Geometric Properties of Assur Graphs
Metric Geometry
2016-09-08 v1 Combinatorics
Abstract
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.
Cite
@article{arxiv.0801.4113,
title = {Geometric Properties of Assur Graphs},
author = {Brigitte Servatius and Offer Shai and Walter Whiteley},
journal= {arXiv preprint arXiv:0801.4113},
year = {2016}
}