## 4 Dynamics Simulation and Configuration Optimization Method
### Vibration Suppression Effects of Different Postures
\begin{array}{l}F_{x}=\sum\limits_{j=1}^{N}\sum\limits_{l=1}^{M}\left(- \mathrm{d}F_{\rm{r}jl}\cos\phi_{jl}-\mathrm{d}F_{\rm{r}jl}\sin\phi_{jl}\right) \\ F_{y}=\sum\limits_{j=1}^{N}\sum\limits_{l=1}^{M}\left(-\mathrm{d}F_{\rm{r}jl} \cos\phi_{jl}+\mathrm{d}F_{\rm{r}jl}\sin\phi_{jl}\right)\\ F_{z}=\sum\limits_{j=1}^{N}\sum\limits_{l=1}^{M}\mathrm{d}F_{\rm{a}jl}\end{array} \right. \tag{22}\]  
where \(jl\) represents the \(l\)th cutting microelement on the cutting blade \(j\), \(\phi_{jl}\) is the angular displacement of the microelement, while \(\mathrm{d}F_{\rm{r}jl}\), \(\mathrm{d}F_{\rm{r}jl}\), and \(\mathrm{d}F_{\rm{a}jl}\) are the forces on the feed, normal, and axial direction, respectively. The milling parameters in Table 1 are adopted to simulate the vibration suppression effects of different \(RxRyRz\) at three heights, and the variation laws of the overall workpiece responses are shown in Figure 9a-c, respectively. where \(x_{\rm end}=1.8\) m, \(y_{\rm end}=0\) m, and \(z_{\rm end}=1.0\) m, \(1.2\) m, \(1.4\) m. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Feed Rate** & **Rotational Speed** & **Milling Width (mm)** & **Milling Depth** \\
**(mm/s)** & **(r/min)** & **Milling Width (mm)** & **(mm)** \\ \hline
2.5 & 6000 & 8.0 & 1.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Milling parameters. Figure 8: Configuration change in the clamping robot under different workpiece fixed angles. Figure 7: The simplified diagram of the workpiece. The three axes in Figure 9 represent the angles of \(Rx\), \(Ry\), and \(Rz\), and the color represents the amplitudes of the responses, which are determined by the acceleration response legend on the right side of the figure. Each figure is composed of six faces, of which the middle three groups of intersecting faces are the responses of different configurations when \(Rx=0^{\circ}\), \(Ry=0^{\circ}\), and \(Rz=0^{\circ}\), and the three faces at the edge are the responses when \(Rx=45^{\circ}\), \(Ry=-45^{\circ}\), and \(Rz=-45^{\circ}\). From the face corresponding to \(Ry=0^{\circ}\) in Figure 9a, it can be seen that as \(Rz\) gradually changes from \(-45^{\circ}\) to \(45^{\circ}\), the responses tend to gradually increase, indicating that the vibration suppression effect of the clamping robot is gradually reduced. In addition, it can be seen from the face of \(Rx=45^{\circ}\) and \(Rz=-45^{\circ}\) that when \(Ry>0^{\circ}\), the responses are greater than \(Ry<0^{\circ}\). Moreover, Figure 9b,c presents the same pattern of response changes. As can be seen from the simulation results of different heights, the overall responses of the workpiece show a downward trend as the height increases from 1.0 m to 1.4 m. Additionally, the maximum values of the overall responses at the three heights are approximately 55 m/s\({}^{2}\), 54 m/s\({}^{2}\), and 53 m/s\({}^{2}\), respectively. The maximum change range of responses throughout the simulation interval is 7 m/s\({}^{2}\). Furthermore, the change ranges caused by \(Rx\) and \(Rz\) are significantly smaller than that of \(Ry\). This is because the conversion around \(Rx\) is mainly completed by the robot's fourth and sixth joints, which will not produce a large configuration change. Moreover, the \(RxyRz\) of the robot are almost symmetrical when rotating around the positive and negative directions of \(Rz\), and the differences of vibration suppression effect of the corresponding \(RxyRz\) are minor. In contrast, the configuration change around \(Ry\) is large and asymmetric, and responses also change greatly. It can be seen from Figure 9 that when Ry is greater than 0, the responses are significantly greater, which indicates that the vibration suppression effect corresponding to the clamping direction B in Figure 7 is better than the clamping direction A.