Wrench-Closure Condition of Cable-Driven Parallel Manipulators

Abstract

Cable-driven parallel manipulators (CDPM) have parallel structures that consist of moving platforms connected to the fixed platform through many flexible cables. The moving platform is driven by many winches, and because of the unidirectional property of cables (cables can only pull and not push in the moving platform), some specific workspaces of CDPM are limited and often do not exist (Gouttefarde and Gosselin 2006). Therefore, determining workspaces for CDPM become an important task, in order to easily plan the trajectory or control the robot. In this paper, we are interested in a set of poses of moving platforms, in which CDPM is always able to generate wrenches that balance any given external wrench exerted on the moving platform. This set of poses is also called wrench-closure workspace (WCW). In this work, we propose a novel procedure used to determine whether a pose of moving platform belongs to WCW. The condition used to check the feasibility of a certain pose in WCW is also called wrench closure condition (WCC). The proposed WCC is able to apply to completely or redundantly restrained CDPM. By analyzing the geometric properties of CDPM and applying the method used to check the feasibility of a system of inequalities, the algorithm used to check the presence of a given pose in WCW is established. To verify the performance of the proposed WCC, the test has been done in two different CDPMs that are clearly described in the introduction section.