the concept has to be similar: compliance will describe how a trajectory changes consequently to an infinitesimal perturbation of the loads, or conversely stiffness concerns load changes required to produce corres-ponding trajectory perturbations. In the following, we will apply these concepts to control a system actuated by Feldman ’ s actuators, and we will prove its controllability for a simple case.

Let us consider the one-dimensional case of a system described by Eq. (28.16) (see Fig. 28.2 ):

φ( ) ( ) ( ) ( , ) ( )x x x x x H x K t�� �� � � � � � (28.16)

where x ( t ) is the status of the system at time t , � ( x ), ( x ), � ( x ) represent the ordinary coefficients of a mechanical second order system (i.e. the coefficient derived from the Lagrangian function of the sys-tem), H ( x , � ) represents the generalized forces exerted by muscles (controlled by � ) and K ( t ) the exter-nal loads. Since � ( x ) represents either a mass or an inertial momentum, we can suppose that � ( x ) � 0 and by dividing we obtain

�� �x x x M x L tx� � �� � �( ) ( , ) ( ), (28.17)

where v ( x ) � ( x )/ � ( x ), L x, � ( t ) � K ( t )/ � ( x ) and M ( x, � ) � � H ( x , � )/ � ( x ) � � ( x )/ � ( x ). We wrote L x, � ( t ) to represent loads in order to emphasize that this time function depends on the con-

trols and on the trajectory x ( t ) realized by the evolution of the system. The map x � L x, � between the space of trajectories and the space of loads, which will supposed in the following as time Hilbert ’ s spaces, is generally not linear and depends on system geometry and on the muscle model. According to the static case, stiffness (or compliance) has to be defined as the differentials of this functional (or the differential of its inverse one). In particular, considering the stiffness of the system, its differential (with respect to the trajectory) will act on the tangent bundle of the space of possible trajectories to the tangent bundle of the space of possible loads. This differential can be calculated and quantify the dynamic stiffness.

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Stiffness Control of Biomimetic Systems Through Recruitment of Bundle Elastomeric Actuators 297

In order to explicit an expression for this differential, let us consider a small variation of the system trajectory x ( t ) by adding with a small perturbation x ( t ). The load required to perform the new trajectory is a solution of

�� �� � �x x x x x x x x M x x L tx x� � � � � � � � � � � � �( ) ( ) ( , ) ( ),

(28.18)

By subtracting Eq. (28.17) by Eq. (28.18), we obtain

��

��

� � �

� �L

xx x

x

xxx x x

M x

xxx,

( )( )

( )( , )

� � ��� � � +

(28.19)

where the differences between correspondent terms have been replaced by their first order differentials. ( � L x, � )/( � x ), which is the dynamic stiffness indicator we consider, represents the infinity-dimensional derivative (or Frechet ’ s differential [6] ) of the operator associating trajectories and loads. It is important to note that ( � L x, � )/( � x ) depends on the chosen controls � s. In particular, in kinematic chains actuated by using Feldman ’ s muscles, different controls can perform the same trajectory even if stiffness or com-pliance result different.

In [7] it is possible to find further details on the matter together with numeric examples of the stiff-ness computation for several mechanical systems. One of the main results reached in the same work is that the choice of certain controls instead of others allows the minimization of the effect on trajectories of a particular class of load perturbation, and this set increases with the redundancy of controls with respect to geometrical state variables.

In the rest of this section we will prove, for the considered system represented in Fig. 28.2 , the exis-tence and uniqueness of control couples with prescribed stiffness. This implies the uniqueness of the controls to let the system follow a given trajectory x ( t ) with an assigned stiffness acting on a fixed per-turbation v ( t ). By joining Eqs. (28.18) and (28.19), we obtain:

mx k x k l x L t

m k x k l xL

��

��

� � � � � �

� � � � � �

( ) ( ) ( )

2 ( ) 2 ( )

12

22

1 2

� �

� � � � �� xx

x,

[ ]�

��

⎧⎨⎪⎪⎪

⎩⎪⎪⎪

(28.20)

By replacing � � x � � 1 and � � l � x � � 2 , the first equation represents a hyperbola (in � , � ) having centre in (0, 0) and asymptote slopes 1 while the second equation represents a line r having slope � 1. It is trivial that the system (28.20) allows a unique solution if and only if r does not pass through the

centre of the hyperbola, i.e. ��

�L

xv mvx,

[ ] � ��.

28.5 THE COMPLIANCE OPERATOR

To deal with compliance instead of stiffness implies a complexity increase because stiffness functional inversions are not trivial. In previous section, we defined the stiffness (related to particular controls) as a correspondence between the (Hilbert) tangent space to trajectory perturbations and the tangent space to the load perturbations:

S T X T Px x x� � �, , ,: ( ) ( )→ (28.21)

In few words, chosen two Hilbert bases for the function spaces, the operator S can be thought as an infinite-dimensional unbounded matrix. The operator C ( compliance operator ) is the inverse of S and so it maps the tangent space to the load perturbations into the tangent space to the trajectory perturbations:

C T P T Xx x x� � �, , ,: ( ) ( )→ (28.22)

S � ,x can be approximated by a sequence of n -dimensional operators S n . In [8] it is proved that the norm of the eigenvalues of S n increases with n , and consequently the norm of the eigenvalues of the inverse operators C n decreases. This implies that the operator C is continuous and bounded, and that, choosing arbitrarily a tolerance � � 0, it is possible to approximate it with a n -dimensional matrix C n , for a certain n , such that the norm of the difference C � ,x � C n (as Hilbert space operator) is smaller than � . In this way, it is possible to operate by finite-dimensional linear algebra instruments to control

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298 Chapter 28

system stiffness or compliance by committing errors smaller than a fixed tolerance. In [8] this fact is exhaustively demonstrated and adequately supported by explicit examples.

28.6 CONCLUSIONS

In the first part of this study, a simple treatment of the control strategy of a kinematic chain in a static case, according to Feldman ’ s guidelines, was introduced from a mathematical point of view. Moreover, by employing dielectric elastomers, a method to realize pseudomuscular actuators enabling this strategy was presented. The last two parts of this chapter regards the introduction of dynamic stiffness and com-pliance and gives an overview on the complexity of the treatment from a mathematical point of view. In spite of this, the treated mono-dimensional example opens up new prospects in control strategy and points out the difficulties that this method may present. Several mathematical instruments needed to solve the particular control problem are yet unexplored. On the other hand, as proved in [7] and intro-duced in Section 28.4, certain important results have still to be widely analysed form a conceptual and biological point of view. The possibility to co-activate muscles only to preserve the system from a cer-tain perturbation, for example, lets the reader suppose that either a biological system is strictly related with the environment where it operates and ‘ knows ’ the possible common perturbation, or that it tries to protect itself against its own singularities, as perturbations characterized by the same oscillation res-onance of the system. Anyway, this research is rather young and future studies will be devoted to clarify these problems, both from a technical and from a conceptual point of view.

ACKNOWLEDGEMENTS

The authors acknowledge Dr Federico Carpi for the results on the electroactive materials and Dr Piero Orsini for precious advices on motion control theories.

References

[1] Feldman , A. ( 1986 ). Once more on the equilibrium-point hypothesis (model) for motor control . J. Motor Behav. , 18 , 17 – 54 .

[2] Pei , Q. , Rosenthal , M. , Standford , S. , Prahlad , H. and Pelrine , R. ( 2004 ). Multiple degrees-of-freedom elec-

troelastometer roll actuators . Smart Mater. Struct. , 13 , N86 – N92 .

[3] Pei , Q. , Pelrine , R. , Standford , S. , Kornbluh , R. and Rosenthal , M. ( 2003 ). Electroelastomer rolls and their

application for biomimetic walking robots . Synth. Met. , 135–136 , 129 – 131 .

[4] Uno , Y. , Kawato , M. and Suzuky , R. ( 1989 ). Formation and control of optimal trajectory in human multijoint

arm movement: minimum torque-change model . Biol. Cybernet. , 61 , 89 – 101 .

[5] Flash , T. and Hogan , N. ( 1985 ). The co-ordination of arm movements: an experimentally confirmed math-

ematical model . J. Neurosci. , 7 , 1688 – 1703 .

[6] Ambrosetti , A. and Prodi , G. ( 1972 ). On the inversion of some differentiable mappings with singularities

between Banach spaces . Ann. Mat. Pur. Appl. , 4 ( 93 ) , 231 – 246 .

[7] Lorussi, F., Caudai, C., Galatolo, S. and De Rossi, D. (2006). Compliance control and Feldman ’ s muscle

model. Proceedings of the International Conference on Biomedical Robotics and Biomechatronics , Pisa,

Italy.

[8] Lorussi, F., Caudai, C., Galatolo, S. and De Rossi, D. Stiffness and compliance control of kinematic chains

and Feldman ’ s muscle model, work in progress.

[9] De Rossi , D. , Di Puccio , F. , Orsini , P. and Tognetti , A. ( 2002 ). Feldman ’ s muscle model: implementation and

control of a kinematic chain driven by pseudo-muscular actuators . Acta Bioeng. Biomech. , 4 ( 1 ) , 224 – 225 .

[10] Ghelardi, A., Lorussi, F., De Rossi, D. and Bicchi, A. (2003). Modellistica, progettazione e controllo di

un ’ interfaccia cinestetica. Università degli studi di Pisa.

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V.III

Commercial Applications

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COMMERCIAL ACTUATORS AND ISSUES

Charlie Duncheon

Artificial Muscle, Inc., Menlo Park, CA, USA

Abstract

This chapter describes the strategy developed and executed by Artificial Muscle, Inc. (AMI) to commercialize the

Electroactive Polymer Artificial Muscle (EPAM TM ) technology developed at SRI International. Specific activity in

enhancing lifetime, focusing on a single but broad application-based EPAM configuration, the Universal Muscle

Actuator (UMA TM ). Also described is the development of an automated manufacturing process that improves prod-

uct quality and reliability as well as reducing costs. The steps taken to reduce the cost and size of the EPAM power

supply and controls are also detailed. EPAM improvements in environmental range and performance characteristics

are addressed as well as some specific applications including pumps and valves.

Keywords : Commercialization, electroactive polymer, electroactive polymer artificial muscle, universal muscle

actuator.

29.1 INTRODUCTION

The various advantages promised by dielectric elastomer transducers are becoming a reality with Electroactive Polymer Artificial Muscle (EPAM TM ) technology. In 2004, after roughly 12 years of development in the laboratories of SRI International, Artificial Muscle, Inc. (AMI) was spun out from SRI International to commercialize EPAM technology and bring to the world the first viable mass mar-ket alternative actuation technology in over 50 years.

AMI was granted an exclusive, permanent, worldwide license to over 30 of SRI International ’ s US and foreign issued and pending EPAM-related patents. To help ensure the successful commercialization of the technology, several EPAM technology inventors and developers left SRI International and joined the AMI team. Professionals with extensive backgrounds in materials development, electronics, and manufacturing were recruited to join the AMI developers. In addition, several other SRI EPAM tech-nology inventors as well as other experienced manufacturing professionals became active members of the AMI Technical Board of Advisors.

