A high precision micropositioner with five degrees of freedom based on anelectromagnetic driving principleWanjun Wang and Tian He Citation: Review of Scientific Instruments 67, 312 (1996); doi: 10.1063/1.1146587 View online: http://dx.doi.org/10.1063/1.1146587 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/67/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Note: Development of a high resolution six-degrees-of-freedom optical vibrometer for precision stage Rev. Sci. Instrum. 82, 056101 (2011); 10.1063/1.3585021 A high-precision five-degree-of-freedom measurement system based on laser collimator and interferometrytechniques Rev. Sci. Instrum. 78, 095105 (2007); 10.1063/1.2786272 Development of a three-degree-of-freedom laser linear encoder for error measurement of a high precision stage Rev. Sci. Instrum. 78, 066103 (2007); 10.1063/1.2743165 Development of a laser-based high-precision six-degrees-of-freedom motion errors measuring system for linearstage Rev. Sci. Instrum. 76, 055110 (2005); 10.1063/1.1915520 A high precision micropositioner based on magnetostriction principle Rev. Sci. Instrum. 63, 249 (1992); 10.1063/1.1142967

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A high precision micropositioner with five degrees of freedom based on anelectromagnetic driving principle

Wanjun Wang and Tian HeMechanical Engineering Department, Louisiana State University, Baton Rouge, Louisiana 70803

~Received 30 August 1995; accepted for publication 11 October 1995!

A five degrees of freedom high precision micropositioner based on spring suspension andelectromagnetic driving has been designed, constructed, and tested. The device consists of two parts:a moving part and a stationary part. The moving part, named as ‘‘motor’’, is formed with a rigidframe and three groups of coils fixed on it. The stationary part of the device, called ‘‘stator’’,includes a chassis and twelve U-shaped magnetic ‘‘shoes’’. The motor is attached to the stator withflat springs whose linear suspension allows it to move in all dimensions except the rotation aroundz axis. The coils have been laid out in such a way that fractions of them pass through the air gapsbetween the facing magnets in the magnetic shoes. When electrical currents are supplied to the coils,the resultingLorenzforces drive the motor to move in the five degrees of freedom allowed by thespring suspension. Since the system is inherently stable and there is no mechanical friction, theopen-loop resolutions of the device are found to be limited only by that of the 12-bit D/A boardused. A closed-loop translation resolution of 0.3mm has been achieved over a working space of 180mm by 180mm by 680mm. A closed-loop rotation resolution of 2.7331026 rad has been achievedover a working space of 1.3831023 rad. Potentially the device can be used for high precisionmicroprobing and testing, cellular biology, microsurgery, and testing of micromechanical devices inthe fast developing MEMS area. ©1996 American Institute of Physics.@S0034-6748~96!05501-X#

I. INTRODUCTION

High precision, micropositioning devices are very essen-tial in such applications as high precision microprobing,probing and analysis of integrated-circuit structures, manipu-lations of individual cells and micro-organisms, microsur-gery, and testing of micromachines. Therefore, a largeamount of research work has been dedicated to the field ofmicropositioning and microactuation in the past ten years.Different mechanisms and methods have been introducedand investigated for various purposes. In general, these re-search efforts can be divided into several major categories:stages for scanning probe microscopy~SPM!, microposition-ing or micromanipulating devices, diamond turning ma-chines, and the area of microelectromechanical systems~MEMS!.

