# Analysis Method of Articulated Torque of Heavy-Duty Six-Legged Robot under Its Quadrangular Gait
## 5 Applications and Experiments  
Based on the analysis method of the static articulated torques in this article and the real data parameters of robot, the prototype of electrically driven heavy-duty six-legged robot is developed. Its climbing experiments are executed, as shown in Figure 25. The maximum walking speed of the prototype is only 0.1 m/s on the flat terrain, which is slow. Thus, it can be considered that the walking speed has no influence on the analysis of the articulated torques when the robot climbs the maximum slope under the low walking speed. The walking experiments of the robot can be employed to check whether the theoretical analysis and simulation of static articulate torque are available or not. If the prototype of electrically driven heavy-duty six-legged robot can successfully traverse the maximum slope, the analysis method of articulated torque in this article can be viewed as reasonable. This method is suitable for analyzing articulated torque when the heavy-duty six-legged robot walks by the quadrangular gait.  
When the crab-type quadrangular gait is employed to pass the maximum slope for the heavy-duty six-legged robot, the distance is 350 mm from the underside of the bearing platform to the slope. The swing sequences of legs in one period are legs 3 and 6 in the 1/3 gait, legs 1 and 4 in the 2/3 gait, and legs 2 and 5 in the last 1/3 gait. Due to the large mass of the heavy-duty six-legged robot, it is necessary to increase the stability of robot when it passes the maximum slope. Thus, the initial rotation angles of the abductor joints are set as 10\({}^{\circ}\) for legs 1, 3, 4 and 6.  
Although the data of the articulated torques are not collected because there are no torque sensors in the robot, the generalized forces of feet can be discretely collected by the six-dimension force  
Figure 25: Climbing maximum slope experiments of robot under crab-type quadrangular gait.  
sensors of the feet. The generalized force curves are shown in Figure 26. To keep the real data of the generalized forces, the generalized force curves are not smoothed. In Figure 26, the generalized force curves exhibit little perturbations. Two main reasons can be illustrated as follows. First, the rubber slabs and steel meshes are installed on the slope for enhancing the adhesion forces of the robot's feet. They produce little deformation when the robot walks. Second, the quadrangular gait leads to the statically indeterminate problem. One leg may bear the small or big normal contact force in the short or long time. Although the generalized force curves present partial perturbations, they still have the much higher value in use.  
The feet of legs 1, 3, 4 and 6 undertake the \(y\)-direction forces due to their abductor joints of \(10^{\circ}\). Although the \(y\)-direction forces lead to the torques of abductor joints, the values of articulated torques are smaller. The torques of the hip joints and knee joints can be estimated based on the generalized force curves of feet and corresponding poses of the robot. Then, it is found that the values of articulated  
Figure 26: Generalized force curves of feet: (**a**) leg 1; (**b**) leg 2; (**c**) leg 3; (**d**) leg 4; (**e**) leg 5; and (**f**) leg 6.  
torques are in the allowable range. Based on Figure 26, it can be concluded that the torques of feet are much small in the directions \(x\) and \(y\) and approximate zero in the direction \(z\). This conclusion is consistent with the actual working conditions.  
In addition, when the crab-type quadrangular gait is used to transit the maximum slope for the heavy-duty six-legged robot, it is found that the all joints can work normally. The braking phenomenon does not occur because the driving devices and actuating devices cannot provide the enough output torques. The robot can independently overpass the maximum slope. Therefore, the results of experiments can prove that the analysis method of the articulated torque is reasonable in this article.