A family of deployable polygons and polyhedra

A new linkage type for resizing polygonal and polyhedral shapes is proposed. The single degree-of-freedom planar linkages considered mainly consist of links connected by revolute joints. It is shown that the group of mechanisms obtained realize Cardanic Motion. The polyhedral linkages proposed are constructed by implementing the proposed planar linkages on the faces and interconnecting them by links at the vertices to retain the solid angles of the polyhedral shape of interest.