Design and Analysis of Translational Joint Using Corrugated Flexure Units with Variable thickness Segments

  • Nianfeng WangEmail author
  • Zhiyuan Zhang
  • Xianmin Zhang
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


The paper introduces a new type of translational joint using corrugated flexure (CF) beams that are formed by serially connecting variable thickness segments. Double elliptical curves are employed to construct the variable thickness segment and Mohr’s integral method is applied to derive the compliance of it. Modeling of the CF beam and the translational joint with variable thickness segments are further carried out through stiffness matrix method, which are confirmed by finite element analysis (FEA). Discussions about the variable thickness of the double elliptical curve segments are then conducted, which enable the translational joint to achieve both high off-axis/axial stiffness ratio and large motion. Experiments were also carried out to test the motion of the optimal design. The derived analytical model provides a new opinion on the design of the CF beam.


Corrugated flexure unit Variable thickness segment Mohr’s integral method FEA 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The authors would like to gratefully acknowledge the reviewers’ comments. This work is supported by


  1. [1]
    H. Zhao and S. Bi, “Accuracy characteristics of the generalized cross-spring pivot,” Mechanism & Machine Theory, vol. 45, no. 10, pp. 1434-1448, 2010.Google Scholar
  2. [2]
    V. K. Venkiteswaran and H. J. Su, “Pseudo-rigid-body models for circular beams under combined tip loads,” Mechanism & Machine Theory, vol. 106, pp. 80-93, 2016.CrossRefGoogle Scholar
  3. [3]
    R. Wang and X. Zhang, “Design and test of a novel planar 3-dof precision positioning platform with a large magnification,” in International Conference on Manipulation, Manufacturing and Measurement on the Nanoscale, pp. 236-243, 2015.Google Scholar
  4. [4]
    R. Wang and X. Zhang, “A planar 3-dof nanopositioning platform with large magnification,” Precision Engineering, vol. 46, pp. 221-231, 2016.CrossRefGoogle Scholar
  5. [5]
    X. Chen and Y. Li, “Design and analysis of a new high precision decoupled xy compact parallel micromanipulator,” Micromachines, vol. 8, no. 3, p. 82, 2017.CrossRefGoogle Scholar
  6. [6]
    S. Wan and Q. Xu, “Design and analysis of a new compliant xy micropositioning stage based on roberts mechanism,” Mechanism & Machine Theory, vol. 95, pp. 125-139, 2016.CrossRefGoogle Scholar
  7. [7]
    N. Wang, X. Liang, and X. Zhang, “Stiffness analysis of corrugated flexure beam used in compliant mechanisms,” Chinese Journal of Mechanical Engineering, vol. 28, no. 4, pp. 776-784, 2015.CrossRefGoogle Scholar
  8. [8]
    N. Wang, Z. Zhang, X. Zhang, and C. Cui, “Optimization of a 2-dof micropositioning stage using corrugated flexure units,” Mechanism & Machine Theory, vol. 121, pp. 683-696, 2018.CrossRefGoogle Scholar
  9. [9]
    N. Wang, X. Liang, and X. Zhang, “Pseudo-rigid-body model for corrugated cantilever beam used in compliant mechanisms,” Chinese Journal of Mechanical Engineering, vol. 27, no. 1, pp. 122-129, 2014.CrossRefGoogle Scholar
  10. [10]
    N. Lobontiu, “In-plane compliances of planar flexure hinges with serially connected straight-and circular-axis segments,” Journal of Mechanical Design, vol. 136, no. 12, p. 122301, 2014.CrossRefGoogle Scholar
  11. [11]
    B. Zettl, W. Szyszkowski, and W. J. Zhang, “On systematic errors of two-dimensional finite element modeling of right circular planar flexure hinges,” Journal of Mechanical Design, vol. 127, no. 4, pp. 782-787, 2005.CrossRefGoogle Scholar
  12. [12]
    N. Lobontiu, J. S. N. Paine, E. Garcia, and M. Goldfarb, “Corner-filleted flexure hinges,” Journal of Mechanical Design, vol. 123, no. 3, pp. 346-352, 2001.CrossRefGoogle Scholar
  13. [13]
    G. Chen, X. Liu, and Y. Du, “Elliptical-arc-fillet flexure hinges: Toward a generalized model for commonly used flexure hinges,” Journal of Mechanical Design, vol. 133, no. 8, p. 081002, 2011.CrossRefGoogle Scholar
  14. [14]
    N. Lobontiu, J. S. N. Paine, E. OMalley, and M. Samuelson, “Parabolic and hyperbolic flexure hinges: exibility, motion precision and stress characterization based on compliance closed-form equations,” Precision Engineering, vol. 26, no. 2, pp. 183-192, 2002.CrossRefGoogle Scholar
  15. [15]
    R. R. Vallance, B. Haghighian, and E. R. Marsh, “A unified geometric model for designing elastic pivots,” Precision Engineering, vol. 32, no. 4, pp. 278-288, 2008.CrossRefGoogle Scholar
  16. [16]
    Q. Meng, Y. Li, and J. Xu, “A novel analytical model for flexure-based proportion compliant mechanisms,” Precision Engineering, vol. 38, no. 3, pp. 449-457, 2014.CrossRefGoogle Scholar
  17. [17]
    N. Lobontiu, “Modeling and design of planar parallel-connection flexible hinges for in- and out-of-plane mechanism applications,” Precision Engineering, vol. 42, no. 1, pp. 113-132, 2015.CrossRefGoogle Scholar
  18. [18]
    Y. Li, S. Xiao, L. Xi, and Z. Wu, “Design, modeling, control and experiment for a 2-dof compliant micro-motion stage,” International Journal of Precision Engineering and Manufacturing, vol. 15, no. 4, pp. 735-744, 2014.CrossRefGoogle Scholar
  19. [19]
    B. Zhu, X. Zhang, and S. Fatikow, “A multi-objective method of hinge-free compliant mechanism optimization,” Structural & Multidisciplinary Optimization, vol. 49, no. 3, pp. 431-440, 2014.MathSciNetCrossRefGoogle Scholar
  20. [20]
    N. Wang, H. Guo, C. Cui, X. Zhang, and K. Hu, “A boundary reconstruction algorithm used in compliant mechanism topology optimization design,” in Mechanism and Machine Science, pp. 657-666, Springer, 2017.Google Scholar
  21. [21]
    N. Wang, Z. Zhang, and X. Zhang, “Stiffness analysis of corrugated flexure beam using stiffness matrix method,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, p. 0954406218772002, 2018.Google Scholar
  22. [22]
    C. Zhang and S. Di, “New accurate two-noded shear-flexible curved beam elements,” Computational Mechanics, vol. 30, no. 2, pp. 81-87, 2003.CrossRefGoogle Scholar
  23. [23]
    J. Marquis and T.Wang, “Stiffness matrix of parabolic beam element,” Computers & structures, vol. 31, no. 6, pp. 863-870, 1989.CrossRefGoogle Scholar
  24. [24]
    L. L. Howell, Handbook of Compliant Mechanisms. 2013.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Guangdong Provincial Key Laboratory of Precision Equipment and Manufacturing Technology, School of Mechanical and Automotive EngineeringSouth China University of TechnologyGuangzhouChina

Personalised recommendations