The issues and challenges facing the AMI team were to improve reliability, performance, and the environmental operating range for devices using EPAM material. In addition, AMI needed to develop a low cost, small form factor power supply to address the high volume market opportunities. Lastly, a high volume manufacturing process had to be developed that not only provided low cost devices but high quality actuators that demonstrated highly repeatable unit-to-unit performances.

By late 2006, AMI had engaged over 50 clients, 30 of which were Fortune 1000 corporations, through development contracts for Original Equipment Manufacturer (OEM) applications or through the direct sale of AMI Development Kits. And as of late 2006, Artificial Muscle was also in discussions with over 100 potential clients for various actuator, sensor, and power generation applications.

29.2 UMA PLATFORM

With all the commercialization challenges facing AMI it became clear that working from a standard actuator product platform would accelerate the path towards commercialization and high volume manu-facturing of EPAM actuators. A common actuator platform would simplify the scope of the first volume manufacturing process and line at AMI while also providing a standard configuration for the extensive

Chapter 29

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testing required for commercialization. While AMI had built actuator prototypes in several config-urations including linear rolls, bending rolls, planars, and diaphragms AMI marketing was challenged to find the single configuration platform that would bring the benefits of standardization while still addressing the maximum range of early applications.

The application chosen for the standard platform was that of the double diaphragm, named the Universal Muscle Actuator TM (UMA). This two-phase configuration addressed close to 80% of AMI ’ s early customer applications including pumps, valves, lens positioners, sensors, and power genera-tors. Limiting design configurations to the UMA allowed AMI engineers to narrow their focus as they engaged in product and process development.

29.2.1 Fundamental design

As many readers will be well aware, an EPAM actuator consists of a thin layer of polymer film between two compliant electrodes. When a voltage potential is applied across the electrodes, the two electrodes attract each other through Maxwellian forces, forcing the incompressible film to contract in thickness and expand in area. When mechanical constraints and output areas are fixed to the film, the expansion and contraction of the film can be harnessed for useful work [1].

In its standard form, the UMA is constructed of two independent stacks of film, attached at their centres and separated by a lightweight spacer (see Fig. 29.1 ). Each stack of film is attached to a frame that gives structure to the film and is usually used to anchor the UMA to the host system. Also attached to each stack of film is an output disc, by which force and stroke are transmitted from the expanding film to the load. A stack of film sandwiched between two frames and two output discs is referred to as a cartridge. Products based on this configuration follow.

29.2.2 DA50 positioner

The most versatile application for AMI, from which most other applications were derived, is the DA50 positioner (see Fig. 29.2 ). The DA50 is an analogue actuator, with its output force and stroke simply proportional to an electrical input signal. Unlike electromagnetic proportional positioners, the force–stroke curve for the DA50 is linear, allowing designers to more easily achieve difficult positioning chal-lenges. Additionally, since EPAM technology can be run at high frequencies, the DA50 and other scaled sizes can function as a vibration source, a feature gaining popularity in human–machine interfaces and

Figure 29.1 The universal muscle actuator.

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Commercial Actuators and Issues 303

standard in active vibration damping applications. In addition to the DA50 AMI introduced a DA50-2 which is a two-phase device providing twice the actuation stroke. This configuration was made avail-able for testing on AMI ’ s MC02 test and evaluation controller. The MC02 controller was developed by AMI to insure a consistent, standard test platform for both AMI and AMI customer testing.

29.2.3 DV35 proportional valve

For fluid control applications, the DV35 proportional valve naturally provides a proportional flow rate in a compact package (see Fig. 29.3 ). The DV35 is an analogue 0–5 V variable valve; flow rate is pro-portional to the input voltage. For this and similar products, AMI uses both commercially available and custom driving electronics. Regardless of the electronics source, however, the goal is the same: to make integration of artificial muscle actuators easy and seamless for the OEM.

29.2.4 DP70-2 pump

For pumping applications, the DP70-2 pump is a UMA configuration containing an integrated pumping chamber, suitable for pumping both liquids and gases (see Fig. 29.4 ). The pump can be controlled with the MC-02 muscle controller, or for OEM applications, an AMI customized pump driver circuit.

29.2.5 Case example: closed-loop pneumatic system

As can be seen from the wide array of devices presented above, the base UMA platform can simultan-eously fill the needs of multiple parts of a complex system. In fact, AMI demonstrated the world ’ s first

Figure 29.2 The DA50 positioner.

Figure 29.3 The DV35 proportional valve.

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EPAM closed-loop pneumatic system. This system used the UMA architecture as a platform on which to create an inflatable bladder system composed of one pump, six valves, and three UMA-based pres-sure sensors. Reading inputs from user-controlled switches, an integrated microcontroller processed pressure levels from the EPAM sensors, directed the EPAM valves to release air from the bladders or fill the bladders, in conjunction with the operation of the EPAM pump, until the bladders were filled to the desired level. This system demonstrated the versatility of the UMA platform in simultaneously addressing several client needs. Additionally, since the components were based on a common architec-ture, a common manufacturing process could be used to significantly reduce part count, fabrication, and assembly time, as well as increasing overall system reliability.

29.3 IMPROVEMENTS IN ROBUSTNESS

While there are many configurations of EPAM technology that can be used to address any given appli-cation, one of the reasons AMI decided to focus on the UMA configuration was its elegant simplicity. In contrast to conventional actuators that have more complicated three-dimensional parts, the UMA is composed of a stack of simple two-dimensional component shapes (see Fig. 29.5 ). These shapes are designed for Z -axis fabrication and assembly operations, keeping parts simple and manufacturing costs low.

Figure 29.5 UMA components.

Figure 29.4 The DP70 pump.

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29.3.1 Mechanical robustness

With such a simple and elegant architecture, devices powered by a UMA actuator are mechanically robust. Instead of converting high speed rotary motion for low speed linear motion applications, as is commonly required for conventional rotary motors, the UMA has the ability to directly drive linear positioning devices at frequencies from DC to several hundred hertz. This ability allows designers to remove complicated, fatigue-prone gear reduction and motion conversion power trains, leading to sys-tems that are long lasting and more cost effective. Indeed, it is not uncommon for OEM designers using EPAM devices to reduce their part count by 50% or more.

While EPAM devices are capable of strains on the order of several hundred per cent in laboratory set-tings, for practical devices AMI designs EPAM actuators for operating strains of roughly 10% in order to meet the lifetime requirements of AMI clients. Using EPAM in this regime tends to provide the prod-uct designer with the best combination of reliability and power output while still providing significant advantages over conventional actuation solutions. One of AMI ’ s ongoing development efforts involves modifying the EPAM system to allow designers to achieve higher force and strain levels without sacri-ficing reliability or mechanical power output.

In addition to direct drive applications, EPAM technology can also be used for so-called infinite stroke applications, such as rotary motors and pumps. These UMA applications convert the reciprocat-ing motion of the UMA actuator to single direction motion for motors and pumps by way of clutches or check valves, respectively. Since mechanical performance directly follows the electrical control signal, the output speed is easily controlled by varying the frequency and the output amplitude is controlled by varying the electrical signal amplitude. Thus, with the addition of a few simple parts and control schemes, the standard UMA platform can be used across a wide variety of applications.

One of the fundamental advantages of the UMA design is its inherent shock-absorbing attribute. Unlike other technologies that transmit a mechanical shock from the end of the output shaft back to the heart of the host system, the EPAM UMA actuator bearing cushions and damps external vibra-tions, minimizing undesirable energy transfer to the rest of the system. This inherent advantage allows designers to exchange their existing actuator, shock-absorbing elements, and over-designed parts for a single, rugged, elegant UMA actuator. A good example of this feature is AMI ’ s lens positioning UMA configuration, where the lens in a cell phone camera module easily survives the industry standard 1.5 m drop test due to the shock-absorbing features of the UMA lens positioner configuration (see Fig. 29.6 ).

In many cases designers can use the UMA ’ s built-in, completely frictionless, output shaft bearing in place of a conventional bearing. This film-based bearing allows designers to automatically self-centre and constrain the UMA end of the output shaft without additional parts or features, as would be required when using conventional actuation technology. The simplicity of the UMA, as well as the reduced system part count, contributes to increased mechanical robustness over conventional solutions.

29.3.2 Environmental robustness

Materials development at AMI is also providing customers with high value as well as environmental and reliability improvements. The commercially available industrial polymers and plastics used in UMA actuators provide customers with lightweight actuators that translate to significant cost savings over conventional metal-based technologies. Not only are the raw materials lighter, but since UMA actua-tors are often smaller than conventional actuators, there are even greater savings in the form of weight, volume, and cost.

Figure 29.6 UMA-based lens positioner for camera modules.

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While there has been much discussion over the past few years regarding the environmental relia-bility of dielectric elastomers, AMI has been pursuing various material improvements that expand the temperature range and general stability of the UMA actuators in the presence of harsh environmental conditions. Specifically, AMI has been working towards achieving high performance operation across a broad range of operating temperatures and conditions. AMI researchers tested silicone dielectrics with highly consistent performance over temperature ranges compared to the first acrylic dielectrics (see Fig. 29.7 ). These new material developments, along with proper isolation techniques, also promise improvements in moisture and chemical resistance.

29.3.3 Reliability

Another subject around which there has been much recent discussion is the topic of fundamental die-lectric elastomer reliability. To address this challenge, Artificial Muscle engaged a team of researchers and experts to extend the lifetime of the UMA actuator. Much of the improvement techniques are AMI trade secrets but as can be seen in Fig. 29.8 , the AMI team has increased the actuator lifetime by more than 8000% since 2003. Such orders of magnitude improvements in reliability are making the adoption of EPAM technology feasible for a wide range of applications.

Reliability improvement

0

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100

1000

10 000

100 000

1 000 000

2003 2004 2005 2006 2007 2008Year

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impr

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Figure 29.8 EPAM reliability improvement.

Stroke versus temperature

05

101520253035404550556065707580859095

100105

�40 �20 0 20 40 60 80 100 120Temperature (°C)

Str

oke

(%)

Figure 29.7 Early environmental tests for new AMI dielectric.

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29.4 MANUFACTURING PROCESS DEVELOPMENT

The Artificial Muscle manufacturing team also contributed to improve the robustness of the UMA actuators by developing bench top, pilot line, and high volume manufacturing systems. These manufac-turing capabilities moved dielectric elastomer technology out of the laboratory and towards integration in OEM applications. Through implementation of automated processes for depositing electrodes UMA assembly, reductions in part-to-part variation led to higher yield and more repeatable system operation. In addition, the manufactured quality of the devices increased, providing benefits in UMA ruggedness and reliability. As part of the Artificial Muscle ’ s commitment to provide its customers with high qual-ity products, AMI began the steps towards ISO and CE certification and plans to have full certification in 2008.

