Reconfigurable polyhedral mechanisms using scissor-like elements with cantellation transformation between dual geometries

Deployable polyhedron mechanisms (DPMs) have garnered significant interest in architecture, aerospace, and robotics, where reconfigurable and space-efficient structures are crucial. This paper presents a tangential design method for DPMs using scissor-like elements (SLEs). Scissor units are placed along the edges of an equilateral polyhedron, tangential to its midsphere. This method enables the mechanisms to transform between a polyhedron and its dual, following the cantellation operation. Using screw theory, the kinematic properties of these mechanisms are analyzed. Results show that the DPMs exhibit 1-degree of freedom (DOF) under normal conditions and gain additional DOFs at multifurcation points, allowing for reconfigurable motion modes. Physical models based on various geometries, including Platonic, Archimedean, Johnson, and Catalan solids, help to validate the method's feasibility. Observations indicate that this method is only applicable to equilateral supporting polyhedra. The transformability and reconfigurability observed in these mechanisms demonstrate the potential of this approach for applications in architecture, aerospace, and robotics.