Analysis of Symmetry in Epicyclic Gear Trains
An investigation to symmetry in epicyclic gear trains (EGTs) is carried out in this research. As a consequence of the graph theoretic framework for EGTs, an EGT graph serves as an isomorphic substitute for its kinematic structure. In this work, Nauty & Traces software package is employed for an EGT graph for determining the automorphism group and orbits of its vertices or edges. The procedure is applied to all the rotationally non-isomorphic graphs available in the published atlases, with and up to 7 links and results are presented. It was inferred that only few percentage of distinct EGT chains (graphs) exhibit any symmetry at all.
KeywordsSymmetry Rotation Graph Epicyclic Gear Train Automorphism Group
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