S.Y. Kim and D.J. Braun, Variable Stiffness Floating Spring Leg: Performing net-zero energy cost tasks not achievable using fixed stiffness springs, vol. 8, no. 9, pp. 5400-5407, 2023.
Sitting down and standing up from a chair and, similarly, moving heavy objects up and down between factory lines are examples of cyclic tasks that require large forces but little to no net mechanical energy. Motor-driven artificial limbs and industrial robots can help humans do these tasks, but motors require energy to provide force even if they supply no net mechanical energy. Springs are energetically conservative mechanical elements useful for building robots that require no energy when performing cyclic tasks. However, conventional springs can be limited by their non-customizable force-deflection behavior — for example, when they cannot meet the force demand despite storing enough energy to perform a cyclic task. Variable stiffness springs are a special type of spring with customizable force-deflection behavior, but most typical variable stiffness springs require energy to amplify force similar to motors. In this paper, we introduce a new type of variable stiffness spring design which is energetically conservative despite having a customizable force-deflection behavior. We present the theory of these springs and demonstrate their utility in performing a net-zero mechanical energy cost lifting task that requires force amplification and as such is not realizable using conventional springs. Energetically conservative springs with customizable force-deflection behavior may find their place in assistive devices, exoskeletons, and industrial robots that can perform a larger class of tasks than conventional springs using little to no external energy.