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A 3D Pseudo-Rigid-Body Model for Large Spatial Deflections of Rectangular Cantilever Beams

[+] Author Affiliations
Nathan O. Rasmussen

Caterpillar, Inc., Mossville, IL

Jonathan W. Wittwer

Sandia National Laboratories, Albuquerque, NM

Robert H. Todd, Larry L. Howell, Spencer P. Magleby

Brigham Young University, Provo, UT

Paper No. DETC2006-99465, pp. 191-198; 8 pages
  • ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2: 30th Annual Mechanisms and Robotics Conference, Parts A and B
  • Philadelphia, Pennsylvania, USA, September 10–13, 2006
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4256-8 | eISBN: 0-7918-3784-X
  • Copyright © 2006 by ASME


The design of compliant mechanisms has been aided by the development of pseudo-rigid-body models to predict the motion of flexible members undergoing large displacements. Many of these models are based on the fact that the end of a cantilever beam follows a near-circular path when planar loads are applied. This paper shows that the application of 3-dimensional end-loading causes a beam to follow a near-spherical path, even for beams with non-circular cross-sections. A 3D pseudo-rigid-body model is presented that allows the motion of an end-loaded rectangular beam to be predicted using a rigid link and a spherical joint. Two sets of deflection limits for 0.5% error are presented and shown to be dependent upon the aspect ratio of the cross-section of the beam. The model has the potential for aiding in the design of spatial compliant mechanisms and analysis of planar compliant mechanisms undergoing large out-of-plane motions.

Copyright © 2006 by ASME



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