## 3 Results
### Description of Response to Perturbation for Kinematic and Kinetic Parameters-Perturbed Limb  
#### 3.2.1 Ground Reaction Forces  
Figure 4 shows the clustering of vertical ground reaction force (GRF) patterns of perturbed left lower limbs, highlighting distinct adaptation strategies in older and young adults. Principal Component Analysis (PCA) was applied to reduce the complexity of the GRF data, with the first two principal components (PC1 and PC2) capturing the most relevant variability in movement patterns. In the older adult group (Figure 4A), PC1 and PC2 accounted for 51.6% and 22.7% of the total variance, respectively-together explaining 74.3% of the dataset's variability. For the young adult group (Figure 4B), PC1 explained 45.1% and PC2 25.5%, totaling 70.6% of the variance. These high percentages indicate that the majority of meaningful differences in GRF patterns are well represented in the two-dimensional PCA space. K-means clustering (3 clusters, 10 replicates) iden  
Figure 3: The means and standard deviations of (**A**) joint angles, (**B**) joint torques and (**C**) ground reaction forces of the gait cycle for young (pink) and elderly (blue) groups, PD–vertical component, AP–anterior-posterior component, ML–medial-lateral component. On the right axis, the SPM[t] statistic is shown as a function of the gait cycle with the critical threshold (t) values. The areas highlighted in gray show the ranges where statistically significant differences are present.  
tified clear groupings of subjects based on their GRF characteristics, with each point representing an individual and colors denoting cluster membership. The distinct separation between clusters suggests varied loading behaviors, with noticeable differences between age groups-indicating that older and younger adults employ different compensatory strategies, likely influenced by age-related changes in neuromuscular control and balance response.  
The extreme values of each component of ground reaction forces from the elderly group were compared with those recorded for the young group for each extracted behavioral strategy and treadmill gait (Figure 5).  
Statistically significant differences were noted for all variables between the younger and older groups for treadmill gait (Figure 5D) and for Strategy III (Figure 5C). For Strategy II, significantly higher values were reported in the elderly group compared to those recorded in the young group for the maximum values of the ML component, the minimum values of the vertical component, and both the minimum and maximum values of the AP component (Figure 5B). In Strategy I, the maximum values for the ML and PD components were significantly higher in the elderly group (Figure 5A).  
It is worth noting that, for most variables, the values recorded in the elderly group were higher or significantly higher than those in the young group. The exceptions were noted for (1) the minimum value of the anterior-posterior component of GRF in Strategy I; (2) the maximum value of the anterior-posterior component of GRF in Strategy II; (3) the minimum value of the ML component of GRF in Strategy III; (4) and the minimum value of the vertical and anterior-posterior components of GRF and treadmill gait.  
Figure 4: Clustering of vertical ground reaction force patterns for perturbed limb using PCA and K-Means. Scatter plots illustrate the distribution of subjects in a reduced feature space defined by the first two principal components (PC1 and PC2) extracted from vertical GRF data. Each point represents a subject, colored by their k-means cluster assignment (3 clusters, 10 replicates). PC1 and PC2 capture the majority of variance, enabling clear visualization of individual differences in loading behavior: (**A**) Older adults, (**B**) Young adults.