## 2 Dynamic Modeling of 6R Robot System
### Simulation Verification of Dynamic Parameter Identification Model  
According to the rigid body dynamics model, Equation (49), in order to identify the mass \(m_{i}\) and the principal moment of inertia \(J_{i_{11}}^{(i)},I_{i_{22}}^{(i)},I_{i_{33}}^{(i)}\) of a single rigid body \(B_{i}\), the following parameters of the rigid body must be known. 1. The three components of the Cardano angles of \((O_{i},e_{-}^{(i)})\) relative to \((O_{0},e_{-}^{(0)})\),
2. The three components of \(F_{i}\) in \((O_{0},e_{-}^{(0)})\),
3. The three components of \(M_{i}\) in \((O_{0},e_{-}^{(0)})\),
4. The three components of the acceleration of rigid body's center of mass in \((O_{0},e_{-}^{(0)})\),
5. The three components of the angular velocity of rigid body in \((O_{0},e_{-}^{(0)})\),
6. The three components of the angular acceleration of rigid body in \((O_{0},e_{-}^{(0)})\). To simultaneously identify the dynamic parameters of all rigid bodies with one simulation (only one movement), that is, the parameters collected in this movement can be used to identify each single rigid body, it is necessary for each rigid body to generate the above parameters at the same time in this movement to ensure that the data corresponding to each discrete time is real-time for each rigid body. This is the premise that the measured parameters can be used to identify the dynamic parameters of each rigid body at the same time. To achieve the above purpose, the simulation is set to make the rigid body \(B_{1}\) move along the \(e_{1}^{(0)}\) direction (that is, the guide rail direction) with an acceleration of 2 m/s\({}^{2}\), while the joint \(O_{1}\) and the joint \(O_{2}\) rotate around the joint axis at the angular acceleration of 9.5493 rad/s\({}^{2}\) (that is, 30\({}^{\circ}\)/s\({}^{2}\)), all other joints are locked so that they do not rotate around the joint axis. Set the initial state to the static state, and the posture is shown in Figure 9, which is the posture shown in Figure 2. The simulation termination time is 2 s and the number of \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Physical Quantity** & **Length** & **Mass** & **Force** & **Time** & **Angle** & **Frequency** \\ \hline Unit & m & kg & N & s & 1 (rad) & Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The unit of each physical quantity. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Rigid Body \(B_{i}\)** & \(B_{1}\) & \(B_{2}\) & \(B_{3}\) & \(B_{4}\) & \(B_{5}\) & \(B_{6}\) \\ \hline Length (m) & 1.045 & 1.245 & 1.21 & 0.315 & 0.29 & 0.3 \\ Radius (m) & 0.5 & 0.3 & 0.2 & 0.2 & 0.2 & 0.3 \\ \(m_{1}\)(kg) & 6402.6012 & 2746.0726 & 1186.1661 & 308.7953 & 284.2877 & 661.7042 \\ \(J_{i_{11}}^{(i)}\)(kg\(\cdot\)m\({}^{2}\)) & 800.3251 & 123.5733 & 23.7233 & 6.1759 & 5.6858 & 29.7767 \\ \(J_{i_{22}}^{(i)}\)(kg\(\cdot\)m\({}^{2}\)) & 982.8126 & 416.4934 & 156.5838 & 5.6413 & 4.8353 & 19.8511 \\ \(J_{i_{33}}^{(i)}\)(kg\(\cdot\)m\({}^{2}\)) & 982.8126 & 416.4934 & 156.5838 & 5.6413 & 4.8353 & 19.8511 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Physical parameters of each rigid body \(B_{i}\). steps is 100. When the simulation is terminated, the robot posture is shown in Figure 10. The motion process generates various required parameters, and the ADAMS software is used to measure various parameters. The 6R robot system will inevitably be disturbed during the movement, which will cause errors between the measured data and the true value. To reduce the identification accuracy error caused by data error when a single set of data is used for identification, multiple sets of data can be used to identify dynamic parameters according to the mathematical model of Equation (56) to improve the accuracy and stability of the obtained parameters. Theoretically, the more data is taken, the better the identification effects, but too much data will increase the complexity and time-consuming of calculation.