Predicting the Biomechanics of Walking - Human Motion Simulation: Predictive Dynamics - page 173

The solid black curves in the figure represent the predicted determinants, the
dashed curves are the experimental mean value of the determinants, and the curves
with shorter dashes show the 95% confidence interval (C.I.) of the statistical means.
The six simulated determinants lie close to the mean of the experimental data;
major parts of the motion are in the confidence region and have trends as those of
the statistical mean. The peak values of ankle motion, pelvic rotation, and pelvic
lateral displacement occur earlier than the experimental data. This is because the
six determinants represent a complex coupled motion, and the optimal solution is
only a compromise motion. Furthermore, ankle motion is the major passive move-
ment due to GRF. It has shown a larger plantar flexion at 60% of gait cycle.
These differences are expected due to approximations in the mechanical model of
the human body.
7.11.1.2 Dynamics
Since we are using a rigid skeleton model, the energy absorption of muscle ten-
dons and ligaments and joint tissue are ignored at heel strike and toe-off. This
results in some jerks in GRF and joint torques. Therefore, the Butterworth low-
pass filter with a cutting frequency of 8 Hz is used to obtain plots for the GRF
and joint torques. Figure 7.18 depicts the torque profiles of the hip, the knee and
the ankle for a stride. Here, HS denotes heel strike, FF foot flat, HO heel off, and
TO toe-off. The figure also shows torques data (digitized) obtained from the liter-
ature ( Simpson and Jiang, 1999; Stansfield et al., 2006 ).
In Figure 7.18 , the hip torque begins to flex the hip at the heel strike and this
torque reaches its maximum extension torque at the terminal stance phase. At the
knee joint, the reaction force flexes the knee during the early stance, but the knee
torque then reverses into an extension torque. Before the swing phase, the knee is
flexed for a second time. The ankle starts with a plantar torque just after heel
strike and reverses into a dorsiflexion torque continuously during the stance,
reaching its peak at terminal stance and then dropping quickly until toe-off.
Figure 7.19 shows the GRFs for the predicted walking motion. The vertical
GRF has a familiar double-peak pattern, and the maximum vertical force is devel-
oped soon after heel strike and then again during terminal stance (push-off). In
the walking direction, the fore-aft GRF, there is a decelerating force early in the
stance phase, and an acceleration force at push-off. Meanwhile, the foot also
pushes laterally during the entire stance phase.
The above resulting joint torques and GRF have shown general agreement
with the experimental results presented in the literature ( Simpson and Jiang,
1999; Stansfield et al., 2006 ). However, there are discrepancies at the beginning
and end of the gait cycle. Since we do not impose symmetry conditions on joint
angle accelerations, the predicted forces show impact phenomena with discontinu-
ities at the boundaries. The discrepancies may also be due to the approximate
models used and approximate simulation of impacts during walking motion. In
addition, the GRF are linearly distributed between the feet during the double sup-
port phase and this may also result in some inaccuracies.