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Mobility Determination of Mechanisms Based on Rigidity Theory

[+] Author Affiliations
Michael Slavutin, Offer Shai

Tel Aviv University, Tel Aviv, Israel

Andreas Müller

Institute of Mechatronics, Technical University, Chemnitz, Germany

Paper No. DETC2012-71289, pp. 1615-1628; 14 pages
  • ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 4: 36th Mechanisms and Robotics Conference, Parts A and B
  • Chicago, Illinois, USA, August 12–15, 2012
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4503-5
  • Copyright © 2012 by ASME


Rigidity theory deals mostly with the topological computation in mechanical systems, i.e. it aims at making generic statements. Mechanism theory is mainly concerned with the geometrical analysis but again also with generic statements. Even more so for mobility analysis where one is interested in both the generic mobility and that of a particular mechanism. In rigidity theory the mathematical foundation is the topology representation using bar-joint and body-bar graphs, and the corresponding rigidity matrix. In this paper novel geometric rules for constructing the body-bar rigidity matrix are derived for general planar mechanisms comprising revolute and prismatic joints. This allows, for the first time, the treatment of general planar mechanisms with the body-bar approach. The rigidity matrix is also derived for spatial mechanisms with spherical joints. The bar-joint rigidity matrix is shown to be a special case of body-bar representation. It is shown that the rigidity matrices allow for mobility calculation as shown in the paper. This paper is aimed at supplying a unified view and as a result to enable the mechanisms community to employ the theorems and methods used in rigidity theory. An algorithm for mobility determination — the pebble game — is discussed. This algorithm always finds the correct generic mobility if the mechanism can be represented by a body-bar graph.

Copyright © 2012 by ASME



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