Design of compliant mechanisms using continuum topology optimization: A review

Abstract Compliant mechanisms have become an important branch of modern mechanisms. Unlike conventional rigid body mechanisms, compliant mechanisms transform the displacement and force at least partly through the deformation of their structural components, which can offer a great reduction in friction, lubrication and assemblage. Therefore, compliant mechanisms are particularly suitable for applications in microscale/nanoscale manipulation systems. The significant demand of practical applications has also promoted the development of systematic design methods for compliant mechanisms. Several methods have been developed to design compliant mechanisms. In this paper, we focus on the continuum topology optimization methods and present a survey of the state-of-the-art design advances in this research area over the past 20 years. The presented overview can be helpful to those engaged in the topology optimization of compliant mechanisms who desire to be apprised of the field’s recent state and research tendency.

[1]  Prabhat Kumar,et al.  Synthesis of C0 Path-Generating Contact-Aided Compliant Mechanisms Using the Material Mask Overlay Method , 2016 .

[2]  D. Benson,et al.  Geometrically constrained isogeometric parameterized level-set based topology optimization via trimmed elements , 2016 .

[3]  Fupei Wu,et al.  Topology Optimization of Spatially Compliant Mechanisms with an Isomorphic Matrix of a 3-UPC Type Parallel Prototype Manipulator , 2018, Micromachines.

[4]  O. Sigmund.  Morphology-based black and white filters for topology optimization , 2007 .

[5]  S. Rahmatalla,et al.  CONTINUUM TOPOLOGY OPTIMIZATION OF BUCKLING-SENSITIVE STRUCTURES , 2002 .

[6]  Bo Wang,et al.  Diverse competitive design for topology optimization , 2018 .

[7]  Nicolae Lobontiu,et al.  Modeling and design of planar parallel-connection flexible hinges for in- and out-of-plane mechanism applications , 2015 .

[8]  Ole Sigmund,et al.  Toward the topology design of mechanisms that exhibit snap-through behavior , 2004 .

[9]  Michael Yu Wang,et al.  Mechanical and geometric advantages in compliant mechanism optimization , 2009 .

[10]  T. E. Bruns,et al.  Numerical methods for the topology optimization of structures that exhibit snap‐through , 2002 .

[11]  George I. N. Rozvany,et al.  DCOC: An optimality criteria method for large systems Part I: theory , 1992 .

[12]  Ole Sigmund,et al.  Topology synthesis of large‐displacement compliant mechanisms , 2001 .

[13]  Krishnan Suresh,et al.  Hinge-Free Compliant Mechanism Design Via the Topological Level-Set , 2013 .

[14]  Xianmin Zhang,et al.  Design of flexure hinges based on stress-constrained topology optimization , 2017 .

[15]  J. Korvink,et al.  Using artificial reaction force to design compliant mechanism with multiple equality displacement constraints , 2009 .

[16]  Andres Tovar,et al.  An efficient 3D topology optimization code written in Matlab , 2014 .

[17]  A. Saxena,et al.  An Improved Material-Mask Overlay Strategy for Topology Optimization of Structures and Compliant Mechanisms , 2010 .

[18]  Osvaldo M. Querin,et al.  A sequential element rejection and admission (SERA) topology optimization code written in Matlab , 2018 .

[19]  Panos Y. Papalambros,et al.  Panos Papalambros a Survey of Structural Optimization in Mechanical Product Development , 2022 .

[20]  Nianfeng Wang,et al.  Topology optimization of hinge-free compliant mechanisms with multiple outputs using level set method , 2013 .

[21]  Bijan Shirinzadeh,et al.  Topology optimisation of bridge input structures with maximal amplification for design of flexure mechanisms , 2018 .

[22]  Yi Min Xie,et al.  A further review of ESO type methods for topology optimization , 2010 .

[23]  Haim Waisman,et al.  Layout design of a bi-stable cardiovascular stent using topology optimization , 2016 .

[24]  Xianmin Zhang,et al.  Topological and Shape Optimization of Flexure Hinges for Designing Compliant Mechanisms Using the Level Set Method , 2019 .

[25]  Lei Li,et al.  Volume preserving projection filters and continuation methods in topology optimization , 2015 .

[26]  Ole Sigmund,et al.  Stress-constrained topology optimization for compliant mechanism design , 2015 .

[27]  G. K. Ananthasuresh,et al.  Design of Distributed Compliant Mechanisms , 2003 .

[28]  Gang-Won Jang,et al.  Topology optimization using moving morphable bars for versatile thickness control , 2017 .

[29]  Noboru Kikuchi,et al.  Topology optimization of thermally actuated compliant mechanisms considering time-transient effect , 2004 .

[30]  Glaucio H. Paulino,et al.  Multi‐actuated functionally graded piezoelectric micro‐tools design: A multiphysics topology optimization approach , 2009 .

[31]  Qingsong Xu,et al.  Design and modeling of constant-force mechanisms: A survey , 2018 .

[32]  Michael Yu Wang,et al.  Design and Development of a Topology-Optimized Three-Dimensional Printed Soft Gripper. , 2018, Soft robotics.

[33]  Dan M. Frangopol,et al.  Reliability-based design of MEMS mechanisms by topology optimization , 2003 .

[34]  Xianmin Zhang,et al.  Topology optimization of bistable mechanisms with maximized differences between switching forces in forward and backward direction , 2019 .

[35]  Ole Sigmund,et al.  Design of multiphysics actuators using topology optimization - Part I: One-material structures , 2001 .

