The Direct Kinematics of Objects Suspended From Cables

Abstract

This work addresses the problem for determining the position and orientation of an object with regular polygon suspended from n cables with the same length when the n robots form a regular polygon on the horizontal plane. First, an analytic algorithm based on resultant elimination is presented to determine all possible equilibrium configurations of the planar 4-bar linkage. As the nonlinear system can be reduced to a polynomial equation in one unknown with a degree 8, this algorithm is more efficient than numerical search algorithms. Then, considering that the motion of the 3D cable system in its vertical planes of symmetry can be regarded as the motion of an equivalent planar 4-bar linkage, the proposed algorithm is used to solve the direct kinematic problem of objects suspended from multiple cables. Then, case studies with three to six cables are conducted for demonstration. Finally, experiments are conducted for validation.