Dynamics analysis of spatial parallel robot with rigid and flexible links

To analyze the rigid-flexible coupling effects on the dynamic performance of a robot system, a dynamic model of a parallel robot with flexible spatial links is derived in detail using a floating frame of reference (FFR) formulation. Compared to the previous rigid-flexible coupling model where the kinematic chains are all flexible links or where the joints are all flexible components, the inertia matrix and the stiffness matrix are not constant matrix which leading to the differences in respect of dynamic performance in model. To verify the correctness of the derived dynamics equations, the dynamics solutions of the spatial parallel robot from an ideal rigid-body model and the FFR model containing rigid and flexible coordinates were established by an FFR formulation. Furthermore, a finite element analysis (FEA) model, which included rigid links and flexible spatial links, was constructed for comparison. The comparison of the three models showed that the trajectory trends were the same, but the motion trajectories of the end-effector obtained by the FFR and FEA models varied within a certain range, and the maximum variations occurred at the peaks of the trajectories. However, since the FFR model considered the coupling effects of rigid and flexible links and the micro-displacement of the end-effector, the amount of deformation was the largest.