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Workspace analysis and optimization is a critical issue in robot manipulator design. For a cable-driven parallel manipulator (CDPM), due to the unilateral driving properties of the cables, maintaining positive cable tension is essential to maneuver the moving platform. As a result, its workspaces are always determined and characterized by the tension status of its driving cables. It has been realized that the tension factor (TF) reflecting the relative tension distribution among the driving cables is an appropriate measure to evaluate the quality of force closure for CDPMs. However, in a fully restrained CDPM, since redundant cables are employed to drive the moving platform, the TF values are not unique even for a particular moving platform pose. Therefore, how to obtain the optimal TF value so as to generate an optimized workspace becomes the major subject of this paper. It is proved that the optimal TF value can be efficiently determined through a linear optimization approach, although it is essentially a nonlinear optimization problem. Subsequently, a global tension index is proposed to evaluate the quality of the entire workspace, which is achieved by integrating the local TF values (i.e., the optimal TF values at every moving platform poses) over the workspace. Computation examples are provided to demonstrate the effectiveness of the proposed algorithms
Yang et al. (Sun,) studied this question.
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