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A Numerical Method for Position Analysis of Compliant Mechanisms With More Degrees of Freedom Than Inputs

[+] Author Affiliations
Quentin T. Aten, Shannon A. Zirbel, Brian D. Jensen, Larry L. Howell

Brigham Young University, Provo, UT

Paper No. DETC2010-28474, pp. 491-502; 12 pages
doi:10.1115/DETC2010-28474
From:
  • ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2: 34th Annual Mechanisms and Robotics Conference, Parts A and B
  • Montreal, Quebec, Canada, August 15–18, 2010
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4410-6 | eISBN: 978-0-7918-3881-5
  • Copyright © 2010 by ASME

abstract

An under-actuated or underconstrained compliant mechanism may have a determined equilibrium position because its energy storage elements cause a position of local minimum potential energy. The minimization of potential energy (MinPE) method is a numerical approach to finding the equilibrium position of compliant mechanisms with more degrees of freedom (DOF) than inputs. Given the pseudo-rigid-body model of a compliant mechanism, the MinPE method finds the equilibrium position by solving a constrained optimization problem: minimize the potential energy stored in the mechanism, subject to the mechanism’s vector loop equation(s) being equal to zero. The MinPE method agrees with the method of virtual work for position and force determination for under-actuated 1-DOF and 2-DOF pseudo-rigid-body models. Experimental force-deflection data is presented for a fully compliant constant-force mechanism. Because the mechanism’s behavior is not adequately modeled using a 1-DOF pseudo-rigid-body model, a 13-DOF pseudo-rigid-body model is developed and solved using the MinPE method. The MinPE solution is shown to agree well with non-linear finite element analysis and experimental force-displacement data.

Copyright © 2010 by ASME

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