[36]  Anders Clausen,et al.  Efficient topology optimization in MATLAB using 88 lines of code , 2011 .

[37]  Hong Zhou,et al.  Shape and Size Synthesis of Compliant Mechanisms Using Wide Curve Theory , 2006 .

[38]  Yang Chen,et al.  Topology Optimization and Prototype of a Three-Dimensional Printed Compliant Finger for Grasping Vulnerable Objects With Size and Shape Variations , 2018, Journal of Mechanisms and Robotics.

[39]  Jonathan B. Hopkins,et al.  Synthesis of multi-degree of freedom, parallel flexure system concepts via freedom and constraint topology (FACT). Part II: Practice , 2010 .

[40]  Ashwin A. Seshia,et al.  On the optimization of compliant force amplifier mechanisms for surface micromachined resonant accelerometers , 2004 .

[41]  Li-Ping Chen,et al.  Topology synthesis of thermomechanical compliant mechanisms with geometrical nonlinearities using meshless method , 2009, Adv. Eng. Softw..

[42]  Mary Frecker,et al.  Topology optimization of compliant mechanisms with multiple outputs , 1999 .

[43]  Glaucio H. Paulino,et al.  PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes , 2012 .

[44]  Mattias Schevenels,et al.  Topology optimization with geometric uncertainties by perturbation techniques , 2012 .

[45]  Grégoire Allaire,et al.  Optimal design of micro-mechanisms by the homogenization method , 2002 .

[46]  Yangjun Luo,et al.  Design of Large-Displacement Compliant Mechanisms by Topology Optimization Incorporating Modified Additive Hyperelasticity Technique , 2017 .

[47]  Sridhar Kota,et al.  An intrinsic geometric framework for the building block synthesis of single point compliant mechanisms , 2011 .

[48]  Ole Sigmund,et al.  Topology optimized electrothermal polysilicon microgrippers , 2008 .

[49]  Shusheng Bi,et al.  An effective pseudo-rigid-body method for beam-based compliant mechanisms , 2010 .

[50]  M. M. Neves,et al.  Generalized topology design of structures with a buckling load criterion , 1995 .

[51]  Lei Wang,et al.  Motion error based robust topology optimization for compliant mechanisms under material dispersion and uncertain forces , 2018 .

[52]  Estrella Veguería,et al.  An element addition strategy for thermally actuated compliant mechanism topology optimization , 2010 .

[53]  Xianmin Zhang,et al.  The Development of a New Piezoresistive Pressure Sensor for Low Pressures , 2018, IEEE Transactions on Industrial Electronics.

[54]  Hong Zhou,et al.  The Modified Quadrilateral Discretization Model for the Topology Optimization of Compliant Mechanisms , 2011 .

[55]  D. Rus,et al.  Design, fabrication and control of soft robots , 2015, Nature.

[56]  Glaucio H. Paulino,et al.  Topology optimization using polytopes , 2013, 1312.7016.

[57]  Xianmin Zhang,et al.  A new topology optimization method for planar compliant parallel mechanisms , 2016 .

[58]  Zhang,et al.  Topology Optimization of Compliant Mechanisms with Geometrical Nonlinearities Using the Ground Structure Approach , 2011 .

[59]  Noboru Kikuchi,et al.  Advances in computational design and optimization with application to MEMS , 2001 .

[60]  Chih-Hsing Liu,et al.  Topology Synthesis and Optimal Design of an Adaptive Compliant Gripper to Maximize Output Displacement , 2018, J. Intell. Robotic Syst..

[61]  Chao Sun,et al.  Topology optimization of compliant adaptive wing leading edge with composite materials , 2014 .

[62]  Dung-An Wang,et al.  A constant-force bistable mechanism for force regulation and overload protection , 2011 .

[63]  Sergej Fatikow,et al.  Design and analysis of a high-accuracy flexure hinge. , 2016, The Review of scientific instruments.

[64]  Xianmin Zhang,et al.  Jacobian-Based Topology Optimization Method Using an Improved Stiffness Evaluation , 2018 .

[65]  Matteo Bruggi,et al.  Synthesis of auxetic structures using optimization of compliant mechanisms and a micropolar material model , 2016, Structural and Multidisciplinary Optimization.

[66]  James K. Guest,et al.  Topology optimization with multiple phase projection , 2009 .

[67]  Kang Tai,et al.  Design of Grip-and-Move Manipulators Using Symmetric Path Generating Compliant Mechanisms , 2008 .

[68]  Min Liu,et al.  Design and analysis of a multi-notched flexure hinge for compliant mechanisms , 2017 .

[69]  Boyan Stefanov Lazarov,et al.  Maximum length scale in density based topology optimization , 2017 .

[70]  M. Bendsøe.  Optimal shape design as a material distribution problem , 1989 .

[71]  Xianmin Zhang,et al.  A level set method for reliability-based topology optimization of compliant mechanisms , 2008 .

[72]  Shinji Nishiwaki,et al.  Piezoresistive sensor design using topology optimization , 2008 .

[73]  Xianmin Zhang,et al.  A multi-objective method of hinge-free compliant mechanism optimization , 2014 .

[74]  Yongsheng Ma,et al.  A survey of manufacturing oriented topology optimization methods , 2016, Adv. Eng. Softw..

[75]  Xianmin Zhang,et al.  Error modelling and motion reliability analysis of a planar parallel manipulator with multiple uncertainties , 2018, Mechanism and Machine Theory.

