Variable stiffness actuators realize a novel class of actuators, which are capable of changing the apparent output stiffness independently of the output position. This is mechanically achieved by the internal introduction of a number of elastic elements and a number of actuated degrees of freedom (DOFs), which determine how the elastic elements are sensed at the output. During the nominal behavior of these actuators, the power flow from the internal actuated DOFs can be such that energy is undesirably stored in the elastic elements because of the specific kinematic structure of the actuator. In this study, we focus on the analysis of the power flow in variable stiffness actuators. More specifically, the analysis is restricted to the kinematic structure of the actuators, in order to show the influence of the topological structure on the power flow, rather than on the realization choices. We define a measure that indicates the ratio between the total amount of power that is injected by the internal actuated DOFs and the power that is captured by the internal elastic elements which, therefore, cannot be used to do work on the load. In order to define the power-flow ratio, we exploit a generic port-based model of variable stiffness actuators, which highlights the kinematic properties of the design and the power flows in the actuator structure.
Carloni, R., Visser, L. C., & Stramigioli, S. (2012). Variable Stiffness Actuators: A Port-Based Power-Flow Analysis. IEEE transactions on robotics, 28(1), 1-11. https://doi.org/10.1109/TRO.2011.2168709