Summary
All rigid motions of a wire forming a closed loop are determined under the hypothesis that the wire is inextensible, perfectly flexible and free of external forces.
It is found that all rigid motions of the wire are uniform rotations and that there exist countably many non trivial configurations of the wire that are consistent with a rigid motion. All these configurations have multiple points.
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Fusco, G. Rigid free motions of a perfect wire forming a closed loop. Acta Mechanica 51, 227–249 (1984). https://doi.org/10.1007/BF01177074
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DOI: https://doi.org/10.1007/BF01177074