In this study, we introduce new types of planar 2 degree-of-freedom robot modules resembling the musculoskeletal structure of the human arm with actuation redundancy. First, for the given actuator sizes the performance analysis for the manipulator with redundant actuation and without redundant actuation is performed with respect to maximum load handling capacity, maximum hand velocity, and maximum hand acceleration. Secondly an algorithm which decides optimal actuator sizes for the given operational performances is introduced, and the optimal actuator sizes for a robot module with four redundant actuation are obtained. The algorithms employed in this paper will be useful to analyze the robot performances and to determine the actuator sizes for general robot manipulators.