[76]  Yi Min Xie,et al.  Topology optimization of compliant mechanisms with desired structural stiffness , 2014 .

[77]  T. Ray,et al.  Design Synthesis of Path Generating Compliant Mechanisms by Evolutionary Optimization of Topology and Shape , 2002 .

[78]  Hai-Jun Su,et al.  Screw Theory Based Methodology for the Deterministic Type Synthesis of Flexure Mechanisms , 2011 .

[79]  Ole Sigmund,et al.  On the usefulness of non-gradient approaches in topology optimization , 2011 .

[80]  Jie Yuan,et al.  A new three-dimensional topology optimization method based on moving morphable components (MMCs) , 2017 .

[81]  L. Valdevit,et al.  Multistable Shape‐Reconfigurable Architected Materials , 2016, Advanced materials.

[82]  Benliang Zhu,et al.  An augmented formulation of distributed compliant mechanism optimization using a level set method , 2016 .

[83]  A. Saxena.  Synthesis of Compliant Mechanisms for Path Generation using Genetic Algorithm , 2005 .

[84]  Cristina Alonso,et al.  A Sequential Element Rejection and Admission (SERA) method for compliant mechanisms design , 2013 .

[85]  G. Rozvany.  Stress ratio and compliance based methods in topology optimization – a critical review , 2001 .

[86]  Zhong Chen,et al.  Realtime in-plane displacements tracking of the precision positioning stage based on computer micro-vision , 2019 .

[87]  Ole Sigmund,et al.  On the Design of Compliant Mechanisms Using Topology Optimization , 1997 .

[88]  J. Petersson,et al.  Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima , 1998 .

[89]  Hejun Du,et al.  Use of functional specifications as objective functions in topological optimization of compliant mechanism , 2001 .

[90]  Mary Frecker,et al.  Dynamic Topology Optimization of Compliant Mechanisms and Piezoceramic Actuators , 2004 .

[91]  O. Pironneau,et al.  Shape and topology optimization based on the convected level set method , 2016 .

[92]  Anupam Saxena,et al.  A Material-Mask Overlay Strategy for Continuum Topology Optimization of Compliant Mechanisms Using Honeycomb Discretization , 2008 .

[93]  Mei Yulin,et al.  A level set method for structural topology optimization and its applications , 2004 .

[94]  N. Wang,et al.  Topology optimization of compliant mechanisms using pairs of curves , 2015 .

[95]  Mattias Schevenels,et al.  On the implementation and effectiveness of morphological close-open and open-close filters for topology optimization , 2016 .

[96]  G. Allaire,et al.  Thickness control in structural optimization via a level set method , 2016, Structural and Multidisciplinary Optimization.

[97]  Xianmin Zhang,et al.  TOPOLOGY OPTIMIZATION OF MULTIPLE INPUTS AND OUTPUTS COMPLIANT MECHANISM WITH COUPLING TERMS CONTROL , 2006 .

[98]  T. Shi,et al.  Constraints of distance from boundary to skeleton: For the control of length scale in level set based structural topology optimization , 2015 .

[99]  Esben Lindgaard,et al.  On compliance and buckling objective functions in topology optimization of snap-through problems , 2013 .

[100]  Jianhua Zhou,et al.  A Moving Morphable Void (MMV)-based explicit approach for topology optimization considering stress constraints , 2018, Computer Methods in Applied Mechanics and Engineering.

[101]  Vivien J. Challis,et al.  A discrete level-set topology optimization code written in Matlab , 2010 .

[102]  Tobias Tiemerding,et al.  Automated Robotic Manipulation of Individual Colloidal Particles Using Vision-Based Control , 2015, IEEE/ASME Transactions on Mechatronics.

[103]  M. Zhou,et al.  Generalized shape optimization without homogenization , 1992 .

[104]  Cristina Alonso,et al.  Topology synthesis of multi-material compliant mechanisms with a Sequential Element Rejection and Admission method , 2014 .

[105]  Jian Zhang,et al.  Explicit structural topology optimization based on moving morphable components (MMC) with curved skeletons , 2016 .

[106]  O. Sigmund,et al.  Topology optimization considering material and geometric uncertainties using stochastic collocation methods , 2012 .

[107]  Ole Sigmund,et al.  A 99 line topology optimization code written in Matlab , 2001 .

[108]  Charles Kim,et al.  A Building Block Approach to the Conceptual Synthesis of Compliant Mechanisms Utilizing Compliance and Stiffness Ellipsoids , 2008 .

[109]  Xiaoyuan Liu,et al.  Elliptical-Arc-Fillet Flexure Hinges: Toward a Generalized Model for Commonly Used Flexure Hinges , 2011 .

[110]  Hae Chang Gea,et al.  A strain based topology optimization method for compliant mechanism design , 2014 .

[111]  A. Ismail-Yahaya,et al.  Multiobjective robust design using physical programming , 2002 .

[112]  Michael Yu Wang,et al.  Design of multimaterial compliant mechanisms using level-set methods , 2005 .

[113]  Robert J. Wood,et al.  An integrated design and fabrication strategy for entirely soft, autonomous robots , 2016, Nature.

[114]  Kalyanmoy Deb,et al.  Generation of Compliant Mechanisms using Hybrid Genetic Algorithm , 2014 .

[115]  Mattias Schevenels,et al.  Efficient reanalysis techniques for robust topology optimization , 2012 .

[116]  S. M. Giusti,et al.  Topology design of thermomechanical actuators , 2017 .

[117]  M. Wang,et al.  A new level set method for systematic design of hinge-free compliant mechanisms , 2008 .

