Tension cable distribution of a membrane antenna frame based on stiffness analysis of the equivalent 4-SPS-S parallel mechanism

Stiffness has significant influence on the surface accuracy of reflector of membrane antennas. This paper proposes a method to analyze the stiffness of a membrane antenna frame supported by compliant booms and tensioned with cables. An equivalent 4-SPS-S parallel mechanism of the membrane antenna frame is established. Velocity Jacobian matrix is obtained through kinematic analysis. Stiffness of the actuating SPS branches and the constrained central strut is constructed. Based on the force-equilibrium equation and the principle of virtual work, total stiffness matrix of the mechanism, which has been decomposed into the SPS branches stiffness matrix and the central strut stiffness matrix, is derived. Influences of cable distribution and platform pose on stiffness are identified by using the stiffness index - the reflector surface accuracy and the minimal eigenvalue. Accuracy of the proposed approach is evaluated. On account of stiffness, numerical simulations have been performed for acquiring the optimal distribution of tension cables and pose of the platform in the design of antennas.