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Design of single-axis flexure hinges using continuum topology optimization method

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Abstract

The design of compliant hinges has been extensively studied in the size and shape level in the literature. This paper presents a method for designing the single-axis flexure hinges in the topology level. Two kinds of hinges, that is, the translational hinge and the revolute hinge, are studied. The basic optimization models are developed for topology optimization of the translational hinge and the revolute hinge, respectively. The objective for topology optimization of flexure hinges is to maximize the compliance in the desired direction meanwhile minimizing the compliances in the other directions. The constraints for accomplishing the translational and revolute requirements are developed. The popular Solid Isotropic Material with Penalization method is used to find the optimal flexure hinge topology within a given design domain. Numerical results are performed to illustrate the validity of the proposed method.

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References

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

    Google Scholar 

  2. Wang H, Zhang X. Input coupling analysis and optimal design of a 3-dof compliant micro-positioning stage. Mech Mach Theroy, 2008, 43: 400–410

    Article  MATH  Google Scholar 

  3. Fatikow S. Automated Nanohandling by Microrobots. 1st ed. London: Springer, 2007

    Google Scholar 

  4. Bendsøe M P, Sigmund O. Topology Optimization: Theory, Methods and Applications. Berlin: Springer, 2003

    Google Scholar 

  5. Zhu B L, Zhang X M. A new level set method for topology optimization of distributed compliant mechanisms. Int J Numer Meth Eng, 2012, 91: 843–871

    Article  Google Scholar 

  6. Zhu B L, Zhang X M, Wang N F. Topology optimization of hinge-free compliant mechanisms with multiple outputs using level set method. Struct Multidisc Optim, 2013, 47: 659–672

    Article  MATH  MathSciNet  Google Scholar 

  7. Lobontiu N. Compliant mechanisms: Design of flexure hinges. CRC Press, 2003

    Google Scholar 

  8. Tian Y, Shirinzadeh B, Zhang D, et al. Three flexure hinges for compliant mechanism designs based on dimensionless graph analysis. Precis Eng, 2010, 34: 92–100

    Article  Google Scholar 

  9. Paros J M, Weisbord L. How to design flexure hinges. Mach Des, 1965, 37: 151–156

    Google Scholar 

  10. Smith S T, Badami V G, Dale J S, et al. Elliptical flexure hinges. Rev Sci Instrum, 1997, 68: 1474–1483

    Article  Google Scholar 

  11. Lobontiu N, Paine J S N, Garcia E, et al. Corner-filleted flexure hinges. J Mech Design, 2001, 123: 346–352

    Article  Google Scholar 

  12. Lobontiu N, Paine J S, Garcia E, et al. Design of symmetric conic-section flexure hinges based on closed-form compliance equations. Mech Mach Theory, 2002, 37: 477–498

    Article  MATH  Google Scholar 

  13. Lobontiu N, Paine J S, O’Malley E, et al. Parabolic and hyperbolic flexure hinges: Flexibility, motion precision and stress characterization based on compliance closed-form equations. Precis Eng, 2002, 26: 183–192

    Article  Google Scholar 

  14. Lobontiu N, Garcia E, Hardau M, et al. Stiffness characterization of corner-filleted flexure hinges. Rev Sci Instrum, 2002, 75: 4896–4905

    Article  Google Scholar 

  15. Tseytlin Y M. Notch flexure hinges: An effective theory. Rev Sci Instrum, 2002, 73: 3363–3368

    Article  Google Scholar 

  16. Awtar S, Slocum A H, Sevincer E. Characteristics of beam-based flexure modules. J Mech Design, 2007, 129: 625–639

    Article  Google Scholar 

  17. Smith S T. Flexures: Elements of Elastic Mechanisms. New York: Gordon and Breach, 2000

    Google Scholar 

  18. Schotborgh W O, Kokkeler F G, Tragter H, et al. Dimensionless design graphs for flexure elements and a comparison between three flexure elements. Precis Eng, 2005, 29: 41–47

    Article  Google Scholar 

  19. Bona F D, Munteanu M G. Optimized flexural hinges for compliant micromechanisms. Analog Integr Circ S, 2005, 44: 163–174

