Differential Kinematics of Spherical and Spatial Motions Using Kinematic Mapping

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

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

B. Ravani

Department of Mechanical Engineering, University of Wisconsin, Madison, WI 53706

J. Appl. Mech 53(1), 15-22 (Mar 01, 1986) (8 pages) doi:10.1115/1.3171705 History: Received November 27, 1984; Revised May 21, 1985; Online July 21, 2009


This paper develops the basic framework for studying differential kinematics of spherical and spatial motions using a mapping of spatial kinematics. Relationships are derived relating the intrinsic properties of the image curves corresponding to a mapping of spherical and spatial kinematics and the instantaneous invariants of the corresponding spherical and spatial motions. In addition, in the case of spherical motions, the equations for the inflection cone and cubic cone of stationary geodesic curvature, important in spherical mechanism synthesis, are derived in terms of the curvature and torsion of corresponding image curves. Similar relationships defining the polhodes of spherical motions and their curvature at the reference instant are recast as well. A simple example involving a special spherical four-bar motion is also presented.

Copyright © 1986 by ASME
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