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Screw System Analysis of Parallel Mechanisms and Applications to Constraint and Mobility Study

[+] Author Affiliations
Jian S. Dai

University of London, London, UK

Zhen Huang

Yanshan University, Qinhuangdao, Hebei, P. R. China

Harvey Lipkin

Georgia Institute of Technology, Atlanta, GA

Paper No. DETC2004-57604, pp. 1569-1582; 14 pages
  • 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


The Kutzbach-Grübler mobility criterion calculates the degrees-of-freedom of a general mechanism. However, the criterion can break down for mechanisms with special geometries, and in particular, the class of so-called overconstrained mechanisms. The problem is that the criterion treats all constraints as active, even redundant constraints, which do not affect the mechanism degrees-of-freedom. This paper examines the screw systems of a parallel mechanism to identify the redundant constraints. The screw system characteristics and relationships are then investigated for physical properties. Then a new approach to mobility analysis is proposed based on screw system decompositions. A new version of the mobility criterion is presented to eliminate the redundant constraints and correctly predict the platform degrees-of-freedom. Several examples of overconstrained mechanisms from the literature illustrate the results.

Copyright © 2004 by ASME



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