[118]  O. Sigmund,et al.  Topology optimization approaches , 2013, Structural and Multidisciplinary Optimization.

[119]  Michael Yu Wang,et al.  Design of piezoelectric actuators using a multiphase level set method of piecewise constants , 2009, J. Comput. Phys..

[120]  T. Shi,et al.  Topology optimization of compliant mechanism and its support through a level set method , 2016 .

[121]  Guo Feng Huang,et al.  An Evolutionary Soft-Add Topology Optimization Method for Synthesis of Compliant Mechanisms With Maximum Output Displacement , 2017 .

[122]  N. P. Dijk,et al.  A level-set based topology optimization using the element connectivity parameterization method , 2010 .

[123]  A. Saxena,et al.  Synthesis of Path Generating Compliant Mechanisms Using Initially Curved Frame Elements , 2007 .

[124]  J. Petersson.  Some convergence results in perimeter-controlled topology optimization , 1999 .

[125]  Charles J. Kim,et al.  An Instant Center Approach Toward the Conceptual Design of Compliant Mechanisms , 2006 .

[126]  Jian Zhang,et al.  A new topology optimization approach based on Moving Morphable Components (MMC) and the ersatz material model , 2016 .

[127]  O. Sigmund,et al.  Higher‐order multi‐resolution topology optimization using the finite cell method , 2017 .

[128]  Xianda Xie,et al.  A new isogeometric topology optimization using moving morphable components based on R-functions and collocation schemes , 2018, Computer Methods in Applied Mechanics and Engineering.

[129]  Hejun Du,et al.  Convex analysis for topology optimization of compliant mechanisms , 2001 .

[130]  Estrella Veguería,et al.  3D compliant mechanisms synthesis by a finite element addition procedure , 2010 .

[131]  Gang-Won Jang,et al.  Topology optimization of pressure-actuated compliant mechanisms , 2010 .

[132]  Ole Sigmund,et al.  Length scale and manufacturability in density-based topology optimization , 2016, Archive of Applied Mechanics.

[133]  Estrella Veguería,et al.  A simple evolutionary topology optimization procedure for compliant mechanism design , 2007 .

[134]  Geert Lombaert,et al.  Topology optimization of fail-safe structures using a simplified local damage model , 2014 .

[135]  Cristina Alonso,et al.  Electro-thermal compliant mechanisms design by an evolutionary topology optimization method , 2013 .

[136]  G. K. Ananthasuresh,et al.  Synthesis of contact‐aided compliant mechanisms for non‐smooth path generation , 2007 .

[137]  Ole Sigmund,et al.  Optimal design of robust piezoelectric microgrippers undergoing large displacements , 2017 .

[138]  G. Allaire,et al.  A level-set method for shape optimization , 2002 .

[139]  Hong Zhou.  Topology Optimization of Compliant Mechanisms Using Hybrid Discretization Model , 2010 .

[140]  G. K. Ananthasuresh,et al.  Design of a Compliant Mechanism to Modify an Actuator Characteristic to Deliver a Constant Output Force , 2006 .

[141]  S. Yamasaki,et al.  A level set based topology optimization method using the discretized signed distance function as the design variables , 2010 .

[142]  Salam Rahmatalla,et al.  Sparse monolithic compliant mechanisms using continuum structural topology optimization , 2005 .

[143]  M. I.Z. Ridzwan,et al.  Methodology of Compliant Mechanisms and its Current Developments in Applications: A Review , 2007 .

[144]  Dongjin Kim,et al.  Topology optimization for continuous and discrete orientation design of functionally graded fiber-reinforced composite structures , 2018, Composite Structures.

[145]  M. Diehl,et al.  Robust topology optimization accounting for misplacement of material , 2012, Structural and Multidisciplinary Optimization.

[146]  Ole Sigmund,et al.  Topology optimization for optical microlithography with partially coherent illumination , 2017 .

[147]  Zhen Luo,et al.  Topology optimization for thermo-mechanical compliant actuators using mesh-free methods , 2009 .

[148]  Kang Tai,et al.  Design of 2-DOF Compliant Mechanisms to Form Grip-and-Move Manipulators for 2D Workspace , 2010 .

[149]  Xianmin Zhang,et al.  Origami Kaleidocycle-Inspired Symmetric Multistable Compliant Mechanisms , 2019 .

[150]  C J Shih,et al.  A two-stage topological optimum design for monolithic compliant microgripper integrated with flexure hinges , 2006 .

[151]  A. Saxena.  Topology design with negative masks using gradient search , 2011 .

[152]  Tam H. Nguyen,et al.  Improving multiresolution topology optimization via multiple discretizations , 2012 .

[153]  G. K. Ananthasuresh,et al.  Topology optimization of compliant mechanisms with multiple materials using a peak function material interpolation scheme , 2001 .

[154]  Kang Tai,et al.  Design of structures and compliant mechanisms by evolutionary optimization of morphological representations of topology , 2000 .

[155]  Emílio C. N. Silva,et al.  Integral Piezoactuator System with Optimum Placement of Functionally Graded Material — A Topology Optimization Paradigm , 2010 .

[156]  G. K. Ananthasuresh,et al.  Topology Synthesis of Compliant Mechanisms for Nonlinear Force-Deflection and Curved Path Specifications , 2001 .

[157]  Hong Zhou,et al.  Topology Optimization of Compliant Mechanisms Using the Improved Quadrilateral Discretization Model , 2012 .

