## 4 Dynamics Analysis
### Dynamics Modeling  
The prototype machine works in a harsh environment underground, the working conditions are complex, and the structure of the prototype machine model is also relatively complex. In order to facilitate problem solving, the longitudinal model of the walking mechanism is simplified, and the prototype machine adopts rubber tracks, which is inconvenient for carrying out dynamics analysis, so the tracks are viewed as a section of the track plate connected together, and in accordance with the dynamics modeling theory and method, the discrete body dynamics modeling method is adopted, and the tracks are concentrated into a mass block. Other structures of the travel system are simplified in the longitudinal plane such as the drive wheel, guide wheel, support wheel, track frame, half shaft, driven gear, active gear, drive shaft and motor, etc. The following assumptions are made to simplify the dynamic model of the prototype travel system for easy analysis:  
1. The MSES virtual prototype driving system passes through the same ground conditions on both sides of the tracks;
2. There is longitudinal symmetry of the prototype driving system, body, etc., to the center of mass;
3. The parts of the driving system of the prototype ignore their elastic variations, and the mass of each part is concentrated at the center of each part;
4. The driving system dynamics is described by a rigid system with spring stiffness and damping stiffness at the joints of the parts;
5. The track plates are of the same specification, with the same elastic properties, linear properties, stiffness coefficients and damping coefficients, and the ground attachment coefficient and sliding friction coefficient to the tracks are unchanged. Based on the above analysis, the longitudinal 14-degree-of-freedom dynamics model of the prototype driving system was established, as shown in Figure 10.  
In this figure, I, II, III and IV represent the driving wheel, guide wheel, front supporting wheel and rear supporting wheel, respectively. \(M\) is the driving moment. \(m_{1},\ m_{2},\ m_{3},\) and \(m_{4}\) are the centralized mass of the lower supporting track of the crawler travel system, respectively. \(x_{1},\ x_{2},\ x_{3},\ \text{and}\ x_{4}\) are the longitudinal vibration displacement of the lower supporting track of the crawler travel system, respectively. \(k_{1},\ k_{2},\ k_{3},\ \text{and}\ k_{4}\) are the stiffness coefficients of the lower support track of the crawler travel system, respectively. \(c_{1},\ c_{2},\ c_{3},\ \text{and}\ c_{4}\) are the damping coefficients of the lower support track of the crawler travel system, respectively. \(m_{5}\) is the centralized mass of the upper support track of the crawler travel system. \(x_{5}\) is the longitudinal vibration displacement of the upper support track of the crawler travel system. \(k_{5}\) and \(k_{6}\) are the stiffness coefficient. \(c_{5}\) and \(c_{6}\) are the damping coefficients of the upper support track of the crawler travel system. \(m_{6},\ m_{7},\ m_{8},\ m_{9},\ \text{and}\ \ m_{10}\) are the masses of the half-shaft, driven gear, active gear, drive shaft and crawler frame, respectively. \(x_{6},\ x_{7},\ x_{8},\ x_{9},\ \text{and}\ x_{10}\) are the longitudinal vibration displacement of the half-shaft, driven gear, active gear, drive shaft and crawler frame, respectively. \(\theta_{1},\ \theta_{2},\ \theta_{3},\ \text{and}\ \theta_{4}\) are the turning angles of the driving wheel, guide wheel, front support wheel and rear support wheel, respectively. \(k_{e}\) and \(c_{e}\) are the meshing stiffness and damping coefficient between the driving wheel and the track, respectively. \(k_{7}\) and \(c_{7}\) are the stiffness coefficient and damping coefficient between the driving wheel and the half-shaft, respectively.