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An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip

[+] Author Affiliations
Marijn Nijenhuis, Just L. Herder, Dannis M. Brouwer

University of Twente, Enschede, The Netherlands

J. P. Meijaard

Olton Engineering Consultancy, Enschede, The Netherlands

Shorya Awtar

University of Michigan, Ann Arbor, MI

Paper No. DETC2015-46591, pp. V05AT08A008; 11 pages
  • ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5A: 39th Mechanisms and Robotics Conference
  • Boston, Massachusetts, USA, August 2–5, 2015
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5712-0
  • Copyright © 2015 by ASME


A flexure strip has constraint characteristics, such as stiffness properties and error motions, that limit its performance as a basic constituent of flexure mechanisms. This paper presents a framework for modeling the deformation and stiffness characteristics of general three-dimensional flexure strips that exhibit bending, shear and torsion deformation. The formulation is based on a finite strain discrete spatial beam element with refinements to account for plate-like behavior due to constrained cross-sectional warping. This framework is suited for analytical calculations thanks to the accuracy of the beam element, while its discrete nature allows for easy implementation in numeric software to serve as calculation aid. As case study, a closed-form parametric analytical expression is derived for the lateral support stiffness of a parallel flexure mechanism. This captures the deteriorating support stiffness when the mechanism moves in the intended degree of freedom. By incorporating relevant geometric nonlinearities and a warping constraint stiffening factor, an accurate load-displacement and stiffness expression for the lateral support direction is obtained. This result is verified by nonlinear finite element analysis.

Copyright © 2015 by ASME



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