Abstarct: The optimal design of the robot structure has been the attention of researchers for a long time. In this research, a pneumatic cylinder is used as a redundant actuator to improve the CDPR performance. Various criteria have been proposed for the performance of the robot, among which manipulability and dexterity are important. The problem with the usual criteria is that they lack comprehensiveness and lose their physical meaning in the case that the CDPR has both rotational and translational degrees of freedom. On the other hand, the subject of one-sidedness and positive cable tension in the case of the cable robot has also been ignored in the previous criteria. For this reason, new criteria for manipulability and dexterity are introduced. In this thesis, a new index is extracted from the combination of kinematic and dynamic dexterity, and finally the cable parallel robot is designed baxsed on this dexterity. In the following, using the theory of optimal control as the main approach of the thesis, the optimal trajectory is selected according to various cost functions, such as reducing forces, reducing changes in forces, or reducing jerk for the assumed robot. In this research, the problem of optimal control is adapted to parallel robot dynamics. In solving the problem of optimal control, different direct and indirect approaches are comprehensively investigated. Despite the advantages of the indirect approach using the Pontryagin method, it will not lead to the correct answer due to reasons such as the excessive complexity of the equations and dependence on the initial guess, therefore the main approach in this research is the direct approach. In the direct approach, various methods have been proposed, and in this thesis, these methods are examined. Among the different trajectory planning methods, in this research, the appropriate approach for the trajectory planning of the cable-parallel robot is adopted using the direct collocation method and the direct shooting method. By using this strategy, it is possible to reach a path that is optimal baxsed on the selected criteria, while in this research, the appropriate distribution of cable tension is considered.