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Rigidity of frameworks supported on surfaces

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<mark>Journal publication date</mark>2012
<mark>Journal</mark>SIAM Journal on Discrete Mathematics
Issue number4
Number of pages25
Pages (from-to)1733-1757
Publication StatusPublished
<mark>Original language</mark>English


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.