29.5 IMPROVEMENTS IN PERFORMANCE

Many of the advantages of EPAM technology over conventional actuator technologies can be classified in the category of electromechanical performance. Artificial Muscle has been working hard to transfer the theoretical advantages of EPAM technology from the laboratory to practical OEM devices.

29.5.1 Power density and energy density

As has already been mentioned, one of the fundamental advantages of the UMA platform is that it is composed primarily of lightweight polymers and plastics. The use of lightweight active and passive subcomponents has been one factor that has helped AMI in improving power and energy densities over the past few years (see Fig. 29.9 ). Another contributing factor to improve power density has been the recent development of high speed operation, from DC up to thousands of hertz.

Such improvements in power density have enabled AMI to produce pumps with power densities on par with commercially available pumping solutions. Similarly, increases in energy density have allowed AMI to develop devices that have significant advantages over conventional devices, both in terms of performance as well as yielding savings in weight and volume.

29.5.2 Efficiency

Efficiency is another area where EPAM devices have inherent advantages over conventional technolo-gies in many applications. For instance, in applications where high speed rotary motion is converted to

Power and energy densities

2003 2004 2005Year

Den

sity

impr

ovem

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Power density Energy density

Figure 29.9 Power and energy density improvements.

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low speed linear motion, as mentioned earlier, the EPAM solution achieves the desired result as a direct drive solution with a low-loss power transmission system; this is in comparison to a conventional solu-tion involving many gears and bearings, each of which contributes frictional losses to the system.

From an electrical point of view, EPAM devices are variable capacitors. This means that they con-sume little power when actively holding a position and return their stored electrical energy when they are discharged. Thus, an EPAM actuator can be significantly more efficient than a conventional electro-magnetic solution, especially in DC or low frequency applications (see Fig. 29.10 ). In cyclic or higher frequency EPAM embodiments, Artificial Muscle is actively developing ways to recover and reuse elec-trical energy from one cycle to the next and plans to have that power supply available in 2008.

29.5.3 Fundamental EPAM advantages

In terms of mechanical work, EPAM actuators tend to have linear force–stroke curves, which make it rela-tively easy for designers to find the appropriate operating point for a given application (see Fig. 29.11 ). In the case of a pump, the pressure–flow curve is fairly linear, again offering designers ease in integrating EPAM technology into their application.

For high precision positioning applications, such as lens positioners or other industrial positioners, EPAM technology is inherently precise, allowing controllable movement down to at least the micron level or better. Since EPAM is an analogue technology, in most cases the motion accuracy depends on the quality of the feedback sensor.

There are also more methods to control EPAM actuators than are readily available for traditional solutions. For instance, in controlling a conventional electromagnetic motor, designers usually set a specific operating voltage, tied to the motor specifications, and control the speed of the motor, if neces-sary, via duty cycle variation or pulse width modulation (PWM). For an EPAM motor, however, since the EPAM movement follows the electrical input signal, in addition to PWM control, the designer can also vary the voltage, frequency, and waveform. This leads to more design flexibility when a particular behaviour is desired. In addition, these additional ‘ axes ’ of actuator control allow EPAM actuators to operate in ways that are significantly more difficult to achieve with conventional technology.

29.5.4 Designed flexibility

The UMA platform also has two main characteristics that enable it to serve a wide variety of customer applications: modularity and scalability. The UMA platform was designed from the ground up to be a modular platform, able to provide different levels of stroke and force with the simple reconfiguration

Power draw

Pow

er d

raw

EPAM® COTS solenoid

Figure 29.10 EPAM efficiency advantage over conventional solenoid.

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of the component parts. This enables AMI to rapidly respond to customer requests for differing levels of functionality. Similarly, since there are common standard sizes and mounting patterns, both active and passive system elements can be rapidly reconfigured to accommodate new design challenges. In add ition, the EPAM technology is inherently scalable, allowing AMI to fabricate devices in the UMA family measuring several millimetres on a side to devices measuring over 100 m on a side. These mod-ular and scalable characteristics are paying off in terms of significantly reduced development time and increased manufacturing throughput.

29.6 IMPROVEMENTS IN MANUFACTURING

Beginning with the SRI International manufacturing techniques, the AMI manufacturing team is trans-forming EPAM manufacturing technology from a laboratory process into a high volume process cap-able of producing many million units per year by the end in 2008. AMI has scaled up the production capacity of EPAM devices from under 1000 devices per year at SRI International during 2000–2003 to 5000 devices manufactured at AMI in 2004 and 30 000 devices manufactured in 2005. With the introduction of the new high volume process, AMI expects to have the capacity to manufacture at least 20 million EPAM devices in 2008 and over 100 million devices in 2009. To accomplish these goals, AMI is developing a proprietary manufacturing process.

29.6.1 Manufacturing strategy

At the core of this proprietary process is the concept of ‘ printing actuators ’ ; EPAM UMA actuators will be printed using existing and custom techniques for high volume printing. AMI is leveraging the emerging field of Printed Electronics by utilizing the same equipment and development strategies that are enabling low cost electronics. Printed Electronics manufacturing techniques are being developed for a wide range of applications, many of which have similar requirements to EPAM devices. Such applica-tions include radiofrequency identification (RFID) tags, organic light emitting diodes (OLEDs), and elemental organic electronic devices such as transistors, resistors, capacitors, batteries, and solar cells. AMI has developed an automated batch mode processing of devices and is currently designing a fully automated manufacturing process that should be operational in late 2007. Such a high volume approach will enable AMI to provide significant value to its customers while keeping costs low.

With the goal of high volume manufacturing in sight, the UMA design team has employed Design for Assembly (DFA) and Design for Manufacturing (DFM) techniques to aid both internal and OEM development. One of the key features of the UMA platform is that the UMA assembly is composed largely of two-dimensional shapes that are easily fabricated and assembled via Z -axis fabrication and assembly equipment.

Since the UMA platform is designed to be inherently modular and scalable to serve as many applica-tions as possible, the manufacturing lines themselves are also being designed to be both adaptable and reconfigurable on the fly, with little if any changeover time. CAD/CAM driven manufacturing will help

Pump performance

Flow rate

Pre

ssur

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AMI pump COTS pump

Actuator performance

Stroke

For

ce

AMI actuator COTS solenoid

Figure 29.11 EPAM device performance compared to conventional pump and solenoid.

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AMI to serve a wide variety of customers and applications with quality products within short response times.

The AMI manufacturing process is designed to release the manufacturing location from all con-straints except supply chain logistics. Most notably, the automated manufacturing system allows AMI and its customers to be independent of the requirements for low-cost labour. Thus, the location of AMI automated cells will be logistics/supply chain driven and not labour cost driven.

29.6.2 Economies of scale

As may already be evident, all of AMI ’ s activities have been geared towards taking advantage of econ-omies of scale, from design, to testing, all the way through to manufacturing and integration into OEM products. The UMA system allows designers to maintain and develop a common platform across appli-cations, reducing the time to market and helping to foster EPAM integration into both existing and emerging applications.

Common UMA system components allow EPAM designers to create multiple configurations with many possible applications per configuration. For instance, with the same film cartridge, an EPAM designer can create a variable or binary positioner, a vibration generator, a valve, or a pump. Additionally, multiple identical cartridges can be stacked to increase force output. Such interchangeable base elements allow the AMI manufacturing team the freedom to focus on producing the highest quality manufactured devices while simultaneously offering the AMI design team the benefits of rapid prototyping. Since the components are similar in both design and construction, the manufacturing process is able to be quickly reconfigured to accommodate variations.

29.7 ELECTRONICS AND POWER SUPPLIES

While applications for electroactive polymers have shown good efficiencies and lower power consump-tion as compared to conventional electromagnetic solutions, they run at high operating voltages that require a ‘ step-up ’ power supply. As stated earlier, a low cost, small form factor power supply was one of the challenges for electroactive polymer commercialization.

Faced with the challenge, AMI did extensive development work to create two families of power sup-plies for electroactive polymer devices, one for testing devices under variable operating parameters and a second for high volume, standard electroactive polymer products that had to be designed for min-imum size and cost.

By its design, EPAM is an electrostatic polymer structure with high voltage and low current oper-ation. Since applications for electroactive polymer actuator products begin with conventional low volt-age input EPAM actuators require power supplies that take low level (0–24 V) variable input and step up through the power supply to high level operating voltage. During the development stages of EPAM in the SRI laboratories the operating voltage was as high as 6 kV but the commercialization activity at AMI has led to lower maximum operating voltages in the 1.2–2.5 kV levels with further voltage reduc-tion in the product roadmap.

AMI attacked the power supply challenge on two fronts mentioned below.

29.7.1 Lower operating voltage

AMI performed development with the structure of the EPAM layers to reduce operating voltage in half by the end of 2005 and had some configurations reduced by another half by mid-2006. This led to both a dramatic reduction in cost as well as size. ( e.g. , 4 mm � 8 mm for lens positioner power supply and controls). The product roadmap at AMI has further operating voltage reductions planned. Figure 29.12 displays the small lens positioner power supply and controller.

29.7.2 Power supply volumes

Power supplies are being developed for both DC and AC applications and will be capable of delivering a broad range of power. These power supplies are designed around common architectures and components, again yielding benefits for high volume manufacturing including low costs for AMI. Early power sup-plies are shown in Fig. 29.13 .

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The first standard power supply developed for EPAM was the MC01. The MC01 was designed to accommodate the testing and evaluation of various EPAM configurations under variable frequencies and voltages. The user could set voltage and frequencies manually or connect the MC01 to a function box for a programmed test. AMI then released a second controller for testing and evaluation, the MC02 (see Fig. 29.14 ). This controller had all the features of the MC01 but accommodated much higher fre-quencies (up to 500 Hz) and allowed the user to run in sine or square wave generation.

The MC01 and MC02 controllers allowed AMI to create a standard testing platform for both internal and customer testing of EPAM devices. This strategy provided a more reliable testing database in AMI ’ s commercialization process.

Figure 29.12 Lens positioner controller and power supply.

Figure 29.13 AMI electronics commercial power supplies.

Figure 29.14 MC02 test and evaluation controller.

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29.8 INTEGRATION OF POWER SUPPLY ELECTRONICS AND THE MUSCLE ACTUATOR

AMI established an early design goal to have an integrated EPAM actuator and power supply/controller in the device, whether that device be a lens positioner, a pump, or a valve. In Fig. 29.15 , the integration of a power supply/controller and the EPAM-based proportional valve is shown. With this design the valve customer only deals with the low input voltage as he or she would with conventional valves.

29.9 ELECTRONICS SUMMARY

When AMI began commercialization of EPAM the power supplies utilized were large, expensive, and not designed for integration into high volume devices. In less than 3 years AMI was providing devices with small, internally integrated power supplies and controls with conventional low voltage inputs. The power supplies will only get smaller in the future as AMI continues to reduce voltage as well as build high volume power supplies designed with all passive components etched on substrates. In essence, AMI has made operating voltage a non-issue with EPAM.

