## 2 Materials and Methods
### Dynamics Modeling and Analysis of Multifunctional Tracked Vehicle
#### 2.2.3 Analysis Details Related to the Loading of a Single Bee Frame  
To conduct vibration analysis of a bee frame, one bee frame was placed in a loading box made of stainless steel with a slot spacing of 485 mm. The bee frame was made of wood, and its length was 480 mm, loaded with a margin of 2.5 mm on each side of the dismantling panels in the loading box. As the tracked vehicle moves, the bee frame will shake inside the loading box and come into contact with the grooved surface. Owing to material limitations in RecurDyn, the stiffness coefficient was used as a contact parameter for the wood-iron contact surface, while the elasticity coefficient was empirically set to approximately one-thousandth of the stiffness coefficient. Table 2 shows the stiffness contact coefficients of different materials in RecurDyn. Vibrations of the bee frame inside the loading box were calculated using the relative coordinate difference. The difference between the center of mass of the bee frame A and the center of mass of the loading box B was used as the basis of calculation in the simulation. The change in center of mass displacement on each axis was used to represent the oscillation of the bee frame in the loading box. Figure 7 shows the bee frame when it is loaded in the loading box. The D function was used to calculate the relative coordinates, where \(DX\), \(DY\), and \(DZ\) denote the differences in the coordinates along the X, Y, and Z directions, respectively. Let us consider direction \(DX\) as an example. Equation (2) is the general relative coordinate calculation formula in the simulation. According to this equation, any change in \(A.CM\) and \(B.CM\) in the X-direction can be considered relative to \(C.CM\). \[DX(A.CM,B.CM,C.CM) \tag{2}\]  
where \(A.CM\) and \(B.CM\) denote the centers of mass of objects A and B, respectively, and \(C.CM\) denotes the reference coordinate system for the change in center of mass. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Properties** & **Clayey Soil** & **Dry Sand** & **Upland Sandy Loam** \\ \hline Terrain Stiffness \(k_{c}\) (kN/\(m^{n+1}\)) & 0.41710 & 0.00048 & 0.03740 \\ Terrain Stiffness \(k_{\varphi}\) (kN/\(m^{n+2}\)) & 0.02190 & 0.00077 & 0.00100 \\ Exponential Number \(n\) & 0.50000 & 1.10000 & 1.10000 \\ Cohesion \(c\) (kpa) & 0.00410 & 0.00100 & 0.00330 \\ Shearing Resistance Angle \(\phi\) (\({}^{\circ}\)) & 13.0000 & 28.0000 & 33.7000 \\ Shearing Deformation Modulus \(k\) & 25.0000 & 25.0000 & 25.0000 \\ Sinkage Ratio & 0.05000 & 0.05000 & 0.05000 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Physical property of various soils [21; 22]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Steel** & **Aluminum** & **Bronze** & **Oak Wood** & **Plastic** & **Rubber** \\ \hline
**Steel** & 108,786 & 54,955 & 80,559 & 11,210 & 2636 & 25 \\ \hline
**Aluminum** & - & 36,763 & 46,690 & 10,182 & 2575 & 25 \\ \hline
**Bronze** & - & - & 63,963 & 10,819 & 2614 & 25 \\ \hline
**Oak Wood** & - & - & - & 5909 & 2177 & 25 \\ \hline
**Plastic** & - & - & - & - & 1334 & 25 \\ \hline
**Rubber** & - & - & - & - & - & 13 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: RecurDyn stiffness contact coefficient table. 2.2.4. Analysis Details of Box Fully Loaded with Bee Frames and Fully Loaded with Beehives  
Considering the complexity and duration of analysis, the vibration of the bee frame inside the hive was analyzed by conducting a single-frame experiment. Vehicle safety performance was determined by analyzing its stability when fully loaded with bee frames. Figure 8a shows the vehicle dynamics model when the vehicle is fully loaded with bee frames. Meanwhile, Figure 8b shows the vehicle dynamics model when the vehicle is fully loaded with beehives. In actual application, it is necessary to secure the beehives by using fastening ropes to ensure they are not dropped during operation. However, fixation relationships were used instead of fastening ropes in the dynamics analysis.