A class of reconfigurable deployable platonic mechanisms

This paper deals with the design of a new class of reconfigurable deployable Platonic mechanisms (RDPMs). At first, reconfigurable angulated element (RAE) with four half-platforms is designed and analyzed based on the reconfigurable property of angulated element. Using RAE as module, a method of synthesizing RDPMs is then proposed and three RDPMs are constructed. Starting from Type I generalised angulated element (GAE), a reconfigurable generalised angulated element (RGAE) comprised of two GAEs is investigated with its reconfigurable conditions identified. n pairs of straight elements (SE) and n pairs of angulated elements (AE) are further inserted into 2-RGAEs to construct n-SEs-2-RGAEs and n-AEs-2-RGAEs. The fully-retracted state and fully-expanded state of n-SEs-2-RGAEs and n-AEs-2-RGAEs are also detailed. Using 1-AE-2-RGAEs, three RDPMs with large magnification ratio are constructed in 3D software and fabricated using aluminum to verify their feasibility. This work provides a systematic approach to the design of RDPMs which can switch between two kinds of conventional deployable polyhedral mechanisms, including deployable polyhedral mechanisms with radially reciprocating motion and Hoberman spheres.