Generalized Ray-Based Lattice Generation and Graph Representation of Wrench-Closure Workspace for Arbitrary Cable-Driven Robots

This paper presents a new generalized ray-based approach to the generation and representation of the wrench-closure workspace (WCW) for cable-driven robots (CDRs). Existing WCW studies have yet to address two significant problems, first is the lack of a generalized approach to generate the WCW with continuity information for all degrees-of-freedom (DoFs) and arbitrary CDRs, and second is a workspace representation for higher DoF robots. The proposed work addresses these issues using a generalized ray-based lattice WCW generation approach that can be applied in all DoFs. Furthermore, a new graph workspace representation is introduced with a range of advantages in the way CDR workspace can be visualized and studied. Such a representation is powerful since it: can be used for any other type of workspace beyond the WCW; can be visualized in two-dimensions regardless of the number of DoFs of the system; allows metric information to be included; and opens up the use of well-established graph theory techniques to study the workspace. Through three different CDR examples, a 3-DoF planar cable-driven parallel robot (CDPR), a 4-DoF multilink robot, and a 6-DoF CDPR, the characteristics and advantages of the proposed method are highlighted.