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The robot drive system has been previously designed to achieve optimal performance in the acceleration space by matching the gear ratios and actuator impedances. In this paper, the design effort on the robot drive system is continued to achieve the optimal performance measured in the velocity and angular velocity space. Design variables are first identified to be actuator gains. Then, the speed hull geometry of a design is analyzed and an appropriate performance measurement of this design is explored. To locate the optimal design, efficient algorithms dedicated to speed hull constructions are identified and the steepest descent direction, is derived to assist in searching for the optimal design. It is found that the objective function of the optimal design problem is not convex and a local optimal design shouldn't be mistaken as the global optimal design. However, for drive systems built with low gear ratios, the nonlinear effects are negligible and the objective function is convex. Therefore, a local optimal design is the global optimal design.