M.Sc Thesis
M.Sc Student Wischnitzer Yonatan Wire-Driven Parallel Robot: Expending the Workspace by Permitting Collisions between Wires Department of Mechanical Engineering Professor Moshe Shoham

Abstract

In spatial designs of wire-driven parallel robots, collisions between the wires may occur. The common practice is to avoid collisions between wires is by limiting platform trajectories. However, as opposed to rigid links, wires may tangle. 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 involving two colliding wires is formulated. The equations were 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) by elimination to provide accurate results.

A two motorized wires experimental setup was built and the theoretical and experimental results for some test cases are hereby presented. Theory provides a reasonable agreement for obtuse wires angles.

Velocities and forces mappings for the wire-driven parallel robot under wire collisions were formulated, as well. It should be noted that unlike those for 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 we hereby define and formulate.

Finally workspace expansion is demonstrated for a redundant 6 DOF design. To this end conditions for feasible and positive wrench closures were defined. Permitting collisions enabled large platform movements that were outside the workspace if collisions were avoided.