# Uncertainty Analysis of Spherical Joint Three-Dimensional Rotation Angle Measurement
## 5 Conclusions
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{(\(\alpha\), \(\beta\), \(\gamma\))} & **Angle of** & **The Best** & **Standard** & **Interval** & **Extension** \\  & **Component** & **Estimate** & **Uncertainty** & & **Uncertainty** \\ \hline \multirow{2}{*}{(\(-5^{\circ}\), \(-5^{\circ}\), \(0^{\circ}\))} & \(\alpha\) & \(-4^{\circ}59^{\prime}55^{\prime\prime}\) & \(1^{\prime}33^{\prime\prime}\) & \([-5^{\circ}27^{\prime\prime}\), \(-4^{\circ}59^{\prime}22^{\prime\prime}]\) & \(2^{\prime}39^{\prime\prime}\) \\  & \(\beta\) & \(-5^{\circ}1^{\prime\prime}\) & \(1^{\prime}31^{\prime\prime}\) & \([-5^{\circ}229^{\prime\prime}\), \(-4^{\circ}57^{\prime}31^{\prime\prime}]\) & \(2^{\prime}29^{\prime\prime}\) \\  & \(\gamma\) & \(49^{\prime\prime}\) & \(1^{\prime}3^{\prime\prime}\) & \([-16^{\prime\prime},1^{\prime}53^{\prime\prime}]\) & \(1^{\prime}5^{\prime\prime}\) \\ \hline \multirow{2}{*}{(\(-5^{\circ}\), \(5^{\circ}\), \(5^{\circ}\))} & \(\alpha\) & \(-5^{\circ}\) & \(1^{\prime}33^{\prime\prime}\) & \([-5^{\circ}233^{\prime\prime}\), \(-4^{\circ}59^{\prime}22^{\prime\prime}]\) & \(2^{\prime}33^{\prime\prime}\) \\  & \(\beta\) & \(5^{\circ}\) & \(1^{\prime}30^{\prime\prime}\) & \([4^{\circ}57^{\prime}31^{\prime\prime}\), \(5^{\circ}27^{\prime\prime}\)] & \(2^{\prime}29^{\prime\prime}\) \\  & \(\gamma\) & \(5^{\circ}16^{\prime\prime}\) & \(42^{\prime\prime}\) & \([4^{\circ}59^{\prime}11^{\prime\prime},5^{\circ}121^{\prime\prime}]\) & \(1^{\prime}6^{\prime\prime}\) \\ \hline \multirow{2}{*}{(\(5^{\circ}\), \(-5^{\circ}\), \(0^{\circ}\))} & \(\alpha\) & \(4^{\circ}1^{\prime\prime}\) & \(1^{\prime}1^{\prime\prime}\) & \([3^{\prime}7^{\prime\prime}28^{\prime},5^{\circ}223^{\prime\prime}]\) & \(1^{\prime}73^{\prime\prime}\) \\  & \(\beta\) & \(-5^{\circ}1^{\prime\prime}\) & \(1^{\prime}31^{\prime\prime}\) & \([-5^{\circ}27^{\prime\prime},4^{\prime\prime},5^{\prime\prime}31^{\prime\prime}]\) & \(2^{\prime}29^{\prime\prime}\) \\  & \(\gamma\) & \(5^{\circ}59^{\prime\prime}\) & \(36^{\prime}59^{\prime\prime}\) & \([44^{\circ}45^{\prime\prime},2^{\prime\prime}38^{\prime\prime}44^{\prime}]\) & \(56^{\prime}59^{\prime\prime}\) \\ \hline \multirow{2}{*}{(\(5^{\circ}\), \(5^{\circ}\), \(5^{\circ}\))} & \(\alpha\) & \(4^{\circ}47^{\prime}20^{\prime\prime}\) & \(39^{\prime}18^{\prime\prime}\) & \([4^{\circ}33^{\prime}40^{\prime\prime},6^{\prime\prime}21^{\prime}52^{\prime\prime}]\) & \(54^{\prime}6^{\prime\prime}\) \\  & \(\beta\) & \(5^{\circ}19^{\prime}17^{\prime\prime}\) & \(27^{\prime}29^{\prime\prime}\) & \([4^{\circ}28^{\prime}4^{\prime},5^{\prime\prime}36^{\prime\prime}26^{\prime \prime}]\) & \(43^{\prime}51^{\prime\prime}\) \\  & \(\gamma\) & \(5^{\circ}33^{\prime}18^{\prime\prime}\) & \(33^{\prime}20^{\prime\prime}\) & \([4^{\circ}30^{\prime}44^{\prime\prime},5^  
**Author Contributions:** Conceptualization, writing--original draft, investigation, software, J.Z. and P.H. ; resources, data curation, supervision, Q.Y. ; methodology, validation, formal analysis, L.Y. ; writing--review and editing, P.H. All authors have read and agreed to the published version of the manuscript. **Funding:** This work was supported in part by the National Natural Science Foundation of China under Grant 52175505. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Not applicable. **Conflicts of Interest:** The authors declare no conflict of interest.