Background: Dexterity is an important index for evaluating the motion performance of a robot. The size of the robot connecting rods directly affects the performance of flexibility. Objective: The purpose of this study is to provide an overview of optimal design methods from many pieces of literature and patents, and propose a new optimal design method for ensuring the robot completes its tasks flexibly and efficiently under workspace constraints. Methods: The kinematics and working space of the robot are analyzed to determine the range of motion of each joint. Then, a dexterity index is established based on the mean value of the global spatial condition number. Finally, an improved cuckoo algorithm is proposed, which changes the step size control factor with the number of iterations. Taking the dexterity index as the objective optimization function and the working radius as the constraint condition, the improved cuckoo search algorithm is used to optimize the size of the robot rod. Results: The improved cuckoo algorithm and proposed rod size optimized method are fully evaluated by experiments and comparative studies. The optimization design process shows that the proposed method has better solution accuracy and faster convergence speed. The optimized design results show that the robot's dexterity index has increased by 26.1%. Conclusion: The proposed method has better solution accuracy and faster convergence speed. The method was suitable for optimizing the rod parameters of the robot, and it was very meaningful to improve the motion performance of the robot.