[158]  Hejun Du,et al.  Techniques to suppress intermediate density in topology optimization of compliant mechanisms , 2001 .

[159]  Ole Sigmund,et al.  On projection methods, convergence and robust formulations in topology optimization , 2011, Structural and Multidisciplinary Optimization.

[160]  Yi Min Xie,et al.  Evolutionary topology optimization of hinge-free compliant mechanisms , 2014 .

[161]  O. Sigmund,et al.  Rapid prototyping of nanotube-based devices using topology-optimized microgrippers , 2008, Nanotechnology.

[162]  R. Bharanidaran,et al.  A modified post-processing technique to design a compliant based microgripper with a plunger using topological optimization , 2017 .

[163]  R. Sauer,et al.  Combined gradient‐stochastic optimization with negative circular masks for large deformation topologies , 2013 .

[164]  Xianmin Zhang,et al.  Design of single-axis flexure hinges using continuum topology optimization method , 2014 .

[165]  Peter D. Dunning,et al.  Simultaneous material and structural optimization by multiscale topology optimization , 2016 .

[166]  Lei Li,et al.  Topology optimization of structures with length-scale effects using elasticity with microstructure theory , 2015 .

[167]  Xiaoming Wang,et al.  Color level sets: a multi-phase method for structural topology optimization with multiple materials , 2004 .

[168]  Nianfeng Wang,et al.  Exploration of Translational Joint Design Using Corrugated Flexure Units With Bézier Curve Segments , 2019 .

[169]  Patrick V. Hull,et al.  Optimal synthesis of compliant mechanisms using subdivision and commercial FEA , 2006 .

[170]  Ramana V. Grandhi,et al.  A survey of structural and multidisciplinary continuum topology optimization: post 2000 , 2014 .

[171]  Yi Min Xie,et al.  Basic Evolutionary Structural Optimization , 1997 .

[172]  Xianmin Zhang,et al.  A 213-line topology optimization code for geometrically nonlinear structures , 2018, Structural and Multidisciplinary Optimization.

[173]  G. K. Ananthasuresh,et al.  A Comparative Study of the Formulations and Benchmark Problems for the Topology Optimization of Compliant Mechanisms , 2009 .

[174]  Justus Laurens Herder,et al.  Design of a statically balanced fully compliant grasper , 2015 .

[175]  Liping Chen,et al.  Topology synthesis of geometrically nonlinear compliant mechanisms using meshless methods , 2008 .

[176]  Thomas Schlinquer,et al.  Displacement Amplifier Mechanism for Piezoelectric Actuators Design Using SIMP Topology Optimization Approach , 2018, 2018 IEEE International Conference on Robotics and Automation (ICRA).

[177]  Tsuyoshi Nomura,et al.  Compliant mechanism design based on the level set and arbitrary Lagrangian Eulerian methods , 2012 .

[178]  Xianmin Zhang,et al.  Optimal design of a planar parallel 3-DOF nanopositioner with multi-objective , 2017 .

[179]  M. Zhou,et al.  Checkerboard and minimum member size control in topology optimization , 2001 .

[180]  Qingsong Xu,et al.  Design of a Large-Stroke Bistable Mechanism for the Application in Constant-Force Micropositioning Stage , 2017 .

[181]  Sridhar Kota,et al.  Design of Compliant Mechanisms: Applications to MEMS , 2001 .

[182]  Erik Andreassen,et al.  On filter boundary conditions in topology optimization , 2017 .

[183]  Xianmin Zhang,et al.  Imposing minimum length scale in moving morphable component (MMC)-based topology optimization using an effective connection status (ECS) control method , 2019, Computer Methods in Applied Mechanics and Engineering.

[184]  S. Yamasaki,et al.  A consistent grayscale‐free topology optimization method using the level‐set method and zero‐level boundary tracking mesh , 2015 .

[185]  Arun L. Gain,et al.  Phase-field based topology optimization with polygonal elements: a finite volume approach for the evolution equation , 2012 .

[186]  S. Bi,et al.  A unified approach to type synthesis of both rigid and flexure parallel mechanisms , 2011 .

[187]  George I. N. Rozvany,et al.  A critical review of established methods of structural topology optimization , 2009 .

[188]  Shawn A. Chester,et al.  Printing ferromagnetic domains for untethered fast-transforming soft materials , 2018, Nature.

[189]  James K. Guest,et al.  Eliminating beta-continuation from Heaviside projection and density filter algorithms , 2011 .

[190]  Hongliang Ren,et al.  Topology Optimized Design, Fabrication, and Characterization of a Soft Cable-Driven Gripper , 2018, IEEE Robotics and Automation Letters.

[191]  Michael Yu Wang,et al.  An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions , 2018 .

[192]  Larry L. Howell,et al.  On the Nomenclature, Classification, and Abstractions of Compliant Mechanisms , 1994 .

[193]  Noboru Kikuchi,et al.  TOPOLOGY OPTIMIZATION OF COMPLIANT MECHANISMS USING THE HOMOGENIZATION METHOD , 1998 .

[194]  Rouhollah Tavakoli,et al.  Alternating active-phase algorithm for multimaterial topology optimization problems: a 115-line MATLAB implementation , 2014 .

[195]  Peter D. Dunning,et al.  Minimum length-scale constraints for parameterized implicit function based topology optimization , 2018, Structural and Multidisciplinary Optimization.

[196]  Michael Yu Wang.  A Kinetoelastic Formulation of Compliant Mechanism Optimization , 2009 .

