| Summary: | The tetrahedral elements that make up the large deployable reflector (LDR) are a kind of metamorphic element, which belongs to the multi-loop coupling mechanism. Firstly, the method of combining topology with screw theory is put forward. The parametric model and the constrained matrix are established to analyze the malleability of 3RR-3RRR tetrahedral element. Secondly, the kinematics expression of each motion pair is deduced by the relationship between the velocity and the motion spinor. Finally, the configuration of the metamorphic element is optimized to make the parabolic antenna fully folded, so that the antenna can meet the maximum folding ratio. The results show that the 3RR-3RRR element is a single-degree of freedom (DOF) mechanism. What’s more, three new configurations 3RS-3RRR, 3SR-3RRR and 3UU-3RRR are obtained on the basis of optimization. In particular, it proves to be that the LDR which consists of the 3RS-3RRR metamorphic element can achieve the maximum folding ratio. This paper provides a theoretical basis for the computer-aided design of the truss antennas, which has an excellent applicability in the field of aerospace and other multi-loop coupling mechanism.
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