Journal Article Infinitesimal Rigidity of Symmetric Bar-Joint Frameworks

Schulze, Bernd  ,  Tanigawa, Shin-ichi

29 ( 3 )  , pp.1259 - 1286 , 2015-07-16 , Society for Industrial and Applied Mathematics
We propose new symmetry-adapted rigidity matrices to analyze the infinitesimal rigidity of bar-joint frameworks of arbitrary-dimension with Abelian point group symmetries. These matrices define new symmetry-adapted rigidity matroids on group-labeled quotient graphs. Using these new tools, we establish combinatorial characterizations of infinitesimally rigid two-dimensional bar-joint frameworks whose joints are positioned as generically as possible subject to the symmetry constraints imposed by a reflection, a half-turn, or a threefold rotation in the plane. For bar-joint frameworks which are generic with respect to any other cyclic point group in the plane, we provide a number of necessary conditions for infinitesimal rigidity.

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