Analysis of Symmetry in Epicyclic Gear Trains

  • V. R. ShanmukhasundaramEmail author
  • Y. V. D. Rao
  • S. P. Regalla
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


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.


Symmetry Rotation Graph Epicyclic Gear Train Automorphism Group 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • V. R. Shanmukhasundaram
    • 1
    Email author
  • Y. V. D. Rao
    • 1
  • S. P. Regalla
    • 1
  1. 1.Birla Institute of Technology and Science (BITS), Pilani – Hyderabad CampusHyderabadIndia

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