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On Calculating the Degrees of Freedom or Mobility of Overconstrained Linkages

[+] Author Affiliations
José María Rico

Instituto Tecnológico de Celaya, Celaya, Guanajuato, México

Bahram Ravani

University of California at Davis, Davis, CA

Paper No. DETC2004-57181, pp. 489-512; 24 pages
doi:10.1115/DETC2004-57181
From:
  • ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2: 28th Biennial Mechanisms and Robotics Conference, Parts A and B
  • Salt Lake City, Utah, USA, September 28–October 2, 2004
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4695-4 | eISBN: 0-7918-3742-4
  • Copyright © 2004 by ASME

abstract

This paper reformulates and extends the new, group theoretic, mobility criterion recently developed by the authors, Rico and Ravani [1]. In contrast to the Kutzbach-Grübler criterion, the new mobility criterion, and the approach presented apply to a large class of overconstrained linkages. The criterion is reformulated, in terms of the well known Jacobian matrices, for exceptional linkages; it is extended to linkages with partitioned mobility as well as trivial linkages. In addition, an extension of the criterion is presented that would allow the computation of degrees-of-freedom of several cases of paradoxical linkages. The case of classical paradoxical linkages such as the Bennett and Goldberg linkages still remains unsolved but some insight into the application of the new mobility criterion for these linkages is also presented.

Copyright © 2004 by ASME

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