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.
Highlights
The main difference between them is that, in the Cable-driven parallel manipulators (CDPM), the rigid links are replaced by the flexible light-weight cables, and their lengths are adjusted by winches that are usually mounted on the fixed platform
Constant orientation wrench closure workspace (COWCW): For in visualization, we can plot the Total orientation wrench closure workspace (TOWCW) of 3-dof CDPM. 6-dof CDPM, we can visualize the projection of itsclosure on up to 3-dimensional workspace
Constant position wrench closure workspace (CPWCW) is the projection of TOWCW when the projected space was only related to As shown in Figure 7, wrench-closure workspace (WCW) of the first configuration CDPM shown in Figure 1 the orientation of moving platform, i.e., position is constant
Summary
The cable-driven parallel manipulators (CDPMs) have a similar structure to the traditional parallel kinematic machines that consist of a moving platform (end-effector), the robot’s fixed platform, and many links used to connect the moving platform to the fixed platform. Due to the unilateral property of the cable tension force, the cable can only be pulled but not be pushed, resulting in the wrench matrix of CDPM perhaps being in full rank, but not providing any solution This leads to the limitation of a workspace of this kind of mechanism. We are interested in a set of poses of the moving platform in which CDPM can balance any external wrench by stretching the cables through winches. This set of poses is called wrench-closure workspace (WCW). In this paper, the method that determines whether a pose of the moving platform belongs to WCW is of interest
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