Orientation Workspace and Stiffness Optimization of Cable-Driven Parallel Manipulators With Base Mobility

Abstract

Cable-driven parallel manipulators (CDPM) potentially offer many advantages over serial manipulators, including greater structural rigidity, greater accuracy, and higher payload-to-weight ratios. However, CDPMs possess limited moment resisting/exerting capabilities and relatively small orientation workspaces. Various methods have been contemplated for overcoming these limitations, each with its own advantages and disadvantages. The focus of this paper is on one such method: the addition of base mobility to the system. Such base mobility gives rise to kinematic redundancy, which needs to be resolved carefully in order to control the system. However, this redundancy can also be exploited in order to optimize some secondary criteria, e.g., maximizing the size and quality of the wrench-closure workspace with the addition of base mobility. In this work, the quality of the wrench-closure workspace is examined using a tension-factor index. Two planar mobile base configurations are investigated, and their results are compared with a traditional fixed-base system. In the rectangular configuration, each base is constrained to move along its own linear rail, with each rail forming right angles with the two adjacent rails. In the circular configuration, the bases are constrained to move along one circular rail. While a rectangular configuration enhances the size and quality of the orientation workspace in a particular rotational direction, the circular configuration allows for the platform to obtain any position and orientation within the boundary of the base circle. Furthermore, if the bases are configured in such a way that the cables are fully symmetric with respect to the platform, a maximum possible tension-factor of one is guaranteed. This fully symmetric configuration is shown to offer a variety of additional advantages: it eliminates the need to perform computationally expensive nonlinear optimization by providing a closed-form solution to the inverse kinematics problem, and it results in a convergence between kinematic singularities and wrench-closure singularities of the system. Finally, we discuss a particular limitation of this fully symmetric configuration: the inability of the cables to obtain an even tension distribution in a loaded configuration. For this reason, it may be useful to relax the fully symmetric cable requirement in order to yield reasonable tensions of equal magnitude.