# 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  
To conveniently execute the analysis of the articulated torques, the electrically driven heavy-duty six-legged robot is called the heavy-duty six-legged robot for short. The mechanism of robot and the structure of leg are shown in Figure 1. Every leg of the robot has three joints, including an abductor joint, hip joint, and knee joint. The axes of the abductor joints follow the direction of \(z\)-axis. The axes of the hip joints and knee joints run parallel to the \(y\)-axis. Based on Figure 1, it can be concluded that the mass of robot is mainly undertaken by the hip joints and knee joints. The maximum walking speed can be achieved by the abductor joint. Thus, the drive devices and actuating devices need to output large articulated toque for the hip joints and knee joints, and to output large rotating speed for the abductor joints. In Figure 1, the abductor joint, hip joint, and knee joint are, respectively, defined as \(A_{i}\), \(H_{i}\), \(K_{i}\) (\(i=1,\,\ldots,\,6\)). The lengths of the coxa, thigh, and shin, respectively, set as \(l_{c}\), \(l_{t}\) and \(l_{s}\). The included angle between the coxa of leg \(i\) and the thigh of leg \(i\) is defined as \(\beta_{i}{}^{\prime}\) (\(i=1,\,\ldots,\,6\)). \(\beta_{i}\) (\(i=1,\,\ldots,\,6\)) is regarded as the included angle between the coxa of leg \(i\) and the shin of leg \(i\). The relations between \(\beta_{i}{}^{\prime}\) and \(\beta_{i}\) are \(0^{\circ}\leq\beta_{i}{}^{\prime}\leq\beta_{i}\leq 90^{\circ}\). The body coordinate system of robot is set as \(\sum_{\text{B}}\); it locates at the center of body. The gravity vector and the principal moment of the robot are, respectively, defined as \(F_{\text{B}}\) and \(M_{\text{B}}\). The abductor joint coordinate system of leg \(i\) contains \(z_{1}^{(i)}\) axis, \(x_{1}^{(i)}\) axis, and \(y_{1}^{(i)}\) axis. The \(z_{1}^{(i)}\) axis is parallel to the \(Z_{\text{B}}\) axis. The \(x_{1}^{(i)}\) axis keeps parallel with the coxa of leg \(i\). The leg \(i\) lies in the plan \(z_{1}^{(i)}x_{1}^{(i)}\). The foot coordinate systems \(\sum_{o_{i}}\) and \(\sum_{f_{i}}\) of leg \(i\) are, respectively, parallel to the body coordinate system \(\sum_{\text{B}}\) and the abductor joint coordinate system of leg \(i\). \(\sum_{\text{G}}\) expresses the coordinate system of ground. Four kinds of typical waking ways under the quadrangular gait can be obtained for the heavy-duty six-legged robot (Figure 2). In Figure 2, the straight lines \(l_{1}\), \(l_{2}\) and \(l_{3}\) are orthogonal to the relevant axes of abductor joints. \(\theta_{i}{}^{\prime}\) and \(\theta_{i}\) (\(i=1,\,\ldots,\,6\)) are defined as the rotation angles of the abductor joint under the crab type and ant type walking ways, respectively. Figure 1: Electrically driven heavy-duty six-legged robot: (**a**) mechanism; and (**b**) structure of leg. One period of the quadrangular gait contains three steps: 1/3 gait, 2/3 gait and 3/3 gait (it represents the last 1/3 gait). When the stability and articulated torques are not considered for the heavy-duty six-legged robot, the sum of swing sequences of the legs is 720 kinds under the quadrangular gait. Whereas, when the robot traverses a slope, it is necessary to consider the stability and articulated torques. The number of the support phase legs should be two for the rear and front legs, respectively. Then, the total swing sequences of the legs are 36 kinds. Based on the configuration of robot, 18 kinds of the higher-stable swing sequences of the legs can be obtained under the quadrangular gait to pass a slope (Table 1). Based on Figures 1 and 2a, the expressions of the tangential forces of feet can be gained for legs 1, 2, 3, 4, 5 and 6 when the value of \(\theta_{i}^{\prime}\) is zero.