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Rigidity of frameworks supported on surfaces

Research output: Contribution to journalJournal article

Published

Journal publication date2012
JournalSIAM Journal of Discrete Mathematics
Journal number4
Volume26
Number of pages25
Pages1733-1757
Original languageEnglish

Abstract

A theorem of Laman gives a combinatorial characterisation of the graphs that
admit a realisation as a minimally rigid generic bar-joint framework in $\bR^2$. A more general theory is developed for frameworks in $\bR^3$ whose vertices are constrained to move on a two-dimensional smooth submanifold $\M$. Furthermore, when $\M$ is a union of concentric spheres, or a union of parallel planes or a union of concentric cylinders, necessary and sufficient combinatorial conditions are obtained for the minimal rigidity of generic frameworks.