Combinatorial characterization of the Assur graphs from engineering

We introduce the idea of Assur graphs, a concept originally developed and exclusively employed in the literature of the kinematics community. This paper translates the terminology, questions, methods and conjectures from the kinematics terminology for one degree of freedom linkages to the terminolog...

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Bibliographic Details
Published in:European journal of combinatorics 2010-05, Vol.31 (4), p.1091-1104
Main Authors: Servatius, Brigitte, Shai, Offer, Whiteley, Walter
Format: Article
Language:English
Subjects:
Combinatorial analysis
Communities
Graphs
Kinematics
Linkages
Mathematical analysis
Rigidity
Terminology
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Summary:We introduce the idea of Assur graphs, a concept originally developed and exclusively employed in the literature of the kinematics community. This paper translates the terminology, questions, methods and conjectures from the kinematics terminology for one degree of freedom linkages to the terminology of Assur graphs as graphs with special properties in rigidity theory. Exploiting the recent works in combinatorial rigidity theory we provide mathematical characterizations of these graphs derived from ‘minimal’ linkages. With these characterizations, we confirm a series of conjectures posed by Offer Shai, and offer techniques and algorithms to be exploited further in future work.
ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2009.11.019