Kinematic analysis of bevel epicyclic gear trains using graph notation

Carl A. Nelson, Raymond J. Cipra

Research output: Contribution to conferencePaperpeer-review


A kinematic analysis technique is introduced to find the 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. Computer software has been developed to demonstrate its usefulness. This discussion is limited to gear trains whose input and output axes are collinear, such as automotive automatic transmissions, although the methodology presented is readily extended to other cases besides the case of collinear input and output axes.

Original languageEnglish (US)
Number of pages7
StatePublished - 2002
Externally publishedYes
Event27th Biennial Mechanisms and Robotics Conference - Montreal, Que., Canada
Duration: Sep 29 2002Oct 2 2002


Conference27th Biennial Mechanisms and Robotics Conference
CityMontreal, Que.


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

ASJC Scopus subject areas

  • General Engineering


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