Optimal force distribution based on slack rope model in the incompletely constrained cable-driven parallel mechanism of FAST telescope

Abstract

This paper addressed the determination of the tension distribution in the slack steel wires of the incompletely constrained cable-driven parallel mechanism of FAST telescope. Slack rope hung with piecewise uniform mass is specially investigated. First, the general formulation based on the wrench matrix was derived. Then the analytical model of slack rope was built to give the quantized relation between direction and amplitude of tension vector. The wrench matrix is not only platform pose dependent but influenced by rope geometry. Finally, a performance index based on minimal tension variance is selected to optimize the tension distribution among steel wires. Levenberg-Marquardt method is applied to solve the quadratic program and a discrete-mesh plan is proposed for the whole focal surface. An example of computation is given to verify the effect of the resolution.