Abstract: In high-speed motion, the elastic deformation and vibration of the Delta parallel robot cannot be ignored, which have an impact on the motion performance. To address the problem of high equation dimensions and difficulty in being suitable for active control when discretizing flexible rods using finite element method, dynamic modeling of Delta rigid flexible coupled parallel robots was conducted using the assumed mode method and Kane method. By adding the position, velocity and acceleration constraint equations of the closed chain rigid flexible coupling system, the rigid flexible coupling dynamic equations of the closed chain Delta parallel robot are established. In order to solve the problem of high complexity of the rigid flexible coupling dynamic model of Delta parallel robot, the rigid flexible coupling dynamic model is decomposed into fast changing and slow changing subsystems according to the time scale by using the Singular perturbation method. In order to avoid disturbance and ensure convergence, a nonsingular terminal sliding mode controller is designed for slow varying systems. To suppress the influence of elastic vibration on motion, an LQR optimal controller was designed for fast changing systems, and merge the controllers of the two subsystems into a nonlinear hybrid controller of the rigid flexible coupling system. Simulation comparative experiments have shown that the designed hybrid controller maintains higher precision trajectory tracking and achieves significant vibration suppression effects, providing a new approach for active tracking control and vibration suppression of Delta rigid flexible coupled parallel robots.

Key words: parallel robot, rigid flexible coupling, assumed mode method, Kane method, singular perturbation