Characterizing redundant rigidity and redundant global rigidity of body-hinge graphs
We characterize the redundant rigidity and the redundant global rigidity of body-hinge graphs in Rd R d in terms of graph connectivity. Our result implies that both edge-redundancy for rigidity and edge-redundancy for global rigidity can be checked via efficient graph-connectivity algorithms. Our result is contrasted with the fact that the problem of augmenting a Laman graph (i.e., the graph corresponding to a minimally rigid generic bar-joint framework in 2-dimension) to a 2-edge-rigid bar-joint graph with a minimum number of added edges is NP-hard.
redundant rigidity global rigidity body-hinge graph algorithms combinatorial rigidity edge-connectivity mixed-connectivity