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Mobility of symmetry-regular bar-and-joint frameworks

Research output: Contribution in Book/Report/ProceedingsChapter (peer-reviewed)

Published

Publication date06/2014
Host publicationRigidity and symmetry
EditorsRobert Connell, Asia Ivić Weiss , Walter Whiteley
Place of publicationNew York
PublisherSpringer
Pages117-130
Number of pages14
ISBN (Electronic)9781493907816
ISBN (Print)9781493907809
Original languageEnglish

Publication series

NameFields Institute Communications
PublisherSpringer
Volume70
ISSN (Print)1069-5265

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.