# A Linkage Representation of the Human Hand Skeletal System Using CT Hand Scan Images
## 4 Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Finger**} & \multicolumn{3}{c}{**\(x\)**} & \multicolumn{3}{c}{**\(y\)**} & \multicolumn{3}{c}{**\(z\)**} \\ \cline{2-11}  & **Actual** & **Estimated** & **Difference** & **Actual** & **Estimated** & **Difference** & **Actual** & **Estimated** & **Difference** \\ \hline Thumb & \(-\)22.8 & \(-\)24.5 & \(-\)1.7 & 21.0 & 20.8 & \(-\)0.2 & \(-\)18.1 & \(-\)21.2 & \(-\)3.1 \\ Index & \(-\)24.7 & \(-\)24.8 & \(-\)0.1 & 88.5 & 87.1 & \(-\)1.4 & 0.0 & 0.0 & 0.0 \\ Middle & 0.0 & 0.0 & 0.0 & 86.1 & 86.6 & 0.5 & 0.0 & 0.0 & 0.0 \\ Ring & 18.2 & 19.6 & 1.4 & 79.0 & 79.6 & 0.6 & \(-\)7.0 & \(-\)5.3 & 1.7 \\ Little & 35.1 & 37.9 & 2.8 & 68.3 & 71.8 & 3.5 & \(-\)12.3 & \(-\)10.2 & 2.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Differences between the coordinates of the carpometacarpal (CMC) joint center of the thumb and the metacarpophalangeal (MCP) joint centers of the other four fingers estimated from the proposed regression models with the actual coordinates (unit: mm). surfaces for different hand postures by registration of each bone segment from the template posture to that from each of other postures, (3) estimation of finite joint centers among different postures, and (4) determination of joint centers as the centroid of the estimated finite joint centers. The use of 3D hand skeleton motions ensures that joint centers are kinematically estimated. The use of the same bone surfaces for different hand postures makes sure that the same centerlines of the distal bone segments of a given joint at different postures are identified so that an accurate finite joint center can be determined by the intersection point of the centerlines at different postures. A finite joint center estimated between two different postures represents the center of the relative rotation between two adjacent body segments from one posture to the other. The centroid of all the finite joint centers estimated among different postures can most closely approximate the centers of the relative rotations between the two adjacent body segments. Thus the participant-specific linkages built from the derived joint centers can satisfy the optimal criteria stated. Finite joint centers vary with the change of flexion-extension of the hand, as shown in Figure 6. Mean distance between the finite joint centers of a hand joint in the present study ranged from 0.5 mm to 1.4 mm, indicating that the variation of finite joint centers was quite small during flexion-extension of the hand. Such a small variation might not have a significant effect on the motion of a hand joint during ergonomic analysis. The proposed method for estimation of the location of a joint center showed high intra- and interobserver precision. The interobserver variation was slightly higher than the intraobserver variation. The high intra- and interobserver precision of the proposed method were because of its high automation level. The slightly higher interobserver variation was mainly caused by the estimation of the wrist joint center. A 2 mm difference was found in the \(y\)-coordinate of the estimated wrist joint center between two observers, caused by the difference in identifying the location of distal wrist crease by the two observers. The present study established regression models to predict internal hand link lengths from hand lengths and the locations of CoRs of the thumb CMC joint and the MCP joints of the other four fingers from hand length and hand breadth. The regression models can be used to effectively build a general linkage by measuring the hand length and the hand breadth of a particular person. Our models have higher \(R^{2}\) values (0.883 to 0.999) than those (0.30 to 0.99) of [PERSON] et al. 's models. The maximum standard error of the coefficients of our models is 0.008, whereas that of [PERSON] et al. 's models is 0.010.