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 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.

• Type: Journal
• Year: 2010
• Where: EJC
• Authors: Brigitte Servatius, Offer Shai, Walter Whiteley
• Keywords: Assur Graphs, EJC 2007, EJC 2010, Isostatic Pinned Frameworks, Singular Realizations