Design of a Folded Leaf Spring with high support stiffness at large displacements using the Inverse Finite Element Method

  • J. RommersEmail author
  • J. L. Herder
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


Compliant (flexure) elements provide highly precise motion guiding because they do not suffer from friction or backlash. However, their support stiffness drops dramatically when they are actuated from their home position. In this paper, we show that the existing Inverse Finite Element (IFE) method can be used to efficiently design flexure elements such that they have a high support stiffness in their actuated state. A folded leaf spring element was redesigned using an IFE code written in Matlab™. The design was validated using the commercial Finite Element software package Ansys™, showing the desired high support stiffness in the actuated state. The proposed method could aid in the design of more compact flexure mechanisms with a larger useful range of motion.


Compliant mechanisms Flexures Inverse Finite Elements Precision Support stiffness 


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This work is part of the research programme Möbius with project number 14665, which is (partly) financed by the Netherlands Organisation for Scientific Research (NWO).


  1. 1.
    Larry L Howell, Spencer P Magleby, and Brian M Olsen. Handbook of compliant mechanisms. John Wiley & Sons, 2013.Google Scholar
  2. 2.
    Herman Soemers. Design Principles for precision mechanisms. T-Pointprint, 2011.Google Scholar
  3. 3.
    Shorya Awtar, Alexander H Slocum, and Edip Sevincer. Characteristics of beam-based flexure modules. Journal of Mechanical Design, 129(6):625–639, 2007.CrossRefGoogle Scholar
  4. 4.
    D. M. Brouwer, J. P. Meijaard, and J. B. Jonker. Large deflection stiffness analysis of parallel prismatic leaf-spring flexures. Precision Engineering, 37(3):505–521, 2013.CrossRefGoogle Scholar
  5. 5.
    Marijn Nijenhuis, J. P. Meijaard, Dhanushkodi Mariappan, Just L. Herder, Dannis M. Brouwer, and Shorya Awtar. An analytical formulation for the lateral support stiffness of a spatial flexure strip. Journal of Mechanical Design, 139(5), 2017.Google Scholar
  6. 6.
    DH Wiersma, SE Boer, Ronald GKM Aarts, and Dannis Michel Brouwer. Design and performance optimization of large stroke spatial flexures. Journal of computational and nonlinear dynamics, 9(1):011016, 2014.CrossRefGoogle Scholar
  7. 7.
    M. Naves, D. M. Brouwer, and R. G. K. M. Aarts. Building block-based spatial topology synthesis method for large-stroke flexure hinges. Journal of Mechanisms and Robotics, 9(4), 2017.CrossRefGoogle Scholar
  8. 8.
    Dannis Michel Brouwer, Jacob Philippus Meijaard, and Jan B Jonker. Elastic element showing low stiffness loss at large deflection. In Proceedings of the 24th Annual Meeting of the American Society of Precision Engineering, Monterey, CA, pages 30–33, 2009.Google Scholar
  9. 9.
    Steven E Boer, RGKM Aarts, Dannis M Brouwer, and J Ben Jonker. Multibody modelling and optimization of a curved hinge flexure. In The 1st joint international conference on multibody system dynamics, Lappeenranta, pages 1–10, 2010.Google Scholar
  10. 10.
    Brian P Trease, Yong-Mo Moon, and Sridhar Kota. Design of large-displacement compliant joints. Journal of mechanical design, 127(4):788–798, 2005.CrossRefGoogle Scholar
  11. 11.
    Guangbo Hao and Haiyang Li. Extended static modeling and analysis of compliant compound parallelogram mechanisms considering the initial internal axial force. Journal of mechanisms and robotics, 8(4):041008, 2016.MathSciNetCrossRefGoogle Scholar
  12. 12.
    Hasan Malaeke and Hamid Moeenfard. A novel flexure beam module with low stiffness loss in compliant mechanisms. Precision Engineering, 48:216–233, 2017.CrossRefGoogle Scholar
  13. 13.
    Mohsen Bakhtiari-Shahri and Hamid Moeenfard. Topology optimization of fundamental compliant mechanisms using a novel asymmetric beam flexure. International Journal of Mechanical Sciences, 135:383–397, 2018.CrossRefGoogle Scholar
  14. 14.
    Sanjay Govindjee and Paul A Mihalic. Computational methods for inverse finite elastostatics. Computer Methods in Applied Mechanics and Engineering, 136(1-2):47–57, 1996.CrossRefGoogle Scholar
  15. 15.
    Alejandro E. Albanesi, Martn A. Pucheta, and Vctor D. Fachinotti. A new method to design compliant mechanisms based on the inverse beam finite element model. Mechanism and Machine Theory, 65:14–28, 2013.CrossRefGoogle Scholar
  16. 16.
    Allan F Bower. Applied mechanics of solids. CRC press, 2009.Google Scholar
  17. 17.
    R D. Cook, D S. Malkus, M E. Plesha, and R J. Witt. Concepts and Applications of Finite Element Analysis: 4th Edition. 01 2002.Google Scholar
  18. 18.
    Arjo Bos. Position actuator for the ELT primary mirror. PhD thesis, Eindhoven University of Technology, The Netherlands, 2017.Google Scholar
  19. 19.
    L.A Cacace. An Optical Distance Sensor: Tilt robust […]. PhD thesis, Eindhoven University of Technology, The Netherlands, 2009.Google Scholar
  20. 20.
    Just L Herder. Design of spring force compensation systems. Mechanism and machine theory, 33(1-2):151–161, 1998.CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Precision and Microsystems EngineeringDelft University of TechnologyDelftThe Netherlands

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