Singularity analysis of fully-constrained six-DOF cable-driven parallel robots with seven cables

Singularity analysis of parallel robots is an important issue. A parallel robot could be out of control or crash in a singular configuration. 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. This paper discusses various categories of singularities of fully-constrained cable-driven parallel robots. 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. 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. A method of identifying force-closure singularities of fully-constrained six-DOF cable-driven parallel robots with seven cables is proposed with mathematical proof. Understanding of the natures of singularities is important for the design and control of cable-driven parallel robots.