A robot design system, and associated method, that is particularly well-suited for legged robots (e.g., monopods, bipeds, and quadrupeds). The system implements three stages or modules: (a) a motion optimization module; (b) a morphology optimization module; and (c) a link length optimization module. The motion optimization module outputs motion trajectories of the robot's center of mass (COM) and force effectors. The morphology optimization module uses as input the optimized motion trajectories and a library of modular robot components and outputs an optimized robot morphology, e.g., a parameterized mechanical design in which the number of links in each of the legs and other parameters are optimized. The link length optimization module takes this as input and outputs optimal link lengths for a particular task such that the design of a robot is more efficient. The system solves the problem of automatically designing legged robots for given locomotion tasks by numerical optimization.