On the Classification of Motions of Paradoxically Movable Graphs

Edge lengths of a graph are called flexible if there exist infinitely many non-congruent realizations of the graph in the plane satisfying these edge lengths. It has been shown recently that a graph has flexible edge lengths if and only if the graph has a special type of edge coloring called NAC-coloring. We address the question how to determine paradoxical motions of a generically rigid graph, namely, proper flexible edge lengths of the graph. We do so using the set of all NAC-colorings of the graph and restrictions to 4-cycle subgraphs.