On the workspace of suspended cable-driven parallel robots

摘要

Workspace calculation for cable-driven parallel robot (CDPR) differs from the one for robots with rigid legs as the main limiting factor is the satisfaction of the mechanical equilibrium, being given a model for the cable behavior. We are considering here 6-dof CDPR with n ≥ 6 cables and are investigating the calculation of horizontal cross-sections of the workspace under the assumption that the orientation of the platform is constant. We show that for non deformable or elastic mass-less cables it is possible to calculate the border of the workspace under the constraints τ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> ≤ τ ≤ τ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> where τ is the cable tension and τ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> , τ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> are constant thresholds. For sagging cables the calculation is much more complex: we present however a preliminary, computer intensive algorithm that allow to obtain an approximation of the cross-section as a set of boxes. We also emphasize that for CDPR the definition of the workspace as the set of poses that can be reached has to be considered stricto sensu and cannot be used for other purpose: for example the inclusion of a trajectory in the workspace is not a proof of the feasibility of this trajectory.