Wire-driven Parallel Robot: Permitting Collisions Between Wires

Abstract

In spatial designs of wire-driven parallel robots, collisions between wires by limiting platform trajectories. The common practice for avoiding collisions between wires is by limiting the moving platform trajectories. However, as opposed to rigid links, wires may tangle and the robot may still be functional. Hence, the purpose of this work is to examine the possibility of permitting wire collisions and thus expanding the workspace of the robot. Under the assumptions of negligible wire mass and diameter and negligible friction between the wires, the inverse kinematics of a robot with two colliding wires is formulated and was solved numerically. In addition, linearization was performed and found to be accurate excluding the initial steps of collision. To resolve this, approximated systems were solved analytically (up to univariate high-order polynomials) using an elimination method that provides accurate results. An experimental setup with two motorized wires was built and the theoretical and experimental results are presented. Velocities and forces mappings for the wire-driven parallel robot under wire collisions were also forrnulated. It should be noted that unlike the collisions-free case, these two mappings are not identical. As a result, two different types of singularities arise, static singularity and kinematic singularity, which are defined and forrnulated. Finally, workspace expansion is demonstrated for a six-degree-of-freedom redundant robot design for which feasible and positive wrench closures were defined. Permitting wire collisions enables a significantly larger workspace compared with the collisions-free case.