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A brief review on nonlinear modeling methods and applications of compliant mechanisms

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Abstract

Compliant mechanisms (CMs) have become one of the most popular research themes in mechanisms and robotics because of their merits. This paper aims to provide a brief systematic review on the advances of nonlinear static modeling approaches and the applications of CMs to promote interdisciplinary/multidisciplinary development for associated theories and other new applications. It also predicts likely future directions of applications and theory development.

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References

  1. Howell L L. Compliant Mechanisms. New York: Wiley, 2001

    Google Scholar 

  2. Lobontiu N. Compliant Mechanisms: Design of Flexure Hinges. Boca Raton: CRC Press, 2002

    Book  Google Scholar 

  3. Howell L L, Magleby S P, Olsen B M. Handbook of Compliant Mechanisms. New York: Wiley, 2013

    Book  Google Scholar 

  4. Smith S T. Flexures: Elements of Elastic Mechanisms. London: Taylor and Francis, 2003

    Google Scholar 

  5. Howell L L, Midha A. Parametric deflection approximations for end-loaded, large-deflection beams in compliant mechanisms. Journal of Mechanical Design, 1995, 117(1): 156–165

    Article  Google Scholar 

  6. Saggere L, Kota S. Synthesis of planar, compliant four-bar mechanisms for compliant-segment motion generation. Journal of Mechanical Design, 2001, 123(4): 535–541

    Article  Google Scholar 

  7. Kota S, Lu K J, Kreiner K, et al. Design and application of compliant mechanisms for surgical tools. Journal of Biomechanical Engineering, 2005, 127(6): 981–989

    Article  Google Scholar 

  8. Awtar S, Slocum A H. Constraint-based design of parallel kinematic XY flexure mechanisms. Journal of Mechanical Design, 2007, 129 (8): 816–830

    Article  Google Scholar 

  9. Awtar S, Slocum A H, Sevincer E. Characteristics of beam-based flexure modules. Journal of Mechanical Design, 2007, 129(6): 625–639

    Article  Google Scholar 

  10. Chen G, Liu X, Du Y. Elliptical-arc-fillet flexure hinges: Toward a generalized model for commonly used flexure hinges. Journal of Mechanical Design, 2011, 133(8): 081002–081010

    Article  Google Scholar 

  11. Hao G, Kong X, Reuben R L. A nonlinear analysis of spatial compliant parallel modules: Multi-beam modules. Mechanism and Machine Theory, 2011, 46(5): 680–706

    Article  MATH  Google Scholar 

  12. Sen S, Awtar S. A closed-form non-linear model for the constraint characteristics of symmetric spatial beams. Journal of Mechanical Design, 2013, 135(3): 031003–031013

    Article  Google Scholar 

  13. Sen S, Awtar S. Nonlinear constraint model for symmetric threedimensional beams. In: Proceedings of the ASME 2010 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference. Montreal, 2010

    Google Scholar 

  14. Chen G, Bai R. Modeling large spatial deflections of slender bisymmetric beams in compliant mechanisms using chained spatialbeam-constraint-model (CSBCM). In: Proceedings of the ASME 2010 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference. Boston, 2015

    Google Scholar 

  15. Venkiteswaran V K, Su H J. A parameter optimization framework for determining the pseudo-rigid-body model of cantilever-beams. Precision Engineering, 2015, 40: 46–54

    Article  Google Scholar 

  16. Chen G, Ma F. Kinetostatic modeling of fully compliant bistable mechanisms using Timoshenko beam constraint model. Journal of Mechanical Design, 2015, 137(2): 022301–022310

    Article  Google Scholar 

  17. Kim C, Ebenstein D. Curve decomposition for large deflection analysis of fixed-guided beams with application to statically balanced compliant mechanisms. Journal of Mechanisms and Robotics, 2012, 4(4): 041009–041017

    Article  Google Scholar 

  18. Holst G L, Teichert G H, Jensen B D. Modeling and experiments of buckling modes and deflection of fixed-guided beams in compliant mechanisms. Journal of Mechanical Design, 2011, 133(5): 051002–051011

    Article  Google Scholar 

  19. Zhang A, Chen G. A comprehensive elliptic integral solution to the large deflection problems of thin beams in compliant mechanisms. Journal of Mechanisms and Robotics, 2013, 5(2): 021006–021015

