## 3 Results and Discussion
### Optimal Parameters Considering the Excitation Source, Rod Thickness and Damping  
As mentioned in Sections 3.1-3.3, the three factors of excitation source, Moment 3, the thickness of end g bar and the damping value of driving rod 1 have the greatest influence on the end displacement amplitude. Therefore, when comprehensively exploring the optimal design of the excitation source, rod thickness and damping value on the end vibration of the welding robot actuator, these three factors are used in the central composite design for optimal design.  
This test adopts three factors and two levels (the three factors are Moment 3, end g thickness and damping value of driving rod 1, respectively), and a set of 20 central composite design (CCD) tests are performed. The resulting data are shown in Table 8.  
The maximum end harmonic response displacement amplitude of the actuator of the controllable mechanism welding robot occurs at multiple frequencies of 16 Hz, 18 Hz, 25 Hz and 43 Hz. Taking the vibration end amplitude displacement value of 0 mm as the optimization goal, the optimization results obtained through the response optimizer are shown in Figure 22.  
The optimization results of Figure 22 are detailed in Table 9.  
As can be seen from Figure 22 and Table 9, when the target displacement amplitude of the actuator end is 0 mm at 16 Hz, 18 Hz, 25 Hz and 43 Hz, the optimal result is achieved when the values of Moment 3, swing arm g thickness and driving rod 1 damping are 1300 N\(\cdot\)mm, 8.7735 mm and 0.050, respectively, the amplitude displacement value of the actuator end reaches the optimal value, and the displacement values at 16 Hz, 18 Hz, 25 Hz and 43 Hz are 0.0879 mm, 0.01243 mm, 0.0983 mm and 0.0000 mm, respectively.  
The displacement amplitude response curve of the execution end obtained after optimization is shown in Figure 23.  
As shown in Figure 23, when the excitation frequency is 25 Hz, the amplitude of the execution end is the largest with a value of 0.0744 mm.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Order** & **Moment 3** & **Thickness of** & **Damping Value of** & **Moment 3** & **Thickness of** & **Damping Value of** \\  & **(N\(\cdot\)mm)** & **End g (mm)** & **Driving Rod 1** & **Order** & **(N\(\cdot\)mm)** & **End g (mm)** & **Driving Rod 1** \\ \hline
1 & 1300 & 8 & 0.0500 & 11 & 1100 & 9 & 0.0260 \\
2 & 1300 & 8 & 0.0020 & 12 & 1100 & 9 & 0.0260 \\
3 & 900 & 10 & 0.0500 & 13 & 1100 & 10.633 & 0.0260 \\
4 & 900 & 10 & 0.0020 & 14 & 773.4 & 9 & 0.0260 \\
5 Figure 23: Amplitude response curve of the terminal surface after comprehensive optimization.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Response** & **Fitting Value** & **Fitting Value Error** & **95\% Confidence Interval** & **95\% Prediction Interval** \\ \hline Deformation (16 Hz) & 0.0879 & 0.0257 & (0.0297, 0.1461) & (\(-\)0.0227, 0.1985) \\ Deformation (18 Hz) & 0.0124 & 0.0078 & (\(-\)0.00518, 0.03004) & (\(-\)0.02103, 0.04588) \\ Deformation (25 Hz) & 0.0983 & 0.0244 & (0.0430, 0.1535) & (\(-\)0.0067, 0.2032) \\ Deformation (43 Hz) & 0.0000 & 0.0119 & (\(-\)0.0270, 0.0270) & (\(-\)0.0513, 0.0513) \\ \hline \hline \end{tabular}
\end{table}
Table 9: Optimization graph results of coupling effects design.  
Figure 22: Optimization diagrams of coupling effects design.