Slackening effects in 2D exact positioning in cable-driven parallel manipulators

An analytical model of elastic cables is presented to evaluate the influence of the cables sag in the exact positioning of a point mass end-effector in a two-dimensional space within the context of cable-driven parallel manipulators. Direct and inverse kinematic problems are formulated by means of 3n nonlinear equations expressing compatibility, equilibrium, and targeting conditions. Examples with an increasing number of cables are proposed to show that, in specific regions of the workspace, solving the inverse kinematics problem implies very slack configurations of redundant cables.