Research on Inverse Dynamics of a Spatial Parallel Robot with Flexible Links

The inverse dynamic model for a rigid-flexible 3-RRRU parallel robot is deduced by Lagrange's equations, wherein the rigid links and flexible links are described by natural coordinate formulation (NCF) and absolute nodal coordinate formulation (ANCF), respectively. To eliminate the Poisson locking effect, the elastic forces of the flexible links are calculated by a selective reduced integration scheme. The generalized-a method is employed to solve the dynamic equations under kinematic constraints. Because of the differences in convergence rates of the coordinates for the rigid links and flexible links, the rigid geometric constraints are subject to be violated during the iterative process. Therefore, a new method based on NCF, called Transient Rigid Kinematic Correction (TRKC), is proposed to preserve the constraints for the multibody system. The dynamic solution results are compared with rigid robotic system, which show that flexible links affect the angular displacement, velocity and torque of the actuated joints.