Fig. 5

Schematic overview of the calculation steps for the mean symmetry values of kinematic synergies. In Step 1, joint angles of the hip, knee, and ankle concerning flexion–extension, abduction–adduction, internal–external rotation, and trunk and pelvis motions including lateral tilt, forward tilt, and rotation angles were derived from the 3DGA model. These 15 independent variables were presented during one gait cycle for each side, which were then pooled together to form an original matrix. In Step 2, Principal Component Analysis (PCA) was utilized to decompose the original matrix into two components, namely, synergy weight and timing coefficient. In Step 3, the scalar dot product was employed to compute the similarities between all possible combinations of the synergy weight on the left and right sides. The highest value pair was then eliminated from the pool, and the process was repeated until all kinematic synergies were matched. Step 4 involved the comparison of the weight of synergies on both sides of each pair with the scalar dot product. The mean weight symmetry value was determined by averaging the symmetry value of all comparisons. In Step 5, the Pearson correlation coefficient (r) was utilized to assess the similarity of the corresponding timing coefficients for each pair. Fisher’s r-to-z transformation was employed to normalize the r values, which were then averaged across all comparisons. The inverse z-transformation was applied to transform the averaged z value back to r, representing the mean timing symmetry value