Deployable origami polyhedrons with one-DOF radial motion

Deployable polyhedrons, especially transformable polyhedrons, are mathematically interesting yet kinematically challenging. This paper presents a synthesis method for constructing a group of origami polyhedrons with synchronized radial motion and deployable transformability. First, an origami-synchronized mechanism with a threefold-symmetric motion feature is proposed by integrating a spatial 9R linkage and three pairs of spherical 4R linkages. Subsequently, by embedding the proposed origami-synchronized mechanism cells into the surface of Archimedean polyhedrons, three one-DOF transformable polyhedral mechanisms with distinct symmetries are constructed, the corresponding prototypes are fabricated to verify their kinematic properties. Further, referring to the dimensional shortening operations, structural variations of origami polyhedrons with mechanism topology isomorphism are demonstrated to realise various poly-hedral transformations with different volumetric deployable ratios. The newly found kinematic strategy and construction method can be readily extended to other polyhedron groups with po-tential applications in the fields such as deployable structures for aerospace exploration and ar-chitecture, as well as unit cells for mechanical metamaterials.