**3. Experimental Results**

Normal gait requires sophisticated interaction of many systems of the body, such as strength, coordination, and sensation. For example, aging is an increasing global public health issue. When aging causes weakening strength and sensation, the interacting systems may result in abnormal gait or walking abnormality. In this section, a preliminary experimental result for the recognition of normal and abnormal gait types from the calculated sets of 3-D hip and knee joint angles (Equations (12)–(17)) are described. Hemiplegic gait is one of the results of post-stroke patients who have weak flexor muscle movement during the gait cycle. The knee is stiff, hyperextends during stance, and does not regularly flex during the swing. The contralateral step often advances to meet the position of the paralyzed limb, instead of periodically moving forward beyond it. These movements include raising the pelvis to clear the paralyzed leg and circumduction, an abnormal shift. As a result, the toe traces a semicircle on the floor, first moving outward and then inward as it advances, instead of a normal straightforward movement [20–23] (Figure 4).

**Figure 4.** Description of a human leg movement during hemiplegic gait experiment.

This experiment provides the results of three-dimensional gait analysis performed on a single participant (i.e., an author). The experiments were performed multiple times to ensure the repeatability of the results and to obtain a statistically significant data set. A PC was then used to record and process the data. The experiments were completed the same way each time but on different days. There was only a single individual that performed the test, and thus, the sampling size was not statistically significant. However, for proof of concept purposes, the test was successful and serves as motivation to repeat the tests on a larger sample size in the future. Figure 5 shows the two kinds of gait patterns that were considered: hemiplegic and normal gaits. Three-dimensional kinematics of the hip and knee joint angles were recorded and calculated. The figure shows the relative angles of the hip and knee during the gait cycle along with extension and flexion in the sagittal plane, the frontal plane, and the transverse plane. From the figure, it can be noticed the changed coordination phase of the hip and knee movements of the Hemiplegic gait.

**Figure 5.** An example of calculated 3-D hip and knee joint angle patterns associated with normal (**a**) (periods of 1.3 s) and simulated hemiplegic walking (**b**) (periods of 1.8 s).

In this paper, a new method to calculate the parameter of the three-dimensional phase difference angles between the hip and knee movements is described to identify biomechanical changes in gait patterns. The phase difference angle analysis aims to establish the distinct conditions for mapping of the characteristic patterns of the joint motions in the performing of specific leg movements. The phase difference angles at time t and the *i*th-directional plane (i.e., sagittal, frontal, and transverse) is given by

$$
\rho\_t^i = 360^\circ \, f \, \Delta t,\tag{25}
$$

where *f* is gait cycle frequency and Δt is the time difference (PD) between the hip and the knee angles.

This study uses the instantaneous signal (i.e., the temporal derivative of the oscillation) since it is useful for describing the non-monochromatic nature of the joint angle signals. Further, it also helps to reduce the effect on noises in IMU signal measurement, such as the signal shift and offset errors. Figure 6 shows the normalized gait phase diagrams of the hip and knee joint angles of Figure 5. From the diagram, the phase deference angles (i.e., hip-sagittal vs. knee-sagittal; hip-sagittal vs. knee-frontal; hip-sagittal vs. knee-transverse) are calculated using Equation (25). All phase deference angles of the two gait patterns are summarized in Figure 7. The figure indicates that all the sagittal, frontal, and transverse directions show a different pattern between the normal and the hemiplegic gait of the subject. Table 1 summarizes the experimental results from multiple trials of the subject.


**Table 1.** The experimental results of the normalized gait phase angles with normal and simulated hemiplegic walking.

<sup>1</sup> The gait cycle frequency is 0.77 Hz. <sup>2</sup> The gait cycle frequency is 0.56 Hz.

**Figure 6.** The normalized gait phase diagrams of the hip and knee joint angles of Figure 5 with normal (**a**) and simulated hemiplegic walking (**b**) (hip-sagittal vs. knee-sagittal).

**Figure 7.** The normalized gait phase diagrams of the hip and knee joint angles of Figure 5 (i.e., hipsagittal vs. knee-sagittal).
