Time-optimal trajectory planning (TOTP) is a well-studied problem in robotics and manufacturing, which involves the minimization of the time required for the operation point of a mechanism to follow a path, subject to a set of constraints. A TOTP technique, designed for fully specified paths that include abrupt changes in direction, was previously introduced by the first author of this paper: an incremental approach called minimum-time trajectory shaping (MTTS) was used. In the current paper, MTTS is converted to a dynamic technique and adapted for use with cable-driven parallel robots, which exhibit cable tension and motor torque constraints. For many applications, cable tensions along a path are verified after trajectory generation, rather than imposed during trajectory generation. For the technique proposed in this paper, the cable-tension constraints are imposed directly and fully integrated with MTTS, during trajectory generation, thus maintaining a time-optimal solution. MTTS is applied to a test system and path, and compared to the bang–bang technique. With the same constraints, the results obtained with both techniques are found to be very close. However, MTTS can be applied to a wider variety of paths, and accepts constraints on jerk and total acceleration that would be difficult to apply using the bang–bang approach.