Kinematic Geometry of Spherical Evolutes

[+] Author and Article Information
J. A. Schaaf

Department of Mechanical Engineering, Washington University, St. Louis, MO 63130

An Tzu Yang

Department of Mechanical Engineering, University of California, Davis, CA 95616

J. Mech. Des 114(1), 109-116 (Mar 01, 1992) (8 pages) doi:10.1115/1.2916903 History: Received March 01, 1990; Revised July 01, 1990; Online June 02, 2008


In this paper, we define spherical evolutes corresponding to the trajectory of a point in spherical kinematics. We derive general expressions for the curvature properties of the nth spherical evolute in terms of the geodesic curvature and the derivative of the geodesic curvature for the (n-1)the spherical evolute. The results are illustrated by numerical examples for the motion of a circular cone rolling on a fixed circular cone, of a spherical turning-block linkage, and of a spherical four-bar linkage.

Copyright © 1992 by The American Society of Mechanical Engineers
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