Rigidity of Frameworks Supported on Surfaces
Nixon, A. · Owen, J. C. · Power, S. C.
Original · EN
A theorem of Laman gives a combinatorial characterisation of the graphs that admit a realisation as a minimally rigid generic bar-joint framework in ². A more general theory is developed for frameworks in ³ whose vertices are constrained to move on a two-dimensional smooth submanifold. Furthermore, when 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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