# 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
### Support Phase Analysis of Crab-Type Quadrangular Gait  
The crab-type quadrangular gait is employed to overpass a slope for the heavy-duty six-legged robot, as shown in Figure 3. The three kinds of typical working conditions of the support phase are gained based on the crab-type quadrangular gait, the rotation angle \(\theta_{i}{{}^{\prime}}\) of \(0^{\circ}\), and Table 1: working condition I, II and III. In working condition I, the support phase contains legs 1, 3, 4 and 6, as shown in Figure 4. In working condition II, the support phase includes legs 1, 2, 4 and 5, or legs 2, 3, 5 and 6, as shown in Figure 5. In working condition III, the support phase comprises legs 1, 2, 4 and 6, or legs 2, 3, 4 and 6, or legs 1, 3, 4 and 5, or legs 1, 3, 5 and 6, as shown in Figure 6.  
Based on Figures 4-6, the working condition III can be viewed as a combination by the working conditions I and II. The state effects of the support phases in Figure 6a,b are equal to each other; they are defined as working condition III-1. The state effect of the support phase in Figure 6c is same as that in Figure 6d; they are named working condition III-2. Figure 4: Working condition I of support phase: (**a**) support phase involving legs 1, 3, 4 and 6; and (**b**) equivalent support phase of legs 1, 3, 4 and 6. Figure 3: Simplified 3-D model of robot using crab-type quadrangular gait to pass slope. A variable \(w\), referring to the typical working conditions I, II, III-1 and III-2, is introduced for analyzing the articulated torques of robot. The active forces from the ground to the foothold of leg \(i\) are, respectively, defined as \(F_{\textit{avri}}\), \(F_{\textit{avri}}\) and \(F_{\textit{vri}}\) in three directions. The static torques of the hip joint and knee joint of the leg \(i\) are, respectively, regarded as \(M_{\textit{whi}}\) and \(M_{\textit{wiki}}\). \(F_{\textit{euraj}}\), \(F_{\textit{euraj}}\) and \(F_{\textit{euraj}}\) represent the active forces of equivalent leg \(j\) (\(j\) =1,..., 6) from the ground in three directions. \(M_{\textit{ewhi}}\) and \(M_{\textit{euraj}}\) are the static articulated torques of equivalent leg \(j\) for the hip joint and knee joint. Based on the above analysis, the rearmost leg in the support phase has the maximum torques of the hip joint and knee joint when the rotation angle \(\theta_{i}^{\prime}\) is zero. The static torques of the hip joint and knee joint of leg \(i\) mainly depend on \(F_{\textit{zi}}\) and \(F_{\textit{xi}}\). \(F_{\textit{yi}}\) can be approximately ignored because of little influence on solving the torques of joints. To make it easier to explain the analysis of the static articulated torques, it is to assume that the homogeneous joints in the same phase have the equal rotation angles of the joints. The bottom surface of bearing platform keeps parallel with the slope. To discuss the analysis method of the torque of joint in this paper, some parameters of robot are assumed. For example, the mass of the robot is supposed to be 250 kg. The mass of the rated load is presumed to be 50 kg. The total mass of one leg is assumed to be 25 kg, including the mass \(m_{\rm c}\) of one coxa, the mass \(m_{\rm t}\) of one thigh and the mass \(m_{\rm s}\) of one chin. Meanwhile, \(m_{\rm c}\) includes the mass of the driving device and actuating device for one abductor joint. \(m_{\rm t}\) contains the mass of the driving devices  
Figure 5: Working condition II of support phase: **(a)** support phase involving legs 1, 2, 4 and 5; and **(b)** support phase involving legs 2, 3, 5 and 6. Figure 6: Working condition III of support phase: **(a)** support phase involving legs 1, 2, 4 and 6; **(b)** support phase involving legs 2, 3, 4 and 6; **(c)** support phase involving legs 1, 3, 4 and 5; and **(d)** support phase involving legs 1, 3, 5 and 6.  
and actuating devices for one hip joint and one knee joint.