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.