Simplified kinematic analysis of bevel epicyclic gear trains with application to power-flow and efficiency analyses

Carl A. Nelson, Raymond J. Cipra

Research output: Contribution to journalArticle

54 Scopus citations


A kinematic analysis technique is introduced to find the angular velocities of all links in bevel epicyclic gear trains. The method relies on previous work in graph theory. It improves on existing techniques used for analysis of planar geared mechanisms in its ability to accurately solve the kinematics of spatial geared mechanisms, particularly bevel gear trains, in a simpler manner. Usefulness of the method is demonstrated through its application to power-flow and efficiency analyses as well as its implementation in computer software. This discussion is limited to gear trains whose input and output axes are collinear, such as automotive automatic transmissions.

Original languageEnglish (US)
Pages (from-to)278-286
Number of pages9
JournalJournal of Mechanical Design, Transactions of the ASME
Issue number2
Publication statusPublished - Mar 1 2005



  • Bevel gear trains
  • Epicyclic gear trains
  • Graph notation
  • Kinematic analysis
  • Planetary gear trains
  • Spatial kinematics

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design

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