Rigidity of multi-graphs. I. Linking rigid bodies in n-space

@article{Tay1984RigidityOM,
  title={Rigidity of multi-graphs. I. Linking rigid bodies in n-space},
  author={Tiong-Seng Tay},
  journal={J. Comb. Theory, Ser. B},
  year={1984},
  volume={36},
  pages={95-112}
}
A linkage of rigid bodies in n-space consists of a set of n-dimensional rigid bodies in n-space, certain pairs of which are linked together by one or more rigid bars using universal (ball) joints. Such a structure is canonically associated (bodies to vertices, bars to edges) with a multi-graph. We show that a multi-graph can be realized as a rigid linkage of rigid bodies in n-space if and only if it contains n(n + I)/2 edge disjoint spanning trees. Some techniques for generating rigid linkages… CONTINUE READING
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