Skip to main content

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

  • Conference paper
  • First Online:
Advances in Mechanism and Machine Science (IFToMM WC 2019)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 73))

Included in the following conference series:

Abstract

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.

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 429.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 549.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 549.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Larry L Howell, Spencer P Magleby, and Brian M Olsen. Handbook of compliant mechanisms. John Wiley & Sons, 2013.

    Google Scholar 

  2. Herman Soemers. Design Principles for precision mechanisms. T-Pointprint, 2011.

    Google Scholar 

  3. Shorya Awtar, Alexander H Slocum, and Edip Sevincer. Characteristics of beam-based flexure modules. Journal of Mechanical Design, 129(6):625–639, 2007.

    Google Scholar 

  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.

    Google Scholar 

  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. 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.

    Google Scholar 

  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.

    Google Scholar 

  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. 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. Brian P Trease, Yong-Mo Moon, and Sridhar Kota. Design of large-displacement compliant joints. Journal of mechanical design, 127(4):788–798, 2005.

    Google Scholar 

  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.

    Google Scholar 

  12. Hasan Malaeke and Hamid Moeenfard. A novel flexure beam module with low stiffness loss in compliant mechanisms. Precision Engineering, 48:216–233, 2017.

    Google Scholar 

  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.

    Google Scholar 

  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.

    Google Scholar 

  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.

    Google Scholar 

  16. Allan F Bower. Applied mechanics of solids. CRC press, 2009.

    Google Scholar 

  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. Arjo Bos. Position actuator for the ELT primary mirror. PhD thesis, Eindhoven University of Technology, The Netherlands, 2017.

    Google Scholar 

  19. L.A Cacace. An Optical Distance Sensor: Tilt robust […]. PhD thesis, Eindhoven University of Technology, The Netherlands, 2009.

    Google Scholar 

  20. Just L Herder. Design of spring force compensation systems. Mechanism and machine theory, 33(1-2):151–161, 1998.

    Google Scholar 

Download references

Acknowledgment

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).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. Rommers .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Rommers, J., Herder, J.L. (2019). Design of a Folded Leaf Spring with high support stiffness at large displacements using the Inverse Finite Element Method. In: Uhl, T. (eds) Advances in Mechanism and Machine Science. IFToMM WC 2019. Mechanisms and Machine Science, vol 73. Springer, Cham. https://doi.org/10.1007/978-3-030-20131-9_209

Download citation

Publish with us

Policies and ethics