Geometric Properties of Assur Graphs

Details Geometric Properties of Assur Graphs Geometric Properties of Assur Graphs

2008-01-27

arxiv.org/abs/0801.4113v1

Mathematics

Metric Geometry

Scientific paper

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.

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