Analytical workspace delineation of a translational underconstrained cable-based robot

Abstract

This paper presents the analytical controllable workspace boundaries of a crane-type cable-based robot with purely translational motions. The underconstrained cable robot is composed of eight cables which support the weight of a mobile platform, restricting its motions into the vertical plane of a static platform. The analytic equations are developed so that its workspace fulfills the tensionable condition for a given set of minimum and maximum tension limits. The all-tensionable workspace is obtained by analyzing slackness conditions with constant orientation of the mobile platform and by solving the all-positive cable tension redundancy. The minimum two-norm cable tension formulation results in a quadratic equation which admits a minimum value by equaling its derivative to zero.