# A Linkage Representation of the Human Hand Skeletal System Using CT Hand Scan Images
## 3 Results
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Finger** & **Segment 1** & **Segment 2** & **Segment 3** & **Segment 4** \\ \hline Thumb & 0.190 \(\pm\) 0.003 (0.996, & 0.233 \(\pm\) 0.002 (0.998, & 0.179 \(\pm\) 0.002 (0.998, & 0.137 \(\pm\) 0.002 (0.998, \\  & \(-\)4.0-3.7, [0.184, 0.196]) & \(-\)2.5-3.7, [0.229, 0.237]) & \(-\)2.7-3.0, [0.175, 0.183]) & \(-\)2.1-2.2, [0.133, 0.141]) \\ Index & 0.476 \(\pm\) 0.005 (0.998, & 0.231 \(\pm\) 0.002 (0.999, & 0.128 \(\pm\) 0.001 (0.999, & 0.109 \(\pm\) 0.002 (0.996, \\  & \(-\)7.0-4.9, [0.465, 0.487]) & \(-\)2.2-2.7, [0.227, 0.235]) & \(-\)1.5-2.1, [0.126, 0.130]) & \(-\)2.7-1.8, [0.105, 0.113]) \\ Middle & 0.458 \(\pm\) 0.004 (0.999, & 0.258 \(\pm\) 0.002 (0.999, & 0.151 \(\pm\) 0.001 (0.999, & 0.116 \(\pm\) 0.002 (0.997, \\  & \(-\)4.8-5.8, [0.449, 0.467]) & \(-\)3.5-2.2, [0.254, 0.262]) & \(-\)2.1-2.2, [0.149, 0.153]) & \(-\)2.3-1.8, [0.112, 0.120]) \\ Ring & 0.433 \(\pm\) 0.004 (0.999, & 0.241 \(\pm\) 0.003 (0.999, & 0.145 \(\pm\) 0.001 (0.999, & 0.118 \(\pm\) 0.002 (0.997, \\  & \(-\)5.6-4.0, [0.424]) & \(-\)3.8-3.0, [0.235, 0.247]) & \(-\)1.5-1.4, [0.143, 0.147]) & \(-\)2.8-1.8, [0.114, 0.122]) \\ Little & 0.425 \(\pm\) 0.004 (0.999, & 0.192 \(\pm\) 0.002 (0.999, & 0.100 \(\pm\) 0.003 (0.991, & 0.105 \(\pm\) 0.002 (0.997, \\  & \(-\)7.0-3.3, [0.416, 0.434]) & \(-\)1.8-3.0, [1.188, 0.196]) & \(-\)3.2-2.6, [0.094, 0.106]) & \(-\)2.8-1.4, [0.101, 0.109]) \\ \hline \hline \end{tabular} Note: For the thumb, Segment 1 is the carpal segment, 2 the metacarpal, 3 the proximal phalangeal, and 4 the distal phalangeal. For the four fingers, Segment 1 is the carpometacarpal segment, 2 the proximal phalangeal, 3 the middle phalangeal, and 4 the distal phalangeal.  
\end{table} 
Table 2: Coefficients for estimating link length or segment length from hand length (A, where link length = A \(\times\) hand length) based on 15 male hands (mean \(\pm\) standard error, \(R^{2}\), maximum residual range, and 95% confidence interval). Figure 5: Linkage representation (blue) of a participant’s right hand by connecting the estimated joint centers (red). The \(x\)-coordinates of the CMC joint center of the thumb and the MCP joint centers of the other four fingers were modeled as a linear function of hand breadth (HB): \(x\) = B \(\times\) HB \(\pm\) error. The \(y\)-coordinates were modeled as a linear function of hand length: \(y\) = C \(\times\) HL \(\pm\) error. The \(z\)-coordinates were modeled as a linear function of hand breadth or hand length using stepwise regression: \(z\) = D \(\times\) HB/HL \(\pm\) error. Coefficients for these models are shown in Table 3. \(R^{2}\) values ranged from 0.883 to 0.999. Standard errors for these models were below 1.7 mm. The proposed regression models were validated with another participant (hand length = 189 mm and hand breadth = 94 mm) besides the 15 participants. As shown in Table 4, the differences between the internal hand link lengths estimated from the proposed regression models and the actual internal hand link lengths ranged from -2.6 to 3.9 mm. As shown in Table 5, the differences between the coordinates of the CMC joint center of the thumb and the MCP joint centers of the other four fingers estimated from the proposed regression models with the actual coordinates ranged from \(-\)3.1 to 3.5 mm.