Most of the research efforts on micropositioning for ap-plications in SPM are based on the converse piezoelectriceffect of the piezoelectric ceramic materials.1–7 These stageshave very limited travel ranges, mostly in the range of sev-eral microns, therefore cannot be used for the investigationof large area specimens. Special means such as multiplyingflexures, or an inertial slider mechanism must be used toachieve larger travel ranges. For example, Bordoniet al.have achieved a large working range and a step size down to5 nm using an inertial slider piezoelectric micropositioner.2

Blackfordet al. have obtained a step size as small as 10 nmin two dimensions by the inertial slider method.3,4 Similarresults with similar approaches have also been reported byLiboulle et al.5 Curtiset al. developed a compact piezoelec-tric micropositioner with a 1.4 cm range of motion.6 A three-dimensional micropositioner based on inertial slip-stick mo-tion has also been reported by Goken.7 However, the mainconcerns in these devices are the scanning speed, the step

size, and the working range, and not for a specific targetposition. It is also very difficult to add any more degrees offreedom than three translations inx, y, z dimensions tothese devices. They do not have enough load capacity andrequire a high voltage power supply. Efforts have also beenmade to develop high precision positioning devices based onother mechanisms, such as the magnetostrictive effect. Wangand Busch-Vishniac also reported a novel two degrees offreedom precision micropositioner based on Terfenol-D mag-netostrictive material.8 It is capable of addressing a 100mmworkspace with open-loop repeatability of 50 nm. Its open-loop accuracy is limited by the thermal expansion and hys-terisis effect.

In the fast-developing field of microelectromechanicalsystems~MEMS!, many devices capable of one degree-of-freedom movement have also been reported.9–13 However,these systems are themselves in microsizes, and can onlyhandle microscopic objects. They are not in the same cat-egory as the positioning system described in this article.

In conventional machining~especially in ultraprecisiondiamond turning! and lithography applications, there are alsorequirements for high precision positioning. The main con-cerns in these cases are the precision rotation of shafts or theprecision feed of tools. Accuracy of nanometer or submicronscale has been achieved.14,15 The accuracy is usually ob-tained by ball screws, air bearings, hydraulic bearings andmagnetic bearings, which results in complicated configura-tion and big, heavy structures.

Since mechanical friction is one of the most importantfactors limiting the resolution and accuracy of high precisionpositioning devices, magnetic levitation technology has beenused by some researchers to eliminate friction and achievehigh resolution. Magnetic actuation for high precision appli-cations has been strongly advocated by Busch-Vishniac.16

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Jeong and Busch-Vishniac reported a magnetic levitationbased microrobot which has six degrees of freedom withfingertip size and a weight of several grams.17 It has an ac-curacy of about 10mm and a very limited payload. Holliset al. also reported a magnetically levitated, six degrees offreedom ‘‘fine motion wrist’’ with a very complicated struc-ture and high nonlinearity.18 Hunteret al. reported a micro-manipulator which allows manipulation and mechanical test-ing of single cells with a resolution of around 10 nm withina working space of a 1 mmsphere.19 The main disadvantageof the magnetically levitated, free-floating positioning de-vices is that they are inherently unstable without closed-loopcontrol. Their accuracy and resolution are therefore limitedby the sensing systems and require heavy computation fordigital control.

The high precision five degrees of freedom microposi-tioner presented in this article is based on spring suspensionand electromagnetic driving. This combination helps toeliminate mechanical friction without introducing the inher-ent unstability of the electromagnetically levitated systems.This means that the device has open-loop stability. Thereforeits displacement resolution becomes independent of the sens-ing system and the computation burden is dramatically re-duced. The prototype device has an overall physical size of 3in.33 in.33.5 in. and only has a single moving element andno mechanical joints. The micropositioner has been designedto have five degrees of freedom: linear translationsx, y, zand rotationsf and c out of thex-y plane, with the bestaccuracy possible. It may also be called a ‘‘multi-degrees offreedom micromotor.’’

The next section will discuss the design and analysis ofthe micropositioner. Experimental results are presented inSec. III, and concluding remarks are made in last section.

