# A Parametric Identification Method of Human Gait Differences and its Application in Rehabilitation
## 3 Results  
### Normal Group  
Figure 4 shows the flexion angle curves (black lines) and their average curves [42] (dark green lines) of the three lower limb joints on the sagittal plane in the normal group. From this figure, the distribution ranges of black lines and the dark green lines are equivalent to the grey area and the solid line in Figure 2e. Therefore, the dark green lines, the three average curves, were applied to the fitting calculation of Equation (1), then the curve fitting results of different numbers of commonality points are shown in Figure 5 and Table 1. Specifically, Figure 5a displays three fitting conditions of four, five, and six commonality points according to the shape characteristics of the hip joint. After comparison, the goodness of fit in five and six commonality points were both 1 with a good fitting degree while the former had not only fewer points but also better correspondence of the numbers between shape parameters and waves than the latter. The average curve of the knee joint was best fitted when  
Figure 4: The curves of participants and their average curves of three lower joints in normal ranges: (**a**) Ten angle curves (black line) and the average curve (dark green line) from the hip joint in one gait cycle; (**b**) The curves of knee flexion; (**c**) The ankle joint curves. Figure 3: The process of investigating the mathematical models of three joints and obtaining the shape parameters of normal group and patient group, thus analyzing whether the patient is well recovered or poor recovered. controlled by six points according to Table 1. Yet, the correspondence between three waves and four parameters was not clear enough. Although the fitting curve controlled by five commonality points did not fit the original curve completely (see Figure 5b), the proper reflection of the waveform property and the correspondence of three waves to three parameters still expressed the advantages. As for the average curve of the ankle joint, seven parameters exactly corresponded to seven fluctuations when controlled by nine points. Nevertheless, on the principle of minimizing parameters, smaller amplitudes that have little effects on gait feature analysis could be omitted for matching. Through the comparison of the first two fitting curves in Figure 5c, the goodness of fit and the parametric correspondence achieved better satisfaction when controlled by eight points. Figure 5: The fitting curves of three groups of commonality points to each joint: (**a**) The average curve (dark green line) of the hip was fitted through four, five, and six commonality points, respectively. The fitting curve (red line) at five points had the similar matching effect as six points, but with fewer points; (**b**) The three relationships among the fitting and average curves at four, five, and six points of the knee joint; (**c**) The average ankle joint curves were fitted by seven, eight, and nine commonality points. The ultimate determined number of commonality points of three joints and the distribution ranges of the curve shapes in the normal group are presented in Figure 6. Table 2 exhibits the commonality point coordinates of each group of joint curves. Precisely, when the average curves of the hip and knee were both controlled by five commonality points and three shape parameters, respectively, and the ankle curve was determined by eight commonality points and six shape parameters, they exactly represented the nature of the curves with the least parameters. On the whole, the fitting curve retains the feature of the original waveforms and contains the minimum points and shape parameters, and the local shape corresponding to each point has a sufficient adjustment range.