Expandable polyhedral mechanisms based on polygonal one-degree-of-freedom faces

In this article, a new family of expandable mechanisms is presented. The proposed mechanisms are expandable polyhedra built using one-degree-of-freedom (one-DOF) planar linkages. The latter planar linkages have the shape of polygons and can be expanded while preserving their shape in any of their configurations. The planar mechanisms are used to form the faces of a polyhedron. They are assembled using spherical joints at the vertices of the polyhedron. The result is a one-DOF movable polyhedron which can be expanded while preserving its shape. The application of the principle on regular polyhedra is first presented. For the five Platonic solids, theoretical maximum expansion ratios are computed, simulation results are given, and two prototypes are shown. Then, two additional examples are provided to illustrate the application of the principle to irregular polyhedra.