Geometric properties of Assur graphs

Authors:
Brigitte Servatius;Offer Shai;Walter Whiteley
Affiliations:
Mathematics Department, Worcester Polytechnic Institute, United States;Faculty of Engineering, Tel-Aviv University, Israel;Department of Mathematics and Statistics, York University Toronto, ON, Canada
Venue:
European Journal of Combinatorics
Year:
2010

Citing 5
Cited 1

The algebraic geometry of motions of bar-and-body frameworks

SIAM Journal on Algebraic and Discrete Methods
Construction of self-dual graphs

American Mathematical Monthly
Rigidity and scene analysis

Handbook of discrete and computational geometry
Constraining Plane Configurations in Computer-Aided Design: Combinatorics of Directions and Lengths

SIAM Journal on Discrete Mathematics
Combinatorial characterization of the Assur graphs from engineering

European Journal of Combinatorics

Directed graphs, decompositions, and spatial linkages

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

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.