Motor selection via impedance-matching for driving nonlinearly damped, resonant loads

This paper presents a novel method for selecting the most appropriate motor–gearhead combination for nonlinearly damped, resonant loads. The method extends to the nonlinear damping case the impedance-matching condition which is used to guarantee a maximum power transfer in linear network theory. In particular, the method is applicable in general to resonant loads where the damping is an odd and memoryless nonlinear function of the velocity. This condition is very common in biomimetic robotics, in particular when designing propulsion systems based on flapping appendages, such as wings or fins, in viscous fluids, such as air or water. The method is graphical in nature and is based on a power vs. impedance-mismatch factor. Such a factor is function of the ratio of the motor armature resistance to the load equivalent resistive impedance reflected at the motor armature, where the latter is nonlinear and depends on the desired kinematics as well as on the transmission ratio and efficiency. The method allows comparing, for a given desired appendage kinematics, all motor–gearhead combinations at once while taking into account all possible constraints such as maximum current, power, and torque.