Fig 1.
Minimal bipedal walking model.
The human body is modelled as a point mass m. The two legs are modelled as massless telescopic actuators that can change length and orientation, exert forces, and perform work on the upper body. The walker walks on level ground in a gravity field with field strength g. Figure adapted from [20].
Fig 2.
(a) Bipedal walking model. (b) Free body diagram of the point mass together with a diagram of the forces exerted by the model to the support. Figure adapted from [20].
Fig 3.
Stance leg switching and double stance phase.
The trajectory of the CoM from measured data, where midstance is at the maxima, marked by a green dot, and the discrete switch from swing leg to stance leg is by definition at the minima, marked by a red dot. The double stance phase, which starts with a heel strike and ends at the toe off, is from the measured data, and is indicated by the grey area. The step length d is defined from midstance to midstance.
Fig 4.
Three synthetic walking motions: (a) pendular, (b) level, and (c) sinusoidal. The configuration at mid stance is drawn in grey, whereas the black configuration is at the discrete switch from swing leg to stance leg.
Fig 5.
Pendular walking motion, with (a) dimensionless leg extension velocity and pendular velocity
, (b) dimensionless leg extension force F/(mg) and pendular motion force M(mgl0), and (c) and dimensionless applied leg extension power PF/(mgv0) and pendular motion power PM/(mgv0), as a function of dimensionless time t/tstep, for one step from midstance to midstance.
Table 1.
Synthetic gait energy balance per step and cost of transport.
Fig 6.
Level walking motion, with (a) dimensionless leg extension velocity and pendular velocity
, (b) dimensionless leg extension force F/(mg) and pendular motion force M(mgl0), and (c) dimensionless applied leg extension power PF/(mgv0) and pendular motion power PM/(mgv0), as a function of dimensionless time t/tstep, for one step from midstance to midstance.
Fig 7.
Sinusoidal walking motion, with (a) dimensionless leg extension velocity and pendular velocity
, (b) dimensionless leg extension force F/(mg) and pendular motion force M(mgl0), and (c) dimensionless applied leg extension power PF/(mgv0) and pendular motion power PM/(mgv0), as a function of dimensionless time t/tstep, for one step from midstance to midstance.
Fig 8.
Measured CoM trajectories for subject 1 and 2, where x is forward, and y is vertically upwards.
Midstance is indicated by a gray dot at the y maxima, and the discrete change from swing leg to stance leg is marked by a white dot at the y minima. Heel strike is the dashed vertical line before and toe-off the dashed vertical line after the discrete change from swing leg to stance leg.
Fig 9.
Position, velocity and acceleration of the CoM coordinates as a function of time, where x is forward and y is vertically upward, for subject 1.
Midstance is indicated by a gray dot at the y maxima, and the discrete change from swing leg to stance leg is indicated by a white dot at the y minima. Heel strike is the dashed vertical line before and toe-off the dashed vertical line after the discrete change from swing leg to stance leg.
Fig 10.
Position, velocity and acceleration of the CoM coordinates as a function of time, where x is forward and y is vertical up, for subject 2.
Midstance is indicated by a gray dot at the y maxima, and the discrete change from swing leg to stance leg is indicated by a white dot at the y minima. Heel strike is the dashed vertical line before and toe-off the dashed vertical line after the discrete change from swing leg to stance leg.
Fig 11.
Tangential pendulum velocity (solid line) and leg extension velocity
(dashed line), pendulum torque force M/l (solid line) and leg extension force F (dashed line), and applied pendular motion power PM (solid line) and applied leg extension power PF (dashed line), as a function of time, for Subject 1 and 2.
The straight horizontal dash-dotted line at the leg extension force is the static gravity force mg. Midstance is indicated by a dash-dot vertical line, and the discrete change from swing leg to stance leg is indicated by a dotted vertical line, where the heel strike is the dashed vertical line before and the toe-off the dashed vertical line after a dotted vertical line.
Table 2.
Energy expenditure and step length per step for the two subjects.
Fig 12.
Measured ground reaction forces from force plate 1 (FP1 red solid lines) and force plate 2 (FP2 green solid lines) together with the ground reaction forces calculated from the model, Fx and Fy, where x is forward and y vertically upwards.
Midstance is indicated by a dash-dot line, and the discrete change from swing leg to stance leg is indicated by a dotted line, where the heel strike is the dashed line before and the toe-off the dashed line after a dotted line.