Logical foundations of kinematic chains: Graphs, line graphs, and hypergraphs

Frank Harary, Hong Sen Yan

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


In terms of concepts from the theory of graphs and hypergraphs we formulate a precise structural characterization of a kinematic chain. To do this, we require the operations of line graph, intersection graph, and hypergraph duality. Using these we develop simple algorithms for constructing the unique graph G(KC) of a kinematic chain KC and (given an admissible graph G) for forming the unique kinematic chain whose graph is G. This one-to-one correspondence between kinematic chains and a class of graphs enables the mathematical and logical power, precision, concepts, and theorems of graph theory to be applied to gain new insights into the structure of kinematic chains.

Original languageEnglish
Pages (from-to)79-83
Number of pages5
JournalJournal of Mechanical Design, Transactions of the ASME
Issue number1
Publication statusPublished - 1990 Mar

All Science Journal Classification (ASJC) codes

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


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