[197]  Shahaboddin Shamshirband,et al.  Development of a new type of passively adaptive compliant gripper , 2013, Ind. Robot.

[198]  Anderson Pereira,et al.  PolyMat: an efficient Matlab code for multi-material topology optimization , 2018, Structural and Multidisciplinary Optimization.

[199]  S. Fatikow,et al.  Bi-directional evolutionary level set method for topology optimization , 2015 .

[201]  Sridhar Kota,et al.  Strategies for systematic synthesis of compliant mems , 1994 .

[202]  Spencer P. Magleby,et al.  Cylindrical cross-axis flexural pivots , 2018 .

[203]  Shinji Nishiwaki,et al.  Shape and topology optimization based on the phase field method and sensitivity analysis , 2010, J. Comput. Phys..

[204]  Fluid flow topology optimization in PolyTop: stability and computational implementation , 2016 .

[205]  Kai A. James,et al.  Optimal design of compliant mechanisms using functionally graded materials , 2017 .

[206]  Takayuki Yamada,et al.  Design of Compliant Thermal Actuators Using Structural Optimization Based on the Level Set Method , 2011, J. Comput. Inf. Sci. Eng..

[207]  Qi Xia,et al.  Bi-directional Evolutionary Structural Optimization on Advanced Structures and Materials: A Comprehensive Review , 2016, Archives of Computational Methods in Engineering.

[208]  H. Berg,et al.  Cats' Paws and Catapults: Mechanical Worlds of Nature and People , 1998 .

[209]  Dongwoo Sheen,et al.  Topology optimization using non‐conforming finite elements: three‐dimensional case , 2005 .

[210]  Thomas A. Poulsen.  A simple scheme to prevent checkerboard patterns and one-node connected hinges in topology optimization , 2002 .

[211]  Zhan Kang,et al.  Topological design of compliant smart structures with embedded movable actuators , 2014 .

[212]  Antoine Laurain,et al.  A level set-based structural optimization code using FEniCS , 2018 .

[213]  Zhen Luo,et al.  Shape and topology optimization for electrothermomechanical microactuators using level set methods , 2009, J. Comput. Phys..

[214]  K. Abdel-Malek,et al.  Compliant mechanism design using multi-objective topology optimization scheme of continuum structures , 2005 .

[215]  Xu Guo,et al.  Explicit feature control in structural topology optimization via level set method , 2014 .

[216]  Michael Yu Wang,et al.  Compliant Mechanism Optimization: Analysis and Design with Intrinsic Characteristic Stiffness , 2009 .

[217]  Yi Min Xie,et al.  A simple and compact Python code for complex 3D topology optimization , 2015, Adv. Eng. Softw..

[218]  Rolf Lammering,et al.  Topology synthesis of large‐displacement compliant mechanisms with specific output motion paths , 2012 .

[219]  Xianmin Zhang,et al.  Line-based calibration of a micro-vision motion measurement system , 2017 .

[220]  G. K. Ananthasuresh,et al.  On an optimal property of compliant topologies , 2000 .

[221]  C. R. Sundararajan,et al.  Probabilistic Structural Mechanics Handbook: Theory and Industrial Applications , 1995 .

[222]  Kalyanmoy Deb,et al.  Domain-specific initial population strategy for compliant mechanisms using customized genetic algorithm , 2011 .

[223]  Ole Sigmund,et al.  Manufacturing tolerant topology optimization , 2009 .

[224]  Xianmin Zhang,et al.  Level Set-Based Topology Optimization of Hinge-Free Compliant Mechanisms Using a Two-Step Elastic Modeling Method , 2014 .

[225]  N. Wang,et al.  Design of dielectric elastomer actuator using topology optimization method based on genetic algorithm , 2019, Smart Materials and Structures.

[226]  O. Sigmund,et al.  Robust topology optimization accounting for spatially varying manufacturing errors , 2011 .

[227]  K. Saitou,et al.  Multi-material topology optimization using ordered SIMP interpolation , 2016, Structural and Multidisciplinary Optimization.

[228]  Cristina Alonso,et al.  Topology synthesis of Multi-Input-Multi-Output compliant mechanisms , 2014, Adv. Eng. Softw..

[229]  Seungjae Min,et al.  A note on hinge‐free topology design using the special triangulation of design elements , 2005 .

[230]  Xianmin Zhang,et al.  Topology Optimization of Compliant Mechanisms , 2018 .

[231]  A. Saxena,et al.  On honeycomb representation and SIGMOID material assignment in optimal topology synthesis of compliant mechanisms , 2007 .

[232]  X. Tong,et al.  Optimal fiber orientation and topology design for compliant mechanisms with fiber-reinforced composites , 2017 .

[233]  M. Wang,et al.  Design of distributed compliant micromechanisms with an implicit free boundary representation , 2008 .

[234]  Zhang Xianmin.  Reliability-based Topology Optimization of Compliant Mechanisms by Using Foundation Structure Approach , 2010 .

[235]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[236]  D. Floreano,et al.  Versatile Soft Grippers with Intrinsic Electroadhesion Based on Multifunctional Polymer Actuators , 2016, Advanced materials.

[237]  Xiaoming Wang,et al.  A level set method for structural topology optimization , 2003 .

[238]  Qingsong Xu,et al.  Design and analysis of a micro-gripper with constant force mechanism , 2016, 2016 12th World Congress on Intelligent Control and Automation (WCICA).

[239]  R. Bharanidaran,et al.  A new method for designing a compliant mechanism based displacement amplifier , 2016 .

