## 3 Proposed Method
Figure 2c,f expresses the starting and ending moment of a gesture together; the dashed line  
Figure 2: Joint trajectories with respect to grab and pinch gestures (right hand): (**a**) grab (at start); (**b**) grab (at end); (**c**) grab (combined (**a,b**)); (**d**) pinch (at start); (**e**) pinch (at end); (**f**) pinch (combined (**d,e**)). means the hand at the starting moment, and the solid line means the hand at the ending moment. In Figure 2c,f, although it is possible to approximately check the degree of the joint information changed in each gesture, it is difficult to confirm the degree of change with respect to each joint. The degree of change with respect to each joint was calculated to confirm it more accurately. Figure 3 indicates the degree of change with respect to each joint information according to grab and pinch gestures. In the case of the thumb, there is no intermediate joint, so 0 was assigned in the intermediate of the thumb. The other joints are expressed in blue for fewer changes (0 in Figure 3a,b) and green for more changes (0.1 in Figure 3a and 0.05 in Figure 3b), depending on the degree of change. As a result, in the case of grab, it was confirmed that the tip joint greatly changed. In the case of pinch, it was confirmed that the tip joint and the distal joint of the index finger greatly changed. Additionally, in the case of pinch, the tip joint of the other fingers showed a tendency to change significantly compared to other joints of each finger. Based on this, we selected the tip joint of each finger as a representative value of the hand for classifying the grab and pinch gesture. However, additional information is required because it is impossible to determine the hand's movement only with the tip joint. For example, Figure 4a,b shows the cases where the tip joint greatly changed. It is difficult to distinguish the cases shown in Figure 4 with only the information that the tip joint changed greatly. Even if additional information is used, the representativeness of the tip joint should be maintained, so the metacarpal joint and proximal joint were additionally selected, which had the least degree of change due to the review result of Figure 3. The selected joints were used to help classify the gesture without compromising the representativeness of the tip joint. In particular, the selected joints can help to check the overall degree of the hand. Meanwhile, the more joints included when classifying a gesture, the larger the size of the  
Figure 4: Cases that the tip joint greatly change: (**a**) case of right angle; (**b**) case of diagonal. Figure 3: Degree of change with respect to each joint information according to grab and pinch gestures: (**a**) grab; (**b**) pinch. dataset and the longer the computation time. Therefore, we did not select a distal joint that showed the most degree of change after the tip, for which the change of degree was almost similar to the tip. Eventually, in this study, joint angles for each finger were calculated using the tip joint, the metacarpal joint, and the proximal joint by Equations (1)-(3):  
\[\overrightarrow{v_{1}}=position_{Metacarpal}-position_{Proximal} \tag{1}\]  
\[\overrightarrow{v_{2}}=position_{Tip}-position_{Proximal} \tag{2}\]  
\[\theta_{jointangle}=\cos^{-1}\left(\frac{\overrightarrow{v_{1}}\cdot \overrightarrow{v_{1}}}{\|\overrightarrow{v_{1}}\|\|\overrightarrow{v_{2}}\| }\right) \tag{3}\]  
where \(position_{Metacarpal}\), \(position_{Proximal}\), and \(position_{Tip}\) are 3D points of the metacarpal joint, the proximal joint, and the tip joint, respectively; \(\theta_{jointangle}\) is an internal angle calculated using the metacarpal, proximal, and tip joints. These five calculated joint angles (\(\theta_{1}-\theta_{5}\)) are shown in Figure 5 and these values were used as representative values representing the hand. When classifying a gesture, only using information at a specific moment cannot reflect information from consecutive movements, so it is difficult to find the user's intention.