A novel construction method is proposed to construct multimode deployable polyhedron mechanisms (DPMs) using symmetric spatial RRR compositional units, a serial kinematic chain in which the axes of the first and the third revolute (R) joints are perpendicular to the axis of the second R joint. Single-loop deployable linkages are first constructed using RRR units and are then assembled into polyhedron mechanisms by connecting the single-loop linkages using RRR units. The proposed mechanisms are over-constrained and can be deployed. The prism mechanism constructed using two Bricard linkages and six RRR chains has one degree-of-freedom (DOF). When removing three of the RRR chains, the mechanism will have one additional 1-DOF motion mode. The DPMs based on 8R and 10R linkages also have multiple modes, and several mechanisms have variable-DOF. The DPMs can switch among different motion modes through transition positions. Prototypes are 3D-printed to verify the feasibility of the mechanisms.

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