Low leg compliance permits grounded running at speeds where the inverted pendulum model gets airborne. (7th June 2020) - Andrada, Emanuel; Blickhan, Reinhard; Ogihara, Naomichi; Rode, Christian
Highlights: The model predicts three-humped ground reaction force profiles for slow grounded running. Minimal single-humped grounded running speed of the model roughly coincides with the transition speed from vaulting to bouncing mechanics in bipeds. Compliant legs permit animals to use grounded running at speeds at which they should become airborne according to inverted pendulum predictions. When accounting for real contact times, stiffer legs used in human walking and running, preclude periodic grounded running. Compliant legs enable different gaits and speeds with similar leg parameters, stiff legs require parameter adaptations. Abstract: Animals typically switch from grounded (no flight phases) to aerial running at dimensionless speeds u ^ < 1. But some birds use grounded running far above u ^ = 1, which puzzles biologists because the inverted pendulum becomes airborne at this speed. Here, we combine computer experiments using the spring-mass model with locomotion data from small birds, macaques and humans to understand the relationship between leg function (stiffness, angle of attack), locomotion speed and gait. With our model, we found three-humped ground reaction force profiles for slow grounded running speeds. The minimal single-humped grounded running speed is u ^ = 0.4. This speed value roughly coincides with the transition speed from vaulting to bouncing mechanics in bipeds. Maximal grounded running speed in the model is not limited. In experiments, animals changed from grounded to aerial running at dimensionless contact time around 1. Considering these real-world contact times reduces the solution space drastically, but experimental data fit well. The model still predicts maximal grounded running speed u ^ > 1 for low stiffness values used by birds but decreases below u ^ = 1 for increasing stiffness. For stiffer legs used in human walking and running, periodic grounded running vanishes. At speeds at which birds and macaques change to aerial running, we found periodic aerial running to intersect grounded running. This could explain why animals can alternate between grounded and aerial running at the same speed and identical leg parameters. Compliant legs enable different gaits and speeds with similar leg parameters, stiff legs require parameter adaptations.