II. DESIGN AND ANALYSIS OF THEMICROPOSITIONING SYSTEM

The block diagram of the micropositioning system isshown in Fig. 1. It consists of four subsystems: the micropo-sitioner, the sensing system~including position sensitive de-tectors and signal processing circuits!, the power driving cir-cuits, and the microcomputer with 12-bit D/A and A/Dboards. The microcomputer takes in the specified target po-sition and the digitized position signals from the sensing sys-tem. The digital controller compares the measured positionwith the target one and sends control signals to correct anyexisting error. The 12 bit D/A board transfers these digitalsignals into analog form and then supplies them to drivingcircuits, where the voltage signals are converted to current

signals. These current signals are then sent to the electricalcoils to drive the micropositioner to the target position.

A. Design of the micropositioner

The design of the micropositioner is shown in the sche-matic diagrams of Fig. 2. The micropositioner consists of astationary part and a moving part. The stationary part of thedevice, hereafter called the ‘‘stator’’, includes an aluminumalloy chassis and twelve U-shaped magnetic ‘‘shoes’’ fixedon it. As shown schematically in Fig. 3~A!, the magneticshoe is formed by two rare-earth permanent magnets facingeach other in opposite poles fixed on a steel bracket func-tioning as magnetic flux path. Very thing steel plates are puton the surfaces of permanent magnets to achieve a uniformmagnetic field in the air gaps of the magnetic shoes. Themoving part, hereafter called the ‘‘motor’’, is formed with arigid frame on which three groups of coils are fixed. Thesecoils are reinforced mechanically against bending. Each

FIG. 1. Block diagram of the system.

FIG. 2. Schematic design of micropositioner.

FIG. 3. Schematic designs of flat springs, magnetic ‘‘shoes’’.

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group of coils and their reinforcing holder is referred to as an‘‘arm’’ hereafter. The arms providing motions in thex-yplane are called ‘‘translational arms’’, and the arm providingthe z-dimensional movement and the out-of-plane rotationsis called the ‘‘rotational arm.’’

The motor is suspended at its two ends by twoberyllium-copper flat springs as shown in Fig. 3~B!. Thesprings are fixed on the chassis and are connected togetherby the frame of the motor at their centers. There is only asingle moving part~the motor! and no mechanical joints inthe device, therefore no mechanical friction is involved.

The magnetic shoes are fixed in such a way that thestraight fractions of the coils on the motor pass through theirair gaps evenly. Thex-direction coils on the top and bottomtranslational arms are in series electrically, so are the twoy-direction coils on the translation arms. This arrangementhelps to increase the translational driving force, thereforeincreasing the working ranges while helping to maintain dy-namic balance. The four coils on the rotational arm can beindividually controlled. They provide thez-directional trans-lation and two rotationsf andc out of thex-y plane. Whenelectrical currents are supplied to the coils,Lorenz forcesexerted on the two translational arms drive the motor tomove inx andy dimensions. TheLorenzforces implied onthe rotational arm translate the motor inz dimension androtate it inf andc dimensions. By controlling the electricalcurrents in the coils, the movements in all five degrees offreedom can be manipulated.

B. Dynamic model of the micropositioner

The electrical coils and the magnetic shoes have beendesigned to eliminate dimensional crosstalk and avoid non-linearity, thus keep the system control straightforward. Tosimplify the modeling of the system, the following assump-tions can be made without introducing significant errors: themagnetic fields in air gaps are uniform; the motor itself is arigid body and is symmetric with respect to the body coor-dinate systemx-y-z; there is no rotation within thex-yplane; and finally the fringe effects and damping are negli-gible. With these assumptions the following equations can beobtained for the system:

X01Kx

MX05

4BNL

Mi 11

BNL

Msin c~ i 41 i 6!, ~1!

Y01Ky

MY05

4BNL

Mi 22

BNL

Msin f~ i 31 i 5!, ~2!

