## 3 Results
### Orthogonal Rotation Combination Design Test
#### 3.2.1 Establishment of the Regression Model and Analysis of Variance  
The test results are shown in Table 8. ANOVA analysis and data fitting were performed using Design-Expert software. Multiple regression equations were established by combining the three independent variables of output air pressure \(X_{1}\), pulling angle \(X_{2}\) and pulling speed \(X_{3}\) with the response values of rape uprooted removal rate \(Y_{1}\), rape removal breakage rate \(Y_{2}\) and pulling force \(Y_{3}\). \[ \begin{array}{l}Y_{1}=82.66+3.75X_{1}-3.33X_{2}-1.25X_{3}+1.67X_{1}X_{2}+0.83 5X_{1}X_{3}\\ -11.75X_{1}{}^{2}-5.91X_{2}{}^{2}-1.75X_{3}{}^{2}\end{array}  \tag{4}\]  
\[ \begin{array}{l}Y_{2}=9.33+6.25X_{1}+1.67X_{2}+1.25X_{3}+1.66X_{1}X_{2}-0.82 5X_{1}X_{3}\\ -0.0025X_{2}X_{3}-2.58X_{1}{}^{2}+6.59X_{2}{}^{2}+0.748X_{3}{}^{2}\end{array}  \tag{5}\]  
\[ \begin{array}{l}Y_{3}=89.72-X_{1}+14.61X_{2}+2.99X_{3}-0.3X_{1}X_{2}-0.75X_{ 1}X_{3}\\ +1.72X_{2}X_{3}-0.4725X_{1}{}^{2}+4X_{2}{}^{2}+0.8525X_{3}{}^{2}\end{array}  \tag{6}\]  
Analysis of variance and significance test results are shown in Table 9. The regression model of rape uprooted removal rate \(Y_{1}\), rape removal breakage rate \(Y_{2}\) and pulling force \begin{table}
\begin{tabular}{l l l l l} \hline
**No.** & **Pulling Speed/(cm\(\cdot\)s\({}^{-1}\))** & **Rape Uprooted Removal Rate/\%** & **Rape Removal Breakage Rate/\%** & **Pulling Force/N** \\ \hline
1 & 8 & 85 & 5 & 85.7 \\
2 & 10 & 85 & 10 & 89.5 \\
3 & 12 & 75 & 15 & 93.4 \\ \hline \end{tabular}
\end{table} 
Table 7: The influence of the pulling speed on the test indicators. \begin{table}
\begin{tabular}{l l l l l l} \hline
**No.** & **Pulling Speed/(cm\(\cdot\)s\({}^{-1}\))** & **Rape Uprooted Removal Rate/\%** & **Rape Removal Breakage Rate/\%** & **Pulling Force/N** \\ \hline
1 & 8 & 85 & 5 & 85.7 \\
2 & 10 & 85 & 10 & 89.5 \\
3 & 12 & 75 & 15 & 93.4 \\ \hline \end{tabular}
\end{table} 
Table 7: The influence of the pulling speed on the test indicators. \begin{table}
\begin{tabular}{l l l l l l} \hline
**No.** & **Output Air** & **Pulling Angle** & **Pulling Speed** & **Rape Uprooted** & **Rape Removal Breakage** & **Pulling** \\  & **Pressure X\({}_{1}\)/MPa** & **X\({}_{2}\)\({}^{o}\)** & **X\({}_{3}\)/(cm\(\cdot\)s\({}^{-1}\))** & **Removal Rate Y\({}_{1}\)/\%** & **Rate Y\({}_{2}\)/\%** & **Force Y\({}_{3}\)/N** \\ \hline  
\hline \end{tabular}
\end{table} 
Table 8: Experimental program and results. \(Y_{3}\) was extremely significant (\(p<0.05\)), indicating that the regression equation had a good fitting degree. The \(R^{2}\) for \(Y_{1}\), \(Y_{2}\) and \(Y_{3}\) are 0.989, 0.980 and 0.986, respectively, indicating that more than 90% of the response values could be explained by the regression model. In summary, the key operating parameters of the clamping manipulator can be analyzed and optimized by this model, and the test has research significance. The size of the \(p\) value can indicate the significance of each regression term's influence on the regression model. In the \(Y_{1}\) regression model, the primary terms \(X_{1}\) and \(X_{2}\) had extremely significant effects (\(p<0.01\)) and \(X_{3}\) had significant effects (\(p<0.05\)), the interaction \(X_{1}\), \(X_{2}\) had significant effects (\(p<0.05\)), the square terms \(X_{1}{}^{2}\) and \(X_{2}{}^{2}\) had extremely significant effects (\(p<0.01\)) and \(X_{3}{}^{2}\) had significant effects (\(p<0.05\)). In the \(Y_{2}\) regression model, the effects of the primary terms \(X_{1}\) and \(X_{2}{}^{2}\) were highly significant (\(p<0.01\)) and \(X_{3}\) was significant (\(p<0.05\)), the interaction \(X_{1}X_{2}\) was significant (\(p<0.05\)), and the square terms \(X_{1}{}^{2}\) and \(X_{2}{}^{2}\) were highly significant (\(p<0.01\)). In the \(Y_{3}\) regression model, the effects of the primary terms \(X_{2}\) and \(X_{3}\) were highly significant (\(p<0.01\)), the interaction \(X_{2}X_{3}\) was significant (\(p<0.05\)), and the secondary term \(X_{2}{}^{2}\) was highly significant (\(p<0.01\)).