On the Properties and the Determination of the Wrench-Closure Workspace of Planar Parallel Cable-Driven Mechanisms

Abstract

This paper presents a detailed analysis of the constant-orientation wrench-closure workspace of planar three-degree-of-freedom parallel mechanisms driven by four cables. The constant-orientation wrench-closure workspace is defined as the subset of the plane wherein, for a given orientation of the moving platform, any planar wrench applied on the moving platform can be balanced by the cable-driven mechanism. Based on mathematical observations, this workspace is proved to be the union of two disconnected sets that may or may not exist. Moreover, if the constant-orientation wrench-closure workspace (WCW) exists, its boundary is shown to be composed of portions of conic sections. Then, an algorithm that determines the constant-orientation wrench-closure workspace by means of a graphical representation of its boundary is introduced. Several examples are also included.

Workspace Classification and Quantification Calculations of Cable-Driven Parallel Robots

“…In general, a workspace of a cable robot is defined as the set of all poses (positions and orientations) for which any wrench of a given set of wrenches can be applied on the platform by pulling the latter with the cables [31]. It means the end effector can physically reach the workspace when (1) all the cables are in tension and (2) all other specific motion and/or force constraints are satisfied [32].…”

“…A few researchers in [31,47,55,56] proposed analytical approaches to find the SEW and WCW issue. Bosscher et al in [46] proposed an approach to find boundaries of the WFW.…”

Analytical Solution to Find the Interference Boundaries of Planar Cable-Driven Mechanisms

“…For instance none of A 2 -C 1 , A 3 -C 1 , A 4 -C 1 could happen anymore and the largest interference-free workspace was obtained As a conclusion to this paper, the interference space of a planar CDM is compared with the wrench closure workspace (WCW). Based on [8], if the constant-orientation WCW exists, its boundary is composed of portions of conic sections. On the other hand, we have shown that the interference boundaries for a given angle are lines.…”

“…The set of all poses in which a range of external wrenches can be generated using a limited range of cable tensions is called wrench feasible workspace (WFW) [6][7][8][9]. A special case of WFW happens when both cable tension and the wrench sets are unbounded which is called wrench closure workspace (WCW) [8,9].The former depends on external loading, static or dynamic equilibrium and cable properties while the latter only depends on the manipulator kinematics. Knowing the WCW is a necessary but not sufficient condition for safe operation of a CDM since interference may occur between two cables or between a cable and the EE referred to as Cable-Cable (C-C) and Endeffector-Cable (E-C) interference, respectively.…”

On the Ability of a Cable-Driven Robot to Generate a Prescribed Set of Wrenches

“…This paper does not address the workspace of cable robots. The latter challenging problem was addressed in several papers over the recent years [10,11,12,19,25]. Before looking globally at the workspace, all proposed methods must go through the intermediate step of assessing the capability of a mechanism to generate a given set of wrenches.…”