Fig. 4

Schematic overview of the calculation steps for the mean symmetry values of kinematic synergies. Step 1: participants underwent a 3DGA model with total-body kinematics using a motion capture system. Step 2: from the 3DGA model, the joint angles of the hip, knee, and ankle were calculated concerning the flexion–extension (Flex), abduction–adduction (Abd), and internal–external rotation (Rot). In this example, the angle of the three lower joints is presented during one gait cycle. The joint angles involving the 9 DoFs were pooled together as an original joint matrix. Step 3: PCA was employed to decompose the original joint matrix into two components, synergy weight, and timing coefficient. Step 4: the similarities of all possible combinations of the synergy weight on the left to the right side were calculated with the scalar dot product [23]. The pair with the highest value was removed from the pool and the process continues until all kinematic synergies were matched. Step 5: the weight of synergies on both sides of each pair was compared with the scalar dot product [69, 70], while the symmetry value of all comparisons was averaged as the mean weight symmetry value. Step 6: the similarity of the corresponding timing coefficients for each pair was evaluated with the Pearson correlation coefficient (r). These correlation values were normalized using Fisher’s r-to-z transformation and then averaged across all comparisons. Inverse z-transformation was finally performed to transform the averaged z value back to r, which was considered as the mean timing symmetry value