Abstract:

For the deployable truss antenna composed of tetrahedral elements, the degree of freedom (DOF) of 3RR-3RRR element and multi-element was analyzed based on the screw theory, and the complexities of the over-constraint and the singularity analysis of the structural element were reduced. Firstly, the position and characteristics of the motion pair could be expressed simultaneously by the screw theory, so the motion spinors of hinges of the 3RR-3RRR element were established, and the number of the over-constraints was solved. Secondly, according to the modified Kutzbach-Grubler formula, the DOF of 3RR-3RRR element was solved, and the singularity and instantaneity of the special configuration were analyzed. Finally, the equivalent structure method was used to simplify the network’s structure and solve the DOF of the reflector. Then the relative distance between two disks was calculated to verify the deployable coordination of the antenna. The results show that the tetrahedral element has one degree of freedom and four over-constraints, and the constraint singularity is obtained under the special position of the hinge. After networking, the reflector is a single DOF mechanism, which can be fully deployed by the control of a single drive to realize the coordination of the deployable antenna at work, and has a good application in spatial mechanism field.

Key words: screw theory, degree of freedom, over-constraint, singularity, tetrahedral element,  , deployableantenna