Workspace analysis of fully restrained cable-driven manipulators

For Cable-Driven Parallel Manipulators (CDPMs), employing redundant driving cables is necessary to obtain the full manipulation of the moving platform because of the unilateral driving property of the cables. Unlike rigid-link manipulators, the workspace of CDPMs is always determined and characterized by positive tension status of driving cables. In addition, 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 tension restraint for CDPMs. However, since redundant cables are employed to drive the moving platform, the TF values are not unique for a particular moving platform pose. Therefore, how to determine the workspace and obtain the optimal TF value so as to generate a workspace with optimized performance become the major subjects of this paper. It is shown that the workspace can be generally formed from tension conditions verified by a recursive dimension-reduction approach and that the optimal TF value at every pose can be efficiently determined through a linear optimization approach, although it is essentially a nonlinear optimization problem. Computational examples are provided to demonstrate the effectiveness of the proposed algorithms.