29.10 COMMERCIALIZATION CONCLUSION

As a result of Artificial Muscle ’ s development of the UMA actuator and electronics, commercial actu-ators will be available in high volumes in 2007 Through the modular, scalable architecture of the UMA, Artificial Muscle is developing the robustness, performance, and value that users expect from actu-ation technologies. Increases in temperature operating range and overall reliability have made it realis-tic for corporations to begin the process of migrating systems using conventional actuation technologies over to EPAM technology. Performance breakthroughs have demonstrated significant advantages of artificial muscle actuation over conventional solutions, offering incentives to market leaders to be early technology adopters. Through a flexible, automated, high volume manufacturing process and by capi-talizing on economies of scale, UMA actuator configurations for a wide variety of applications will soon be available in high volumes. Using AMI ’ s integrated electronics control modules, OEM product designers will be able to incorporate EPAM technology into existing and emerging applications with minimal risk. These and other developments like the small, low cost power supplies are actively contrib-uting to demonstrate the advantages of artificial muscle EPAM technology in commercial applications.

Reference

[1] Pelrine , R. , Kornbluh , R. , Pei , Q. and Joseph , J. ( 2000 ). High-speed electrically actuated elastomers with strain

greater than 100% . Science , 287 , 836 – 839 .

Figure 29.15 Integrated power supply and controller in EPAM proportional valve.

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DIELECTRIC ELASTOMER LOUDSPEAKERS

Richard P. Heydt , Roy Kornbluh , Joseph Eckerle and Ronald Pelrine

SRI International, Menlo Park, CA, USA

Abstract

Dielectric elastomer (DE) loudspeakers are similar to electrostatic loudspeakers in that they are based on thin dielec-

tric films that radiate sound in response to oscillating applied voltages. DE speakers operate at high voltage – on

the order of 1 kV, depending on the film thickness – and like electrostatic speakers are typically driven with a DC

bias and AC modulation. Since the electric field is applied directly across the elastomer thickness, the DE speaker

film thickness changes as it radiates sound. High sound pressure levels can be generated with loudspeakers of mod-

erate size. Harmonic distortion is inherent to DE loudspeakers because film deformation varies as the square of the

applied field. Harmonic distortion can be reduced by implementing a push–pull configuration. One of the unique

capabilities of DE loudspeakers is that their shape, and thus the sound radiation directivity, is adjustable by chan-

ging how the speakers are biased mechanically. DE loudspeakers can conform to any surface profile and, like other

DE actuators, they are lightweight and potentially very inexpensive.

Keywords : Concave, convex, dielectric elastomer, directivity, electrostatic loudspeaker, film loudspeaker, harmonic

distortion.

30.1 INTRODUCTION

Film- and membrane-type loudspeakers are not quite as familiar as voice-coil-driven cone speakers but have been in use since electrostatic loudspeakers were developed in the 1920s and 1930s [1] . A recent entry to the film loudspeaker category that has achieved some commercial success is the distributed-mode loudspeaker invented by NXT [2] . Dielectric elastomer (DE) loudspeakers [3] , discussed in this chap-ter, are another new type. Film loudspeakers have become more common in response to the demand for flat and lightweight speakers in computers, televisions, and handheld communication devices, and for conforming loudspeakers on curved surfaces, such as automobile headliners.

In this chapter, DE loudspeakers will also be referred to as electroactive polymer (EAP) loudspeakers, with the understanding that there are other types of EAPs. DE loudspeakers are analogous to electrostatic speakers: they are both high-voltage devices in which charge is moved onto and off of a dielectric film, causing the film to vibrate and emit sound. A fundamental difference is that the electrostatic film oscil-lates under an applied electric field but the film does not deform mechanically. In contrast, when voltage is applied to a DE film its thickness decreases and its area increases. The film oscillates if a bias force is used to take advantage of the changing area. Scheinbeim [4] was among the first to suggest that elasto-meric polymers could generate sound under the application of high voltage across the polymer thickness, using the electrostrictive response of polyurethane and other polymer actuators [5] . Unlike electrostric-tive polymers, film deformation in DEs results from electrostatic forces. Loudspeakers based on thin DE films are capable of generating large vibration amplitudes and sound pressures.

30.2 DESIGN AND OPERATION

Loudspeakers can be built with any of several different DEs. Acrylics and silicones are attractive because of their high dielectric constant and breakdown strength [6] . As with other DE actuators, a loudspeaker is made by first fabricating a thin elastomer film, with a typical loudspeaker film thickness being 50 � m. The film is maintained in tension by a rigid frame or an enclosure.

Chapter 30

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314 Chapter 30

The actuation thickness strain s of a DE film under an applied electric field or voltage is [6]

s

E

Y h Y� �

� � � � �r r02

02

2 (30.1)

where E is the applied electric field, v is the applied voltage, h is the film thickness, Y is the Young ’ s modulus, � r is the relative dielectric constant, and � 0 is the permittivity of free space.

Like an electrostatic speaker, a DE loudspeaker is usually operated with a DC bias voltage and an AC drive voltage, as indicated by Fig. 30.1 . Voltage requirements depend on film thickness and desired sound output. In practice, for a 50 � m speaker film (nominal thickness after film prestrain) the DC bias is typically in the range from 1 to 2 kV and the AC drive in the range from tens to hundreds of volts.

In addition to the electrical bias and drive voltages, the elastomer film must have a mechanical bias force to generate sound ( Fig. 30.1 ). In an electrostatic speaker the dielectric film is attracted across an air gap towards a stationary plate ( Fig. 30.2 ), and no bias force other than the initial film tension is necessary. With a DE loudspeaker, however, the film tension relaxes when voltage is applied so a mechanical bias is required to cause the film to oscillate in the normal direction. The mechanical bias can be applied by stretching the film across a backing material, such as a porous foam, or by applying a small positive or negative air pressure. Figure 30.3 shows a square DE loudspeaker biased with lightweight foam [7] . Even including the foam backing, this speaker is essentially two dimensional, which illustrates one of the advantages of DE technology for generating sound.

DE film

Mechanicalbias force

Vibration

Soundradiation

Electrodes

AC drivevoltage

DC voltage

Film

RH-314522-2A

Figure 30.1 Operational schematic of a DE loudspeaker. The electroded film vibrates when it is driven electric-ally by a DC bias voltage and an AC drive voltage. A mechanical bias force keeps the film in tension and causes it to vibrate unidirectionally when voltage is applied.

Soundradiation

Stationary electrode

Stationary electrodeRI-314522-3

Vibrating diaphragm

�VAC�

�VAC�

VDC

Figure 30.2 Operational schematic on an electrostatic loudspeaker. The diaphragm vibrates when it is attracted across an air gap towards a stationary electrode. In the ‘ push–pull ’ configuration shown, there are stationary elec-trodes on each side of the diaphragm. Like a DE speaker, an electrostatic speaker is usually operated with a DC bias and an AC drive voltage.

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Dielectric Elastomer Loudspeakers 315

30.3 PERFORMANCE

Figure 30.4 shows a representative measurement of on-axis frequency response magnitude for a DE loudspeaker. The acrylic film of the speaker has a diameter of 10 cm and is mounted on a rigid frame over a shallow (2 cm deep) plenum. For this DE loudspeaker the fundamental acoustic resonance is at 1050 Hz. The sound pressure level (SPL) drops below the resonance level by about 6 dB at 10 kHz and by about 14 dB at 20 kHz. Beginning at approximately 6 kHz, the response decays at an average rate of 8 dB per octave. The overall response in the middle part of the audible frequency range – between 1 and 10 kHz – is fairly good. In general, loudspeaker designers like the frequency response (SPL) to be reasonably flat past the fundamental resonance. Note that the loudspeaker was built to demonstrate functionality and was not engineered for optimal performance, so improvements in the response are possible. There are several minor nulls and resonances in the frequency response that reflect specific details of the loudspeaker construction, such as cavity dimensions, damping, and so forth. The primary resonance frequency is a function of cavity depth and film tension. The primary resonance frequency would be lower if the DE film had been mounted on a larger-volume speaker housing.

The SPL varies directly with applied voltage. If the voltage on the DE loudspeaker film is v = B + A* sin( � t ), where B is the DC bias and A is the amplitude of the AC drive voltage, then the time-varying response amplitude corresponding to the film strain in Eq. (30.1) is

s

h YBA AAC

r� �� �0

222( ) (30.2)

where s AC is the amplitude of the film vibration, h is the film thickness, Y is the Young ’ s modulus, � r is the relative dielectric constant, and � 0 is the permittivity of free space.

At a given frequency SPL is proportional to the film vibration amplitude. Figure 30.5 shows the acoustic response at two drive voltages that differ by a factor of three. Based on Eq. (30.2) the predicted

90

80

70

60

50

400 0.2 0.4 0.6 0.8 1 1.2

Frequency (Hz)

SP

L (d

B)

1.4 1.6 1.8

�1042

Figure 30.4 Frequency response of a 10 cm diameter EAP loudspeaker plotted on a linear frequency scale. The SPL is measured on-axis at 1 m from the speaker surface. The response is reasonably flat between the resonance frequency (1050 Hz for this loudspeaker) and 20 kHz.

Figure 30.3 A conventional electromagnetic loudspeaker and a DE speaker. The square DE loudspeaker is 15 cm on a side, and is biased mechanically with foam. The conventional loudspeaker is heavier and thicker for the same cross-sectional area because of the magnet and voice coil.

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316 Chapter 30

change in SPL is 10.3 dB, which is consistent with the measured difference of 8–10 dB over the audible frequency range.

The on-axis SPL is a function of frequency, voltage, and film area. The SPL is ultimately limited by the electric field strength of the elastomer film, although large sound pressures are possible well below the breakdown field limits. Sound pressures of almost 90 dB (at 1 m) in the vicinity of the resonance fre-quency have been measured with a 12.5 cm diameter loudspeaker film, at an applied voltage of 1.5 kV DC and 400 V AC [7] .

Like electrostatic speakers, DE loudspeakers are capacitive and the film impedance is a reactance that decreases with increasing frequency. Representative values of the impedance for a 10 cm diameter speaker are listed in Table 30.1 . Not included in the table entries is a resistive part of the impedance, resulting from current leakage through the speaker film, which varies directly with the applied field. Since the loudspeaker film presents a primarily capacitive load to the driver amplifier, the conventional ‘ sensitivity ’ – the SPL resulting from 1 W power dissipation in an 8 � speaker load – used to compare the efficiency of sound production in electromagnetic speakers is not very relevant to DE loudspeakers.

30.4 HARMONIC DISTORTION

The acoustic pressure generated by a DE loudspeaker is proportional to the volume acceleration of air generated by the vibration of the film. Since the vibration is related to film strain and the strain varies as the square of the applied voltage (to first order), the acoustic response will always have har-monic distortion. As Eq. (30.2) indicates, the harmonic distortion becomes greater as drive amplitude ( A ) increases relative to bias voltage ( B ). Table 30.2 illustrates this point with measured data at a single drive frequency. Therefore, to obtain good fidelity one would ideally keep the AC drive voltage less

Table 30.1 Representative values of the loudspeaker reactive impedance as a function of frequency for a 10 cm diameter dielectric elastomer loudspeaker. The film is primarily a capacitive load with an assumed nominal capacitance of 5.6 nF. The impedance values do not include the contribution of the DC film resistance.

