an innovative design method for compliant mechanisms combining structural optimisations and designer...
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Journal of Engineering DesignVol. 20, No. 2, April 2009, 125154
An innovative design method for compliant mechanismscombining structural optimisations and designer creativityMasakazu Kobayashia*, Shinji Nishiwakib, Kazuhiro Izuib and Masataka Yoshimurab
aDepartment of Information-aided Technology, Toyota Technological Institute, Nagoya City, Japan;bDepartment of Aeronautics and Astronautics, Kyoto University, Kyoto City, Japan
(Received 9 February 2007; final version received 11 July 2007 )
This paper proposes an innovative, integrated design method for the design of practical and sophisticatedcompliant mechanisms. The approach consists of two optimisation methods, topology and shape optimi-sation, plus a scheme to implement designer input of ideas. In the first step, a designer explores the mostfruitful design concepts for mechanisms that achieve the design specifications, by combining compliantmechanisms created by the topology optimisation with additional mechanisms prepared by the designer.In this first step, a support method based on the visualisation of the designers thinking processes assiststhe designer in his or her exploration of new ideas and design concepts. In the second step, the shapeoptimisation yields a detailed optimal shape based on the design concept. The combination of compliantmechanisms with the additional mechanisms enables the creation of devices having increased capabilityor higher performance than would be possible using a single compliant mechanism designed by topol-ogy optimisation alone. Executing the shape optimisation after initial design concepts have been exploredfacilitates the determination of a detailed optimal shape, and also enables to consider non-linear analy-sis and stress concentration and to make accurate quantitative performance evaluations, which topologyoptimisation cannot provide.
Keywords: optimal design; compliant mechanism; topology optimisation; shape optimisation; designercreativity; creative support system
In mechanical design, mechanisms consisting of rigid parts linked to moveable joints are oftenused, and in such mechanisms the relative motion of the links is constrained by the joints. Onthe other hand, compliant mechanisms (Howell 2001) utilise a structures flexibility to achieve aspecified motion, by deforming the structure elastically, instead of relying on joint movements.Such compliant mechanisms often consist of fewer parts than rigid-link mechanisms, or caneven be monolithic, and, compared with rigid-link mechanisms, have several merits (Howell2001, Ananthasuresh and Kota 1995), such as reduced wear and operation noise, zero backlash,
*Corresponding author. Email: firstname.lastname@example.org
ISSN 0954-4828 print/ISSN 1466-1837 online 2009 Taylor & FrancisDOI: 10.1080/09544820701565017http://www.informaworld.com
126 M. Kobayashi et al.
freedom from lubrication requirements, weight savings, manufacturing advantages, and ease ofminiaturisation. Therefore, the use of compliant mechanisms in mechanical products, medicalinstruments and micro-electro mechanical systems (Howell 2001, Larsen et al. 1997) can beexpected to increase.
For such promising compliant mechanisms, many design methods have been developed overthe past few decades, and these can be classified into the following two types. The first method typeis based on kinematics, where the designer creates a traditional rigid-link mechanism consistingof rigid parts and joints, and then creates a compliant mechanism by converting the joints toflexural parts. Her and Midah (1987) proposed a methodology for obtaining all possible compliantmechanisms from a given rigid body kinematic chain. Howell and Midah (1994) proposed ananalysis and synthesis method using a pseudo-rigid-body model. The advantage of a kinematicsapproach is that the designer can utilise an already well-developed body of knowledge concerningkinematics and rigid-link mechanisms. However, such methods require trial and error processeson the part of the designer, to find the best conversion, and the best traditional mechanism doesnot always result in the best compliant mechanism.
The second method type is based on topology optimisation (Bendse and Kikuchi 1988), wherethe designer configures the design domain, boundary conditions and the location and directionof the input and output forces of the target mechanism, and then the topology optimisation isconducted to calculate an optimal shape under these conditions. Sigmund (1997) proposed adesign approach using topology optimisation based on the density method, and Larsen et al. (1996)also proposed a similar design approach. On the other hand, the approach proposed by Nishiwakiet al. (2001) was based on the homogenisation design method. The advantage of a topologyoptimisation-based approach is that knowledge of kinematics is not required and fully optimalconfigurations can be yielded without the designers trial and error processes.
