The purpose of this article is to propose a system approach based on graph theory to represent planetary gear trains with any number of degrees of freedoms. A regular graph representation of the kinematic structure of planetary gear train with any number of degrees of freedoms is given using polygonal graph representation. Then, the adjacency matrix rules for planetary gear train with any number of degrees of freedoms were established. The results of this paper provide a powerful tool for the analysing the topological structure of the planetary gear train with any number of degrees of freedoms.
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Lam et al. (2024) studied this question.
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