The split-belt rimless wheel

Abstract

Split-belt treadmill walking, in which the two belts move at different speeds, reveals a mechanism through which energy can be extracted from the environment. When a person walks with positive step length asymmetry on a split-belt treadmill, the treadmill can perform net positive work on the person. Here we use a split-belt rimless wheel model to explore how people could take advantage of the treadmill. We show that a split-belt rimless wheel can passively walk steadily by capturing energy from the treadmill to overcome collision losses, whereas it loses energy on each step with no way to recover the losses when walking on tied belts. Our simulated split-belt rimless wheel can walk steadily for a variety of leg angle and belt speed combinations, tolerating both speed disturbances and ground height variability. The wheel can even capture enough energy to walk uphill. We also built a physical split-belt rimless wheel robot and demonstrated that it can walk continuously without additional energy input. In comparing the wheel solutions to human split-belt gait, we found that humans do not maximize positive work performed by the treadmill. Other aspects of walking, such as costs associated with swing, balance, and free vertical moments, likely limit people’s ability to benefit from the treadmill. This study uses a simple walking model to characterize the mechanics and energetics of split-belt walking, demonstrating that energy capture through intermittent contact with two belts is possible and providing a simple model framework for understanding human adaptation during split-belt walking.

Modeling, analysis and control of robot–object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives

“…(48) (a): this depends on the application in mind. Frictional oscillators can be seen as a simplified case of more complex systems like split-belt rimless wheels [169], which in addition involve impacts. In such systems it is the belt speed difference that may be considered as the control input.…”