Passive knee flexion increases forward impulse of the trailing leg during the step-to-step transition

TL;DR

Enabling passive knee flexion initiation could be beneficial in humanoid robots with passive ankles, and in ankle-knee prostheses and orthoses with passive ankles for saving on control effort, and reducing hardware complexity otherwise required for active knee flexion before the step-to-step transition.

Abstract

Human walking efficiency relies on the elastic recoil of the Achilles tendon, facilitated by a "catapult mechanism" that stores energy during stance and releases it during push-off. The catapult release mechanism could include the passive flexion of the knee, as the main part of knee flexion was reported to happen passively after leading leg touch-down. This study is the first to investigate the effects of passive versus active knee flexion initiation, using the bipedal EcoWalker-2 robot with passive ankles. By leveraging the precision of robotic measurements, we aimed to elucidate the importance of timing of gait events and its impact on momentum and kinetic energy changes of the robot. The EcoWalker-2 walked successfully with both initiation methods, maintaining toe clearance. Passive knee flexion initiation resulted in a 3% of the gait cycle later onset of ankle plantar flexion, leading to 87% larger increase in the trailing leg horizontal momentum, and 188% larger magnitude increase in the center of mass momentum vector during the step-to-step transition. Our findings highlight the role of knee flexion in the release of the catapult, and timing of gait events, providing insights into human-like walking mechanics and potential applications in rehabilitation, orthosis, and prosthesis development.

Figures (6)

• Figure 1: The two main roles of push-off (a) and the expected effect of passive versus active knee flexion initiation (b). The main part of knee flexion, from 5-40deg, occurs passively after LLTD Perry1992. We compare PKFI and AKFI to influence energy flow into the RB and TL by indirectly manipulating SAPF timing. We aim to contribute to the debate on the primary function of ankle push-off in the human swing leg catapult mechanism Zelik2016. a: During a step-to-step transition, push-off plays two main roles: it redirects the center of mass velocity ($\Delta \mathbf{v}_\mathrm{CoM}$) from one inverted pendulum arc to the next, and it increases the velocity of the TL. The drawing was inspired by Fig 1 in Adamczyk2009 and Fig 4 in Lipfert2014. b: We designed the AKFI experiment with earlier knee flexion onset than PKFI experiment to alter the SAPF timing. This results in an earlier SAPF in AKFI, prolonging the positive ankle power ($\mathrm{P}_\mathrm{ank, pos}$) period until LLTD. Before LLTD, the TL bears the whole body weight, while the loading leg (LL) is in swing. The filled part under the positive ankle power curve represents the predicted ankle energy mainly accelerating the RB. Due to the predicted SAPF delay in PKFI experiment, we expect lower ankle energy accelerating the RB in PKFI than in AKFI experiment. Abbreviations:TL: Trailing Leg, LL: Leading Leg, RB: Remaining Body, CoM: Center of Mass, vmin: time of minimum vertical velocity of the CoM (start of Step-to-Step transition period), vmax: second vertical velocity peak of the CoM after vmin (end of Step-to-Step transition period), SAPF: Start of Ankle Plantar Flexion, LLTD: Leading Leg Touch-Down, TO: Toe-Off, AKFI: Active Knee Flexion Initiation, PKFI: Passive Knee Flexion Initiation.
• Figure 2: Hip, knee, and ankle angles during the full gait cycle in the experiments with active knee flexion initiation (AKFI - a), and with passive knee flexion initiation (PKFI - b). Shading shows the standard deviation of the curves. Horizontal axis shows the gait cycle percentage, 0% GC is the touch-down of the trailing leg. In the PKFI experiment, the knee motor torque is zero from the dark pink vertical dotted line (kneeT-off) until the dark pink vertical dashed line (kneeT-on). The continuous cyan line shows the measured joint angles of the robot, while the dashed cyan line shows the commanded joint angles of the hip and the knee. Joint angles of human walking are overlayed (gray lines) for reference. VanderZee2022$^\text{: average of trials 20, 21, and 22}$ Abbreviations:SKF: Start of Knee Flexion, SHF: Start of Hip Flexion, SAPF: Start of Ankle Plantar Flexion, vmin: time of minimum vertical velocity of the CoM, LLTD: Leading Leg Touch-Down, TO: Toe-Off, vmax: second vertical velocity peak of the CoM after vmin.
• Figure 3: Timing of the gait events in gait cycle percentage with active knee flexion initiation (AKFI), and with passive knee flexion initiation (PKFI), and by humansVanderZee2022. 0% GC is the touch-down of the trailing leg. In the PKFI experiment, knee and hip flexion start 5% GC later than in the AKFI experiment (SKF and SHF). LLTD occurs 1%GC earlier with PKFI than with AKFI. The ankle starts to plantarflex (SAPF) 2% GC after LLTD with PKFI, while SAPF occurs 2% GC before LLTD with AKFI. The gait event timing values and their standard deviation values are available in Supplementary Table S2. Abbreviations:$\mdlgblkcircle$ SKF: Start of Knee Flexion, $\mdlgblksquare$ SHF: Start of Hip Flexion, ✘ SAPF: Start of Ankle Plantar Flexion, $\blacktriangledown$ vmin: time of minimum vertical velocity of the CoM, $\blacktriangleright$ LLTD: Leading Leg Touch-Down, $\blacktriangleleft$ TO: Toe-Off, $\blacktriangle$ vmax: second vertical velocity peak of the CoM after vmin.
• Figure 4: Trailing Leg (TL), Remaining Body (RB), and Center of Mass (CoM) instantaneous momentums in horizontal (a, c, and e) and vertical (b, d, and f) directions at the start of the step-to-step transition (vmin), at leading leg touch-down (LLTD), and at the end of the step-to-step transition (vmax) in the active knee flexion initiation (AKFI) and in the passive knee flexion initiation (PKFI) experiments. The vertical black lines at the top of the bars show the standard deviations. The change in TL horizontal momentum is larger with PKFI than with AKFI, and RB horizontal momentum decreases with PKFI. The CoM's vertical momentum increases more in AKFI than in PKFI experiment during the step-to-step transition. The momentum values and their standard deviation values are available in Supplementary Table S3. *** denote significant difference between the momentum changes ($\Delta$) during the step-to-step transition period in the AKFI and in the PKFI experiments with p < 0.001. The exact p values are available in \ref{['tab:statTest_Res']}.
• Figure 5: Center of Mass (CoM) velocity vectors at the start of the step-to-step transition (vmin), at leading leg touch-down (LLTD), and at the end of the step-to-step transition (vmax) in the active knee flexion initiation (AKFI - a) and in the passive knee flexion initiation (PKFI - b) experiments. An arc is drawn with a radius that is equal to the length of the velocity vector at vmin to better show the relation of the vector lengths at the three different times during the step-to-step transition. The length of the velocity vector increases between vmin and vmax more in the PKFI experiment than in the AKFI experiment.