Frameworks with coordinated edge motions

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, subject to a linear constraint for each class. This is a tensegrity-like setup that is amenable to combinatorial “Maxwell-Laman-type” analysis. We describe the generic rigidity of coordinated frameworks in terms of the generic \(d\)-dimensional rigidity properties of the bar-joint framework on the same underlying graph. We also give Henneberg and Laman-type characterizations for generic coordinated rigidity in the plane, for frameworks with one and two coordination classes.