    Article  Google Scholar 

  20. Zhao J, Jia J, He X, et al. Post-buckling and snap-through behaviour of inclined slender beams. Journal of Applied Mechanics, 2008, 75 (4): 041020–041026

    Article  Google Scholar 

  21. Awtar S, Sevincer E, Sen S. Elastic averaging in flexure mechanisms: A three-beam parallelogram flexure case study. Journal of Mechanisms and Robotics, 2010, 2(4): 041006–041017

    Article  Google Scholar 

  22. Hao G, Li H. Nonlinear analytical modeling and characteristic analysis of a class of compound multi-beam parallelogram mechanisms. Journal of Mechanisms and Robotics, 2015, 7(4): 041016–041019

    Article  Google Scholar 

  23. Hao G, Kong X. Nonlinear analytical modeling and characteristic analysis of symmetrical wire beam based composite compliant parallel modules for planar motion. Mechanism and Machine Theory, 2014, 77: 122–147

    Article  Google Scholar 

  24. Pei X, Yu J, Zong G, et al. A novel family of leaf-type compliant joints: Combination of two isosceles-trapezoidal flexural pivots. Journal of Mechanisms and Robotics, 2009, 1(2): 021005–021010

    Article  Google Scholar 

  25. Li H, Hao G. Constraint-force-based (CFB) modelling of compliant mechanisms. In: Proceedings of ASME 2015 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference. Boston, 2015

    Google Scholar 

  26. Awtar S, Ustick J, Sen S. An XYZ parallel-kinematic flexure mechanism with geometrically decoupled degrees of freedom. Journal of Mechanisms and Robotics, 2012, 5(1): 015001–015007

    Article  Google Scholar 

  27. Awtar S, Sen S. A generalized constraint model for two-dimensional beam flexures: Nonlinear strain energy formulation. Journal of Mechanical Design, 2010, 132(8): 081009

    Article  Google Scholar 

  28. Awtar S. Analysis and synthesis of planar kinematic XY mechanisms. Dissertation for the Doctoral Degree. Cambridge: Massachusetts Institute of Technology, 2004

    Google Scholar 

  29. Saxena A, Kramer S N. A simple and accurate method for determining large deflections in compliant mechanisms subjected to end forces and moments. Journal of Mechanical Design, 1998, 120 (3): 392–400

    Article  Google Scholar 

  30. Kumar R, Ramachandra L S, Roy D. Techniques based on genetic algorithms for large deflection analysis of beams. Sadhana, 2004, 29 (6): 589–604

    Article  MATH  Google Scholar 

  31. Banerjee A, Bhattacharya B, Mallik A K. Large deflection of cantilever beams with geometric non-linearity: Analytical and numerical approaches. International Journal of Non-linear Mechanics, 2008, 43(5): 366–376

    Article  MATH  Google Scholar 

  32. Ma F, Chen G. Modeling large planar deflections of flexible beams in compliant mechanisms using chained beam-constraint-Model. Journal of Mechanisms and Robotics, 2015, 8(2): 021018

    Article  Google Scholar 

  33. Morsch F M, Tolou N, Herder J L. Comparison of methods for large deflection analysis of a cantilever beam under free end point load. In: Proceedings of the ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference. San Diego, 2009

    Google Scholar 

  34. Howell L L, Midha A, Norton TW. Evaluation of equivalent spring stiffness for use in a pseudo-rigid-body model of large-deflection compliant mechanisms. Journal of Mechanical Design, 1996, 118 (1): 126–131

    Article  Google Scholar 

  35. Saggere L, Kota S. Synthesis of planar, compliant four-bar mechanisms for compliant-segment motion generation. Journal of Mechanical Design, 2001, 123(4): 535–541

    Article  Google Scholar 

  36. Su H J. A pseudorigid-body 3R model for determining large deflection of cantilever beams subject to tip loads. Journal of Mechanisms and Robotics, 2009, 1(2): 795–810

    Article  Google Scholar 

  37. Awtar S, Sen S. A generalized constraint model for two-dimensional beam flexures: Nonlinear load-displacement formulation. Journal of Mechanical Design, 2010, 132(8): 081008

    Article  Google Scholar 

  38. Sen S, Awtar S. Nonlinear strain energy formulation of a generalized bisymmetric spatial beam for flexure mechanism analysis. Journal of Mechanical Design (New York), 2014, 136(2): 021002–021013

