Walking on Level Surfaces

same applies to the hip joint rotation, which shows no significant change in its values with the different stiffness values. It is noted that the small differences (maximum of 1 degree) occur at some point and continue until the end of the curve. Figure 6.3 represents the hip joint rotation for the different stiffness values of the sole.

Figure 6.2: The simulated moment at the ankle of the prosthetic foot for different stiffness values of the prosthetic foot sole

Figure 6.3: The simulated rotation of the thigh at the hip joint for the different stiffness values of the prosthetic foot sole

Observing the BCoM motion shown in Figure 6.4 indicates that changing the stiffness of the foot sole influences the vertical BCoM motion in the second half of the stance period of the gait such that it is ending at a lower or higher vertical position with respect to the start point. These deviations at the end of the simulation time with respect to the results of simulation using the original stiffness value of 28.5 GPa where found to be −9%, +8%, and +14% corresponding to the stiffness values −10%, +10%, and +20% of the original, respectively.

The differences in the horizontal motion of the BCoM at the end of the simulation time were very small. The maximum difference between the results corresponding to the two stiffness extremities 25.5 GPa and 34.5 GPa was 6 mm, which is less than 1% of the total horizontal displacement.

Figure 6.4: The simulated BCoM motion for four different stiffness values of the foot sole

Since the results of changing the stiffness values of the base spring of the prosthetic foot leads to significant changes in the vertical BCoM displacement without causing any significant changes in the forces and moments acting on the body (according to this numerical model), the model will be further used in evaluating the effect of changing the foot sole stiffness on the motions and forces of an amputee at different walking speeds and different surface inclinations.

6.1.2 Changing the inclination angle of the ankle joint

In this section the effect of the ankle joint inclination is to be studied. Four inclination angles are considered +3, 0, −3, and −6 degrees. Small changes in the inclination angles are considered since larger rotation values have caused large deviations from the normal gait cycle, which make them not suitable for walking on level surfaces. (Note: −3 and −6 degrees mean rotating the foot in the backward direction and +3 degrees in the forward direction).

Figure 6.5 shows the vertical GRF acting on the body of the amputee at the prosthetic side. The small changes in the inclination angle of the ankle joint have caused large changes in the vertical GRF. The first peak values for the −6 and −3 degrees inclination are 801 N and 732 N,

which are 21.2% and 10.7% higher than the value at the normal 0 degree inclination, respectively. On the other hand increasing the angle up to +3 degrees has reduced the peak force value 11.2% (587 N). Also the timing of the peak values has changed, which is already expected since rotating the ankle joint backward accelerates the load response period. In the case of forward rotation (+3 degrees) of the ankle the system has shown two successive peaks because the foot needs more time until it is completely in contact with the ground. Then the second small peak occurs as the forefoot makes contact with the ground and the sound leg completely leaves the ground.

For the second peaks (where the foot sole bears most of the load) the differences in the forces were small. The maximum difference was 4.6%. In general this figure indicates that the changes in angle of the ankle joint are more dominant than the change in the foot sole stiffness studied in the previous section.

Figure 6.5: The simulated vertical GRFs acting on the prosthetic foot for four different ankle joint inclinations

In Figure 6.6 the torques at the ankle are displayed. The most important difference between the curves is the time when the moments are zero. Increasing the angle of inclination increases the time needed to reach zero moment, which means that the heel of the foot stays loaded for a longer time.

Figure 6.6: The simulated moment at the ankle joint of the prosthetic foot for four different ankle joint inclinations

The hip joint rotation shows very small changes by reducing the angle of the ankle joint

−3 degrees but by changing the rotation angle of the ankle joint −6 and +3 degrees, the total rotation of the hip joint has changed −7% and +7%, respectively. Figure 6.7 represents the hip joint rotation for the different inclination of the ankle joint.

Figure 6.7: The simulated rotation of the thigh at the hip joint for four different ankle joint inclinations

The BCoM motion is shown in Figure 6.8. From the figure it can be clearly recognized that the changes in the BCoM are very significant and occur along the path of the body and not just at the second half of the gait cycle (as the case was in the previous section when the stiffness was changed). The vertical displacement of the BCoM has increased 24 mm for a 3 degrees increase in the ankle joint inclination. This is about 55% of the total vertical displacement. However, reducing the inclination angle by 3 degrees has reduced the BCoM vertical displacement just 11% (5 mm). For −6 degrees change in ankle joint inclination the reduction was 45%. The relation between the inclination angle and the changes in the BCoM displacements is not linear.

The differences in the horizontal displacements of the BCoM at the end of the simulation time were larger than that corresponding to the stiffness changes. The maximum difference between the results, corresponding to the two inclination angles 3 and −6 degrees, is 81 mm, which is 9.0% of the total horizontal displacement.

Figure 6.8: The simulated BCoM vertical and horizontal motion for four different ankle joint inclinations

Since the changes in this property of the foot have significantly changed the gait parameters it will also be considered as an important value to be studied in the other gait conditions.