# Optimal Design and Experiment of Manipulator for Camellia Pollen Picking
## 4 Manipulator Workspace Analysis and Simulation  
By solving the working space of the camellia-pollen-picking manipulator, the activity range of the camellia-pollen-picking manipulator in three-dimensional space can be simulated. The cloud diagram of the pollen-picking manipulator workspace is shown in Figure 7.  
Figure 6: Manipulator’s big arm and forearm stress contour. Figure 7: Cloud diagram of the pollen-picking manipulator workspace. (**a**) 3D –space cloud diagram: (**b**) X/Y –plane projection; (**c**) X/Z –plane projection; (**d**) Y/Z –plane projection. The blue part in Figure 7 is the area that the end of the camellia-pollen-picking manipulator can reach in three-dimensional space. The point-cloud distribution in the space is relatively uniform, which shows that the structure and size of the manipulator are reasonable and provide a theoretical basis for further machining the prototype. To verify whether the manipulator with the optimized structure parameters can reach the target picking point, a motion-planning experiment was carried out for the reduced-scale model manipulator used in the laboratory from the initial pose of the working state to the target picking point. The experiment was carried out with eight extreme picking points and seven other arbitrary picking points in the target picking area, as shown in Figure 8.  
After the reduced-scale model manipulator moves to the specified position, the coordinates of the end position of the manipulator are measured with a portable three-coordinate instrument of the Italian COORD3 brand EOS544 model. The measurement results are shown in Table 2.  
As can be seen from Table 2, during the experiments, the reduced-scale model manipulator reached eight extreme picking points and seven other arbitrary picking points in the target picking area for camellia pollen. The reduced-scale model manipulator can move continuously and smoothly, and thus the rationality of the optimal design of the manipulator structure can be verified [25; 26; 27]. However, during the working process of the manipulator, there is a certain positional deviation from the predetermined position. The maximum errors in the \(x\), \(y\), and \(z\) directions are 5.1 mm, 5.7 mm, and 5.1 mm, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multicolumn{3}{c}{**Theoretical Value**} & \multicolumn{3}{c}{**Measured Value**} & \multicolumn{3}{c}{**Absolute Value of Error**} \\ \cline{2-10}  & **Px** & **Py** & **Pz** & **Px\({}^{\prime}\)** & **Py\({}^{\prime}\)** & **Pz\({}^{\prime}\)** & **Ex** & **Ey** & **Ez** \\ \hline
1 & 950 & 725 & 340 & 954.4 & 730.1 & 344.8 & 4.4 & 5.1 & 4.8 \\
2 & 950 & 725 & 1700 & 947.3 & 721.5 & 1695.4 & 2.7 & 3.5 & 4.6 \\
3 & 950 & \(-\)720 & 1700 & 946.2 & \(-\)724.3 & 1704..3 & 3.8 & 4.3 & 4.3 \\
4 & 950 & \(-\)720 & 340 & 945.8 & \(-\)723.8 & 344.6 & 4.2 & 3.8 & 4.6 \\
5 & 320 & 725 & 340 & 316.2 & 722.6 & 336.5 & 3.8 & 2.4 & 3.5 \\
6 & 320 & 725 & 1700 & 317.5 & 729.4 & 1705.1 & 2.5 & 4.4 & 5.1 \\
7 & 320 & \(-\)720 & 1700 & 322.8 & \(-\)717.4 & 1695.1 & 2.8 & 2.6 & 4.9 \\
8 & 320 & \(-\)720 & 340 & 325.1 & \(-\)724.9 & 343.5 & 5.1 & 4.9 & 3.5 \\
9 & 400 & \(-\)600 & 400 & 403.5 & \(-\)604.6 & 403.5 & 3.5 & 4.6 & 3.5 \\
10 & 480 & \(-\)300 & 650 & 483.7 & \(-\)294.3 & 647.1 & 3.7 & 5.7 & 2.9 \\
11 & 640 & \(-\)200 & 900 & 636.8 & \(-\)202.9 & 895.4 & 4.6 & 2.9 & 4.6 \\
12 & 650 & 240 & 1040 & 654.1 & 243.5 & 1044.9 & 4.1 & 2.9 & 4.9 \\
13 & 680 & 300 & 1300 & 678.1 & 302.5 & 1304.2 & 1.9 & 2.5 & 4.2 \\
14 & 700 & 340 & 1530 & 704.6 & 344.2 & 1526.3 & 3.5 & 4.2 & 3.7 \\
15 & 750 & 600 & 1650 & 746.4 & 604.6 & 1646.5 & 3.6 & 4.6 & 3.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Measurement results of the end position of the pollen-picking manipulator. Figure 8: Motion-planning experiment of pollen-picking manipulator. The main reason is the position error caused by the structural parameters of each link of the manipulator due to the deviation of the processing and assembly.