Unified Spherical Curvature Theory of Point-, Plane-, and Circle-Paths

[+] Author and Article Information
Kwun-Lon Ting, Ruj Bunduwongse

Tennessee Technological University, Cookeville, TN 38505

J. Mech. Des 113(2), 142-149 (Jun 01, 1991) (8 pages) doi:10.1115/1.2912762 History: Received March 01, 1988; Online June 02, 2008


This paper presents a unified treatment on the spherical curvature theory of point-, plane-, and circle-, paths or direct and inverse kinematics. It features the use of spherical inverse Euler-Savary equation to identify the kinematic loci such as return cone, double cusp axes, center-axis cone, and Burmester center axes. These results are then applied to the curvature theory of plane-path or circle-path to identify return plane, center plane, Ball’s plane, and Burmester plane. It explains satisfactorily the duality between point- and plant-paths.

Copyright © 1991 by The American Society of Mechanical Engineers
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