## 3 Results
On average, as shown in Figure 7a, the x-direction velocity reaches its minimum and maximum at approximately 0% and 50% of the gait cycle, respectively. Conversely, the load distribution of the first principal motion demonstrates almost opposite characteristics, with maximum and minimum values at roughly 0% and 50% of the gait cycle, respectively. This pattern suggests that individuals with higher first scores exhibit less variation in the x-direction velocity. This observation is further supported by Figure 8a, where gait samples with the highest and lowest first scores are depicted with solid and dotted lines, respectively. Notably, the higher the score, the higher the MoS value and postural stability. The extended center of mass becomes close to the center of the body with low speeds in the x-direction, implying a high postural stability. Therefore, individuals with high first scores and minimal fluctuation in the x-directional speed tend to have large mediolateral MoS values. Figure 7c shows that the dominant feature of the second principal motion is along the z-axis, lagging behind the mean motion by approximately 10%. This delay suggests that individuals with elevated second scores experience delayed peaks in the z-directional velocities, as shown in Figure 8b. Similarly, Figures 7d and 8c show that the defining characteristic of the third principal motion is a reduced walking speed (y-directional velocity), with individuals exhibiting large third scores when walking slowly, probably because of the short strides, as indicated by the reduced vertical movement. Figure 6: Observed and estimated MoS. (**a**) Mediolateral direction and (**b**) anterior direction. MoS values were estimated by 10-fold cross-validation. Figure 9 shows the mean translational velocities of the sacral crest and the first to third principal motions for estimating the anterior MoS. The anterior MoS for the sacral crest was estimated by summing the following three principal motion scores:  
\[\mathbf{m}_{\text{ant}}=0.0792\mathbf{t}_{1}+0.0480\mathbf{t}_{2}+0.0432\mathbf{t}_{3}+\overline{ \mathbf{m}}_{\text{ant}}, \tag{19}\]  
where \(\overline{\mathbf{m}}_{\text{ant}}\) represents the mean anterior MoS value across all samples. Figure 10 compares motion samples with the highest (represented by solid curves) and smallest (represented by dotted curves) scores for each principal motion. Figure 9b shows that the prominent feature of the first principal motion is small velocities in the y-direction, with velocities in the x- and z-directions approximately in the opposite phase to the average motions. Consequently, as shown in Figure 10a, participants with a large first score walk slowly with small velocity amplitudes in the mediolateral (x) and vertical (z) directions, indicating a gait with small strides. The second principal motion is characterized by a lag in the z-direction velocity, as shown in Figures 9c and 10b. A motion sample with a large second score shows a delay in the z-direction phase. Figures 9d and 10c show noticeable differences in motions between large and small third scores, particularly in the x- and z-directions. Compared with the sample with a small score, the sample with a large score advances in phase in the z-direction. Additionally, the sample with a large score exhibits minimal change in the x-directional velocity. Figure 7: Mean translational velocities of the sacral crest and principal motions to estimate the mediolateral MoS. (**a**) Mean translational velocities. (**b**) First principal motion. (**c**) Second principal motion. (**d**) Third principal motion. Figure 8: Examples of gait motions with the highest (rigid curves) and smallest (dotted curves) scores for each principal motion to estimate the mediolateral MoS. Figure 9: Mean translational velocities of the sacral crest and principal motions to estimate the anterior MoS. (**a**) Mean translational velocities (same as Figure 7a). (**b**) First principal motion. (**c**) Second principal motion. (**d**) Third principal motion.