Z01Kz

MZ05

BNL

M~ i 31 i 41 i 51 i 6!, ~3!

f1Kf

I xxf5

BNLd

I xx~ i 42 i 6!, ~4!

c1Kc

I yyc5

BNLd

I yy~ i 52 i 3!, ~5!

whereX0 , Y0 , Z0 are the displacements of the center ofmass of the motor in theX, Y, Z dimensions, respectively;fandc are rotations around theX andY axes;B is the flux

density in the air gap of the magnetic shoes;M is the mass ofthe motor,kx, ky, kz, kf, andkc are the spring constants intheX, Y, Z, f, andc dimensions;i 1 , i 2 , i 3 , i 4 , i 5, andi 6 are the electrical currents supplied to the coils 1, 2, 3, 4, 5,and 6, respectively@see Figs. 2~c! and 2~d!#; N is the numberof turns in each coil;L is the length of each coil contained inthe air gap of the magnetic shoes;d is the distance from thegeometric center of the rotational arm to the straight portionof the coils; andI xx and I yy are the moments of inertia withrespect to body coordinate systemx-y.

From Eqs.~1!–~5!, it can be seen that there exists littledimensional crosstalk. The rotationc is only dependent onthe currents,i 3 and i 5 , the rotationf is only dependent onthe currentsi 4 and i 6 , and i 1 and i 2 control theX and Ytranslations, respectively. The advantage of this dimensionalseparation is that each type of motion can be independentlycontrolled, either in parallel or series.

C. Electromagnetic driving force

The Lorenz force exerted on the current carrying coilscan be estimated theoretically. From magnetic field theory,20

the magnetic flux densityB0 in the middle of the identical,yoked magnets facing each other in attracting positions~as inthe design here! can be expressed as Eq.~6! if the yoke isassumed to have the same thickness as the permanent mag-net:

B052Br

p S tan21AB

2xA4x21A21B2

2tan21AB

2~2l1x!A4~2l1x!21A21B2D , ~6!

whereBr is the flux density of the magnet;A, B, and l arethe width, length, and thickness of the permanent magnet,respectively; 2x is the air gap between the facing magnets.

The magnets used in the design have a size of 10mm320 mm33 mm, the air gap is 6 mm. The NaFeB35rare-earth magnets used have aBr of 12 300 G. For a coil of20 turns with a length contained in the air gap of 20 mm anda current of 5 A supplied, the maximumLorenzforce in thexdimension can be calculated as

~Fx!max54BNLi53.723~Newton!. ~7!

This is a reasonable driving force for the microposi-tioner.

D. Sensing system

A sensing system is needed for two purposes. First, highprecision sensors are necessary for assessing the open-loopperformance of the micropositioner. Second, since the mi-cropositioner is an inherently low-damping system; sensorsare needed for feedback control to avoid oscillatory over-shoot errors when the micropositioner achieves a target po-sition quickly.

For this particular system, a high precision, noncontactsensing scheme is required. Capacitive sensors, acoustic sen-sors~ultrasound type!, and inductive sensors have to be ruled

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out due to the limited measurement range, insufficient accu-racy, and the sensitivity to the electromagnetic fields existingin the micropositioner, respectively.

A sensing system using lateral-effect position sensitivedetectors~PSDs! as the sensing cells is adopted.21–23 Asshown in Figs. 2~A! and 2~B!, three pin-cushion-type PSDs24

and three LEDs are used. The LEDs are fixed on the motorand move with it, and the PSDs are fixed on the chassis.Then the motion of the motor is converted into the relativemovements between the PSDs and LEDs. When the lightbeams from LEDs are projected on the surfaces of the PSDs,photocurrents containing the position information of the mo-tor are generated. These photocurrents are then further pro-cessed by amplifying, adding, subtracting, normalizing, andfiltering. The schematic diagram of the signal processingscheme is given in Fig. 4. To boost the signal to noise ratioand therefore increase the measurement resolution, the lightsignals from LEDs are pulse amplitude modulated~PAM! bysynchronized pulse signals.25–27 Then the modulated photo-current signals are preprocessed and restored to the dc modeby using sample/hold amplifiers. The calibration resultsshows that better than 0.05mm position resolution can beachieved over a working space of 1.2 mm31.2 mm withexcellent linearity using this sensing system. Higher resolu-tion is possible for a smaller working space.

