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A Unified Concept for the Graph Representation of Constraints in Mechanisms

[+] Author Affiliations
Andreas Müller

University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai, China

Offer Shai

Tel-Aviv University, Tel-Aviv, Israel

Paper No. DETC2014-34713, pp. V05AT08A059; 6 pages
  • ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5A: 38th Mechanisms and Robotics Conference
  • Buffalo, New York, USA, August 17–20, 2014
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4636-0
  • Copyright © 2014 by ASME


There are two established approaches to represent constraints: the body-bar (BB) and the bar-joint (BJ) graph that can be used in machine theory. They are referred to as topological graphs as they describe the relation between members of a mechanism. It is known, however, that in many cases these graphs are not unique. Hence any method for kinematic analysis or mobility determination that is based on these topological graphs is prone to failures.

In this paper a generalized and unified concept for the representation of constraints in mechanisms is introduced. It is first shown in which situations BB and BJ representations fail to correctly represent the mechanism. The novel constraint graph is then derived starting from the most general model of constrained rigid bodies. It is shown how BB and BJ graphs result as special cases. Therefore the new graph representation is called the ‘mixed graph’. It is further shown how this novel mixed constraint graph allows for computation of the correct generic (topological) mobility, and thus overcomes the problems of BB and BJ representations.

Copyright © 2014 by ASME



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