[240]  R Bharanidaran,et al.  Numerical simulation and experimental investigation of a topologically optimized compliant microgripper , 2014 .

[241]  Qingsong Xu,et al.  A Totally Decoupled Piezo-Driven XYZ Flexure Parallel Micropositioning Stage for Micro/Nanomanipulation , 2011, IEEE Transactions on Automation Science and Engineering.

[242]  Just L. Herder,et al.  Negative Stiffness Building Blocks for Statically Balanced Compliant Mechanisms: Design and Testing , 2010 .

[243]  Min-Gyu Im,et al.  Reliability-based topology optimization of electro-thermal-compliant mechanisms with a new material mixing method , 2012 .

[244]  Yen-Pin Chiang,et al.  Optimal Design of a Soft Robotic Gripper for Grasping Unknown Objects. , 2018, Soft robotics.

[245]  C. S. Jog,et al.  A new approach to variable-topology shape design using a constraint on perimeter , 1996 .

[246]  M. Wang,et al.  Length scale control for structural optimization by level sets , 2016 .

[247]  Xianmin Zhang,et al.  Input coupling analysis and optimal design of a 3-DOF compliant micro-positioning stage , 2008 .

[248]  A. Takezawa,et al.  Topology optimization of compliant circular path mechanisms based on an aggregated linear system and singular value decomposition , 2012 .

[249]  T. E. Bruns,et al.  Topology optimization of non-linear elastic structures and compliant mechanisms , 2001 .

[250]  Xianmin Zhang,et al.  Topology optimization of distributed flexure hinges with desired performance , 2020, Engineering Optimization.

[251]  Just L. Herder,et al.  Synthesis Methods in Compliant Mechanisms: An Overview , 2009 .

[252]  Masataka Yoshimura,et al.  An innovative design method for compliant mechanisms combining structural optimisations and designer creativity , 2009 .

[253]  Shinji Nishiwaki,et al.  Design of compliant mechanisms considering thermal effect compensation and topology optimization , 2010 .

[254]  N. Kikuchi,et al.  Optimal structural design considering flexibility , 2001 .

[255]  Nianfeng Wang,et al.  Hierarchical optimization for topology design of multi-material compliant mechanisms , 2017 .

[256]  Larry L. Howell,et al.  Kinetostatic modeling of complex compliant mechanisms with serial-parallel substructures: A semi-analytical matrix displacement method , 2018 .

[257]  Cristina Alonso,et al.  Evolutionary optimization of compliant mechanisms subjected to non-uniform thermal effects , 2012 .

[258]  Nianfeng Wang,et al.  Design of a rotary dielectric elastomer actuator using a topology optimization method based on pairs of curves , 2018 .

[259]  Li,et al.  Multi-objective Topology Optimization of Thermo-mechanical Compliant Mechanisms , 2011 .

[260]  K. Tai,et al.  Structural topology optimization using a genetic algorithm with a morphological geometric representation scheme , 2005 .

[261]  Dan M. Frangopol,et al.  Reliability-based analysis and design optimization of electrostatically actuated MEMS , 2004 .

[262]  Ole Sigmund,et al.  Optimum Design of Microelectromechanical Systems , 2001 .

[263]  Jianyuan Jia,et al.  A generalized model for conic flexure hinges. , 2009, The Review of scientific instruments.

[264]  Yingjun Wang,et al.  Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review , 2018, Computer Modeling in Engineering & Sciences.

[265]  Chao-Chieh Lan,et al.  A Constant-Force Compliant Gripper for Handling Objects of Various Sizes , 2014 .

[266]  Christopher B. Williams,et al.  Multiple-Material Topology Optimization of Compliant Mechanisms Created Via PolyJet Three-Dimensional Printing , 2014 .

[267]  Stuart T. Smith,et al.  ELLIPTICAL FLEXURE HINGES , 1997 .

[268]  Karim Abdel-Malek,et al.  Continuum topology optimization for monolithic compliant mechanisms of micro-actuators , 2006 .

[269]  T. Buhl.  Simultaneous topology optimization of structure and supports , 2002 .

[270]  Xianmin Zhang,et al.  TOPOLOGY OPTIMOZATION OF COMPLIANT MECHANISMS , 2003 .

[271]  Shikui Chen,et al.  Parametric structural shape & topology optimization with a variational distance-regularized level set method , 2017 .

[272]  Mary Frecker,et al.  Topological synthesis of compliant mechanisms using multi-criteria optimization , 1997 .

[273]  Gaofei Ouyang.  Reliability-based Topology Optimization of Structures Using the Level Set Method , 2008 .

[274]  Markus Olhofer,et al.  Evolutionary computation for topology optimization of mechanical structures: An overview of representations , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[275]  Grégoire Allaire,et al.  Structural optimization with $\tt{FreeFem++}$ , 2006 .

[276]  Michael Yu Wang,et al.  Shape and topology optimization of compliant mechanisms using a parameterization level set method , 2007, J. Comput. Phys..

[277]  Tielin Shi,et al.  Topology optimization of thermal actuator and its support using the level set based multiple–type boundary method and sensitivity analysis based on constrained variational principle , 2018 .

[278]  Seog-Young Han,et al.  Topology optimum design of compliant mechanisms using modified ant colony optimization , 2015 .

[279]  Prabhat Kumar,et al.  On topology optimization with embedded boundary resolution and smoothing , 2015 .

[280]  S. Fatikow,et al.  Filter the shape sensitivity in level set-based topology optimization methods , 2015 .

