Singularity Analysis of Planar Cable-Driven Parallel Robots

It is well known that parallel robots may have singular configurations that can result in a loss of full control the mechanisms. This paper analyzes two different categories of singularities of planar cable-driven parallel robots with four or more cables. The unidirectional constraint of cables makes the singularity analysis of cable-driven parallel robots different from that of rigid-link parallel robots even if they have similar kinematical architectures. Based on their natures, singularities of cable-driven parallel robots are classified into two categories: the Jacobian singularity and the force-closure singularity. A Jacobian singularity occurs when the Jacobian matrix of a cable-driven parallel robot loses its full rank. Based on rank analysis of Jacobian matrix, a group of Jacobian singularities is reported with mathematical proof. When the Jacobian matrix of a cable-driven parallel robot has a full rank, the cables' inability to generate tension will lead to force-closure singularities, which can always happen to fully-constrained cable-driven parallel robots. An algorithm of identifying force-closure singularities of planar cable-driven parallel robots is proposed. Understanding of the natures of singularities is important for the design and control of cable-driven parallel robots.