# Analysis Method of Articulated Torque of Heavy-Duty Six-Legged Robot under Its Quadrangular Gait
## 2 Walking Ways of Heavy-Duty Six-Legged Robot under Quadrangular Gait
### Typical Walking Ways of Robot under Quadrangular Gait
Thus,  
\[(F_{x1}\quad F_{x2}\quad F_{x3}\quad F_{x4}\quad F_{x5}\quad F_{x6})=\left(-F _{x}^{(f_{1})}\quad-F_{x}^{(f_{2})}\quad-F_{x}^{(f_{3})}\quad F_{x}^{(f_{4})} \quad F_{x}^{(f_{5})}\quad F_{x}^{(f_{6})}\right) \tag{1}\]  
Based on Figure 2, it can be concluded that the crab-ant mixed type I and crab-ant mixed type II can be transformed from the crab type or the ant type. Generally, we all know that the rearmost leg of robot experiences the maximum normal contact force when the robot passes along a slope. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Phase**} & \multicolumn{2}{c}{**1/3 Gait**} & \multicolumn{2}{c}{**2/3 Gait**} & \multicolumn{2}{c}{**3/3 Gait**} & \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Phase**} & \multicolumn{2}{c}{**1/3 Gait**} & \multicolumn{2}{c}{**2/3 Gait**} & \multicolumn{2}{c}{**3/3 Gait**} \\  & & & & & & & & & & **Legs** & **Legs** \\ \hline \multirow{2}{*}{1} & Transfer & 1, 5 & 2, 4 & 3, 6 & Transfer & 2, 5 & 3, 6 & 1, 4 \\ \cline{2-9}  & Support & 2, 3, 4, 6 & 1, 3, 5, 6 & 1, 2, 4, 5 & Support & 1, 3, 4, 6 & 1, 2, 4, 5 & 2, 3, 5, 6 \\ \hline \multirow{2}{*}{2} & Transfer & 1, 5 & 3, 6 & 2, 4 & Transfer & 2, 4 & 3, 6 & 1, 5 \\ \cline{2-9}  & Support & 2, 3, 4, 6 & 1, 2, 4, 5 & 1, 3, 5, 6 & Support & 1, 3, 5, 6 & 1, 2, 4, 5 & 2, 3, 4, 6 \\ \hline \multirow{2}{*}{3} & Transfer & 1, 4 & 2, 5 & 3, 6 & Transfer & 2, 4 & 1, 5 & 3, 6 \\ \cline{2-9}  & Support & 2, 3, 5, 6 & 1, 3, 4, 6 & 1, 2, 4, 5 & Support & 1, 3, 5, 6 & 2, 3, 4, 6 & 1, 2, 4, 5 \\ \hline \multirow{2}{*}{4} & Transfer & 1, 4 & 2, 6 & 3, 5 & Transfer & 3, 6 & 2, 5 & 1, 4 \\ \cline{2-9}  & Support & 2, 3, 5, 6 & 1, 3, 4, 5 & 1, 2, 4, 6 & Support & 1, 2, 4, 5 & 1, 3, 4, 6 & 2, 3, 5, 6 \\ \hline \multirow{2}{*}{5} & Transfer & 1, 4 & 3, 6 & 2, 5 & Transfer & 3, 6 & 2, 4 & 1, 5 \\ \cline{2-9}  & Support & 2, 3, 5, 6 & 1, 2, 4, 5 & 1, 3, 4, 6 & Support & 1, 2, 4, 5 & 1, 3, 5, 6 & 2, 3, 4, 6 \\ \hline \multirow{2}{*}{6} & Transfer & 1, 4 & 3, 5 & 2, 6 & Transfer & 3, 6 & 1, 5 & 2, 4 \\ \cline{2-9}  & Support & 2, 3, 5, 6 & 1, 2, 4, 6 & 1, 3, 4, 5 & Support & 1, 2, 4, 5 & 2, 3, 4, 6 & 1, 3, 5, 6 \\ \hline \multirow{2}{*}{7} & Transfer & 2, 6 & 3, 5 & 1, 4 & Transfer & 3, 6 & 1, 4 & 2, 5 \\ \cline{2-9}  & Support & 1, 3, 4, 5 & 1, 2, 4, 6 & 2, 3, 5, 6 & 1, 3, 4, 6 & Support & 1, 2, 4, 5 & 2, 3, 5, 6 & 1, 3, 4, 6 \\ \hline \multirow{2}{*}{8} & Transfer & 2, 6 & 1, 4 & 3, 5 & Transfer & 3, 5 & 1, 4 & 2, 6 \\ \cline{2-9}  & Support & 1, 3, 4, 5 & 2, 3, 5, 6 & 1, 2, 4, 6 & Support & 1, 2, 4, 6 & 2, 3, 5, 6 & 1, 3, 4, 5 \\ \hline \multirow{2}{*}{9} & Transfer & 2, 5 & 1, 4 & 3, 6 & Transfer & 3, 5 & 2, 6 & 1, 4 \\ \cline{2-9}  & Support & 1, 3, 4, 6 & 2, 3, 5, 6 & 1, 2, 4, 5 & Support & 1, 2, 4, 6 & 1, 3, 4, 5 & 2, 3, 5, 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Higher-stable swing sequences of legs under quadrangular gait. Figure 2: Four kinds of typical walking ways of heavy-duty six-legged robot under quadrangular gait: (**a**) crab type; (**b**) crab–ant mixed type I; (**c**) ant type; and (**d**) crab–ant mixed type II. Then, the joints of the rearmost leg have the maximum values of torques in the homogeneous joints. According to the structure of leg and four kinds of typical walking ways, it can be concluded that the large static torques of the hip joint and knee joint can be obtained when the crab-type quadrangular gait is selected to overpass a slope. Thus, the support phase of the crab-type quadrangular gait can be only analyzed for gaining the torques of the hip joints and knee joints.