Walk run transition in humans and the expanded inverted pendulum model
There is an ongoing debate about the reasons underlying gait transition in terrestrial locomotion. The ‘Compass gait’ is a very reductionist model of walking. It treats stance as an inverted pendulum motion, and gives clear predictions of the effect of step length and gravity on maximum walking speeds. We investigate the extension of the ‘Compass gait’ to incline walking. We evaluate step length and gravity effect on an incline (α=8.8°) and level ground and compare the result with the prediction based on the extended ‘Compass gait’ model.
Stance during the ‘Compass gait’ model of walking. The CoM (blue circle) vaults over a massless rigid leg of constant length. Red arrows indicate centripetal forces provided by gravity, green arrows centrifugal forces due to vaulting. The component of gravity providing centripetal forces – that acting to compress the leg – is largest at mid stance.
Maximum walking speeds are constrained by gravity providing sufficient centripetal force to prevent foot take-off. Take-off conditions are most limiting at the extremes of leg angle (early and late stance) due to the combination of maximum centrifugal forces (as the body moves faster) and a reduced weight component along an angled leg. Limitations to leg angles based on conditions at early and late stance lead to a maximum step length related to speed.
The ‘Compass gait’ model can be extended to incline walking. Again assuming that stance follows an inverted pendulum motion, and the leg does not change length during this vault, leg angles must be symmetrical about the perpendicular to the SURFACE. However, maximum step angles still relate to angles from vertical (defined by GRAVITY). Thus, maximum step lengths fall for both incline and decline walking. With similar constraints on step frequency, top walking speeds are also predicted to fall with greater slope angles – BOTH INCLINE AND DECLINE
Our results show a change in gait transition speeds on an incline and provide further support that ‘normal’ human walking parameters are constrained by the mechanics of vaulting, and demonstrate that treating walking as an ‘inverted pendulum’ gait has predictive—not merely descriptive—power.
Development of a dynamic walking assistance device for rehabilitation purpose
Many walking assistant devices as well as many tools used in rehabilitation, while supporting body weight, suppress the dynamic transition of potential and kinetic energy by limiting the vaulting motion over the stance leg. We investigated the properties of a walking device that aids the natural vaulting motion and allows the patient to gradually improve towards normal walking. Headley court military hospital was consulted for this project.
Walking and running in children – how to become a bipedal specialist
This research explores why animals and humans of different sizes and different speeds walk and run differently. We looked closely at gait and movement of toddlers and young children (age 1-5), comparing them with adults. The aim was to find out why a toddler’s stiff legged waddle is different from an adult’s fluid run. Investigating the force traces and kinematics of children walking and running at self-selected speeds, we also discovered very distinct looking, highly left biased vertical force traces, typical for children between the age 1.6-4 years. Looking for an explanation we believe the predominant reason for the deviation from adult gaits lies in the smaller size of children rather than an underdevelopment of muscles or motor control. Work minimizing gaits require the production of high forces in a very short period of time. There is a trade of between minimized work and minimized power. Due to their smaller size children’s stride frequency is higher than in adults allowing for less time to push off the ground. To compensate they extend their stance period so that the work (despite being greater than absolutely necessary) can be done over a longer duration, and the amount of muscle that has to be activated for the power can be reduced. The gaits of small children, and the greater deviation of their mechanics from work-minimising strategies, may be understood as appropriate for their scale, not merely as immature, incompletely developed sub-optimal gaits.
Figure: Empirical stance durations presented in non-dimensional form for running undergraduates (grey), sprinters (white), children (green) and children with a duty factor greater than 0.5 (black). Children are not dynamically similar to adults: their stance durations are disproportionately high!
The minimisation of muscle volume activated for whichever is more demanding between mechanical work and power successfully provides a simple, general and mechanistic account for features of walking and running mechanics, and their scaling with speed and size in humans. Aspects of small children’s gaits – higher duty factor, more biased walking forces and greater deviation from work- minimising gaits than adults – have similarities with those of medium-sized birds, and may be related to adaptive strategies for limiting the muscle activation demands due to power.
All work was done in collaboration with Dr. Jim Usherwood (webpage)
Hubel, T. Y., & Usherwood, J. R. (2015). Children and adults minimise activated muscle volume by selecting gait parameters that balance gross mechanical power and work demands. Journal of Experimental Biology, 218 (18), 2830-2839 ().
Usherwood, J. R., Channon, A. J., Myatt, J. P., Rankin, J. W. and Hubel, T. Y. (2012). The human foot and heel-sole-toe walking strategy: a mechanism enabling an inverted pendular gait with low isometric muscle force? J.R.Soc. Interface 9, 2396-2402 ().