## 5 Results and Discussion  
The motion state of 3D revolute joint B with different joint clearances of the SCARA robot during the assembly of the wine box base is analyzed in this section. Assuming that all arms of the SCARA robot are rigid, and the rest of the kinematic pairs are perfect, Table 2 lists the geometric dimensions and quality attributes of each arm. Table 3 lists the simulation parameters of the SCARA robot. Table 4 lists the clearance dimensions of 3D revolute joint B. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Arms**} & \multirow{2}{*}{**Length [mm]**} & \multirow{2}{*}{**Mass [kg]**} & \multicolumn{5}{c}{**Characteristics of Inertia [kg m2]**} \\ \cline{3-8}  & & & \(\mathbf{J_{ss}}\) & \(\mathbf{J_{yy}}\) & \(\mathbf{J_{ss}}\) & \(\mathbf{J_{ss}}\) & \(\mathbf{J_{ss}}\) & \(\mathbf{J_{ss}}\) \\ \hline Arm 1 & 329 & 5.78 & 2.569 & 3.080 & 2.537 & \(2.002\times 10^{-5}\) & 2.384 & \(0.007\times 10^{-5}\) \\ Arm 2 & 275 & 4.35 & 1.346 & 0.981 & 1.298 & \(4.871\times 10^{-4}\) & \(-2.258\times 10^{-4}\) & \(-4.22\times 10^{-4}\) \\ Arm 3 & 350 & 3.03 & \(2.087\times 10^{-2}\) & \(2.087\times 10^{-2}\) & \(4.726\times 10^{-5}\) & \(1.005\times 10^{-6}\) & \(3.307\times 10^{-6}\) & \(0.489\times 10^{-6}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Geometric dimensions and quality attributes of the robot arms. Figure 8: The specific action process of the SCARA robot. When there are clearances of different sizes in joint B, the movement trajectory of the end effector of the SCARA robot will change to different degrees. Figure 9a-c show the displacement change curves of the geometric center of the end effector along the \(X\), \(Y\), and \(Z\) axes, respectively, in the \(O-XYZ\) coordinate system during the completion of an operation cycle of the robot. In Figure 9, the motion trajectory of joint B with no clearance is shown by the red curve, the motion trajectory of joint B with clearance \(C_{a}=C_{r}=0.2\) mm is shown by the blue curve, and the motion trajectory of joint B with clearance \(C_{a}=C_{r}=0.5\) mm is shown by the magenta curve. As can be seen in Figure 9, when joint clearance is present, the displacement trajectory will fluctuate slightly. The displacement trajectory when joint clearance is 0.2 mm has smaller fluctuation than that when joint clearance is 0.5 mm. Figure 10a-c show the velocity variation curves of the geometric center of the end effector of the SCARA robot along the \(X\), \(Y\), and \(Z\) axes, respectively, in the frame \(O-XYZ\). Through comparison, it can be found that the joint clearance of different sizes has different influences on the velocity, and the joint clearance of 0.5 mm has a greater influence on the velocity. \begin{table}
\begin{tabular}{l c} \hline
**Case** & **Clearance Dimension (mm)** \\ \hline Case 1 & \(C_{a}=C_{r}=0.2\) \\ Case 2 & \(C_{a}=C_{r}=0.5\) \\ \hline \end{tabular}
\end{table} 
Table 4: Clearance dimension of joint B.  
Figure 9: Displacement curves of the end effector along the \(X\), \(Y\), and \(Z\) axes. (**a**) The displacement curve along the \(X-\)axis direction in the frame \(O-XYZ\); (**b**) the displacement curve along the \(Y-\)axis direction in the frame \(O-XYZ\); and (**c**) the displacement curve along the \(Z-\)axis direction in the frame \(O-XYZ\). According to Figures 9 and 10, the size of joint clearance has a decisive influence on the kinematics analysis of the SCARA robot. The displacement and velocity fluctuations of the robot are also different as a result of the different clearances. The smaller the clearance, the smaller the fluctuation of displacement and velocity will be and the better the smoothness of the robot's movement will be, and the defective rate on the production line will gradually increase. According to Figure 7, the projection of the sucker in the _XOY_ plane is a square. Figure 11 studies the path of the end effector by studying the path of the geometric center of the square.