The three LEDs and PSDs are arranged in the followingway: one LED is fixed on each end of the motor, facing atwo-dimensional PSD fixed on the chassis. These two sen-sors provide information on translations within thex-y planeand rotationf andc out of thex-y plane. A third LED isfixed to the side of the motor, facing a one-dimensional PSDfixed on the chassis forz-dimensional measurement. The co-ordinate systems of these sensors are shown in Fig. 2~B!.These five dimensions are necessary and sufficient for deter-mining the five degrees of freedom of the micropositioner.The main advantage of this sensing scheme is its simplicity.There exists a minor disadvantage: rotations of the micropo-sitioner may cause a small amount of changes in thez read-out even when there is no movement of the micropositionerin the z direction. Since the rotating angles involved in thedevice are very small, these errors are negligible. With this

assumption following kinematic transformation equations forthe sensing system can be derived:

X05X11X2

22X22X1

hZ, ~8!

Y05Y11Y2

22Y22Y1

hZ, ~9!

Z05Z, ~10!

f5arctanSY22Y1

h D , ~11!

c5arctanSX12X2

h D , ~12!

whereX0 , Y0 , Z0, f and c are defined in Eqs.~1!–~5!;X1 , Y1 , X2 , Y2, andZ are sensor coordinates, andh isthe distance between twox-y PSDs as shown in Fig. 2~b!.

III. EXPERIMENTAL RESULTS

A. Open-loop results

The open-loop calibration is carried out to determine thelinearity and open-loop resolution of the micropositioningsystem.

Figure 5 shows the open-loop calibration results for allfive degrees of freedom~x,y,z, f, c!. They were obtained byincreasing the displacement in one dimension while keepingother dimensions stationary. The results show that the maxi-mum working range is about 180mm in both thex and ydimensions, is 680mm in thez dimension, 1.3831023 rad in

FIG. 4. Schematic diagram of the PSD and signal processing circuit.

FIG. 5. Open-loop calibration results.

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the f dimension, and 0.6831023 rad in thec dimension.The system shows very high linearity. There is also verylittle crosstalk between different dimensions, which makes itpossible to control each degree of freedom separately. Thisworking space can be further increased by either increasingthe driving currents, the number of turns in the coils, orreducing the stiffness of the suspension springs. However, itshould be noted that reduction of the spring stiffness maylead to lower response speed.

Since the system has open-loop stability, the open-loopresolution is limited by that of the driving system. The driv-ing circuit is found to have much higher accuracy than thatof the 12-bit D/A board. Therefore, the open-loop resolutionis found to be about 0.05mm ~180 mm/4095! in x and ydimensions and 0.15mm ~600 mm/4095! for thez-dimension, as set by the 12-bit~0–4095! digital to analogconversion board.

B. Closed-loop control and experimental results

As shown in Sec. II, the micropositioner is a typicalspring-mass system and has a very simple mathematicalmodel. This fact lends a great convenience to controller de-sign. However, it is not practical and efficient to design thecontroller directly from this theoretical model because manyphysical parameters of the system, such as the stiffness of thesprings, cannot be easily and accurately assessed. In addi-tion, other important factors such as the equivalent dampingcoefficient also cannot be easily estimated. A practical andeasier way to overcome these difficulties is to analyze thestep response of the system, and then design the controllerbased on it.

1. Step responses without feedback control

Figure 6 shows the step responses of the microposition-ing system in all five degrees of freedom without feedbackcontrol. They were acquired by supplying step inputs~i.e.,raise the output abruptly from zero to a specified level! to themicropositioner. It can be clearly seen from these responsesthat the micropositioner is basically a second-order, under-damped system, whose transfer function must be in the fol-lowing form:

G~s!5vn2

s212jvns1vn2, ~13!

wherevn is the undamped natural frequency of the system,and j is the damping ratio of the system. The damping,which is proportional to the moving speed of the motor,stems from the induced inverse electromotive inside themoving coils. It can be seen from the step responses that thesystem has a very high frequency, which is attributed to thesmall mass of the motor and large stiffness of the springs.The system also has a very low damping effect.

