Wrench-Closure Workspace Generation for Cable Driven Parallel Manipulators Using a Hybrid Analytical-Numerical Approach

Abstract

In this paper, a technique to generate the wrench-closure workspace for general case completely restrained cable driven parallel mechanisms is proposed. Existing methods can be classified as either numerically or analytically based approaches. Numerical techniques exhaustively sample the task space, which can be inaccurate due to discretisation and is computationally expensive. In comparison, analytical formulations have higher accuracy, but often provides only qualitative workspace information. The proposed hybrid approach combines the high accuracy of the analytical approach and the algorithmic versatility of the numerical approach. Additionally, this is achieved with significantly lower computational costs compared to numerical methods. It is shown that the wrench-closure workspace can be reduced to a set of univariate polynomial inequalities with respect to a single variable of the end-effector motion. In this form, the workspace can then be efficiently determined and quantitatively evaluated. The proposed technique is described for a 3 degrees of freedom (3-DOF) and a 6-DOF cable driven parallel manipulator. A detailed example in workspace determination using the proposed approach and comparison against the conventional numerical approach is presented.

An Overview of the Development for Cable-Driven Parallel Manipulator

“…In the kinematic modeling of the cable-driven parallel robots, there are different models to illustrate the cable profile, including straight line model [26][27][28][29][30], parabolic model, and 2 Advances in Mechanical Engineering catenary model [31]. Generally, the straight line model is sufficient for most redundantly constrained robots.…”

Workspace Classification and Quantification Calculations of Cable-Driven Parallel Robots

“…Lau et al addressed the wrench closure condition (WCC) in [51]. The WCC is defined as the set of postures, which, if a set of positive cable forces is satisfied, can be determined for any arbitrary external wrench, velocity, or acceleration of the manipulator without any upper bound to cable force.…”

“…In most studies [48,[51][52][53][54], the numerical approach is used to find out the corresponding workspace for a specific system. It means the entire structure space is discretized and exhaustively searched to find the matching workspace which is defined previously.…”

Design and Analysis of Cooperative Cable Parallel Manipulators for Multiple Mobile Cranes

“…The CPMs have potential advantages in terms of simple and light-weight structure, large reachable workspace, high acceleration capability, and easy reconfigurability [16][17][18]. For the preceding characteristics, the CPMs play an important role in many engineering fields, such as manipulation of heavy payloads for manufacturing and cargo handling, coordinate measurement, aircraft testing, super antenna, haptic devices, rehabilitation and welfare engineering [19][20][21][22]. For the past several decades, the CPMs have been extensively studied.…”