Kinematic Characteristics and Dynamics Analysis of the Tetrahedral Deployable Mechanism Based on the Screw Theory

In order to solve the modeling and analysis problems of the kinematics and dynamics of the spaceborne tetrahedral space deployable antenna, a kinematics and dynamics characteristics analysis method based on screw theory is established. Firstly, configuration and geometric characteristics of the 3RR-3RRR tetrahedral deployable mechanism are analyzed, its screw constrained topology diagram is obtained based on screw theory, and its degree of freedom (DOF) is calculated to be only one. Then, the kinematics analysis of the mechanism is conducted, the velocities of the components are obtained through the combinatorial operation of kinematic twists, and the Jacobian matrix of this mechanism is also obtained. The 6-dimensional acceleration of each component is expressed by the screw derivative, and the angular accelerations and centroid linear accelerations of the node disks and rods are deduced. Finally, the dynamic equation is established based on the Newton-Euler equation and the principle of virtual work, and the numerical calculation and simulation verification are carried out. The simulation results are completely consistent with the numerical results, which verifies the correctness of the kinematics and dynamics characteristics analysis method based on screw theory. Every parameter has clear physical meanings in the analysis based on the proposed method, and the analysis process is easy to program due to its stylization and is suitable for the analysis of such spatial deployable mechanisms.