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Understanding coupled factors that affect the modelling accuracy of typical planar compliant mechanisms


In order to accurately model compliant mechanism utilizing plate flexures, qualitative planar stress (Young’s modulus) and planar strain (plate modulus) assumptions are not feasible. This paper investigates a quantitative equivalent modulus using nonlinear finite element analysis (FEA) to reflect coupled factors in affecting the modelling accuracy of two typical distributed- compliance mechanisms. It has been shown that all parameters have influences on the equivalent modulus with different degrees; that the presence of large load-stiffening effect makes the equivalent modulus significantly deviate from the planar assumptions in two ideal scenarios; and that a plate modulus assumption is more reasonable for a very large out-of-plane thickness if the beam length is large.

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

    Google Scholar 

  6. 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 

  7. Timoshenko S. On the correction for shear of the differential equation for transverse vibrations of prismatic bars. Philosophical Magazine Series 6, 1921, 41(245): 744–746

    Article  Google Scholar 

  8. 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 

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

    Article  Google Scholar 

  10. Zettl B, Szyszkowski W, Zhang W J. On systematic errors of twodimensional finite element modeling of right circular planar flexure hinges. Journal of Mechanical Design, 2005, 127(4): 782–787

    Article  Google Scholar 

  11. Zettl B, Szyszkowski W, Zhang W J. Accurate low DOF modeling of a planar complaint mechanism with flexure hinges: The equivalent beam methodology. Precision Engineering, 2005, 29 (2): 237–245

    Article  Google Scholar 

  12. 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 

  13. Hao G, Kong X. A novel large-range XY compliant parallel manipulator with enhanced out-of-plane stiffness. Journal of Mechanical Design, 2012, 134(6): 061009

    Article  Google Scholar 

  14. Hao G, Kong X. A normalization-based approach to the mobility analysis of spatial compliant multi-beam modules. Mechanism and Machine Theory, 2013, 59(1): 1–19

    Article  MathSciNet  Google Scholar 

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Correspondence to Guangbo Hao.

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Hao, G., Li, H., Kemalcan, S. et al. Understanding coupled factors that affect the modelling accuracy of typical planar compliant mechanisms. Front. Mech. Eng. 11, 129–134 (2016).

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  • coupling factors
  • modelling accuracy
  • compliant mechanisms
  • equivalent modulus