## 4 Simulation Test of the Grouser Effect
### Design of the Simulation Experiment  
#### 4.3.1 The Full Factorial Experimental Design  
According to the structure of the reconfigurable wheel-crawler integration walking mechanism designed above, the track shoe's length was determined to be 129 mm. According to the research results of [PERSON], it was determined that the ratio of the thickness of the rectangular grouser to the length of the track shoe should be between 0.1 and 0.3, so the parameter \(\lambda\in\) [0.1, 0.3] was determined. Since the ratio of the grouser's height to the track shoe's width is rarely more than 0.2 in practice, the grouser's height was set to 5 mm to 25.6 mm, according to the design formula for the track shoe's pitch  
\[l=(1.75\sim 2.3)\sqrt[4]{G}\]  
where \(G\) is the total weight of the robot itself and the load. Because of the combination of its weight and the design load of the reconfigurable wheel-crawler robot, the track pitch \(l\) was selected to be 12 mm to 20 mm. The maximum speed of the robot is 3 km/h. When the robot moves in the triangular crawler mode, the driving mode is changed from the direct drive of the main shaft to the main shaft driving the chain to the driving wheel, and the driving wheel is used to drive the track. Affected by the size of the driving wheel, the maximum moving speed of the robot is 0.893 km/h in the triangular track mode. In order to ensure the quality of the test, 20% and 60% of the maximum moving speed are respectively selected as the minimum moving speed and the maximum moving speed of the simulation test, which are about 0.18 km/h and 0.54 km/h. To further study the effects of four parameters, namely the track shoe's pitch \(l\), the grouser's height \(h\), the ratio \(\lambda\) of the grouser's thickness to the track shoe's length, and the moving speed \(v\) of the crawler robot, on the traction of the track shoe, a complete factorial test was designed according to the literature [24]. The response quantities were \(l\), \(h\), \(\lambda\), and \(v\), and the three levels of the variables (low, medium, and high) are represented by \(-1\) \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Component** & **Quantity** & **Parameters** & \\ \hline \multirow{3}{*}{Driving wheel} & \multirow{3}{*}{1} & Number of Teeth & 15 \\  & & Base Circle Radius/mm & 21.3844 \\  & & Pitch Circle Radius/mm & 22.3844 \\  & & Inner Flange Radius/mm & 26 \\  & & Wheel Radius/mm & 23.5 \\ Induction wheel & 2 & Inner Flange Width/mm & 35 \\  & & Total Width/mm & 45 \\  & & Wheel and Hub Width/mm & 50 \\ Road wheel & 12 & Wheel Radius/mm & 13 \\  & & Hub Width/mm & 30 \\  & & Pin Radius/mm & 1.65 \\  & & Track Link Left Length/mm & 13 \\ Track shoes & Determined by width & Left Pin Height/mm & \(-10.2\), 3 \\  & & Track Link Height/mm & 6 \\  & & Grouser Width/mm & 129 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the main components of the walking mechanism. \begin{table}
\begin{tabular}{c c} \hline \hline
**Definitions** & **Parameters** \\ \hline Terrain Stiffness (\(k_{c}\))/kN\(\cdot\)m\({}^{-(n+1)}\) & \(3.7389\times 10^{-2}\) \\ Terrain Stiffness (\(k_{p}\))/kN\(\cdot\)m\({}^{-(n+1)}\) & \(1.0425\times 10^{-2}\) \\ Exponential Number (\(n\)) & \(1.1\) \\ Cohesion (\(c\))/kPa & \(3.3\times 10^{-3}\) \\ Shearing Resistance Angle/\({}^{\circ}\) & \(33.7\) \\ Shearing Deformation Modulus/MPa & \(25\) \\ Sinkage Ratio & \(1.9\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the soil pavement. 0, and 1, respectively. The specific values assigned are shown in Table 3. To ensure the accuracy of the test, according to the horizontal distribution of the parameter \(\lambda\), in this experiment, a track shoe with a width of 12 mm was used as a benchmark to carry a 100 kg car body. When the track shoe's width was 16 mm, the weight of the loaded car body was 42.3 kg. When the track shoe's width was 20 mm, the weight of the loaded car body was 27.5 kg.