## 2 Materials and Methods
### Kinematic Experiment
#### 2.1.4 Data Analysis  
The data matrix of size 86,400 \(\times\) 21 was used to perform all the analyses. Identifying the joint angles that have the most significant impact on the overall data variance is crucial. The angles with the highest variance must be actively controlled by external motors in the prosthetic hand design for efficient operation. Principal Component Analysis (PCA) was conducted to analyze the variance of each joint angle. It was observed that the MCP F/E angles have a maximum contribution to the first principal component (PC), indicating their higher variance in grasping. Figure 3a shows the cumulative variance of each PC averaged across participants, postures, and trials. It can be observed that \(\sim\)85% of the total variance can be expressed by the first 3 PCs as expected [24]. It is also noted that a significant variance of the MCP Ab/Ad angle is observed only in the 3 rd PC. This can be attributed to the lower ROM of the MCP Ab/Ad angle. The loading chart of the index finger for the first 2 PCs is shown in Figure 3b. It can be seen that the length of the line segment corresponding to the Ab/Ad angle is quite small when compared to the other three angles of the finger, which shows a lower representation of the MCP Ab/Ad angle in the first two PCs.  
Performing only a PCA does not clearly indicate the importance of the Ab/Ad angle in grasping due to the difference in the ROM of the three F/E angles and the Ab/Ad angle. Hence, data normalization needs to be performed to compare variances on a uniform scale. To this end, using the following formula, \"min-max normalization\" was performed for all the joint angles of the index, middle, ring, and little fingers.  
\[x_{new}=\frac{x-x_{min}}{x_{max}-x_{min}} \tag{2}\]  
where \(x\) is the data (individual joint angle) value for any joint angle. \(x_{max}\) and \(x_{min}\) are the maximum and the minimum values of that joint angle dataset.  
The normalized data were then used to perform the variance analysis. The coefficient of variance for the MCP F/E and the Ab/Ad angles was calculated to compare the two joint angles. The results are shown in Figure 4. It was noted that the Ab/Ad angle exhibited a higher coefficient of variance for the index, ring, and little fingers. This finding suggests that the MCP Ab/Ad angle has a significant variance, even within its limited range of  
Figure 3: (a) Cumulative variance of all the principal components of the combined dataset. (b) Loading plot to indicate the relative importance of the 4 angles of the index finger in the first 2 principal components.  
motion, highlighting the need to incorporate this functionality into the design of prosthetic hands. Therefore, the role of the Ab/Ad angle should be considered in the design and control of prosthetic hands to enhance overall dexterity and performance.  
The current section showed the importance of the Ab/Ad angle and provided the basis for incorporating the functionality of the Ab/Ad angle in prosthetic hand design. This work proposes to design a 3 DoF fingers palmar finger orientation analysis. Orientation of each finger in the current work refers to the Ab/Ad angle as measured in the frontal plane with respect to the y-axis (refer to Figure 1). To this end, in the current work, finger orientation analysis is performed based on the kinematic structure of the finger and the fingertip workspace. Since the finger and hand kinematics have already been established, we continue by performing the workspace analysis of the fingertips.