Topology optimisation, however, has several inherent problems, such as numerical problemsthat typically result in checkerboards or hinge patterns numerical difficulties in utilising localphysical quantities, such as stress and displacement during the optimisation process. Topologyoptimisation can also not easily consider large deformations and non-linear analysis, or makedetailed shape decisions, although numerous methods have been developed in an attempt to resolvethese challenges. For the checkerboard pattern problem, methods based on filtering techniques(Sigmund and Petersson 1998, Fujii and Kikuchi 2000, Bourdin 2001) are often used, but suchmethods merely address the symptoms rather than the core difficulty. On the other hand, severalmethods that resolve this problem theoretically have been proposed, such as node-based topologyoptimisation (Matsui and Terada 2004). The appearance of hinges is another numerical obstacle,an outcome of flexibility maximisation when topology optimisation is used for the design ofa structure having flexible regions. Hinges must be avoided due to manufacturing infeasibility.To eliminate hinges, Poulsen (2003) proposed a method based on member size control, andYoon et al. (2004) proposed a method using wavelets. To employ local physical quantities, severalmethods (Pereira et al. 2004, Duysinx and Bendse 1998) tried various ways of considering stressconstraints, but the direct implementation of stress constraints in compliant mechanism designremains problematic at the present time. To precisely assess the quantitative performance of acompliant mechanism during the optimisation process, non-linear and large deformation analysisis desirable. Pedersen et al. (2001) and Bruns and Tortorelli (2001) proposed topology optimisationmethods that include large deformation analysis, but these methods have unwieldy computationalrequirement, and local solutions with physically meaningless shapes may be presented as optimalresults. Furthermore, there is little difference in the optimal results generated by these methodsthat consider large deformations, and those obtained by methods that do not, if we do not explicitlydeal with highly non-linear effects such as buckling phenomena.
Furthermore, in a broad range of product applications, compliant mechanisms are expected tofulfil a variety of mission-specific functions, such as a stopper using bi-stability, or non-linear
Journal of Engineering Design 127
deformation paths. To enable the design of such compliant mechanisms, having increasinglysophisticated functions, a number of design methods have been developed, based on kinematicsand topology optimisation approaches. In the kinematics approach, Midha et al. (2004) proposeda method based on pseudo-rigid-body models and rigid-body mechanism synthesis for function,path and motion generation. Jensen and Howell (2004) considered several mechanism configura-tions involving slider joints, and facilitated the design of bi-stable compliant mechanisms usingdesigners prior knowledge of compliant mechanism configurations. Crane et al. (2004) designeda floating-opposing-arm centrifugal clutch using a pseudo-rigid-body model, manufactured proto-types and tested them. Snmez (2003) introduced the design of compliant long-dwell mechanisms,including straight flexible beams and flexible arcs. Such mechanisms have two stable positions,an initial position and one where the flexible arc works as a bucking stopper. Methods basedon the kinematics approach can achieve complicated compliant mechanism designs by applyingwell-developed kinematics knowledge, but they also suffer from the problems inherent in thekinematics approach, as described above.
As for methods based on topology optimisation, Ohsaki and Nishiwaki (2005) devel-oped a design method for bi-stable compliant mechanisms utilising snap-through behaviour,based on the ground structure approach, by considering geometrical non-linearity. Saxena andAnanthasuresh (2001) proposed a method for the design compliant mechanisms having a desiredoutput trajectory. They also proposed a method that combines topology optimisation and apseudo rigid-body model (Saxena and Ananthasuresh 2003). Mankame and Ananthasuresh(2004a) proposed a method that makes use of the ground structure approach and regularisedcontact modelling, for the design of contact-aided compliant mechanisms that enable non-smooth functions, such as non-smooth output paths, by exploiting contact between variousparts of the compliant mechanism. They also proposed a design method for electrother-mal compliant mechanisms (Mankame and Ananthasuresh 2004b). The methods describedabove use topology optimisation based on discrete element approaches, while the followingmethods employ continuum mechanics approaches. Swan and Rahmatalla (2004) proposed acontrol algorithm within a computationally finite deformation analy