2. Step responses with a PID controller

The foregoing analysis on the system dynamic propertiesshows that the transfer function of the system has a pair ofconjugate complex poles which are very near to the imagi-nary axis. It is these two poles which cause the underdamped

vibration of the micropositioner when it is subjected to a stepinput. To overcome this undesired oscillatory response, thesetwo poles must be eliminated, so the controller to be takenshould be in the following form:

D~s!5s212jvns1vn

2

Ks, ~14!

which is designed to cancel the pair of complex poles. Thevalue ofK can be adjusted to tune the controller. The tuningcriterion is to make the micropositioner reach the target po-sition as soon as possible without overshoot. A PID control-ler was designed. The Tustin method28 is used to transfer itinto the discretized form~in the z-domain!. Then it can beimplemented in the microcomputer.

Real time control over multidimensions is obtained byimplementing a digital controller checking these directionsalternatively at each sampling instance.

The step responses of the micropositioner with a PIDcontroller are shown in Fig. 7. It can be seen that the highoscillation in the open-loop step responses has been elimi-nated and there are no overshoots.

The sensing system used in the experiment has beencalibrated with a precision stage and a translational resolu-tion of 0.05mm was confirmed over the working space of 1.2mm by 1.2 mm inx and y dimensions, and a resolution of0.15mm was confirmed over a range of 1.2 mm inz dimen-sion. However, the 12-bit A/D conversion board used to digi-tize the sensing signals limits the measurement resolution to0.3 mm. This sets the limitation for the resolutions for asystem with closed-loop control.

FIG. 6. Step responses of the system without closed-loop feedback control.

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IV. DISCUSSION

A five degrees of freedom high precision microposi-tioner based on spring suspension and electromagnetic driv-ing has been designed, constructed, and tested. In compari-son with other types of precision positioning devices, theprototype micropositioner has some major advantages. First,it realized high precision positioning over a large workingspace in five degrees of freedom with a very simple design.Particularly, it provides a rotating mechanism which is espe-cially valuable in some cases. Second, the linear spring sus-pension used in the device eliminates the mechanical frictionwhile maintaining inherent open-loop stability. This uniquecharacter provides to the device the advantage of a magneti-cally levitated system and eliminates its inherent unstability.Third, careful design of the flat springs, the coils, and magnetshoes helps to minimize interaction between the differentdimensions and nonlinearity. The simple dynamic model ofthe device also helps to simplify controller design and reducethe computation burden of the computer. Finally, the com-pact size, simple structure, low voltage power supply, andhigh load carrying ability of the device make it potentiallyuseful for different types of applications.

Since the open-loop accuracy of the device is only lim-ited by the resolution of the 12-bit D/A board, higher reso-lution can be expected if a 14- or 16-bit D/A board is used. Alarger working range is possible if a higher driving current,smaller distance between the facing magnets or more turns ofthe coils are adopted.

In conclusion, the prototype micropositioner has the ad-

vantages of high accuracy, large working space, open-loopstability, high linearity, compact size, and high load capacity.These advantages make it potentially useful in such applica-tions as high precision microprobing, probing and analysis ofintegrated-circuit structures, manipulations of individualcells and micro-organisms, microsurgery, and testing of mi-cromachines.

ACKNOWLEDGMENT

The authors wish to thank Dr. Illene Busch-Vishniac ofthe Department of Mechanical Engineering, The Universityof Texas at Austin, for allowing us to use some of the equip-ment in her laboratory and for her helpful discussion.

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FIG. 7. Step responses of the system with closed-loop control.

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