Design and Characterization of Viscoelastic McKibben Actuators with Tunable Force-Velocity Curves

Abstract

The McKibben pneumatic artificial muscle is a commonly studied soft robotic actuator, and its quasistatic force-length properties have been well characterized and modeled. However, its damping and force-velocity properties are less well studied. Understanding these properties will allow for more robust dynamic modeling of soft robotic systems. The force-velocity response of these actuators is of particular interest because these actuators are often used as hardware models of skeletal muscles for bioinspired robots, and this force-velocity relationship is fundamental to muscle physiology. In this work, we investigated the force-velocity response of McKibben actuators and the ability to tune this response through the use of viscoelastic polymer sheaths. These viscoelastic McKibben actuators (VMAs) were characterized using iso-velocity experiments inspired by skeletal muscle physiology tests. A simplified 1D model of the actuators was developed to connect the shape of the force-velocity curve to the material parameters of the actuator and sheaths. Using these viscoelastic materials, we were able to modulate the shape and magnitude of the actuators' force-velocity curves, and using the developed model, these changes were connected back to the material properties of the sheaths.

Figures (6)

• Figure 1: Viscoelastic McKibben Actuator (VMA): (a) Plain McKibben Actuator (control), (b) Ecoflex-30 sheath, (c) Urethane sheath, (d) Ecoflex-30 and Carbopol composite sheath (10mm diameter shown for all). Each VMA contains a plain McKibben actuator at its core, fabricated in the same method as the control.
• Figure 2: Fabrication, Characterization, and Modeling. (a) Each viscoelastic muscle actuator consists of a standard McKibben actuator (fabricated following controlMcKibbenDesign) and a viscoelastic polymer sheath. (b) To characterize the dynamic properties of the actuators, iso-velocity experiments were performed on an Instron 5969 at various velocities and inflation pressures. (c) The dynamics of the actuators were modeled using parallel chains of Standard Linear Solid elements (SLSE), with one arm capturing the dynamics of the McKibben actuator and the other the dynamics of the sheath material. Using this model, an analytical expression for the force-velocity curves can be obtained (d), and the shape of the curve can be related to the material properties of the constituents. The height of this curve above the $v=0$ point, $\Delta FV(v)$, can be related to two material properties of the actuator. Here, shortening velocity (negative of the extension rate) is reported in alignment with standard muscle physiology experiments.
• Figure 3: Investigation of model parameters for a 1-SLSE model ((a) and (b)) and for a 2-SLSE model ((c) and (d)). Here the normalized shortening velocity (negative of the extension strain rate, $v$) is reported in alignment with standard muscle physiology experiments. (a) By varying the stiffness : damping ratio in the viscous arm of the SLSE, the slope of the force-velocity curve can be changed. As $\gamma$ decreases (increased damping time constant), the force-velocity curve approaches a step response, with no velocity dependence. Conversely, as $\gamma$ increases, the curve approaches a linear response. (b) By varying the stiffness ratio between the two arms of the model, the height of the force-velocity curve is changed, with the height increasing with increasing $\kappa$. For (c) and (d), one SLSE in the model was fixed with $\kappa_1=10$ and $\gamma_1=50$, and the parameters of the other arm were varied. (c) By varying $\gamma_2$ in the second arm, the slope of the force-velocity can be tuned, and (d) by varying $\kappa_2$, the height of the force-velocity curve can be adjusted. In both cases, increasing $\beta$ (the stiffness ratio of the two parallel elastic elements), the effect of changing $\kappa_2$ or $\gamma_2$ is amplified. (e) These parameters can grouped into four different material classes. By combining materials of classes, the force-velocity curve can be tuned for a desired dynamic response.
• Figure 4: Characterization and Modeling of the Force-Velocity Curve. (a) An example iso-velocity experiment (6mm control McKibben actuator at 10 PSI) with the individual velocity ramps overlayed. Data from these force responses are used to construct an experimental force-velocity curve. (b) To avoid confounding effects from various amounts of overshoot, the peak force that is normalized by the initial force and the velocity is normalized by the pressurized rest length for the force-velocity curve is taken at the point when the ramp first reaches its target point. This occurs just prior to the extension overshoot.
• Figure 5: Experimental Characterization of Viscoelastic McKibben Actuators. Each column shows the data for a different actuator, and each row shows a different actuator diameter. Along the dashed line, the experimental data is reported as mean $\pm$ 1 standard deviation. The solid line shows the corresponding model fit for that actuator and that pressure. For the control actuators, a 1-SLSE model is used, and for each of the VMA, a 2-SLSE model is used, with the control element parameters set by the corresponding control actuator model. Inset: The 5PSI curve for the 12mm Urethane actuator is inset to allow a smaller axis range for the rest of the 12mm actuators.