The dynamic modeling, redundant-force optimization, and dynamic performance analyses of a parallel kinematic machine with actuation redundancy

SUMMARY This paper discusses a planar 2-DOF (degrees of freedom) parallel kinematic machine with actuation redundancy. Its inverse dynamic model is constructed by utilizing the Newton–Euler method based on the kinematic analysis. However, the dynamic model cannot be solved directly because the number of equations is less than the number of unknowns, which is due to the redundant force. In order to solve this problem, the relationship between the deformations of the links and the position errors of the moving platform are further explored. Then a novel method, which aims at minimizing the position errors of the machine, is proposed to optimize the redundant force. It also enables to solve the dynamic model. Finally, the dynamic performance analyses of this machine and its non-redundant counterpart are provided by numerical examples. Besides, another optimization method proposed for minimizing the constraint forces is also applied for comparison. The results show the effectiveness of the novel methods in improving the position precision of the machine.