Design and kinematics analysis of a parabolic cylinder deployment mechanism with modular over-constrained triangular pyramid

Space missions require novel mechanisms that can have compact form in complex space environments. This study proposes a modular triangular pyramid parabolic cylinder deployment mechanism. The modular deployable unit contains an over-constrained triangular pyramid deployable mechanism and a symmetrical trapezoidal Bricard linkage that drives the longitudinal and transverse motions of the mechanism. A cable net is added between two symmetrical linkages to form a parabolic cylindrical reflector and is analyzed by the force density method. The Denavit-Hartenberg (D-H) coordinate method is used to analyze the kinematic characteristics. Based on the analytical solution for the angular displacement, the degrees of freedom of the mechanism are derived from screw theory. Subsequently, the angular velocity and acceleration of the joint points are obtained. Finally, kinematic models of the modular triangular pyramid parabolic cylinder deployable mechanism are established, and the accuracy of the theoretical model is verified using a numerical method. This novel parabolic cylinder deployable mechanism will have a significant influence in aerospace domain. Crucially, the work has value to design deployment mechanism for parabolic cylinder antenna.