Mobility of symmetry-regular bar-and-joint frameworks

Fowler, Patrick and Guest, Simon and Schulze, Bernd (2014) Mobility of symmetry-regular bar-and-joint frameworks. In: Rigidity and symmetry :. Fields Institute Communications . Springer, New York, pp. 117-130. ISBN 9781493907809

Abstract

In a symmetry-regular bar-and-joint framework of given point-group symmetry, all bars and joints occupy general positions with respect to the symmetry elements. The symmetry-extended form of Maxwell’s Rule is applied to this simplest type of framework and is used to derive counts within irreducible representations for infinitesimal mechanisms and states of self stress. In particular, conditions are given for symmetry-regular frameworks to have at least one infinitesimal mechanism (respectively, state of self stress) within each irreducible representation of the point group of the framework. Similar conditions are found for symmetry-regular body-and-joint frameworks.