Frequency Reactive Impedance Magnitude

100 Hz 284 k � 500 Hz 56.8 k � 1 kHz 28.4 k � 2 kHz 14.2 k � 5 kHz 5.7 k � 10 kHz 2.8 k � 20 kHz 1.4 k �

90

80

70

60

50

40

30

200 0.2 0.4 0.6 0.8 1 1.2

Frequency (Hz)

SP

L (d

B)

1.4 1.6 1.8�104

2

1.5 kV DC, 405 V AC

1.5 kV DC, 135 V AC

Figure 30.5 Effect of voltage on the on-axis SPL of a 10 cm diameter EAP loudspeaker. The DC bias for both response curves is 1.5 kV. The AC drive voltage is 135 V for the lower curve and 405 V for the upper curve. The higher voltage increases SPL by 8–10 dB, which compares well with the 9.5 dB increase in vibration amplitude predicted by Eq. (30.2).

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Dielectric Elastomer Loudspeakers 317

than a few per cent of the DC bias, for example, a drive voltage of 100 V or less with a bias voltage of 5 kV. Although it is feasible to operate a speaker in this regime, film lifetime decreases at high DC bias, especially for large-area DE loudspeaker films. With current film technology it is more prac tical to increase SPL by reducing the bias voltage and increasing the drive voltage.

There are at least two approaches for reducing harmonic distortion. Film vibration amplitude increases approximately as the square of voltage, so it is possible to linearize by driving the film with the square root of signal voltage, as reported in [3] . This can be done either electronically or in software.

A second approach is to build a ‘ push–pull ’ DE loudspeaker [8] . This is the analogue of a push–pull electrostatic loudspeaker, in which harmonics contributing to distortion are cancelled by oscillating the sound-radiating film between two stationary plates, with opposite-polarity AC drive voltages on each plate. A push–pull DE loudspeaker, shown schematically in Fig. 30.6 , consists of sets of identical films biased mechanically such that they have opposite curvature. This is accomplished most readily by biasing the speaker films with small positive and negative air pressures. When two oppositely curved films are driven by the same AC voltages (but 180° out of phase), the higher order harmonics tend to cancel one another in the far field. Note that this configuration is not equivalent to a dipole loudspeaker: the drive voltages are out of phase, but the two films oscillate in the same direction at any moment in time.

Figure 30.7 is an example of harmonic reduction with the push–pull approach. A pair of loudspeak-ers with an array of 5.5 mm radiating elements was driven at 1000 V DC and 300 V (0–p) AC [8] . At this high AC-to-DC voltage ratio (0.3) the total harmonic distortion (THD) for a single loudspeaker operating alone was 5% or more at frequencies above 2 kHz, more than 25% between 1.7 and 2 kHz, and more than 70% at some frequencies below 500 Hz. (Note that high distortion is a problem for many speaker technologies at low frequencies because large vibration amplitudes are required.) When two speakers were operated together in push–pull mode, the THD dropped dramatically at all frequencies and above 2 kHz the THD dropped to less than 1%.

These test results illustrate the potential of push–pull operation for reducing harmonic distortion in DE loudspeakers. Further development is needed to determine the limits of sound fidelity with dis-tortion compensation, especially at low frequencies. The push–pull approach is effective at reducing harmonic distortion when film element diameters are smaller than wavelength. At 10 kHz the acoustic wavelength in air is about 3.4 cm.

Table 30.2 Total harmonic distortion of a dielectric elastomer loudspeaker, measured at a single frequency (1.2 kHz) below but near resonance (1.45 kHz). The THD increases with increasing ratio of AC drive voltage to DC bias voltage.

Ratio of AC-to-DC Voltage Total Harmonic Distortion at 1.2 kHz

0.1 3.5% 0.2 6.1% 0.3 8.7% 0.4 10.4%

Soundradiation

Harmonics cancelin far field

Soundradiation

Concave film

Convex film

Bias force Bias forceRH-314522-1

�VAC�

�VAC�

VDCVDC

Figure 30.6 Depiction of a push–pull pair of EAP loudspeaker films. By biasing two films in opposite directions it is possible to reduce harmonic distortion in the far field. It is assumed that the film diameters are less than the acoustic wavelength.

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318 Chapter 30

30.5 LOUDSPEAKER SHAPE EFFECTS

One can always increase the on-axis sound pressure by increasing the total film area of a DE loud-speaker. However, as the diameter of a flat film sound radiator becomes large compared to wavelength, the sound becomes directional. For application as a general-purpose loudspeaker, a flat film must be segmented to avoid creating highly directional beam patterns at higher frequencies. This approach for producing more isotropic radiation is very effective for DE loudspeakers because the DE film fabrica-tion process lends itself readily to film segmentation.

Another approach is to control directionality via loudspeaker shape and here, too, DE speakers are much more amenable than conventional loudspeakers. A loudspeaker can be biased mechanically so that the film surface is flat, concave, or convex. Negative or positive air pressure is an easy way to bias an EAP film to give it either a concave or convex shape, respectively. The bias is a useful speaker design tool and it can even be altered in situ.

Figure 30.8 [7] shows how the on-axis sound pressure changes when the same DE loudspeaker is biased mechanically to yield a concave or a convex film surface. At high frequencies, when the wavelength is small relative to speaker diameter (10 cm), there is no difference between the two speaker configura-tions. Between 1 and 6 kHz, the SPL of the concave loudspeaker is larger by roughly 5 dB because it focuses the on-axis sound in this frequency range. This type of behaviour is expected theor etically [9] – what is unique is that these results come from the same loudspeaker.

The off-axis response is changed even more significantly by shape differences in the EAP film sur-face. The theoretical directivity of a baffled piston ( Fig. 30.9 ) is representative of the directivity of pla-nar film radiators. The off-axis response drops off relative to the centerline response and radiation nulls appear as frequency increases.

80

60

40

20

00 1 2 3 4

Frequency (kHz)

Tot

al h

arm

onic

dis

tort

ion

(%)

Push–pullUncompensated

Figure 30.7 Comparison of measured total harmonic distortion for an uncompensated EAP loudspeaker and a set of EAP loudspeakers operating in push–pull mode. The AC-to-DC voltage ratio was 0.3 for this set of measure-ments. Above 2 kHz the distortion in push–pull operation was less than 1%.

90

85

80

75

70

60

55

50

65

0 0.2 0.4 0.6 0.8 1 1.2Frequency (Hz)

SP

L(dB

)

1.4 1.6 1.8

�1042

Concave speaker film

Convex speaker film

Figure 30.8 Effect of shape on the on-axis SPL. The response curves are for an EAP loudspeaker operating at 1.5 kV DC and 405 V AC. When the speaker is biased so that its shape is concave, the on-axis SPL between 1 and 6 kHz is higher than when it is biased in a convex shape. The same loudspeaker was used for both measurements.

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Dielectric Elastomer Loudspeakers 319

0

�5

�10

�15

�20

�25

�30

�35

�40

�45

�500 10 20 30 40 50 60 70 80 90

Angle from centerline (deg)

Dire

ctiv

ity (

dB)

1 kHz (ka � 0.9)

f � 1 kHzf � 2 kHz

f � 5 kHzf � 10 kHz

2 kHz (ka � 1.8)5 kHz (ka � 4.6)10 kHz (ka � 9.1)

Figure 30.9 Theoretical directivity for an ideal piston radiator of 10 cm diameter in a rigid baffle. At higher fre-quencies, for which the acoustic wavelength is less than the piston diameter, there are nulls in the off-axis sound radiation. The directivity at all frequencies is normalized to 0 dB at 0° (corresponding to on-axis radiation).

0

�5

�10

�15

�20

�25

�30

�35

�400 10 20 30 40 50 60 70 80 90

Angle from centerline (deg)

Dire

ctiv

ity (

dB)

(1) 2.2 kHz (ka � 2.0)

(2) 5.5 kHz (ka � 5.0)

(3) 6.6 kHz (ka � 6.0)

(4) 8.8 kHz (ka � 8.0)

(1)

(2)

(3)

(4)

Figure 30.10 Measured directivity of a 10 cm diameter EAP loudspeaker, biased so that the speaker has a slightly concave shape (the speaker plenum is at negative pressure). The loudspeaker directivity is similar to that of the ideal piston in Fig. 30.9.

The measured directivity of a DE loudspeaker of the same diameter (10 cm) is shown in Fig. 30.10 . This loudspeaker had a small negative-pressure mechanical bias so that the film surface was slightly concave. A very different directivity response ( Fig. 30.11 ) was obtained when the film was biased with positive pressure so that its shape was convex. Although the SPL compared with the centerline SPL still decreases with angle, there are no major nulls over the frequency range shown (to 8.8 kHz or ka = 8). The convex surface ( Fig. 30.12 ) is much more like an ideal radiator in the sense that its sound radiation is more isotropic.

The capabilities of building segmented loudspeakers from a single film and of building speakers of different surface profiles make DE loudspeakers extremely versatile from an engineering design stand-point. The response at all receive angles can be tailored by choosing appropriate speaker physical shape and segmentation.

30.6 APPLICATIONS

DEs can be implemented into both low-end and high-end loudspeakers. It is straightforward to build simple DE loudspeakers for general-purpose sound reproduction, where high fidelity is not critical. Such loudspeakers can be made very inexpensively and even ‘ throw-away ’ loudspeakers are feasible. High-end loudspeakers, in which fidelity, frequency response, and other characteristics are very import-ant are also possible. These loudspeakers would include compensation for harmonic distortion, and would generally entail a level of engineering and development comparable to any good loudspeaker. In the high-end audio market, well-designed DE loudspeakers could compete with electrostatic loudspeak-ers in performance and potentially be lower in cost.

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320 Chapter 30

Near term applications of DE loudspeakers include distributed sources for active noise control, such as for reducing sound from vibrating panels, or quieting noise in automobile cabins. DEs may also be useful as ultrasonic actuators in applications such as medical imaging.

References

[1] Hunt, F. V., Ed. (1954). Electroacoustics: The Analysis of Transduction, and Its Historical Background. American Institute of Physics (for the Acoustical Society of America), New York.

[2] NXT web site (n.d.). www.nxtsound.com .

[3] Heydt , R. , Pelrine , R. , Joseph , J. , Eckerle , J. and Kornbluh , R. ( 2000 ). Acoustical performance of an electros-

trictive polymer film loudspeaker . J. Acoust. Soc. Am. , 107 ( 2 ), 833–839.

[4] Scheinbeim , J. L. , Newman , B. A. , Zhenyi , M. and Lee , J. W. ( 1992 ). Electrostrictive response of elastomeric

polymers . ACS Polym. Prepr. , 33 ( 2 ) , 385–386.

[5] Zhenyi , M. , Scheinbeim , J. , Lee , J. W. and Newman , B. ( 1994 ). High field electrostrictive response of poly-

mers . J. Polym. Sci. B Polym. Phys. , 32 ( 16 ) , 2721–2731.

