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Many characterizations of fragmentability of topological spaces have been investigated. In this paper we deal with some properties of weak-fragmentability of Banach spaces.

In cable-driven parallel robots (CDPRs), each cable is typically driven by one actuator, and one is led to think that the number of actuators necessarily depends on the number of cables. In this paper, we consider that the number of cables depends on the required workspace while the number of actuators depends on the number of degrees of freedom of the robot. When designing a CDPR, one typically starts from the shape of the desired workspace to determine the required number of cables. Thence, he or she adds as many actuators, assuming that each of them drives one cable. Here, the number of actuators is supposed to be equal to one more than the number of degrees of freedom of the CDPR irrespective of the number of cables. A transmission system is designed for the actuators to drive several cables, first theoretically in the form of a transmission matrix, and then mechanically in the form of the corresponding cable-pulley routing. Two examples are proposed with two and three degrees of freedom respectively; both aim at covering a rectangular workspace. The wrench-closure-workspaces of the resulting robots compare favorably to existing CDPRs with more actuators.