## 4 Simulation Results
### Simulation Results  
The results from the simulation are shown in Figures 8-10. In Figure 8a, we denote the relative position and orientation of the visual servo. (b) Denotes the joint angles of CMM and (c) denotes the joint deflections of CMM. Figure 9 denotes the deflection of the end of the CMM, which is described in the frame of the base of the MMMS. Assuming that the orientation of the EEF and object frames slowly vary with respect to time, we use the ZYX Euler angle to represent the orientations. From Figure 8a, it is seen that, under the visual servo control, the tracking errors are reduced at a relatively steady velocity in the long-range motion and converge to zeros when reaching the desired berth position within one vibration cycle. A low-frequency vibration appeared in the manipulator system due to the rather low natural frequency (0.007 Hz). As shown in Figure 8c, the joint of the CMM mostly moves within \(\pm 0.1^{\circ}\), which is the boundary of the backlash. The joint motion of the CMM will reverse at the backlash boundaries due to a higher stiffness, which will work beyond the backlash. Even though the backlash is small, the deflection of the CMM is nonnegligible, which can be seen in Figure 10. However, with the backlash compensation, the deflection of the CMM converges to zeros when the EEF reaches the desired target. One can see that, acceleration during the start-up period and deceleration near the target period will stimulate the deflection in the backlash. From Figure 9, it can be seen that, at the beginning of the acceleration period, the motion of the EMM inevitably causes a disturbance to the base, leading to the joint oscillation of the CMM in the backlash, the base vibration based on the FTS works at this period due to the dead zone limitation of the FTS. The joint trajectory of EMM is performed with the joint two fixed inverse kinematics, as shown in Figure 8b.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Manipulator** & **Property** & **Mass (kg)** & \(\mathbf{I_{x}(kg\cdot m^{2})}\) & \(\mathbf{I_{y}(kg\cdot m^{2})}\) & \(\mathbf{I_{z}(kg\cdot m^{2})}\) \\ \hline \multirow{8}{*}{CMM} & Joint 1 & 59.5 & 4.322 & 1.438 & 4.121 \\  & Joint 2 & 53.6 & 2.468 & 1.329 & 2.267 \\  & Link 1 & 108.4 & 2.782 & 384.756 & 384.327 \\  & Link 2 & 98.7 & 4.527 & 341.956 & 339.871 \\  & Joint 6 & 53.6 & 2.468 & 1.329 & 2.267 \\  & Joint 7 & 53.5 & 4.322 & 1.438 & 4.120 \\  & EEF & 100.5 & 3.347 & 9.731 & 9.833 \\ \hline \multirow{8}{*}{EMM} & Joint 1 & 31.7 & 0.366 & 0.366 & 0.332 \\  & Joint 2 & 31.7 & 0.366 & 0.366 & 0.332 \\  & Link 1 & 74.7 & 0.881 & 70.702 & 70.554 \\ \cline{1-1}  & Link 2 & 57.5 & 0.730 & 45.040 & 44.918 \\ \cline{1-1}  & Joint 6 & 31.7 & 0.366 & 0.332 & 0.355 \\ \cline{1-1}  & Joint 7 & 31.7 & 0.366 & 0.334 & 0.358 \\ \cline{1-1}  & EEF & 28.9 & 0.52 & 0.527 & 0.421 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Mass properties of the CMM/EMM.  
Figure 8: Base deflection and base energy. (**a**) The relative position and orientation of the visual servo. (**b**) The joint angle of EMM. (**c**) The joint deflection of CMM.  
Figure 10: The end position and orientation of CMM.  
Figure 9: The base force/torque sensor of EMM.