[6] Pelrine , R. , Kornbluh , R. , Pei , Q. and Joseph , J. ( 2000 ). High-speed electrically actuated elastomers with strain

greater than 100% . Science , 287 , 836–839.

[7] Heydt, R., Kornbluh, R., Eckerle, J. and Pelrine, R. (2006). Sound radiation properties of electroactive

polymer loudspeakers. Proceeding of the SPIE Conference on Smart Structures and Materials , San Diego,

California, USA.

[8] Heydt, R., Pelrine, R., Joseph, J. and Eckerle, J. (1998). Lightweight polymer film loudspeaker for active noise

control. International Mechanical Engineering Conference and Exposition , Anaheim, California, USA .

[9] Suzuki , H. and Tichy , J. ( 1981 ). Sound radiation from convex and concave domes in infinite baffle . J. Acoust. Soc. Am. , 69 ( 2 ), 41–49.

Figure 30.12 A 10 cm diameter EAP loudspeaker in the SRI International anechoic test chamber. The loudspeaker is biased with positive air pressure to give the surface a convex shape.

0

�5

�10

�15

�20

�25

�30

�35

�400 10 20 30 40 50 60 70 80 90

Angle from centerline (deg)

Dire

ctiv

ity (

dB)

(1) 2.2 kHz (ka � 2.0)(2) 5.5 kHz (ka � 5.0)(3) 6.6 kHz (ka � 6.0)(4) 8.8 kHz (ka � 8.0)

(1)

(2)

(3)

(4)

Figure 30.11 Measured directivity of the 10 cm diameter EAP loudspeaker, when it is biased so that the speaker has a convex shape (the speaker plenum is at positive pressure). Unlike the flat piston radiator or the concave loud-speaker, there are no major nulls in the off-axis sound radiation.

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INDEX

1, 6-hexanediol diacrylate (HDDA), 44 1-DOF antagonistic module, 274 2-DOF spring roll, 92

bending force of, 97–99 longitudinal expansion and bending angle of, 95–97

3-DOF binary manipulator discrete positions of, 270

3-DOF spring roll longitudinal expansion and bending angle, 97

7-DOF binary manipulator prototype, 273

ABAQUS, 172, 173 Acrylic elastomers, x, 33, 35–37, 44, 151, 279, 280, 313

VHB 4910, 170 Acrylic film, 223, 315

VHB 4910, 280 Acrylonitrile–butadiene rubber (NBR), 65 Active area, 4, 9, 83, 147 Actuation, finite-elasticity models of, 159

finite strain model, 160 infinitesimal strain model, 160–161 temporal dependency

dielectric properties, 164–165 mechanical properties, 165–167

Actuator(s), 3, 146 agonist–antagonist actuators, 129, 288, 289 balloon actuators, 87 bending beam actuators, 231–233 binary actuators, 271–272 bistable actuator, 84 bow actuator, 84 bowtie actuators, 83 buckling actuators, 136, 139 bundle elastomeric actuators, 290 carbon nanotube actuators, 18 circular actuator, 172–173 commercial actuators comparisons, 14 configurations, 82, 89, 103

for coupling, to loads, 82 from DESCE, 103–104 exploit flexibility and conformability, 82 tension maintenance and buckling prevention, 83 of thickness-mode DE, 220–223 thickness mode of operation, 85–86

contractile actuators, 110 contractile monolithic linear actuators, 123 conventional actuator, 13–14, 271, 272, 279, 304 cymbal actuators, 81 diaphragm actuators, 81, 132, 232, 233–234 dielectric elastomer actuator (DEA), 69, 79 discrete electromagnetic actuators, 217, 218 efficiency of, 37 electrostatic elastomer actuators, 110 enhanced-thickness-mode actuator, 86 evaluation, 209–210 extending actuators, 110

flexible frame saddle actuator, 84 folded actuators, 126–128, 130 framed actuators, 83, 84, 229–230 helical actuators, 124–126 ionic actuators, 17, 19 IPMC actuators, 20 microactuators see Small devices miniature rolled DE actuators, 207–215 modules, in earthworm robot, 266–267 monolithic actuators, 217 moonie actuators see Cymbal actuators multi-DOF roll actuators, 91 multilayer actuators, 103, 116 multilayer stack contractile actuators, 109 packaged actuators, 43, 85 performance, of DE, 14 proposed actuator, 264 pseudomuscular actuators, 294–296 rolled actuators, 82, 83, 91, 110, 210, 213, 214, 215,

229, 280–284 rolled, photo of, 83 saddle actuator, 84 sheet processing, 104 spring roll actuators, 254 stack

50-layer, 117 cross section of, 112 micrograph, of 100-layer, 112

stack actuators, 85 structure, 83 Universal Muscle Actuator, 85

Adkins theory, 177, 180 Agonist–antagonist actuators, 129, 288, 289 Air-gap electrostatic devices, 232 Analogous ’ Cauchy method, 180 Annelid, 259 Arm wrestling robot, 279

actuator arrangement, 287–288 actuator banks, 288 actuator length, 286 design, 284–286 force transmission mechanism, 288 operating principle, 286 specification for, 285 structure of, 285 wrapped dielectric film length, 286–287

Arrayed pin actuator system, 242–244 Artificial motor unit fibres, 294–296 Artificial muscle, 193, 195, 251, 301, 306, 307, 308, 312

biomimetic applications of, 198 Artificial Muscle, Inc. (AMI), 85, 102, 301 Artificial muscle technology, 14, 15 Atomic force microscopy (AFM), 73 Axial contraction, 124, 126, 284

of folded actuator with rectangular cross-section, 127

Axisymmetric model, 172

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322 Index

Balloon actuators, 87 Barium titanate (BaTiO 3 ), 60, 64 Benzoyl peroxide, 44 Bi-directional tilters, for pointing/ positioning system,

130–131 Binary actuation, 270–271

binary actuators, 271–272 binary robotic systems with DEAs, 273–275

binary manipulation, 273–274 space exploration robots locomotion, 274–275

DEA properties, 272–273 using DEA, 276

Bioinspired actuation mechanisms, 128–129 Biomedical devices, 224–225 Biomimetic robots

crawling robots, 252 EPAM-enabled robots

first generation of, 253–255 future generation of, 255–257

flying robots, 252 robot actuator properties, 253 swimming robots, 252

Bi-phalangeal finger, 293 Bistable actuator, 84 Bistable module

antagonist, 274 binary manipulator, 273 specifications, 274 using single actuator, 274

Bizzi model, 291 Böttcher equation, 58 Bow actuator, 84 Bowtie actuator, 83

rotary motor based on, 87 Braille cell, assembled, 244 Braille cell layers, 243 Braille display, 118, 223

electrode layout for, 120 Braille display system, 239–240

arrayed pin actuator system, 242–244 cell design

basic actuation principle, 240–242 embedded controller and driving circuit

organization of, 244–245 experimental evaluation of, 246–247 physiological study, for standardization, 240

Braille display unit, 244 Braille tablet, 244 Breakdown field, 53 Breakdown strength see Breakdown field Bruggeman integration method, 59 Buckling actuators, 136, 139

piezocapacitive sensors, 134–135 array of, 139

piezoresistive sensors, 133–134 prototype devices, 135–140 with integrated displacement sensor, 132

Bundle elastomeric actuators artificial motor unit fibres, 294–296 compliance control, to dynamic case, 296–297

compliance operator, 297–298 Feldman ’ s muscle model, 291–294 pseudomuscular actuators, 294–296 stiffness control, of biomimetic systems, 290

Buoy generators, 153, 154

Carbon blacks, 61 percolation threshold for, 71

Carbon nanotube, 19, 20 actuators, 18 fillers

percolation threshold for, 62 Cauchy method, 180 Central control unit (CCU), 296 Central nervous system (CNS), 291 Circuit board architecture, 245 Circular actuators, 172

experiments with, 170–171 finite element calculation of, 172–173

Closed-loop pneumatic system, case study, 303–304 Commercial actuators and issues

electronics and power supply low operating voltage, 310 power supply volumes, 310–311

manufacturing, improvements in economies of scale, 310 strategy, 309–310

manufacturing process development, 307 performance, improvements in

designed flexibility, 308–309 efficiency, 307–308 fundamental EPAM advantages, 308 power density, and energy density, 307

power supply electronics and muscle actuator, integration of, 312

robustness, improvements in, 304 environmental, 305–306 mechanical, 305 reliability, 306

UMA platform, 301–302 closed-loop pneumatic system, 303–304 DA50 positioner, 302–303 DP70-2 pump, 303 DV35 proportional valve, 303 fundamental design, 302

Compliance control, to dynamic case, 296–297 Compliance operator, 297–298 Compliant electrodes

conductive filters, in insulating matrix, 69–70 cured electrodes, 71 particulate electrodes, without binding materials, 71 percolation phenomena, for conducting compos-

ites, 70–71 metal films, 71–73

corrugated electrode deformation, 73–74 soft conducting materials, 69 solutions, materials and technologies, 69 unconventional electrode materials

ion implantation, 75 platinum salt reduction, 75

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Index 323

self-assembled gold nanoparticle, rubber compos-ites, 74–75

Computer controlled actuator electromechanical test stand, 105

Conducting polymers, 17–18, 19, 62 Conductive fillers, 61–62

in insulating matrix, 69–70 cured electrodes, 71 particulate electrodes, without binding materials,

71 percolation phenomena, for conducting compos-

ites, 70–71 Configurations, for DEAs, 79–80

areas, arrays and multifunctionality, 87 for coupling, to loads, 82 design issues and unique features, 80–81 flexibility and conformability, 82 generators, 87 motor configurations, 86–87 sensors, 87 tension maintenance and buckling prevention, 83 thickness mode of operation, 85–86 tunable structures, 87–88

Confocal laser scanning microscopy (CLSM), 73 Constant volume assumption, 5–7 Constitutive model, 171–172 Constitutive stress–strain-field relationship, 182–183 Contractile actuators, 110

space application of, 130 Contractile monolithic linear actuators, 123

applications bi-directional tilters, for pointing/positioning sys-

tem, 130–131 bioinspired actuation mechanisms, 128–129 hand splints, for rehabilitation, 128 lightweight flexible space structures, 129–130

folded actuator, 126–128 helical actuator, 124–126

Conventional actuators, 13–14, 271, 272, 279, 304 Conventional portable FFDs, 209 Conventional windmills, 154 Copper-coated phospholipidic tubules, 65 Copper phthalocyanine olygomer, 60, 62 Corrugated electrode

deformation of, 73–74 design, 72

Counter-opposed dielectric elastomers, 144 Coupling efficiency, 38 Crawling robots, 252 Creep and stress relaxation, 41 Crosslinking reaction see Vulcanization Cured electrodes, 71 Cycle life, 15 Cymbal actuators, 81

