Abstract
This paper presents an efficient method for the identification of the displacement isomorphism of planetary gear trains with any number of gear pairs. For every plantary gear train, the corresponding displacement graph and rotation graph are used to characterize its kinematic structure. Next, a mathematical representation, called the Structural Code, is proposed to represent the topological structure of the displacement graph and rotation graph of a planetary gear train. By comparing the corresponding Structural codes, the linear and rotational displacement isomorphism of planetary gear trains can be identified in an unambiguous way.
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