Cable-driven parallel manipulators with base mobility: A planar case study
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Cable-driven parallel manipulators offer a variety of potential advantages over serial manipulators, including greater structural rigidity, greater accuracy, and higher payload-to-weight ratios. Compared to traditional rigid-link parallel manipulators, they are capable of a much larger translational workspace. Furthermore, their relatively low mass and inertial properties facilitate performance at higher accelerations. However, the fact that cables can pull but not push gives rise to unilateral constraints which add complexity to the modeling and analysis of the system; in order to fully control all degrees of freedom, the cables must always remain tensioned and a minimum of one degree of actuation redundancy is generally required. Cable-driven robots also suffer from limited moment resisting/exerting capabilities and relatively small orientation workspaces. In order to combat these limitations, various methods have been proposed in the literature - each with its own advantages and disadvantages. The focus of this paper is on one such method: the addition of base mobility into the system. It is shown that this base mobility gives rise to kinematic redundancy, which, if carefully resolved and controlled, can be exploited in order to optimally position the bases according to some desired objective - for example, maximizing the size and quality of the wrench-closure workspace. In this work, the quality of the wrench-closure workspace is given by an index known as the tension factor. Two planar mobile base configurations are investigated, and their results 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. It is demonstrated that while a rectangular configuration is capable of improving the size and quality of the orientation workspace in a particular rotational direction, a 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; it results in a convergence between kinematic singularities and wrench-closure singularities of the system; and it allows for some secondary criteria, such as the stiffness of the system, to be optimized. 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.