RESEARCH PAPERS: Mechanisms Papers

The Image Curve of the Planet in a Spherical Epicyclic Gear Train

[+] Author and Article Information
Q. Ge, J. M. McCarthy

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

J. Mech., Trans., and Automation 110(3), 281-286 (Sep 01, 1988) (6 pages) doi:10.1115/1.3267459 History: Received June 03, 1987; Online November 19, 2009


This paper uses the Euler parameters of the motion of the planet of a spherical epicyclic gear train to obtain a curve on the surface of a hypersphere in four dimensions. This curve, called the image curve, represents the rotational motion of the planet as it rolls without slipping on the fixed gear. Two image curves are obtained for two different choices of moving and fixed reference frames and it is shown that they are related by an orthogonal transformation in four dimensional space. The differential properties of the image curve are computed and it is found that the curvature and torsion are constant. A reference position is chosen and the canonical frame and instantaneous invariants of the motion are determined in terms of the dimensions of the gear train.

Copyright © 1988 by ASME
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