RESEARCH PAPERS: Mechanisms Papers

The Opposite Pole Quadrilateral as a Compatibility Linkage for Parameterizing the Center Point Curve

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

Department of Mechanical Engineering, University of California, Irvine, Irvine, CA 92717

J. Mech. Des 115(2), 332-336 (Jun 01, 1993) (5 pages) doi:10.1115/1.2919196 History: Received February 01, 1990; Online June 02, 2008


In planar four-position kinematics, the centers of circles containing four positions of a point in a moving rigid body form the center point curve. This curve can be parameterized by analyzing a “compatibility linkage” obtained from a complex number formulation of the four-position problem. In this paper, we present another derivation of the center point curve using a special form of dual quaternions and the fact that it is identical to the pole curve. The defining properties of the pole curve lead to a parameterization by kinematic analysis of the opposite pole quadrilateral as a four-bar linkage. Thus the opposite pole quadrilateral becomes the compatibility linkage. This derivation generalizes to provide parameterizations for the center point cone of spherical kinematics and the central axis congruence of spatial kinematic theory.

Copyright © 1993 by The American Society of Mechanical Engineers
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