A drawback of many cable-driven parallel robots is a relatively small orientation workspace. In this paper, two design variants for cable-driven parallel robots with nine and twelve cables are proposed that allow for large rotations. It is shown that the platform can perform a 360◦ tive tension in all cables and without collisions amongst the cables. Furthermore, workspace studies of the total orientation workspace are provided. Surprisingly, this family of cable robot is capable to perform an unlimited rotation within a translational workspace of reasonable size. Finally, the efficiency and computation time of force distribution algorithms is compared for cable robots having twelve cables.