Geometric properties of Assur graphs

In our previous paper, we presented the combinatorial theory for minimal isostatic pinned frameworks–Assur graphs–which arise in the analysis of mechanical linkages. In this paper we further explore the geometric properties of Assur graphs, with a focus on singular realizations which have static sel...

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Bibliographic Details
Published in:European journal of combinatorics 2010-05, Vol.31 (4), p.1105-1120
Main Authors: Servatius, Brigitte, Shai, Offer, Whiteley, Walter
Format: Article
Language:English
Subjects:
Combinatorial analysis
Drivers
Graphs
Linkages
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Summary:In our previous paper, we presented the combinatorial theory for minimal isostatic pinned frameworks–Assur graphs–which arise in the analysis of mechanical linkages. In this paper we further explore the geometric properties of Assur graphs, with a focus on singular realizations which have static self-stresses. We provide a new geometric characterization of Assur graphs, based on special singular realizations. These singular positions are then related to dead-end positions in which an associated mechanism with an inserted driver will stop or jam.
ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2009.11.020