## 4 Simulation and Experiment of the Standard Workpiece
### Experimental Measurement of the Centroid of the Standard Workpiece  
The moment of inertia of the standard workpiece was measured 20 times via the measurement system to reduce the changes in the results of the centroid determination caused by sensor deviation. The experimental results are shown in Figure 5, and the three curves represent the measurement values of sensors \(A\), \(B\), and \(C\), respectively. According to Equation (21), we can obtain the average values from the \(A\), \(B\), and \(C\) sensors, which are 8.612 kg, 9.252 kg, and 9.252 kg, respectively, and the average values are used as the final experimental data. The comparison of the centroid of the standard workpiece between the simulation and experimental results is shown in Table 8.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mass (kg)** & **Adams Simulation Coordinates (mm)** & **Solidworks Simulation Coordinate (mm)** & **Deviation (mm)** \\ \hline \(P_{A}=8.880\), & \(x_{s}=-0.032\), & \(x_{s}=-0.032\), & \(\Delta x_{s}=0\) \\ \(P_{B}=8.886\), & \(y_{s}=0.026\), & \(y_{s}=0.032\), & \(\Delta y_{s}=0.006\) \\ \(P_{C}=8.881\) & \(z_{s}=154.989\) & \(z_{s}=154.995\) & \(\Delta z_{s}=0.006\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: Simulation measurement results of the centroid of the standard workpiece in adams.  
Figure 5: Standard workpiece mass data at three points.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Mass (kg)** & **Experimental Value (kg)** & **Theoretical Value (kg)** & **Deviation between Experiment (kg)** & **Experimental Coordinate (mm)** & **Solidworks Theoretical Coordinate (mm)** & **Deviation (mm)** \\ \hline \(P_{A}\) & 8.612 & 8.880 & \(0.268\) & \(x_{s}=0\), & \(x_{s}=-0.032\), & \(\Delta x_{s}=0.032\) \\ \(P_{B}\) & 9.252 & 8.886 & \(-0.366\) & \(y_{s}=4.720\), & \(y_{s}=0.032\), & \(\Delta y_{s}=4.688\) \\ \(P_{C}\) & 9.252 & 8.881 & \(-0.371\) & \(z_{s}=159.663\) & \(z_{s}=154.995\) & \(\Delta z_{s}=4.688\) \\ \hline \hline \end{tabular}
\end{table}
Table 8: The comparison of the centroid of the standard workpiece between simulation and experimental results.  
It can be determined from Table 8 that there are deviations between the experimental and theoretical results in the actual measurement. The main factors that cause these deviations are parts processing deviation, assembly deviation, and weighing sensor deviation. Table 3 shows that the deviation of the weighing sensor is \(\pm 0.05\%\). It is assumed that the deviations are mainly affected by the weighing sensors in the measurement system, and the maximum deviation of the centroid in the \(ox\)-axis direction can be expressed as:  
\[\Delta x_{\max}=\left(1.0005P_{\mathrm{C}}x_{2}-0.9995P_{B}x_{1}\right)/m \tag{22}\]  
When \(P_{\mathrm{C}}=P_{B}=8.88\) kg, \(x_{1}=x_{2}=100\sqrt{3}\) mm, and hence \(\Delta x_{\max}=0.057\) mm, and \(\Delta y_{\max}=0.067\) mm. Table 8 shows that the measurement accuracy in the \(ox\)-axis direction meets the design requirements. According to the principle of moments, the value of the weighing sensors increases as the three points approach the coordinate origin in the direction of the \(oy\)-axis. Table 8 indicates that the experimental coordinates \((y_{1},y_{2},y_{3})\) are \(y_{1}>200\) mm and \(y_{2}=y_{3}<100\) mm. The mass of each millimeter in the \(OA\), \(OB\), and \(OC\) directions is \(q=8.88/200=0.0444\) kg/mm, and therefore, the positions of the actual weighing sensors in the \(oy\)-axis direction are \(y_{1}=200+0.268/0.0444=206\) mm and \(y_{2}=y_{3}=100-0.37\times 0.5/0.0444=96\) mm, respectively. After compensation, the actual position of the centroid is (0, \(-0.09\)), and the deviations are \(\Delta x_{s}=0.032\), \(\Delta y_{s}=0.041\), and \(\Delta z_{s}=0.041\), respectively. The results show that the deviations meet the requirements of precision.