This paper deals with cable-driven mobile platforms that are equipped with a serial robot. The contribution of this paper is twofold. First, a method to determine the maximum payload handled by the serial robot while the mobile platform is maintained in equilibrium by cables is presented. A mobile platform pose is wrench feasible if cables can balance any possible external wrench exerted on the platform such that cable tensions remains within their admissible values. Being given that the wrenches exerted by the serial robot on the platform are configuration dependent, at a given platform pose, wrench feasibility is to be tested for the entire serial robot workspace. The proposed approach is used not only to examine wrench feasibility but also to evaluate the maximum wrench feasible payload handled by the serial robot. To this end, the set of all possible wrenches, referred to as the available wrench set, that can be generated by cables is to be determined in a suitable mathematical representation. The second contribution of this paper is a new computationally-efficient algorithm to determine the available wrench set. Comparison and equivalence with other methods are discussed. Finally, a case study of a 6-DoF cable-suspended mobile platform actuated by eight cables and equipped with a 2-DoF planar serial robot is considered to demonstrate the presented methodology.