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Symbolic Formulation of a Path-Following Joint for Multibody Dynamics

[+] Author Affiliations
Andrew Hall, John McPhee

University of Waterloo, Waterloo, ON, Canada

Chad Schmitke

MapleSoft, Waterloo, ON, Canada

Paper No. DETC2014-35082, pp. V003T01A025; 10 pages
  • ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 3: 16th International Conference on Advanced Vehicle Technologies; 11th International Conference on Design Education; 7th Frontiers in Biomedical Devices
  • Buffalo, New York, USA, August 17–20, 2014
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4634-6
  • Copyright © 2014 by ASME


We present a specialized multibody joint that constrains motion to a spatial path. The joint is used in the reduction of 1 degree-of-freedom systems with complex kinematics. Example applications of the joint are: the reduction of vehicle suspension systems, or the representation of biological joints. The new joint is implemented in the graph-theoretic symbolic multibody modeling environment of MapleSim and is formulated in such a way that a single ordinary differential equation is used to describe the resulting kinematic pair. A particle moving along a planar semi-circular path was chosen as the first example for successful validation of the new joint since a simple closed-form solution in terms of the path length exists. To represent arbitrary curves, the path must first be parameterized in terms of its path length. Next, a differentiable mathematical definition of the curve must be generated. B-splines are generated to define the path. For best performance we minimize the number of knots in the splines and find their optimal locations. Using the spline fitting approach, a planar parabolic path is generated and used to further analyze the performance of our implementation.

Copyright © 2014 by ASME



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