Frameworks with coordinated edge motions

Schulze, Bernd and Serocold, Hattie and Theran, Louis (2022) Frameworks with coordinated edge motions. SIAM Journal on Discrete Mathematics, 36 (4). pp. 2602-2618. ISSN 0895-4801

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Abstract

We develop a rigidity theory for bar-joint frameworks in Euclidean d -space in which specified classes of edges are allowed to change length in a coordinated fashion that requires differences of lengths to be preserved within each class. Rigidity for these coordinated frameworks is a generic property, and we characterize the rigid graphs in terms of redundant rigidity in the standard d -dimensional rigidity matroid. We also interpret our main results in terms of matroid unions.