Cable-driven parallel robots (CDPRs) have several advantages and have been widely used in many industrial fields, especially industrial applications that require high dynamics, high payload capacity, and a large workspace. In this study, a design model for a CDPR system was proposed, and kinematic and dynamic modeling of the system was performed. Experiments were carried out to identify the dynamic modulus of elastic cables based on the dynamic mechanical analysis (DMA) method. A modified kinematic equation considering cable nonlinear tension was developed to determine the optimal cable tension at each position of the end-effector, and the wrench-feasible workspace was analyzed at various motion accelerations. The simulation results show that the proposed CDPR system obtains a large workspace, and the overall workspace is satisfactory and unrestricted for moving ranges in directions limited by the X-axis and the Y-axis from −0.3 to 0.3 m and by the Z-axis from 0.1 to 0.7 m. The overall workspace was found to depend on the condition of acceleration as well as the moving ranges limited by the end-effector. With an increase in external acceleration, the cable tension distribution increased and reached a maximum in the case of 100 m/s2.