Logical Foundations of Kinematic Chains: Graphs, Line Graphs, and Hypergraphs

[+] Author and Article Information
Frank Harary

Department of Computer Science, New Mexico State University, Las Cruces, NM

Hong-Sen Yan

Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan 70101, ROC

J. Mech. Des 112(1), 79-83 (Mar 01, 1990) (5 pages) doi:10.1115/1.2912583 History: Received August 01, 1988; Revised May 01, 1989; Online June 02, 2008


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.

Copyright © 1990 by The American Society of Mechanical Engineers
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