Efficient enumeration and hierarchical classification of planar simple-jointed kinematic chains: Application to 12- and 14-bar single degree-of-freedom chains

Eric Butcher, Chris Hartman

Research output: Contribution to journalArticle

49 Scopus citations


An algorithm to exhaustively enumerate and structurally classify planar simple-jointed kinematic chains using the hierarchical representation of Fang and Freudenstein is proposed in which all isomorphic chains are automatically eliminated in the enumeration procedure such that isomorphism testing on the final set of chains is eliminated. An efficient rule-based technique for eliminating degenerate kinematic chains is also proposed. This efficient scheme allows for the exhaustive enumeration of complicated cases that have received little or no attention in the past due to the difficult and time-consuming aspect of testing the kinematic chains for isomorphisms. For verification, the algorithm is first applied to enumerate the single degree-of-freedom 6-, 8-, and 10-bar cases, then to the 12-bar case (for which the results verify or contradict those reported in three previous papers), and finally to the previously intractable 14-bar case.

Original languageEnglish (US)
Pages (from-to)1030-1050
Number of pages21
JournalMechanism and Machine Theory
Issue number9
Publication statusPublished - Sep 2005
Externally publishedYes



  • Contracted
  • Isomorphism testing
  • Monochrome graphs
  • Planar mechanisms
  • Simplified

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering
  • Mechanical Engineering

Cite this