Kinematic Characteristics Analysis and Assembly Application of the Rectangular Pyramid Deployable Mechanism

Deployable mechanisms have the characteristics of complex loops and strong coupling. As a result, the solution to the degrees of freedom (DOFs) and kinematic characteristics of the basic mechanism unit are often complicated, and the solution for combined mechanisms is rarely reported in the relevant literature. In this paper, the kinematic characteristics of the rectangular pyramid deployable mechanism (RPDM) are analyzed, and the DOFs of the RPDM are calculated based on the screw theory. In addition, the DOF number and properties of its moving components are analyzed. Based on the condition that the nonhomogeneous linear equations have a unique solution, the singularity analysis of the mechanism is complete, which indicates that the mechanism can be continuously deployed and folded. Based on the geometric characteristics of the mechanism, its folded ratio is calculated. Finally, a ring, a planar, and a parabolic truss deployable antenna mechanism are assembled based on the RPDM, and the DOF variation for the different assembly modes is obtained via the screw constraint matrix. This study provides a good reference for the design and analysis of such multi-closed-loop deployable mechanisms, and the large-scale space-deployable mechanisms constructed in this paper have good application prospects in the aerospace field.