Skip to main content

Topology Optimization of Flexure Hinges

  • Chapter
  • First Online:
Topology Optimization of Compliant Mechanisms

Abstract

This chapter is devoted to developing a systematic method for the topology optimization of flexure hinges. The main research work includes: (1) Developing basic topology optimization models for translational and revolute flexure hinges. The objective function for the topology optimization of flexure hinges is to maximize the compliance in the rotational direction while minimizing the compliance in the direction of parasitic motion. (2) Reducing the maximum stress and stress concentration factor by considering the stress constraint in the optimization model. (3) Improving the performances of the common notch flexure hinges by redesigning their configurations using topology optimization approach.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Awtar, S., Slocum, A.H., Sevincer, E.: Characteristics of beam-based flexure modules. J. Mech. Des. 129(6), 625–639 (2007)

    Article  Google Scholar 

  2. Barthelemy, J.F., Haftka, R.T.: Approximation concepts for optimum structural designła review. Structural Optimization 5(3), 129–144 (1993)

    Article  Google Scholar 

  3. Bendsøe, M.P.: Optimal shape design as a material distribution problem. Structural Optimization 1(4), 193–202 (1989)

    Article  Google Scholar 

  4. Bendsoe, M.P., Sigmund, O.: Topology Optimization: Theory, Methods, and Applications. Springer Science & Business Media (2013)

    Google Scholar 

  5. Bruggi, M.: On an alternative approach to stress constraints relaxation in topology optimization. Structural Multidisciplinary Optimization 36(2), 125–141 (2008)

    Article  MathSciNet  Google Scholar 

  6. Chen, Z., Zhou, D., Liao, H., Zhang, X.: Precision alignment of optical fibers based on telecentric stereo microvision. IEEE/ASME Trans. Mechatron. 21(4), 1924–1934 (2016)

    Article  Google Scholar 

  7. Cheng, G., Guo, X.: \(\varepsilon \)-relaxed approach in structural topology optimization. Structural Optimization 13(4), 258–266 (1997)

    Article  Google Scholar 

  8. De Bona, F., Munteanu, M.G.: Optimized flexural hinges for compliant micromechanisms. Analog Integr. Circ. Sig. Process. 44(2), 163–174 (2005)

    Article  Google Scholar 

  9. De Leon, D.M., Alexandersen, J., Fonseca, J.S., Sigmund, O.: Stress-constrained topology optimization for compliant mechanism design. Structural Multidisciplinary Optimization 52(5), 929–943 (2015)

    Article  MathSciNet  Google Scholar 

  10. Holmberg, E., Torstenfelt, B., Klarbring, A.: Stress constrained topology optimization. Structural Multidisciplinary Optimization 48(1), 33–47 (2013)

    Article  MathSciNet  Google Scholar 

  11. 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. 34(2), 259–270 (2010)

    Article  Google Scholar 

  12. Howell, L.L.: Compliant mechanisms. Wiley (2001)

    Google Scholar 

  13. Kirsch, U.: On singular topologies in optimum structural design. Structural Optimization 2(3), 133–142 (1990)

    Article  Google Scholar 

  14. Larsen, U.D., Signund, O., Bouwsta, S.: Design and fabrication of compliant micromechanisms and structures with negative poisson’s ratio. J. Microelectromech. Syst. 6(2), 99–106 (1997)

    Article  Google Scholar 

  15. Le, C., Norato, J., Bruns, T., Ha, C., Tortorelli, D.: Stress-based topology optimization for continua. Structural Multidisciplinary Optimization 41(4), 605–620 (2010)

    Article  Google Scholar 

  16. Lin, R., Zhang, X., Long, X., Fatikow, S.: Hybrid flexure hinges. Review of scientific instruments 84(8), 085,004 (2013)

    Article  Google Scholar 

  17. Lipkin, H., Patterson, T.: Generalized center of compliance and stiffness. In: Proceedings of 1992 IEEE International Conference on Robotics and Automation, pp. 1251–1256. IEEE (1992)

    Google Scholar 

  18. Liu, M., Zhang, X., Fatikow, S.: Topology optimization of large-displacement flexure hinges. In: ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. V05AT08A005–V05AT08A005. American Society of Mechanical Engineers (2015)

    Google Scholar 

  19. Liu, M., Zhang, X., Fatikow, S.: Design and analysis of a high-accuracy flexure hinge. Rev. Scientific Instruments 87(5), 055,106 (2016)

    Article  Google Scholar 

  20. Liu, M., Zhang, X., Fatikow, S.: Design of flexure hinges based on stress-constrained topology optimization. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. p. 0954406216671346 (2016)

    Google Scholar 

  21. Liu, M., Zhang, X., Fatikow, S.: Design and analysis of a multi-notched flexure hinge for compliant mechanisms. Precis. Eng. (2017)

    Google Scholar 

  22. Lobontiu, N.: Compliant mechanisms: design of flexure hinges. CRC Press (2002)

    Google Scholar 

  23. Lobontiu, N., Paine, J.S., Garcia, E., Goldfarb, M.: Corner-filleted flexure hinges. J. Mech. Des. 123(3), 346–352 (2001)