    Article  Google Scholar 

  39. Schitter G, Thurner P J, Hansma P K. Design and input-shaping control of a novel scanner for high-speed atomic force microscopy. Mechatronics, 2008, 18(5–6): 282–288

    Article  Google Scholar 

  40. Kim D, Lee D Y, Gweon D G. A new nano-accuracy AFM system for minimizing Abbe errors and the evaluation of its measuring uncertainty. Ultramicroscopy, 2007, 107(4–5): 322–328

    Article  Google Scholar 

  41. Yu J, Xie Y, Li Z, et al. Design and experimental testing of an improved large-range decoupled XY compliant parallel micromanipulator. Journal of Mechanisms and Robotics, 2015, 7(4): 044503

    Article  Google Scholar 

  42. Hu Y H, Lin K H, Chang S C, et al. Design of a compliant micromechanism for optical-fiber alignment. Key Engineering Materials, 2008, 381–382: 141–144

    Article  Google Scholar 

  43. Thorlabs. https://www.thorlabs.com/navigation.cfm?guide_id = 84&gclid = Cj0KEQiAv5-zBRCAzfWGu-2jo70BEiQAj_-F8oL9nxDhydrBT7Ph5Qx3eFPfWxuXA5QmbGUXci2Q6w60aAley8P8HAQ (in Chinese)

  44. Chen W, Du C, Wu Y, et al. A parallel alignment device with dynamic force compensation for nanoimprint lithography. Review of Scientific Instruments, 2014, 85(3): 035107

    Article  Google Scholar 

  45. Li J, Sedaghati R, Dargahi J, et al. Design and development of a new piezoelectric linear inchworm actuator. Mechatronics, 2005, 15(6): 651–681

    Article  Google Scholar 

  46. Alblalaihid K, Lawes S, Kinnell P. Variable stiffness probing systems for micro-coordinate measuring machines. Precision Engineering, 2016, 43: 262–269

    Article  Google Scholar 

  47. Jin Z, Gao F, Zhang X. Design and analysis of a novel isotropic sixcomponent force/torque sensor. Sensors and Actuators A: Physical, 2003, 109(1–2): 17–20

    Google Scholar 

  48. Hao G, Murphy M, Luo X. Development of a compliantmechanism-based compact three-axis force sensor for high-precision manufacturing. In: Proceedings of the ASME 2015 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE 2015). Boston, 2015

    Google Scholar 

  49. Hansen B J, Carron C J, Jensen B D, et al. Plastic latching accelerometer based on bistable compliant mechanisms. Smart Materials and Structures, 2007, 16(5): 1967–1972

    Article  Google Scholar 

  50. Gao Z, Zhang D. Design, analysis and fabrication of a multidimensional acceleration sensor based on fully decoupled compliant parallel mechanism. Sensors and Actuators A: Physical, 2010, 163 (1): 418–427

    Article  Google Scholar 

  51. Sung E, Slocum A H, Ma R, et al. Design of an ankle rehabilitation device using compliant mechanisms. Journal of Medical Devices, 2011, 5(1): 011001–011007

    Article  Google Scholar 

  52. Chen G, Zhang S. Fully-compliant statically-balanced mechanisms without prestressing assembly: Concepts and case studies. Mechanical Sciences, 2011, 2(2): 169–174

    Article  Google Scholar 

  53. Awtar S, Trutna T T, Nielsen, J M, et al. FlexDexTM: A minimally invasive surgical tool with enhanced dexterity and intuitive control. Journal of Medical Devices, 2009, 4(3): 829–839

    Google Scholar 

  54. Doria M, Birglen L. Design of an under actuated compliant gripper for surgery using nitinol. Journal of Medical Devices, 2009, 3(1): 011007

    Article  Google Scholar 

  55. Liew L A, Tuantranont A, Bright V M. Modeling of thermal actuation in a bulk-micromachined CMOS micromirror. Microelectronics Journal, 2000, 31(9–10): 791–801

    Article  Google Scholar 

  56. Olfatnia M, Cui L, Chopra P, et al. Large range dual-axis microstage driven by electrostatic comb-drive actuators. Journal of Micromechanics and Microengineering, 2013, 23(10): 105008

    Article  Google Scholar 

  57. Olfatnia M, Sood S, Gorman J, et al. Large stroke comb-drive actuators enabled by a novel flexure mechanism. Journal of Microelectromechanical Systems, 2013, 22(2): 483–494

