Polyhedral Linkages Obtained as Assemblies of Planar Link Groups

Abstract

The study aims to devise means of obtaining polyhedral linkages for homothetic deployment of polyhedral shapes by embedding planar link groups in faces of the polyhedral shape of interest. The questions of which polyhedral shapes may be suitable for such a pur-pose and what are the compatibility conditions for spatially assembling planar link groups are addressed. Homohedral and tangential polyhedral shapes are found to be suitable for the task and some examples of linkages are worked out.