In this paper, according to high load capacity and rather large workspace characteristics of cable driven robots (CDRs), maximum dynamic load carrying capacity (DLCC) between two given end points in the workspace along with optimal trajectory is obtained. In order to find DLCC of CDRs, joint actuator torque and workspace of the robot constraints concerning to non-negative tension in cables are considered. The problem is formulated as a trajectory optimization problem, which is fundamentally a constrained nonlinear optimization problem. Then the iterative linear programming (ILP) method is used to solve the optimization problem. Finally, a numerical example involving a 6 DOF CDR is presented and results are discussed.