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Closed-Form Nonlinear Analysis of Beam-Based Flexure Modules

[+] Author Affiliations
Shorya Awtar, Alexander H. Slocum

Massachusetts Institute of Technology, Cambridge, MA

Paper No. DETC2005-85440, pp. 101-110; 10 pages
doi:10.1115/DETC2005-85440
From:
  • ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 7: 29th Mechanisms and Robotics Conference, Parts A and B
  • Long Beach, California, USA, September 24–28, 2005
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4744-6 | eISBN: 0-7918-3766-1
  • Copyright © 2005 by ASME

abstract

The simple beam acts as a constraint element when used in flexure mechanisms. Non-linearities arising from the force equilibrium conditions in a beam significantly affect its properties as a constraint element. Consequently, beam-based flexure mechanisms typically suffer from performance tradeoffs in terms of motion range, accuracy and stiffness. This paper presents simple yet accurate approximations that capture this non-linearity and allow for the closed-form analysis of flexure mechanisms of moderate complexity. These general analytical tools enable a designer to parametrically predict key performance parameters of a conceived mechanism such as mobility, over-constraint, stiffness variation, and error motions, without resorting to tedious numerical or computational methods. To illustrate their effectiveness, these approximations are used in deriving the closed-form force-displacement characteristics of several important beam-based flexure modules, and the results are validated using Finite Element Analysis. Variations in the beam shape and flexure module geometry are also considered analytically.

Copyright © 2005 by ASME

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