RESEARCH PAPERS: Mechanisms Papers

An Application of the Linkage Characteristic Polynomial to the Topological Synthesis of Epicyclic Gear Trains

[+] Author and Article Information
Lung-Wen Tsai

Power Systems Research Department, General Motors Research Laboratories, Warren, MI 48090-9055

J. Mech., Trans., and Automation 109(3), 329-336 (Sep 01, 1987) (8 pages) doi:10.1115/1.3258798 History: Received July 10, 1986; Online November 19, 2009


In this paper, a random number technique for computing the value of a linkage characteristic polynomial is shown to be an effective method for identifying isomorphic graphs. The technique has been applied to the topological synthesis of one-degree-of-freedon, epicyclic gear trains with up to six links. All the permissible graphs of epicyclic gear trains were generated by a systematic procedure, and the isomorphic graphs were identified by comparing the values of their corresponding linkage characteristic polynomials. It is shown that there are 26 nonisomorphic rotation graphs and 80 displacement nonisomorphic graphs from which all the six-link, one-degree-of-freedom, epicyclic gear trains can be derived.

Copyright © 1987 by ASME
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