Generic global rigidity of body-bar frameworks

However, there is a special class of generic frameworks that have polynomial time algorithms for their generic rigidity (and redundant rigidity) in Rd for any d⩾1, namely generic body-and-bar frameworks. Such frameworks are constructed from a finite number of rigid bodies that are connected by bars generically placed with respect to each body. We show that a body-and-bar framework is generically globally rigid in Rd, for any d⩾1, if and only if it is redundantly rigid. As a consequence there is a deterministic polynomial time combinatorial algorithm to determine the generic global rigidity of body-and-bar frameworks in any dimension.