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The Correction to Grubler Criterion for Calculating the Degrees of Freedoms of Mechanisms

[+] Author Affiliations
Offer Shai

Tel Aviv University, Tel Aviv, Israel

Paper No. DETC2011-48146, pp. 413-416; 4 pages
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 35th Mechanisms and Robotics Conference, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5483-9
  • Copyright © 2011 by ASME


It is well known that the widely used Chybychev-Grubler Kutzbach’s criterion does not give the correct mobility for many mechanisms. In this paper we will show that if we add to the known Grubler equation the number of inner forces existing in the mechanism, termed self-stresses, we will derive the correct answer. The unique contribution of this paper is that it enables to find this correction on the given mechanism without any need to write the corresponding matrices or any equations. It should be noted that the correct mobility is obtained from the given configuration of the mechanism; that is the instantaneous mobility and not the global mobility.

Copyright © 2011 by ASME
Topics: Mechanisms



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