STIFFNESS ANALYSIS OF CABLE-DRIVEN PARALLEL MANIPULATORS USING EQUIVALENT MODEL

In most of the analysis of cable-driven parallel manipulators composed of relatively short cables, cables are treated as linear elements that can only be tensioned, and the sag effects due to their self-weight cannot be considered. As a result, the stiffness analysis procedure is the same as that of rigid-link parallel manipulators. In this paper, the static model for long-span cables is constructed using catenary equation to account for the sag effects, and the stiffness matrix of a cable is deduced. An equivalent model in the stiffness sense is presented, in which a cable can be replaced by 3 springs perpendicular to each other. Then a cable-driven parallel manipulator is equivalent to its relative rigid-link counterpart. The stiffness matrix of a long-span cable-driven manipulator can be obtained by referring to the available conclusions of the stiffness analysis. The stiffness of the cable-supporting system for a large radio telescope is presented as a numerical example.