    Article  Google Scholar 

  58. Wilcox D L, Howell L L. Fully compliant tensural bistable micromechanisms (FTBM). Journal of Microelectromechanical Systems, 2005, 14(6): 1223–1235

    Article  Google Scholar 

  59. Xu Q. Design, fabrication, and testing of an MEMS microgripper with dual-axis force sensor. IEEE Sensors Journal, 2015, 15(10): 6017–6026

    Article  Google Scholar 

  60. Aten Q T, Jensen B D, Burnett S H, et al. A self-reconfiguring metamorphic nanoinjector for injection into mouse zygotes. Review of Scientific Instruments, 2014, 85(5): 055005

    Article  Google Scholar 

  61. Hopkins J B, Lange K J, Spadaccini CM. Designing microstructural architectures with thermally actuated properties using freedom, actuation, and constraint topologies. Journal of Mechanical Design, 2013, 135(6): 061004

    Article  Google Scholar 

  62. Lakes R. Foam structures with a negative Poisson’s ratio. Science, 1987, 235(4792): 1038–1040

    Article  Google Scholar 

  63. Kim K, Lee J, Ju J, et al. Compliant cellular materials with compliant porous structures: A mechanism based materials design. International Journal of Solids and Structures, 2014, 51(23–24): 3889–3903

    Article  Google Scholar 

  64. Nelson T G, Lang R J, Pehrson N A, et al. Facilitating deployable mechanisms and structures via developable lamina emergent arrays. Journal of Mechanisms and Robotics, 2015, 8(3): 031006

    Article  Google Scholar 

  65. Fowler R M, Howell L L, Magleby S P. Compliant space mechanisms: A new frontier for compliant mechanisms. Mechanical Sciences, 2011, 2(2): 205–215

    Article  Google Scholar 

  66. Merriam G, Jones J E, Magleby S P, et al. Monolithic 2 DOF fully compliant space pointing mechanism. Mechanical Sciences, 2013, 4 (2): 381–390

    Article  Google Scholar 

  67. Pellegrini S P, Tolou N, Schenk M, et al. Bistable vibration energy harvesters: A review. Journal of Intelligent Material Systems and Structures, 2013, 24(11): 1303–1312

    Article  Google Scholar 

  68. Shaw A D, Neild S A, Wagg D J, et al. A nonlinear spring mechanism incorporating a bistable composite plate for vibration isolation. Journal of Sound and Vibration, 2013, 332(24): 6265–6275

    Article  Google Scholar 

  69. Zhang B, Billings S A, Lang Z Q, et al. Suppressing resonant vibrations using nonlinear springs and dampers. Journal of Vibration and Control, 2009, 15(11): 1731–1744

    Article  MATH  Google Scholar 

  70. Hopkins J B, Panas R M. Eliminating parasitic error in dynamically driven flexure systems. In: Proceedings of the 28th Annual Meeting of the American Society for Precision Engineering. St. Paul, 2013

    Google Scholar 

  71. Hao G, Li H. Extended static modelling and analysis of compliant compound parallelogram mechanisms considering the initial internal axial force. Journal of Mechanisms and Robotics, 2016, 8(4): 041008

    Article  Google Scholar 

  72. Yu J, Lu D, Hao G. Design and analysis of a compliant parallel pantilt platform. Meccanica, 2015, 1–12

    Google Scholar 

  73. She Y, Li C, Cleary J, et al. Design and fabrication of a soft robotic hand with embedded actuators and sensors. Journal of Mechanisms and Robotics, 2015, 7(2): 021007

    Article  Google Scholar 

  74. Zhou L, Marras A, Su H, et al. DNA origami compliant nanostructures with tunable mechanical properties. ACS Nano, 2014, 8(1): 27–34

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Engineering, University College Cork, Cork, T12 YN60, Ireland

    Guangbo Hao & Haiyang Li

  2. School of Mechanical Engineering and Automation, Beihang University, Beijing, 100191, China

    Jingjun Yu

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  1. Guangbo Hao
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  2. Jingjun Yu
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  3. Haiyang Li
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Correspondence to Guangbo Hao.

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Hao, G., Yu, J. & Li, H. A brief review on nonlinear modeling methods and applications of compliant mechanisms. Front. Mech. Eng. 11, 119–128 (2016). https://doi.org/10.1007/s11465-016-0387-9

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