Variable Stiffness Floating Spring Leg: Performing Net-Zero Energy Cost Tasks Not Achievable Using Fixed Stiffness Springs

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 mechan- ical 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.