Constrained Cubic Grid Rigidity Decision with Directed Graph and Applications

Abstract We present a rigidity decision problem of constrained cubic grids in any given bracing pattern. The cubic grid bar and joint frameworks are not rigid. Additional constraints are required for rigidity. These constraints can be pinned down joints and additional bracing elements. Scaffoldings are not rigid cubic grid structures whose specific joints are pinned down. Inserting cable, strut, or rod bracing elements makes the framework rigid. Our model, which provides a linearly complex algorithm, has practical implications in testing the strong connectedness of a corresponding directed graph, contributing to the field of rigidity in structural engineering and motions of cable controlled pinned down cubic mechanisms.