Parametric equations to study and predict lower-limb joint kinematics and kinetics during human walking and slow running on slopes.

Comprehensive data sets for lower-limb kinematics and kinetics during slope walking and running are important for understanding human locomotion neuromechanics and energetics and may aid the design of wearable robots (e.g., exoskeletons and prostheses). Yet, this information is difficult to obtain and requires expensive experiments with human participants in a gait laboratory. This study thus presents an empirical mathematical model that predicts lower-limb joint kinematics and kinetics during human walking and running as a function of surface gradient and stride cycle percentage. In total, 9 males and 7 females (age: 24.56 ± 3.16 years) walked at a speed of 1.25 m/s at five surface gradients (-15%, -10%, 0%, +10%, +15%) and ran at a speed of 2.25 m/s at five different surface gradients (-10%, -5%, 0%, +5%, +10%). Joint kinematics and kinetics were calculated at each surface gradient. We then used a Fourier series to generate prediction equations for each speed's slope (3 joints x 5 surface gradients x [angle, moment, mechanical power]), where the input was the percentage in the stride cycle. Next, we modeled the change in value of each Fourier series' coefficients as a function of the surface gradient using polynomial regression. This enabled us to model lower-limb joint angle, moment, and power as functions of the slope and as stride cycle percentages. The average adjusted R2 for kinematic and kinetic equations was 0.92 ± 0.18. Lastly, we demonstrated how these equations could be used to generate secondary gait parameters (e.g., joint work) as a function of surface gradients. These equations could be used, for instance, in the design of exoskeletons for walking and running on slopes to produce trajectories for exoskeleton controllers or for educational purposes in gait studies.

Mechanics of walking and running up and downhill: A joint-level perspective to guide design of lower-limb exoskeletons.

Lower-limb wearable robotic devices can improve clinical gait and reduce energetic demand in healthy populations. To help enable real-world use, we sought to examine how assistance should be applied in variable gait conditions and suggest an approach derived from knowledge of human locomotion mechanics to establish a 'roadmap' for wearable robot design. We characterized the changes in joint mechanics during walking and running across a range of incline/decline grades and then provide an analysis that informs the development of lower-limb exoskeletons capable of operating across a range of mechanical demands. We hypothesized that the distribution of limb-joint positive mechanical power would shift to the hip for incline walking and running and that the distribution of limb-joint negative mechanical power would shift to the knee for decline walking and running. Eight subjects (6M,2F) completed five walking (1.25 m s-1) trials at -8.53°, -5.71°, 0°, 5.71°, and 8.53° grade and five running (2.25 m s-1) trials at -5.71°, -2.86°, 0°, 2.86°, and 5.71° grade on a treadmill. We calculated time-varying joint moment and power output for the ankle, knee, and hip. For each gait, we examined how individual limb-joints contributed to total limb positive, negative and net power across grades. For both walking and running, changes in grade caused a redistribution of joint mechanical power generation and absorption. From level to incline walking, the ankle's contribution to limb positive power decreased from 44% on the level to 28% at 8.53° uphill grade (p < 0.0001) while the hip's contribution increased from 27% to 52% (p < 0.0001). In running, regardless of the surface gradient, the ankle was consistently the dominant source of lower-limb positive mechanical power (47-55%). In the context of our results, we outline three distinct use-modes that could be emphasized in future lower-limb exoskeleton designs 1) Energy injection: adding positive work into the gait cycle, 2) Energy extraction: removing negative work from the gait cycle, and 3) Energy transfer: extracting energy in one gait phase and then injecting it in another phase (i.e., regenerative braking).