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Journal of Applied Mathematics
Volume 2014, Article ID 350492, 8 pages
http://dx.doi.org/10.1155/2014/350492
Research Article

On the Minimum Cable Tensions for the Cable-Based Parallel Robots

1Key Laboratory of Ministry of Education for Electronic Equipment Structure Design, Xidian University, Xi’an 710071, China
2School of Mechanical and Electronic Engineering, Xidian University, Xi’an 710071, China

Received 19 May 2014; Accepted 15 July 2014; Published 4 August 2014

Academic Editor: Antonio Bandera

Copyright © 2014 Peng Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper investigates the minimum cable tension distributions in the workspace for cable-based parallel robots to find out more information on the stability. First, the kinematic model of a cable-based parallel robot is derived based on the wrench matrix. Then, a noniterative polynomial-based optimization algorithm with the proper optimal objective function is presented based on the convex optimization theory, in which the minimum cable tension at any pose is determined. Additionally, three performance indices are proposed to show the distributions of the minimum cable tensions in a specified region of the workspace. An important thing is that the three performance indices can be used to evaluate the stability of the cable-based parallel robots. Furthermore, a new workspace, the Specified Minimum Cable Tension Workspace (SMCTW), is introduced, within which all the minimum tensions exceed a specified value, therefore meeting the specified stability requirement. Finally, a camera robot parallel driven by four cables for aerial panoramic photographing is selected to illustrate the distributions of the minimum cable tensions in the workspace and the relationship between the three performance indices and the stability.