Rigidity of Frameworks Supported on Surfaces

Details Rigidity of Frameworks Supported on Surfaces Rigidity of Frameworks Supported on Surfaces

2010-09-20

arxiv.org/abs/1009.3772v1

Mathematics

Combinatorics

32 pages, 6 figures

Scientific paper

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.

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