On the Relation Between Kinematic Mappings of Planar and Spherical Displacements

[+] Author and Article Information
J. M. McCarthy

Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104

J. Appl. Mech 53(2), 457-459 (Jun 01, 1986) (3 pages) doi:10.1115/1.3171781 History: Received June 01, 1985; Revised October 01, 1985; Online July 21, 2009


Kinematic mappings, which transform the parameters specifying a rigid displacement into a point in a higher dimensional space, have been the focus of recent study for the purpose of classifying rigid motion, aiding mechanism design, and automating robot task planning. Presented here is the procedure which demonstrates that the particular mapping introduced by Blaschke and Müiller (1956) to study planar kinematics, and used subsequently by other researchers, is a limiting case of a mapping based on the Euler parameters of an orthogonal matrix used by Ravani (1982) for spherical kinematics.

Copyright © 1986 by ASME
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