A Parameterization of the Central Axis Congruence Associated with Four Positions of a Rigid Body in Space

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

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

J. Mech. Des 115(3), 547-551 (Sep 01, 1993) (5 pages) doi:10.1115/1.2919224 History: Received February 01, 1990; Online June 02, 2008


Given four positions of a rigid body in space, there is a congruence of lines that can be used as the central axes of cylindric cranks to guide the body through the four positions. This “central axis congruence” is a generalization of the center point curve of planar kinematics. It is known that this congruence is identical to the screw congruence which arises in the study of complementary screw quadrilateral. It is less well-known that the screw congruence is the “screw surface” of the 4C linkage formed by the complementary screw quadrilateral, and it is this relationship that we use to obtain a parameterization for the screw congruence and in turn, the central axis congruence. This parameterization should facilitate the use of this congruence in computer based design of spatial mechanisms.

Copyright © 1993 by The American Society of Mechanical Engineers
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