DA50 positioner, 302–303 DA50-2, 303 DE loudspeakers, 87, 90

applications, 319–320 design, and operation, 313–314

harmonic distortion, 316–317 performance, 315–316 shape, effects of, 318–319

Debye model, 52, 53 Design for Assembly (DFA), 309 Design for Manufacturing (DFM), 309 Design parameters and modelling, 220–223 Diaphragm actuators, 81, 132, 232, 233–234

based on IPN composite films, 49 Diaphragm configuration, of DE actuators, 180–182 Dielectric breakdown, 53 Dielectric constant, of polymers

improving methods, 54, 56–57 Dielectric elastomer actuators (DEAs), 14, 159, 193,

207, 237, 245, 253, 271 advantages of, 196–197 analytical model, 272 binary robotic systems, 273–275 diaphragm configuration, 180–182 geometry of, 69 configurations for

areas, arrays and multifunctionality, 87 for coupling, to loads, 82 design issues and unique features, 80–81 flexibility and conformability, 82 generators, 87 motor configurations, 86–87 sensors, 87 tension maintenance and buckling prevention, 83 thickness mode of operation, 85–86 tunable structures, 87–88

high-strain actuation of, 159 powered ankle-foot orthosis

application of, 200–201 properties of, 272–273

Dielectric elastomers with smart compliant electrodes (DESCE)

actuator configurations, 103–104 sensor configurations, 106–107 sheet, 106 testing of

active equilibrium electromechanical properties, 105

chemical properties, 105 dynamic electromechanical properties, 106 electrical properties, 105 mechanical properties, 104–105

Dielectric fillers, 60–61 Dielectric mixing rules, 55, 58–60 Dielectric permittivity, of elastomers

field-structured composites, 64 of polymer materials, 53–55 random composites

conductive fillers, 61–62 dielectric fillers, 60–61 dielectric mixing rules, 55, 58–60 dielectric strength of, 63–64 mechanical properties of, 62–63 semiconconductive fillers, 61–62

synthetic polymers, 65–66

Index-I047488.indd 323Index-I047488.indd 323 12/7/2007 7:35:50 PM12/7/2007 7:35:50 PM

324 Index

Dielectric strength failure, 276 Direct compression, 261–263 Discrete electromagnetic actuators, 217, 218 Displacement amplification, 263 Distributed generator application, 154–155 DP70-2 pump, 303, 304 DV35 proportional valve, 303 Dynamic Mechanical Analyzer (DMA), 38 Dynamic scanning actuation (DSA), 245

Earthworm locomotion, 260–261 Earthworm robot

building and operating of, 266–268 Effective mechanical pressure, 261 Effective-medium approximation (EMA), 70 Elastomer helix, 124 Elastomer strains, 10 Elastomers, 25–26 Electrical effects

in continuous dielectric media, 178–179 Electrical safety issues, 214 Electroactive polymer (EAP), 208, 218, 259

applications for, 310 flex, 254

Electroactive polymer artificial muscle (EPAM), 143, 253, 256, 301, 302, 304–312

fin under water testing, 257

single jumping robot, 255 skitter, 254 see also Commercial actuators

Electroactive polymer bicep, 197–199 Electro-elastic membrane theory, 179–180 Electromagnetic generators, 151, 152, 153 Electromechanical axial strains, 124, 127 Electromechanical coupling efficiency, 38 Electromechanical measurement

circular actuator arrangement for, 171 Electromechanical transduction effects, in DEs

analysis of, 7–8 constant volume assumption, 5–7 resultant Maxwell stress, 5–7 sensors, 10 stiffness modulation, 10–12 strain response and stability, 8–9 structure of, 3–5

Electromeric silicone helices, 125 Electrostatic effect, 178 Electrostatic elastomer actuators, 110 Electrostatic pressure

elastic dielectric film deformation, 109 Electrostriction, 69, 178 Electrostrictive effect, 178 Electrostrictive polymers, 16 Embedded controller and driving circuit, 244–245 End-linked curing system, 28 Energy cycles, 150 Energy density

physics basis, for DEs, 227–228 and power density, 307

Enhanced-thickness-mode actuator, 86 for microfluidics and haptics, 233–235

Environmental robustness, 305–306 EPAM-enabled robots

first generation of, 253–255 future generation of, 255–257

Equilibrium Point Theory, 291 European Space Agency (ESA), 129 Extending actuators, 110 Extensional sensor, 108

Feldman ’ s muscle model, 291–294 Ferroelectric polymers, 16 Field-structured composites, 64 Finite element simulation, 172

circular actuator, 172–173 optimization procedure, 173–174 uniaxial behaviour, 174

Finite strain model, 160, 161–164 Flapping wing robot, 257 Flex, 254 Flex-foot cheetah®, 195 Flexible frame saddle actuator, 84 Flocking, 201 Flying robots, 252 Folded actuator, 126–128, 130

with circular cross-section, 126 development of, 128 properties of, 126 protype, 127

bi-directional tilter, 131 with rectangular cross-section, 126

axial contraction of, 127 Force-displacement behaviour, 213 Force feedback demonstration devices, 215 Force feedback devices (FFDs), 207

body-based FFD, 208 demonstration devices, 215 electrical safety issues, 214 actuator evaluation, 209–210 components and principles of operation, 208–209

conceptual approach, 209 ground-based FFD, 207–208 miniature rolled DE actuators, 207–215

design and manufacturing process, 210 experimental characterization of, 213–214 principle of operation, 210 theoretical consideration, 210–213

requirements, 209 Force-voltage behaviour, 213 Framed actuator, 83, 84, 229–230

for micro-optical and electrical devices, 231

Generator mode, devices and applications advantages of, 152 analysis of, 149–150 distributed generator application, 154–155 point generator application, 152–154 practical considerations, 150–152 principle, of DE, 146–149

Index-I047488.indd 324Index-I047488.indd 324 12/7/2007 7:35:50 PM12/7/2007 7:35:50 PM

Index 325

Generators and sensors, 236 Geometrical nonlinearities, 114–115 Gradient IPN, 443–44 Green membrane theory, 177, 178, 180 Ground-based devices, 207–208 GUI interface, 246

Hand splints, for rehabilitation, 128, 129 Haptic displays, 223–224, 234 Harmonic distortion, 313, 316–317 HARRIS ICM7555, 108 Heel-strike generators, 153 Helical actuator, 124–126 High aspect ratio thickness-mode actuators, 86 High-end loudspeaker, 319 High-performance acrylic and silicone elastomer,

35–37 basic model, of operation, 33–34 dynamic response

creep and stress relaxation, 41 efficiency, 37–39 speed, 39–41

environmental considerations, 41 future, 41–42 polymer performance

overview of, 34, 35 High-performance electroactive polymers

conventional actuators, 13–14 ionic actuators, 17

carbon nanotube actuators, 18 conducting polymers, 17–18 ionic polymer/metal composites, 18–19

muscle, 14–16 relaxor ferroelectric polymers, 16–17 shape memory alloys, 19

Hit recognition rate (HRR), 246, 247 Hooke ’ s law, 159, 220 Hyperelastic–viscoelastic models, 169

IEC 60479-2, 214 Inchworm-like propulsion system, 229, 231 Infinitesimal strain model, 160–161 Insulating matrix, 69–70 Interpenetrating polymer networks (IPNs)

concepts for, 43–44 future, 50 preparation of

in highly prestrained elastomer films, 44 synthesis of, 44 VHB-based IPN DE

actuation without external prestrain, 48–49 mechanical properties, 46–48 microstructures, 45–46 preserved prestrain with curable additive, 44–45

Ion implantation, 75 Ionic actuators, 17

carbon nanotube actuators, 18 conducting polymers, 17–18 ionic polymer/metal composites, 18–19

Ionic polymer/metal composites (IPMC), 18–19

Jumping robots, 255

Kerner–Böttcher equation, 58

Lab-on-a-chip microfluidic devices, 224, 225 Landau–Lifshitz mixing rules, 55 Landauer equation, 58 Laser displacement sensor, 265 Latex IPN, 43 Leakage, 151 Life-sized human skeleton model, 198 Lightweight deployable booms, 129 Lightweight flexible space structures, 129–130 Linear-type generators, 153–154 Lithium niobate, 231 Lorentz local field, 64 Lorentz–Lorenz equation, 58 Loss factor, 51 Loss tangent, 51 Loudspeakers see DE loudspeakers Low-end loudspeaker, 319 Lumped parameter model, 147

Magnetic resonance imaging (MRI), 273 Mammalian skeletal muscle, 15 Material modelling, 171–172 Material strength failure, 276 Matrix actuators, for tactile display, 119 Maxwell–Faraday electrostatics theory, 177, 180 Maxwell–Garnett equation, 58 Maxwell stress, ix, 105, 178, 261, 276–277 Maxwell–Wagner equation, 58 Maxwell–Wagner polarization, 52, 61 MC01 controller, 311 MC02 controller, 311 Mechanical robustness, 305 MERbot, 91, 100–101, 254, 255 Metal coatings, 71 Metal films, for compliant electrodes, 71–73

corrugated electrode deformation, 73–74 Metal Rubber™, 75, 237 Microactuators see Small devices Micro-annelid-like robot, actuated by artificial muscles,

259–260 actuation ideas

direct compression preview, 261–263 displacement amplification, 263

earthworm locomotion, 260–261 earthworm robot, building and operating of, 266–268 proposed actuator building, 264 simulation, and experimental results, 265–266

Microbot mission concept, 274 Microbot prototype performing hops, 276 Micro-controller, 244–245 Microelectromechanical systems (MEMS), 118, 227–

228, 232, 236, 237 and small-scale application, 230 see also Small devices

Microfluidic devices see Small devices Micro-optical devices see Small devices

Index-I047488.indd 325Index-I047488.indd 325 12/7/2007 7:35:50 PM12/7/2007 7:35:50 PM

326 Index

Microrobots, 229–230 Miniature rolled DE actuators

blocked strain activation, axial force, 212–213 design and manufacturing process, 210 experimental characterization of, 213–214 non-uniform pressure distribution, 210 non-uniform thickness distribution, 211 principle of operation, 210

MIT SMA powered binary manipulator, 272 Modelling DE membranes, 177

constitutive equation, 182–183 diaphragm configuration, of DE actuators, 180–182 electrical effects, in continuous dielectric media,

178–179 electro-elastic membranes theory, 179 qualitative analysis, numerical results, 183–187

Monolithic actuator, 217 Mooney–Rivlin equation, 165 Mooney–Rivlin model, 182 Moonie actuators see Cymbal actuators Motor configurations, 86–87 Multi-DOF roll actuators, 91

2-DOF spring roll bending force, 97–99 longitudinal expansion and bending angle, 95–97

3-DOF spring roll longitudinal expansion and bending angle, 97

challenges, 99–100 MERbot, 100–101 pivot rolls, 93–94 production outlook, 102 roll fish, 101 spine rolls, 94–95 spring rolls, 92–93 Sushi rolls, 101

Multi-DOF roll fish, 101 Multifunctional electroelastomer rolls (MERs), 91, 254 Multilayer actuator, 103, 116

