RESEARCH PAPERS: Mechanisms Papers

Further Applications of Group Theory to the Enumeration and Structural Analysis of Basic Kinematic Chains

[+] Author and Article Information
E. R. Tuttle

Department of Engineering, University of Denver, Denver, CO 80208

S. W. Peterson

Department of Mechanical Engineering, Vanderbilt University, Nashville, TN 37235

J. E. Titus

Productivity Center, Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455

J. Mech., Trans., and Automation 111(4), 494-497 (Dec 01, 1989) (4 pages) doi:10.1115/1.3259027 History: Received October 01, 1987; Online November 19, 2009


The use of finite symmetry groups to enumerate basic kinematic chains has been extended by making use of the subgroup structure of the symmetry groups. This refinement not only makes the enumeration of kinematic chains considerably more efficient, but also permits the enumeration of all distinct inversions of each of the chains found. As examples, all chains with 2, 3, 4, and 5 independent loops and 1, 2, or 3 degrees of freedom and their inversions have been found on a personal computer.

Copyright © 1989 by ASME
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