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Frameworks symmetry and rigidity

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Published
<mark>Journal publication date</mark>12/2010
<mark>Journal</mark>International Journal of Computational Geometry and Applications
Issue number6
Volume20
Number of pages28
Pages (from-to)723-750
Publication StatusPublished
<mark>Original language</mark>English

Abstract

Symmetry equations are obtained for the rigidity matrix of a bar-joint framework in ℝd. These form the basis for a short proof of the Fowler-Guest symmetry group generalisation of the Calladine-Maxwell counting rules. Similar symmetry equations are obtained for the Jacobian of diverse framework systems, including constrained point-line systems that appear in CAD, body-pin frameworks, hybrid systems of distance constrained objects and infinite bar-joint frameworks. This leads to generalised forms of the Fowler-Guest character formula together with counting rules in terms of counts of symmetry-fixed elements. Necessary conditions for isostaticity are obtained for asymmetric frameworks, both when symmetries are present in subframeworks and when symmetries occur in partition-derived frameworks.

Bibliographic note

The paper was published in December 2010. (No record of acceptance date.)