A cable-driven mechanism based on the idea of BetaBot (2005, “A New Cable-Based Parallel Robot With Three Degrees of Freedom,” Multibody Syst. Dyn., 13, pp. 371–383) is analyzed and geometrical description of its workspace boundary is found. In this mechanism, the cable arrangement eliminates the rotational motions leaving the moving platform with three translational motions. The mechanism has potentials for large scale manipulation and robotics in harsh environments. A detailed analysis of the tensionable workspace of the mechanism is presented. The mechanism, in a tensionable position, can develop tensile forces in all cables to maintain its rigidity under arbitrary external loading. A set of conditions on the geometry of the mechanism is proposed for which the tensionable workspace becomes a well defined convex polyhedron. The geometrical shape of the workspace is then described and the tensionability of the mechanism inside the workspace is proved. The proof is quite general and based on a geometrical approach.