## 4 Dynamics Simulation and Configuration Optimization Method  
### Vibration Suppression Effects of Different Postures  
The configuration of the clamping robot can be divided into two parts: the position \(x_{\text{end}}y_{\text{end}}z_{\text{end}}\) and posture \(Rx RyRz\) of the flange coordinate system relative to the coordinate system \(o_{B}x_{B}y_{B}z_{B}\). Additionally, the values of the position and posture will both affect the configuration of the clamping robot. As shown in Figure 6, the gripper consists of a connecting plate, an air cylinder, two link reinforcement plates, two jaws and two central axes, in which the jaws can adjust around the central axis. Before clamping, the gripper is left open. When the configuration of the clamping robot is determined, the cylinder contracts to clamp the workpiece, and the jaws adaptively adjust the angles to fit the surfaces of the workpiece. The clamping force of the gripper on the workpiece is only related to the air pressure and cylinder performance, and will not change with the clamping position and clamping direction. When the spatial positions of the AGV and workpiece remain unchanged, the gripper can still clamp the workpiece through both the A and B directions. Apparently, the clamping robot has different configurations in the two directions of the gripper. The vibration responses of the workpiece depend on the state vector \(\mathbf{Z}_{31,0}\) of the output point \(P_{\text{m}}\), which can be written as follows:  
\[\mathbf{Z}_{31,0}=\mathbf{U}_{31,30}\mathbf{Z}_{30,31}+\mathbf{U}_{31,32}\mathbf{Z}_{32,31} \tag{21}\]  
As shown in Figure 7, when the gripper is clamping the workpiece in direction A or B, the input points of two directions are equivalent to \(P_{\text{c}}\). Additionally, \(P_{\text{c}}\) is located on the line over the output point \(P_{\text{m}}\) and the input point \(P_{\text{f}}\), and its position is constant relative to \(P_{\text{m}}\) in both directions, A and B. Moreover, the dynamics parameters of the workpiece are unchanged; thus, the transfer matrix \(\mathbf{U}_{31,30}\) is also unchanged. Furthermore, since the fixed position of the workpiece is always unique, then the transfer matrix \(\mathbf{U}_{31,32}\) is also unchanged. In this case, the vibration responses of the workpiece are only related to \(\mathbf{Z}_{30,31}\) and \(\mathbf{Z}_{32,31}\) at different clamping robot configurations. In this paper, the acceleration of the \(P_{\text{m}}\) point in the \(o_{\text{w}}x_{\text{w}}y_{\text{w}}z_{\text{w}}\) coordinate system is used to represent the vibration response of the workpiece. In addition to different \(Rx RyRz\) for the same workpiece, the configurations of the clamping robot facing the same type of workpiece with different fixed angles on the panel will also change. As shown in Figure 8, when the gripper clamping the workpiece in the B direction, the configuration of the clamping robot is constantly changing with the fixed angle of the workpiece. At this time, if the position of the AGV and the fixed stiffness of the workpiece do not change, only \(Rx RyRz\) changes in the robot configuration. The same is true for clamping direction A. For the two cases in Figures 6 and 8, the influence of different \(Rx RyRz\) on the vibration suppression effect of the clamping robot needs to be analyzed to obtain the optimal clamping configuration. Figure 6: Structure of the gripper and two clamping directions. In order to analyze and predict the vibration suppression effect of different clamping robot configurations on the workpiece, the dynamic milling force model of spiral slotting end mill is used as the input, and the instantaneous milling force in \(x_{\rm w},y_{\rm w}\), and \(z_{\rm w}\) direction is as follows:  
\[\left\{