A Fast solution method for end-effector force extremum in redundant cable-driven parallel robots

For the problem of quickly obtaining the range of load forces in a specific direction at the end-effector of an eight-cable, six-degree-of-freedom redundantly driven cable-parallel robot, a method based on geometric approaches in six-dimensional space for judging the extremum of the end-effector platform force is proposed, which involves shifting the convex hull formed by six-dimensional hyperplanes and intersecting it with a line or a two-dimensional section to determine the extremum of the feasible force of the end-effector, enabling rapid judgment of the force range that the platform can generate in any given orientation. Using an eight-cable, six-degree-of-freedom mechanism as an example, the proposed method establishes an end-effector position-acceleration image and utilizes position-acceleration curves to plan motion trajectories. The computed trajectory of cable forces satisfies the imposed constraints.