Research on the dynamic trajectory of spatial cable-suspended parallel manipulators with actuation redundancy

A cable-driven parallel manipulator (CDPM) adopts flexible cables instead of rigid limbs, connecting the base and the end effector. When gravity is considered as a virtual cable, the cable-suspended parallel manipulator (CSPM) takes shape. Due to various advantages, i.e. large workspace, high speed and low cost, the CSPM has drawn the attention of both academia and industry. Dynamic trajectories of the CSPM are deduced by considering the dynamic model instead of the traditional quasi-static or static assumption, which further expands the motion range of the CSPM. Our previous work revealed that redundant actuation helps to improve the dynamic capability of the planar CSPM in terms of the feasible frequency. In this paper, dynamic trajectories of the redundantly actuated spatial CSPM are investigated. By considering the inertial force of the end effector as an additional gravitational force, equivalent gravitation and equivalent projection are proposed, which bridge the gap between static and dynamic workspaces. Feasible frequency ranges of typical dynamic trajectories for 4-cable CSPM are analytically deduced with the three-cable theorem, giving an insight into the problem. The stable and promising pendulum-like frequency is confirmed with physical experiments. Methods established in this paper could be conveniently adopted for the dynamic trajectory analysis of other spatial CSPMs with actuation redundancy.