    Article  Google Scholar 

  20. Zelenika S, Munteanu M G, Bona F D. Optimized flexural hinge shapes for microsystems and high-precision applications. Mech Mach Theory, 2009, 44: 1826–1839

    Article  MATH  Google Scholar 

  21. Trease B P, Moon Y M, Kota S. Design of large-displacement compliant joints. J Mech Design, 2005, 127: 788–798

    Article  Google Scholar 

  22. Yu J J, Li S Z, Su H J, et al. Screw theory based methodology for the deterministic type synthesis of flexure mechanisms. J Mech Robot, 2011, 3: 03100801–03100813

    Article  Google Scholar 

  23. Su H J, Denis V, Dorozhkin et al. A screw theory approach for the conceptual design of flexible joints for compliant mechanisms. J Mech Robot, 2009, 1: 04100901–04100907

    Google Scholar 

  24. Hopkins J B, Culpepper M L. Synthesis of multi-degree of freedom, parallel flexure system concepts via freedom and constraint topology (FACT)-part I: Principles. Precis Eng, 2010, 34: 259–270

    Article  Google Scholar 

  25. Frecker M I, Ananthasuresh G K, Nishiwaki S, et al. Topological synthesis of compliant mechanisms using multi-criteria optimization. J Mech Design, 1997, 119: 238–245

    Article  Google Scholar 

  26. Sigmund O. On the desgn of compliant mechanisms using topology optimization. Mech Based Struct Mach, 1997, 25: 493–524

    Article  Google Scholar 

  27. Nishiwaki S, Min S, Yoo J, et al. Optimal structural design considering flexibility. Comput Methods Appl Mech Eng, 2001, 190: 4457–4504

    Article  MathSciNet  Google Scholar 

  28. Wang M, Wang X M, Guo D M. A level set method for structural topology optimization. Comput Methods Appl Mech Eng, 2003, 192: 227–246

    Article  MATH  Google Scholar 

  29. Allaire G, Jouve F, Toader A M. Structural optimization using sensitivity analysis and a level set method. J Comput Phys, 2004, 194: 363–393

    Article  MATH  MathSciNet  Google Scholar 

  30. Rozvany G I N. A critical review of established methods of structural topology optimization. Struct Multidisc Optim, 2009, 37: 217–237

    Article  MATH  MathSciNet  Google Scholar 

  31. Yu J J, Li S Z, Su H J, et al. Screw theory based methodology for the deterministic type synthesis of flexure mechanisms. J Mech Robot, 2011, 3: 031008

    Article  Google Scholar 

  32. Choi K K, Kim N H. Structural sensitivity analysis and optimization 1: Linear system. New York: Springer-Verlag, 2005

    Google Scholar 

  33. Yong Y K, Lu T F, Handley D C. Review of circular flexure hinge design equations and derivation of empirical formulations. Precis Eng, 2008, 32: 63–70

    Article  Google Scholar 

  34. Svanberg K. The method of moving asymptotes-a new method for structural optimization. Int J Numer Methods Eng, 1987, 24: 359–373

    Article  MATH  MathSciNet  Google Scholar 

  35. Barthelemy J F M, Haftka R T. Approximation concepts for optimum structural design-a review. Struct Multidisc Optim, 1993, 5: 129–144

    Article  Google Scholar 

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Authors and Affiliations

  1. Key laboratory of Precision Equipment and Manufacturing Technology of Guangdong Province, South China University of Technology, Guangzhou, 510640, China

    BenLiang Zhu, XianMin Zhang & Sergej Fatikow

  2. Division Microrobotics Department of Computing Science, Uhlhornsweg 84, A1, 26111, Oldenburg, Germany

    Sergej Fatikow

Authors
  1. BenLiang Zhu
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  2. XianMin Zhang
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  3. Sergej Fatikow
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Correspondence to XianMin Zhang.

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Zhu, B., Zhang, X. & Fatikow, S. Design of single-axis flexure hinges using continuum topology optimization method. Sci. China Technol. Sci. 57, 560–567 (2014). https://doi.org/10.1007/s11431-013-5446-4

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  • DOI: https://doi.org/10.1007/s11431-013-5446-4

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