## 4 Results and Discussions
### Optimization of Gait  
Under different mechanism parameters, i.e., \(m_{per}\), \(m_{hyper}\), \(l_{hyper}\), and \(l_{hyper}\), bipedal robots walking at various walking speeds and step lengths have varying energy consumption requirements. Based on the human body structure parameters and practical aspects of robot design, this section focuses on studying the walking gait features of bipedal robots based on the analysis above; the bipedal robots are set as \(m_{per}=0.3\), \(m_{hyper}=0.3\), \(l_{hyper}=0.15\), and \(l_{hyper}=0\). The push-off impulse \(P_{push}\) and minimum ground reaction force \(N_{min}\) under different step lengths and walking speeds are determined. The minimum ground support force refers to the minimum vertical support force exerted by the ground on the bipedal robot throughout the swing phase. When the support force is less than zero, the robot's legs are off the ground. Figure 15(a) shows that the \(P_{push}\) increases with an increase in walking speed and step length. As shown in Figure 15(b), throughout the swing phase, for small walking speeds, the \(N_{min}\) decreases with an increase in step length. The \(N_{min}\) increases with an increase in step length when the walking speed is large. It is also observed that for moderate walking speed, the \(N_{min}\) remains relatively constant (Figure 16(b), V = 0.3, 0.5, and 0.6). According to optimal mechanism parameters, Figure 16(b) shows the variation in hip joint torque \(\tau_{hip}\) corresponding to different step lengths under the condition of fixed walking speed. The hip joint torque exhibits positive values only during the initial phase of the swing phase. And thereafter, it remains at zero throughout the walking motion. Under the same walking speed, the hip joint torque \(\tau_{hip}\) required for cyclic walking gait decreases with an increase in step length. The ankle joint torque has no effect during motion on flat ground and remains at 0. In this model, the hip joint torque serves as the primary driving force during the swing phase, and it only exists at the beginning of the gait. On the other hand, in the push-off phase, ankle joint torque is the sole driving force in this model, and it only exists when the gait is about to end. Figure 17 shows that when walking with a short step length, a smaller push-off impulse is adequate to successfully complete the swing of the stance leg. The duration of the swing phase is relatively short, so the swing leg needs to generate a larger torque by the hip to complete the swing quickly. As the step length increases, a larger push-off impulse is necessary to enable the swing of the stance leg during the swing phase. At this point, the duration of the swing phase increases, and the swing leg only needs a smaller torque to complete the swing. At the same walking speed, for longer step lengths, the required hip joint torque is smaller, and the push-off impulse is larger during  
Figure 16: (**a**) \(P_{\text{push}}\) at different walking speeds and step lengths; (**b**) \(N_{\text{min}}\) at different walking speeds and step lengths. the swing phase. By comparing with the former study, the above common features can be identified [36; 37]. Therefore, based on the analysis in this paper, the following design recommendations can be derived. In designing the walking gait of a bipedal robot, the swing phase should provide a forward hip joint torque to drive the swing of the swing leg, and at the moment the swing leg leaves the ground, a push-off impulse is provided to complete the ankle joint to push off. These coordinated actions are performed to accomplish the entire walking motion, leading to the subsequent transition to the next step of the cycle. Figure 17: The variation in \(\tau_{hip}\) corresponding to different step lengths under the condition of fixed walking speed. (\(V=0.5\), \(D=0.3\)-\(0.9\)); (a) \(D=0.3\); (b) \(D=0.5\); (c) \(D=0.7\); (d) \(D=0.9\).