In order to solve the problems of microgravity conditions on ground for the complicated driving mechanism of multidimensional framed structure space antenna components, a multidimensional framed structure zero gravity tracking system using constant tension suspension was designed. The system is able to perceive and tracking the intended motion of space two-dimensional pointing mechanism and deployable locking mechanism of antenna in real time, through a novel constant tension suspension controller based on position optimal sliding mode inner loop control strategy to enhance robustness and control accuracy, and solve the impact of parametric perturbation and the external disturbance of constant tension suspension system on the control accuracy. The zero gravity tracking system can provide microgravity conditions on ground for the driving mechanism of space antenna without additional force component in horizontal direction. Experimental results indicate that the control precision of the system meets the task requirements, and validate the correctness and feasibility of the scheme.