Workspace and stiffness analysis of a three-degree-of-freedom spatial cable-suspended parallel mechanism while considering cable mass

Abstract

Most existing research on parallel cable-driven mechanisms has been performed while neglecting cable mass. However, those prior works that did take cable mass into account have shown that such a hypothesis may lead to significant errors in the analysis of these mechanisms. The research presented herein assesses the effect of neglecting cable mass in the analysis of a spatial parallel three-degree-of-freedom suspended cable-driven mechanism. The analysis is based on the elastic catenary model. The inverse displacement problem of the mechanism is solved numerically subject to constraints on the cable tensions and restrictions on cable drooping. This solution is then used in the numerical estimation of the mechanism workspace. The stiffness of the mechanism is evaluated throughout the workspace by mapping intuitive stiffness indices that are extracted from the stiffness matrix. Both the mechanism workspace and stiffness are found to be heavily influenced by cable sagging. The results obtained in this paper support the notion that the effect of cable sagging on a mechanism should be thoroughly assessed prior to pursuing a design based on the assumption of massless cables.