Variable Stiffness Springs for Energy Storage Applications

Theory suggests an inverse relation between the stiffness and the energy storage capacity for linear helical springs: reducing the active length of the spring by 50% increases its stiffness by 100%, but reduces its energy storage capacity by 50%. State-of-the-art variable stiffness actuators used to drive robots are characterized by a similar inverse relation, implying reduced energy storage capacity for increased spring stiffness. This relation limits the potential of the variable stiffness actuation technology when it comes to human performance augmentation in natural tasks, e.g., jumping, weight-bearing and running, which may necessitate a spring exoskeleton with large stiffness range and high energy storage capacity. In this paper, we theoretically show that the trade-off between stiffness range and energy storage capacity is not fundamental; it is possible to develop variable stiffness springs with simultaneously increasing stiffness and energy storage capacity. Consistent with the theory, we experimentally show that a controllable volume air spring, has a direct relation between its stiffness range and energy storage capacity. The mathematical conditions presented in this paper may be used to develop actuators that could bypass the limited energy storage capacity of current variable stiffness spring technology.