This study investigated energetically optimal hopping motions for a one-dimensional (1D) hopper with either parallel elastic actuation (PEA, shown as schematic in (a) and detailed model in (c)) or series elastic actuation (SEA, (b) and (d)). For both hoppers we simultaneously optimized motion trajectories, actuator inputs, and actuation parameters for three different cost functions: positive mechanical motor work, thermal electrical losses, and positive electrical work. The optimization included main body position y, leg length l, motor position u (only for SEA), motor force after the transmission T_o, spring stiffness k, and rotary gearbox ratio n_r (not shown).