A Historical Review of Polyhedral Linkages

Polyhedral linkages are linkages that resemble polyhedral shapes at different configurations. This paper summarizes the necessary geometrical fundamentals of polyhedral geometry and presents a historical and critical review of the polyhedral linkage designs available in the literature. Basic definitions of polyhedral geometry and operations are needed to comprehend and design polyhedral linkages. First, early works on polyhedral linkages are presented, where flexible polyhedra with rigid faces and flexible edges are issued. The final part is reserved to conformal polyhedral linkages, which go through shape transformations while plane, dihedral and solid angles are preserved. Conformal polyhedral linkages are examined in four categories: 1) Jitterbug-like linkages with screwing polygonal links connected to each other with dihedral angle preserving links, 2) polyhedral linkages with planar kinematic chains in radial motion planes, 3) polyhedral linkages with planar kinematic chains on faces, that are connected to each other with dihedral angle preserving links, and 4) other conformal polyhedral linkages.