    Article  Google Scholar 

  24. Lobontiu, N., Paine, J.S., Garcia, E., Goldfarb, M.: Design of symmetric conic-section flexure hinges based on closed-form compliance equations. Mech. Mach. Theory 37(5), 477–498 (2002)

    Article  Google Scholar 

  25. Lobontiu, N., Paine, J.S., OMalley, E., Samuelson, M.: Parabolic and hyperbolic flexure hinges: flexibility, motion precision and stress characterization based on compliance closed-form equations. Precis. Eng. 26(2), 183–192 (2002)

    Article  Google Scholar 

  26. Paros, J.M.: How to design flexure hinges. Mach. Des. 37, 151–156 (1965)

    Google Scholar 

  27. Pilkey, W.D., Pilkey, D.F.: Peterson’s Stress Concentration Factors. Wiley (2008)

    Google Scholar 

  28. Rozvany, G., Sobieszczanski-Sobieski, J.: New optimality criteria methods: forcing uniqueness of the adjoint strains by corner-rounding at constraint intersections. Structural Optimization 4(3–4), 244–246 (1992)

    Article  Google Scholar 

  29. Schotborgh, W.O., Kokkeler, F.G., Tragter, H., van Houten, F.J.: Dimensionless design graphs for flexure elements and a comparison between three flexure elements. Precis. Eng. 29(1), 41–47 (2005)

    Article  Google Scholar 

  30. Sigmund, O.: On the design of compliant mechanisms using topology optimization. Mech. Structures Mach. 25(4), 493–524 (1997)

    Article  Google Scholar 

  31. Smith, S.T.: Flexures: Elements of Elastic Mechanisms. CRC Press (2000)

    Google Scholar 

  32. Smith, S.T., Badami, V.G., Dale, J.S., Xu, Y.: Elliptical flexure hinges. Rev. Sci. Instrum. 68(3), 1474–1483 (1997)

    Article  Google Scholar 

  33. Su, H.J., Dorozhkin, D.V., Vance, J.M.: A screw theory approach for the conceptual design of flexible joints for compliant mechanisms. J. Mech. Robot. 1(4), 041,009 (2009)

    Article  Google Scholar 

  34. Suzuki, K., Kikuchi, N.: A homogenization method for shape and topology optimization. Comput. Methods Appl. Mech. Eng. 93(3), 291–318 (1991)

    Article  Google Scholar 

  35. Svanberg, K.: The method of moving asymptotesła new method for structural optimization. Int. J. Numer. Meth. Eng. 24(2), 359–373 (1987)

    Article  MathSciNet  Google Scholar 

  36. Tian, Y., Shirinzadeh, B., Zhang, D.: Closed-form compliance equations of filleted v-shaped flexure hinges for compliant mechanism design. Precis. Eng. 34(3), 408–418 (2010)

    Article  Google Scholar 

  37. Trease, B.P., Moon, Y.M., Kota, S.: Design of large-displacement compliant joints. J. Mech. Des. 127(4), 788–798 (2005)

    Article  Google Scholar 

  38. Tseytlin, Y.M.: Notch flexure hinges: an effective theory. Rev. Sci. Instrum. 73(9), 3363–3368 (2002)

    Article  Google Scholar 

  39. Wang, M.Y., Wang, X., Guo, D.: A level set method for structural topology optimization. Comput. Methods Appl. Mech. Eng. 192(1), 227–246 (2003)

    Article  MathSciNet  Google Scholar 

  40. Wang, R., Zhang, X.: A planar 3-DOF nanopositioning platform with large magnification. Precis. Eng. 46, 221–231 (2016)

    Article  Google Scholar 

  41. Xie, Y.M., Steven, G.P.: A simple evolutionary procedure for structural optimization. Comput. Structures 49(5), 885–896 (1993)

    Article  Google Scholar 

  42. Xu, W., King, T.: Flexure hinges for piezoactuator displacement amplifiers: flexibility, accuracy, and stress considerations. Precis. Eng. 19(1), 4–10 (1996)

    Article  Google Scholar 

  43. Yong, Y.K., Lu, T.F., Handley, D.C.: Review of circular flexure hinge design equations and derivation of empirical formulations. Precis. Eng. 32(2), 63–70 (2008)

    Article  Google Scholar 

  44. Yu, J., Li, S., Su, H.j., Culpepper, M.: Screw theory based methodology for the deterministic type synthesis of flexure mechanisms. J. Mech. Robot. 3(3), 031,008 (2011)

    Article  Google Scholar 

  45. Zelenika, S., Munteanu, M.G., De Bona, F.: Optimized flexural hinge shapes for microsystems and high-precision applications. Mech. Mach. Theory 44(10), 1826–1839 (2009)

    Article  Google Scholar 

  46. Zhu, B., Zhang, X., Fatikow, S.: Design of single-axis flexure hinges using continuum topology optimization method. Sci. China Technol. Sci. 57(3), 560–567 (2014)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xianmin Zhang .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Zhang, X., Zhu, B. (2018). Topology Optimization of Flexure Hinges. In: Topology Optimization of Compliant Mechanisms. Springer, Singapore. https://doi.org/10.1007/978-981-13-0432-3_2

Download citation

  • DOI: https://doi.org/10.1007/978-981-13-0432-3_2

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-0431-6

  • Online ISBN: 978-981-13-0432-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics