A family of reconfigurable deployable polyhedral mechanisms based on semiregular and Johnson polyhedra

This paper proposes and designs reconfigurable double angulated element (RDAE) and reconfigurable multiple angulated element (RMAE). A family of reconfigurable deployable polyhedral mechanisms (RDPM) based on semiregular and Johnson polyhedra are synthesized by using RDAE and RMAE. The obtained RDPMs can deploy in Hoberman sphere motion (HSM) and Radially Reciprocating Motion (RRM). The constraint conditions and geometric parameters (angles and link lengths) of RDAE are identified by considering the constraints of two pairs of angulated elements and three intersected axes. The kinematics of RDAE in HSM mode and RRM mode are also analyzed. RMAE is further investigated with its constraints and parameters identified. The construction steps of RDPMs based on semiregular and Johnson polyhedra are introduced separately, and reconfigurable deployable triangular prismatic mechanism and reconfigurable deployable triangular cupola mechanism as two examples are constructed in computer as well as in reality to verify the feasibility of RDAE, RMAE and the proposed construction method.