[281]  Xianmin Zhang,et al.  Structural Topology Optimization Using a Moving Morphable Component-Based Method Considering Geometrical Nonlinearity , 2018, Journal of Mechanical Design.

[282]  A. Midha,et al.  A Compliance Number Concept for Compliant Mechanisms, and Type Synthesis , 1987 .

[283]  Allan T. Dolovich,et al.  On understanding of design problem formulation for compliant mechanisms through topology optimization , 2013 .

[284]  Xu Guo,et al.  An explicit length scale control approach in SIMP-based topology optimization , 2014 .

[285]  Rigoberto Burgueño,et al.  Buckling-induced smart applications: recent advances and trends , 2015 .

[286]  Xianmin Zhang,et al.  Design of Planar Large-Deflection Compliant Mechanisms With Decoupled Multi-Input-Output Using Topology Optimization , 2019, Journal of Mechanisms and Robotics.

[287]  Xianwen Kong,et al.  Mobility and Singularity Analysis of a Class of Two Degrees of Freedom Rotational Parallel Mechanisms Using a Visual Graphic Approach , 2012 .

[288]  C. G. Lopes,et al.  Topology design of compliant mechanisms with stress constraints based on the topological derivative concept , 2016 .

[289]  Shusheng Bi,et al.  A Family of Butterfly Flexural Joints: Q-LITF Pivots , 2012 .

[290]  S. Fatikow,et al.  Hybrid flexure hinges. , 2013, The Review of scientific instruments.

[291]  Jian Zhang,et al.  Minimum length scale control in structural topology optimization based on the Moving Morphable Components (MMC) approach , 2016 .

[292]  Liang Gao,et al.  Stress‐based multi‐material topology optimization of compliant mechanisms , 2018 .

[293]  Y. Y. Kim,et al.  Hinge-free topology optimization with embedded translation-invariant differentiable wavelet shrinkage , 2004 .

[294]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[295]  Kurt Maute,et al.  Level-set methods for structural topology optimization: a review , 2013 .

[296]  Anupam Saxena,et al.  Topology design of large displacement compliant mechanisms with multiple materials and multiple output ports , 2005 .

[297]  O. Sigmund,et al.  Design and fabrication of compliant micromechanisms and structures with negative Poisson's ratio , 1996, Proceedings of Ninth International Workshop on Micro Electromechanical Systems.

[298]  K. Maute,et al.  Analytical sensitivity analysis of geometrically nonlinear structures based on the co-rotational finite element method , 2006 .

[299]  Sridhar Kota,et al.  An Energy Formulation for Parametric Size and Shape Optimization of Compliant Mechanisms , 1999 .

[300]  Michael Yu Wang,et al.  Shape feature control in structural topology optimization , 2008, Comput. Aided Des..

[301]  Sang-Hoon Lee,et al.  Level set based robust shape and topology optimization under random field uncertainties , 2010 .

[302]  Gang-Won Jang,et al.  Topology optimization of MEMS considering etching uncertainties using the level‐set method , 2012 .

[303]  Allan T. Dolovich,et al.  Topology optimization of efficient and strong hybrid compliant mechanisms using a mixed mesh of beams and flexure hinges with strength control , 2018 .

[304]  Andrew T. Conn,et al.  Elastic Cube Actuator with Six Degrees of Freedom Output , 2015 .

[305]  Bret Stanford,et al.  Three-Dimensional Topologies of Compliant Flapping Mechanisms , 2014 .

[306]  Bernhard Sendhoff,et al.  Robust Optimization - A Comprehensive Survey , 2007 .

[307]  Osvaldo M. Querin,et al.  Topology optimization of 3D compliant actuators by a sequential element rejection and admission method , 2016 .

[308]  Xianmin Zhang,et al.  Design of fully decoupled compliant mechanisms with multiple degrees of freedom using topology optimization , 2018, Mechanism and Machine Theory.

[309]  J. R. Raney,et al.  Multistable Architected Materials for Trapping Elastic Strain Energy , 2015, Advanced materials.

[310]  Xu Guo,et al.  Structural complexity control in topology optimization via moving morphable component (MMC) approach , 2017 .

[311]  Guo Feng Huang,et al.  A topology optimization method with constant volume fraction during iterations for design of compliant mechanisms , 2016 .

[312]  Yu Wang,et al.  Topology optimization of compliant mechanisms using element-free Galerkin method , 2015, Adv. Eng. Softw..

[313]  Eduardo Lenz Cardoso,et al.  On the influence of local and global stress constraint and filtering radius on the design of hinge-free compliant mechanisms , 2018 .

[314]  Martin Wegener,et al.  Tailored Buckling Microlattices as Reusable Light‐Weight Shock Absorbers , 2016, Advanced materials.

[315]  N. Kikuchi,et al.  A homogenization method for shape and topology optimization , 1991 .

[316]  G. Allaire,et al.  Structural optimization using sensitivity analysis and a level-set method , 2004 .

[317]  Damiano Pasini,et al.  Snapping mechanical metamaterials under tension. , 2015, Advanced materials.

[318]  Takayuki Yamada,et al.  Level set-based topology optimization for the design of a peltier effect thermoelectric actuator , 2017 .

[319]  Xian-min Zhang,et al.  Unified motion reliability analysis and comparison study of planar parallel manipulators with interval joint clearance variables , 2019, Mechanism and Machine Theory.

[320]  Larry L. Howell,et al.  The topological synthesis of compliant mechanisms , 1996 .