Novel Spring Mechanism Enables Iterative Energy Accumulation under Force and Deformation Constraints

TL;DR

It is shown that, by utilizing a novel floating spring mechanism, the weight of a human or robot can be used to iteratively increase spring compression, irrespective of the potential energy stored by the spring.

Abstract

Springs can provide force at zero net energy cost by recycling negative mechanical work to benefit motor-driven robots or spring-augmented humans. However, humans have limited force and range of motion, and motors have a limited ability to produce force. These limits constrain how much energy a conventional spring can store and, consequently, how much assistance a spring can provide. In this paper, we introduce an approach to accumulating negative work in assistive springs over several motion cycles. We show that, by utilizing a novel floating spring mechanism, the weight of a human or robot can be used to iteratively increase spring compression, irrespective of the potential energy stored by the spring. Decoupling the force required to compress a spring from the energy stored by a spring advances prior works, and could enable spring-driven robots and humans to perform physically demanding tasks without the use of large actuators.

Figures (7)

• Figure 1: Repeated squatting with a floating variable stiffness spring. (a) The end points of the spring are fixed (red) while the user compresses the spring with a squat. (b) The end points of the spring are free (blue) while the spring is locked. The mechanical advantage of the human over the spring is increased as the human stands and the spring shifts towards the knee joint. (c) By repeating the energy accumulation cycle (a)-(b), the user can iteratively increase the energy stored by the spring.
• Figure 2: Model of the human augmented with a lower-limb exoskeleton. (a) Mass-spring system. The leg deformation is described by $\Delta l$. The body mass is supported by a spring with stiffness $k_n$ and deformed length $s_n^{\pm}$; the superscripts ${\pm}$ denote the pre-squat and post-squat spring lengths, respectively, and the subscript $n$ denotes the number of squats performed during repeated squatting. (b) An example force-deflection of the human leg $F$ (red) that leads to the average leg force $\bar{F}=\frac{1}{2}mg$ is shown with the red line. The maximum amount of energy accumulated during one squat $E_{1\max}$ is shown with the dark area.
• Figure 3: Model of the variable stiffness floating spring-leg. The leg segments $\overline{HK}$ and $\overline{KA}$ are equal in length. The spring is assumed to remain vertical ($x$ is constant) as the leg deforms by $\Delta l$.
• Figure 4: Simulated behavior for the spring-leg. (a) Force-deflection achieved by repeated squats, subject to a limited force (horizontal line), compared to the force required to achieve the same deformation in a single compression cycle (dashed line). The forces are normalized by the weight of the user (Section \ref{['subsection:fixed']}). (b) Potential energy stored by the spring, normalized by the max amount of energy that can be accumulated in a single squat $E_{1\max}$ (\ref{['eqn:E1max']}) defined in (Section \ref{['subsection:fixed']}). The four squats shown in the figure were the minimum number of squats necessary to achieve full spring deformation.
• Figure 5: Prototype floating spring-leg mechanism. (a) Front view. (b) Top view. The leg segments are of relatively equal length of $205$ mm. The spring has a free length of approximately $114$ mm and a force-deflection rate of $0.9$ N/mm.