Optimization of Compliant Mechanisms by Use of Different Polynomial Flexure Hinge Contours

  • P. GräserEmail author
  • S. Linß
  • L. Zentner
  • R. TheskaEmail author
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 71)


This paper presents the application of different polynomial flexure hinge contours in one compliant mechanism in order to increase both simultaneously the precision and the stroke of the output motion of compliant mechanisms. The contours of the flexure hinges are optimized in dependency of the required elasto-kinematic properties of the mechanism. This new approach for optimization is described in comparison to the use of identical common hinge contours. Based on previously optimized single polynomial flexure hinges, the validity of proposed guidelines is analyzed for a combination of several flexure hinges in two compliant mechanisms for linear point guidance. The rigid-body models of both mechanisms realize an approximated straight line as output motion. The compliant mechanisms are designed through the rigid-body replacement method and with different polynomial flexure hinges with orders varying from 2 to 16. The multi-criteria optimization is performed by use of non-linear FEM simulations. The derived values for the kinematic output parameters are compared for the ideal model and the optimized compliant mechanism. The results are discussed and conclusions for ongoing research work are drawn.


Compliant mechanism Flexure hinge Different polynomial contours Optimization 



The development of this project is supported by the Deutsche Forschungsgemeinschaft (DFG) under Grant No. TH 845/5-2 and ZE 714/10-2.


  1. 1.
    Gräser, P., Linß, S., Zentner, L., Theska, R.: Design and experimental characterization of a flexure hinge-based parallel four-bar mechanism for precision guides. In: Zentner, L., Corves, B., Jensen, B., Lovasz, E.-C. (Eds.), Microactuators and Micromechanisms, Vol. 45 of Mechanisms and Machine Science, pp. 139–152. Springer International Publishing, Cham., 2017
  2. 2.
    Howell, L.L., Midha, A.: A method for the design of compliant mechanisms with small-length flexural pivots. J. Mech. Des. 116, 280–290 (1994). Scholar
  3. 3.
    Howell, L.L., Magleby, S.P., Olsen, B.M.: Handbook of Compliant Mechanisms. Wiley, Chichester (2013)CrossRefGoogle Scholar
  4. 4.
    Linß, S., Erbe, T., Zentner, L.: On polynomial flexure hinges for increased deflection and an approach for simplified manufacturing. In: 13th World Congress in Mechanism and Machine Science, Guanajuato, Mexico, p. A11_512 (2011)Google Scholar
  5. 5.
    Linß, S., Milojevic, A., Pavlovic, N.D., Zentner, L.: Synthesis of compliant mechanisms based on goal-oriented design guidelines for prismatic flexure hinges with polynomial contours. In: 14th World Congress in Mechanism and Machine Science, Taipei, Taiwan. (2015)
  6. 6.
    Linß, S.: Ein Beitrag zur geometrischen Gestaltung und Optimierung prismatischer Festkörpergelenke in nachgiebigen Koppelmechanismen, doctoral thesis, TU Ilmenau, Ilmenau, urn:nbn:de:gbv:ilm1-2015000283 (2015)Google Scholar
  7. 7.
    Lobontiu, N.: Compliant Mechanisms: Design of Flexure Hinges. CRC Press, Boca Raton, Fla. (2003)Google Scholar
  8. 8.
    Tseytlin, Y.M.: Notch flexure hinges: An effective theory. Rev. Sci. Instrum. 73, 3363–3368 (2002). Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Precision Engineering Group, Department of Mechanical EngineeringTechnische Universität IlmenauIlmenauGermany
  2. 2.Compliant Systems Group, Department of Mechanical EngineeringTechnische Universität IlmenauIlmenauGermany

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