A flexure strip has constraint characteristics, such as stiffness properties and error motions, that govern its performance as a basic constituent of flexure mechanisms. This paper presents a new modeling approach for obtaining insight into the deformation and stiffness characteristics of general three-dimensional flexure strips that exhibit bending, shear, and torsion deformation. The approach is based on the use of a discretized version of a finite (i.e., nonlinear) strain spatial beam formulation for extracting analytical expressions that describe deformation and stiffness characteristics of a flexure strip in a parametric format. This particular way of closed-form modeling exploits the inherent finite-element assumptions on interpolation and also lends itself for numeric implementation. As a validating case study, a closed-form parametric expression is derived for the lateral support stiffness of a flexure strip and a parallelogram flexure mechanism. This captures a combined torsion–bending dictated geometrically nonlinear effect that undermines the support bearing stiffness when the mechanism moves in the intended degree of freedom (DoF). The analytical result is verified by simulations and experimental measurements.
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An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip
Marijn Nijenhuis,
Marijn Nijenhuis
Precision Engineering,
University of Twente,
Enschede 7522 NB, The Netherlands
e-mail: m.nijenhuis@utwente.nl
University of Twente,
Enschede 7522 NB, The Netherlands
e-mail: m.nijenhuis@utwente.nl
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J. P. Meijaard,
J. P. Meijaard
Precision Engineering,
University of Twente,
Enschede 7522 NB, The Netherlands;
University of Twente,
Enschede 7522 NB, The Netherlands;
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Dhanushkodi Mariappan,
Dhanushkodi Mariappan
Precision Systems Design Lab,
Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: dhanush@umich.edu
Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: dhanush@umich.edu
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Just L. Herder,
Just L. Herder
Precision Engineering,
University of Twente,
Enschede 7522 NB, The Netherlands
e-mail: j.l.herder@utwente.nl
University of Twente,
Enschede 7522 NB, The Netherlands
e-mail: j.l.herder@utwente.nl
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Dannis M. Brouwer,
Dannis M. Brouwer
Precision Engineering,
University of Twente,
Enschede 7522 NB, The Netherlands
e-mail: d.m.brouwer@utwente.nl
University of Twente,
Enschede 7522 NB, The Netherlands
e-mail: d.m.brouwer@utwente.nl
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Shorya Awtar
Shorya Awtar
Precision Systems Design Lab,
Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: awtar@umich.edu
Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: awtar@umich.edu
Search for other works by this author on:
Marijn Nijenhuis
Precision Engineering,
University of Twente,
Enschede 7522 NB, The Netherlands
e-mail: m.nijenhuis@utwente.nl
University of Twente,
Enschede 7522 NB, The Netherlands
e-mail: m.nijenhuis@utwente.nl
J. P. Meijaard
Precision Engineering,
University of Twente,
Enschede 7522 NB, The Netherlands;
University of Twente,
Enschede 7522 NB, The Netherlands;
Dhanushkodi Mariappan
Precision Systems Design Lab,
Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: dhanush@umich.edu
Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: dhanush@umich.edu
Just L. Herder
Precision Engineering,
University of Twente,
Enschede 7522 NB, The Netherlands
e-mail: j.l.herder@utwente.nl
University of Twente,
Enschede 7522 NB, The Netherlands
e-mail: j.l.herder@utwente.nl
Dannis M. Brouwer
Precision Engineering,
University of Twente,
Enschede 7522 NB, The Netherlands
e-mail: d.m.brouwer@utwente.nl
University of Twente,
Enschede 7522 NB, The Netherlands
e-mail: d.m.brouwer@utwente.nl
Shorya Awtar
Precision Systems Design Lab,
Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: awtar@umich.edu
Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: awtar@umich.edu
1Corresponding author.
Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 1, 2016; final manuscript received January 11, 2017; published online March 20, 2017. Assoc. Editor: Nam H. Kim.
J. Mech. Des. May 2017, 139(5): 051401 (11 pages)
Published Online: March 20, 2017
Article history
Received:
July 1, 2016
Revised:
January 11, 2017
Citation
Nijenhuis, M., Meijaard, J. P., Mariappan, D., Herder, J. L., Brouwer, D. M., and Awtar, S. (March 20, 2017). "An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip." ASME. J. Mech. Des. May 2017; 139(5): 051401. https://doi.org/10.1115/1.4035861
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