Braille application, 119 Multilayer stack contractile actuators, 109

applications peristaltic pump, 120–121 tactile display, 118

characterization dynamic behaviour, 117–118 quasi-static behaviour, 117

modelling electrical model, 115–116 geometrical nonlinearities, 114–115

technology material requirement, 110–111 realization, 111–112 results, 112–113

Muscle, 14–16 Muscle-like actuation, 128, 193, 256 Mylar film, 134

Nafion®, 18 Nanosonic Inc., 237 Natural muscle, 153, 251, 253, 256

vs. direct-drive electric actuation technologies, 196 reverse operation comparison, 203

Negative air pressure, 318 Negative spring constant ’ approach, 84 Neo-Hookean model, 160, 162 Newton ’ s second law, 164, 165 Nonlinearity elasticity theory, 177 Non-prestrain actuator construction, 264 Number recognition rate (NRR), 246

Off-axis response, 318, 319 Ogden equation, 162 Ogden model, 182, 184 On-axis sound pressure, 318 Optimization procedure, 170–171, 173–174 Organic light emitting diodes (OLEDs), 309 Original Equipment Manufacturer (OEM), 301, 305, 312 Orthotics and prosthetics, 193

active system, 195 DEA, advantages of, 195–197 of DEA application, 197

to bionics, 193 design criteria, 194–195 dielectric elastomer-powered VAD, 201–203 electroactive polymer bicep, 197–199

dielectric artificial muscles, biomimetic applica-tion, 198

limitations of, 203–204 passive system, 195 powered ankle-foot orthosis

to drop-foot gait pathology treatment, 199–201

P–Vol curve, 185, 187 Packaged actuator, 43, 85 Particulate electrodes

without binding materials, 71 Passive layer, 218, 220, 221, 223 Passive-matrix configuration

with periodic refreshment, 120 Percolation phenomena

for conducting composites, 70–71 Peripheral control unit (PCU), 296 Peristaltic pump, 120–121 Perspex cylinder, 215 Photolithography, 72, 112 Physical and chemical properties, of DEs

elastic modulus, 26–28 elastomers, 25–26 processing, 31–32 swollen networks, 31 vulcanization, 28–30

Piezocapacitive sensing, 134–135 Piezoceramics, 13, 14 Piezoelectrics, 13, 14, 80, 109, 180, 232, 272 Piezoresistive sensing, 133–134 Pivot rolls, 93–94, 256 Platinum salt reduction, 75 Point generator application, 152–154 Poisson ’ s ratio, 34, 47, 142, 220, 221 Polder–Van Santen equation, 58

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Index 327

Poly(copper phthalocyanine) (poly(CuPc)), 62 Poly(ether urethane)/poly(ethyl methacrylate) (PU/

PEMA), 28 Poly(ethylene-co-vinyl acetate) (EVA), 62 Poly(vinylidene fluoride–trifluoroethylene–chlorotrif-

luoroethylene) (P(VDF–TrFE–CTFE)), 62 Polyacrylates, 27, 181 Polyanilines (PANIs), 62, 65 Polydimethylsiloxane (PDMS), 25, 64, 124, 135 Poly-ethylene–glycol–diacrylate (PEGDA), 60 Polyisoprenes, 27 Polymer engines, 154, 155 Polymer film deformation, constraining

to single output direction, 82 Polymers, 3, 4, 13, 81, 154 Polyphthalocyanines, 62 Polypyrroles, 62, 73 Polythiophenes, 62 Polyurethanes (PUs), 25–26, 28, 50, 61 Polyvinylidenefluoride (PVDF), 16, 17 Positive air pressure, 318, 309 Power density, 307 Power supply electronics, of commercial activators

low operating voltage, 310 and muscle actuator, integration of, 312 power supply volumes, 310–311

Powered ankle-foot orthosis, 199–201 currnet technology

application of DEA, 200–201 Prestrained circular actuator modeling, 169

experimental data circular actuators, 170–171 uniaxial tensile strength, 170 versus simulation, 174–175

finite element simulation, 172 circular actuator, 172–173 optimization procedure, 173–174 uniaxial behaviour, 174

material modelling, 171 constitutive model, 171–172

Processing, in elastomers, 25–26 Programmable surface modification see Thickness-

mode DE Proof-of-concept, 101, 130, 198 Proof-of-principle devices, 236 Proposed actuation mechanism, schematic view, 241 Proposed actuator

building of, 264 simulation and experimental results, 265–266

Proposed Braille display exploded view, 243 psychophysical experiment of, 247

Prototype devices, of buckling actuators, 135–140 Pseudomuscular actuators, 294–296

mechanical system with, 292 Pseudo-Young ’ s moduli, 47 Pull-in-failure, 160, 271, 272, 276 Pulse width modulation (PWM), 308 Push–pull electrostatic loudspeaker, 317, 318 PZT, 80

Qualitative analysis, numerical results, 183–187 Quasilinear viscoelastic constitutive model, 169, 171 Quasilinear visco-hyperelastic model, 175, 176 Quasi-static behaviour, 117

Radial prestraining, 170 Radio frequency identification (RFID), 107, 309 Random composites

conductive fillers, 61–62 dielectric fillers, 60–61 dielectric mixing rules, 55–60 dielectric strength of, 63–64 mechanical properties of, 62–63 semiconconductive fillers, 61–62

Raybot, 256, 257 Rayleigh equation, 58 Recruitment, 15 Refreshable Braille displays, 223, 234, 235 Relative dielectric constant, 51 Relaxor ferroelectric polymers, 16–17 Rivlin–Adkins assumption, 183 Rivlin–Sawyers equation, 165 Robo-Ray, 256 Robot actuator properties, 253 Robotic arm, 279–280

arm wrestling robot actuator arrangement, 287–288 actuator length, 286 actuator system, 286 design, 284–286 operating principle, 286 wrapped dielectric film length, 286–287

rolled actuators actuator design, 280 layers, number of, 282 operating principle, 281–282

Robustness, improvements in, 304 environmental, 305–306 mechanical, 305 reliability, 306

Rolled actuators, 82, 83, 110, 229 actuator design, 280 layers, number of, 282 operating principle, 281–282 schematic depiction of, 281

Saddle actuator, 84 Sartomer Co, 44 Self-assembled gold nanoparticle, rubber composites,

75 SEM micrographs, 114 Semiconductive fillers, 61–62 Semi-IPN, 44 Sensor configuration, 106–107

variety of, 89 Sensors, 10, 236 Sequential IPN, 44, 47 Setae, 260 Shape memory alloys (SMA), 14, 19, 20, 195, 256, 259,

272

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328 Index

Sigma Aldrich, 44 Silicon–oxygen bond, 28 Silicone helices, 124, 125 Silicone KE441, 262, 264 Silicone(s), 111

elastomers, 27, 28, 35–37, 38, 39, 40, 41–42, 50, 71, 103, 151, 306, 313

networks, 29–30 Sillars mixing rules, 55 Simulation, in DE technology, 169

and experimental data, 174–175 and experimental results, 265–266 finite element simulation, 172–174

Simultaneous interpenetrating networks (SIN), 43 Skitter, 100, 254 Small devices

challenges, 236–237 materials, and fabrication basis, 228–229 physics basis, 227–228 representative applications

diaphragm and enhanced-thickness-mode actua-tors, 233–235

framed, and bending beam actuators, 231–233 generators, and sensors, 236 microrobots, 229–231

Smart compliant electrode principles of, 104 see also Compliant electrodes

Snake robots, 255–256 Soft conducting materials, of compliant electrodes,

69 Sound pressure level (SPL), 315–316, 318 Space exploration robots locomotion, 274–275 Speakers see DE loudspeakers Spider configuration, 81, 82 Spine rolls, 94–95 Spring roll actuators, of DE, 254, 280, 282, 283, 284,

287 Spring rolls, 82

multi-DOF spring rolls, 91, 92–93, 254 applications, 100–101 bending force of, 97–99 longitudinal expansion, and bending angle of,

95–97 see also Spring roll actuators

SRI International, 85, 89, 234, 253, 301 Stack actuators, 85

see also Multilayer stack contractile actuators Stack-like actuators, 85, 123 Standard Braille cell, 242, 243 Step-down converters, 150, 151 Step-up converters, 150–151 Stiffness modulation, in DE, 10–12 Stress–strain behaviour, 46, 47, 74, 100 Stress–strain characteristic, 117 Stress–strain curves, 42, 63, 66 Stress–strain relation, 161, 162, 294 Styrene–butadiene rubber (SBR), 27–28 Sushi rolls, 91, 101 Swimming robots, 252–253

Swiss Federal Laboratories for Materials Testing and Research (EMPA), 279, 280, 289

Swollen networks, 31 Synthetic polymers, 65–66

Tactile cell design actuation principle, 240–242

Tactile display, 118–119, 239, 240 Tensile load, 85, 220 Texture feedback, 217, 225 Thermoplastic IPN, 44 Thickness-mode DE, 217–218

actuator configuration, 218–219 applications of

biomedical devices, 224–225 haptic displays, 223–224 mechanical devices, 225

design parameters, and modelling, 220–223 Time-dependent behaviour, of DE, 27, 261 Timoshenko equation, 48 Titanium dioxide (TiO 2 ), 60 Transduction, in DE operation, 240 Trifunctional trimethylolpropane trimethacrylate

(TMPTMA), 44, 45, 46

Unconventional electrode materials ion implantation, 75 platinum salt reduction, 75 self-assembled gold nanoparticle, rubber composites,

74–75 Uniaxial behaviour, 174, 175 Uniaxial tensile strength, 170 Uniaxial tensile test data, 169, 170 Unidirectional compliant electrode, 72 Universal Muscle Actuator TM (UMA) platform, 85,

301–302 closed-loop pneumatic system, 303–304 DA50 positioner, 302–303 DP70-2 pump, 303 DV35 proportional valve, 303 fundamental design, 302

Variable damping, 144–145 devices, 141

Variable stiffness mode, devices and applications, 141–142

principles of, 142–144 variable damping, 144–145

applications, 145 Ventricular assist device (VAD), 201–203

cardiac tissue, mechanical actuation of, 202–203 specific issues, 203

VHB-based IPN DE actuation, without external prestrain, 48–49 mechanical properties

after release, 47–48 before release, 46–47

microstructures, 45–46 preserved prestrain, with curable additive, 44–45

VHB-poly(HDDA), 45, 46, 47, 48, 49

Index-I047488.indd 328Index-I047488.indd 328 12/7/2007 7:35:51 PM12/7/2007 7:35:51 PM

Index 329

VHB-poly(TMPTMA), 45, 46, 47, 48, 49 VHB™ 4190, 166, 167 Viscoelastic behaviour, of DE, 114, 200, 261 Vulcanization, 28–30

Wacker Elastosil P7670, 112, 116 Wacker Elastocil ® RT 625, 103 Wagner theoretical scheme, 55, 58

Wave-power generator, 153, 155 Wind-power generator, 153

Young ’ s modulus, 26, 46, 47, 48, 72–73, 117, 162

Zwick (Z010) machine, 170 Zwick multisens, 170

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