Optimal Selection of Transmission Ratio and Stiffness for Series-Elastic Actuators with Known Output Load Torque and Motion Trajectories

Series Elastic Actuators (SEAs) are multi-degree-of-freedom spring-mass-damper systems that employ elastic transmission elements to reduce mechanical impedance and buffer energy from motor (input) to load (output). This work deals with the mathematical modeling of SEAs and their sizing for given application requirements. In designing traditional actuation systems a common approach is to optimize the speed ratio of the transmission with respect to a given figure of merit, such as the motor rated torque or power, once the output load torque and motion trajectories are given. Taking inspiration from existing techniques developed for the sizing of traditional actuators having just one degree of freedom, a new approach is presented here for two degrees of freedom SEAs, which enables the designer to optimally select at the same time both the ratio and the compliance of the elastic transmission.