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.