# Gait Analysis of Elderly and Young People Based on Joint Angles and Positions
## 4 Results  
### Comparison of PCLs between Elderly and Young People  
We used 3D plots to confirm how the elevation angles differed between elderly and young people. Figure 4 shows three-dimensional plots of the average elevation angles divided by age group for one walking cycle from left heel touch to left heel re-grounding. Elevation angles for the elderly patients are shown in blue, and those for the young patients are shown in red. The mean values were averaged for the elderly and young groups by applying a polynomial approximation to each participant's elevation angles, setting the gait cycle to 100%, and normalizing the gait cycle time. A grid was added to the approximate planes to show the differences. The size of the circle indicates the vertical movement of each participant. Figure 4 shows that the ranges of motion of the elevation angles were smaller for the older patient, as in the conventional treadmill study. Aging has been reported to have no effect on limb coordination [21], and we confirmed that the PCL was established in both  
Figure 4: Comparison of PCLs between the elderly and young people. Figure 3: Relationship between PCL and one cycle of walking. (**a**) Example of PCL for elevation angle and stick figure for one walking cycle. (**b**) Time [%] is expressed in 100% based on one cycle of walking from heel contact to the next heel contact. young and elderly subjects. In addition, the closed circles for the three elevation angles were smaller for the elderly patients. This suggests that elderly people have a decreased range of motion of the lower limbs during walking rather than variations in elevation angles as a result of changes in walking posture (e.g., hunchback). Approximate planes were calculated from the obtained elevation angles, and the cumulative contribution rates shown in Table 3 were used to investigate whether the plane law holds after aging. The cumulative contribution rates were calculated as the sum of the contribution rates of the first and second principal components using the statistical processing software SPSS (IBM Japan, Ltd., Tokyo, Japan; IBM SPSS Statics ver. 24). [PERSON] et al. (2012) reported cumulative contribution rates of 99% or more for all subjects (21-40 years). In their results, there was no significant difference between the elderly group and the young group. In addition, a \(t\)-test was performed between the elderly group and the young group, but there was no significant difference in the cumulative contribution rate. Changes in Elevation Angles \(\theta_{\text{high}}\), \(\theta_{\text{shank}}\), and \(\theta_{\text{foot}}\) during One Gait Cycle  
To examine the differences in elevation angles between the elderly and young, the changes in \(\theta_{\text{high}}\), \(\theta_{\text{shank}}\), and \(\theta_{\text{foot}}\) within one walking cycle were examined. The changes in the angles are shown in Figure 5. For \(\theta_{\text{high}}\), the angles of the elderly participants tended to be smaller than those of the younger participants, indicating that thigh flexion/extension was decreased in the elderly. For \(\theta_{\text{shank}}\), thigh and lower leg flexion tended to be smaller for the elderly population from 60% to 70% of the way through the gait cycle. For \(\theta_{\text{foot}}\), the angles of the elderly patients were lower than those of the young patients from 0 to 50% and from 80% to 100% of the gait cycle, and it was confirmed that the flexion and dorsiflexion from the heel to the toe were decreased. Figure 6 shows the differences between the maximum and minimum values of \(\theta_{\text{high}}\), \(\theta_{\text{shank}}\), and \(\theta_{\text{foot}}\) from Figure 5. The mean values of \(\theta_{\text{high}}\), \(\theta_{\text{shank}}\), and \(\theta_{\text{foot}}\) for the elderly and younger groups are shown, and the standard deviations were calculated for the mean values.