## 4 Results and Discussions
### Optimization of Leg Length Ratio  
After obtaining the optimal value for the leg mass ratio \(m_{per}\) and hip mass ratio \(m_{hyper}\), the mechanism parameters of the bipedal robot are set as \(l_{hyper}=0.2\), \(m_{per}=0.3\), and \(m_{hyper}=0.3\), and the length ratio of body to leg, \(l_{hyper}\), is analyzed.  
Figure 10 shows the variation in the full-range energy consumption \(COT_{ave}\) when \(l_{hyper}\) varies in the range of [0, 0.6]. The \(COT_{ave}\) increases with an increase in \(l_{hyper}\). \(COT_{ave}\) of 0.049126 is observed at \(l_{hyper}=0.3\). When \(l_{hyper}\) varies in the range [0, 0.1], \(COT_{ave}\)  
Figure 8: \(COT\) versus \(m_{hyper}\) with different walking speeds (\(V\)) and step length (\(D\)): (**a**) \(V=0.3\); (**b**) \(V=0.4\); (**c**) \(V=0.5\); (**d**) \(V=0.6\).  
Figure 9: Optimal step length and \(COT\) with \(m_{hyper}=0.3\): (**a**) optimal step length; (**b**) optimal \(COT\).  
consistently remains at a low level. It can be observed that the bipedal robot exhibits higher average efficiency in walking when the distance between the center of mass of the hip and the leg is closer.  
As shown in Figure 11, the energy consumption \(COT\) corresponding to different step lengths is depicted for the range of V = {0.3, 0.4, 0.5, 0.6}, with respect to the variation in \(l_{hipper}\). The \(COT\) increases with an increase in \(l_{hipper}\) when the walking speed remains constant and the step length is short (Figure 11c: \(V\) = 0.5 and \(D\) = 0.4). At longer step lengths, the \(COT_{ave}\) first decreases and then increases with an increase in \(l_{hipper}\), and the overall trend changes steadily. In Figure 11a, when \(V\) = 0.3 and \(D\) = 0.8, the minimum energy consumption value \(COT\) is 0.024812 for \(l_{hipper}\) = 0.3.  
Figure 11: \(COT\) versus \(l_{hipper}\) with different walking speed (\(V\)) and step length (\(D\)): (**a**) \(V\) = 0.3; (**b**) \(V\) = 0.4; (**c**) \(V\) = 0.5; (**d**) \(V\) = 0.6.  
Figure 10: The variation in \(COT_{ave}\) when \(l_{hipper}\) varies in the range of \([0,0.6]\).  
With an increase in \(l_{bper}\), the walking energy consumption significantly increases for a shorter step length; it first decreases and then increases when the step length is long. Therefore, with a decreasing value of \(l_{bper}\), the optimized configuration exhibits a more stable walking gait.  
Figure 15 shows the variation in the optimal step length with the walking speed when \(l_{bper}=0.4\) and the \(COT\) values correspond to the optimal step length. The optimal step length increases with an increase in walking speed.  
The above research results show that reducing the ratio of leg mass in the total mass, concentrating the mass of the entire body at the hip joint, reducing the ratio of the upper  
Figure 14: \(COT\) versus \(l_{bper}\) with different walking speeds (\(V\)) and step lengths (\(D\)): (**a**) \(V=0.3\); (**b**) \(V=0.4\); (**c**) \(V=0.5\); (**d**) \(V=0.6\).  
Figure 15: Optimal step length and \(COT\) with \(l_{bper}=0.4\): (**a**) optimal step length; (**b**) optimal \(COT\).  
body to total body length, and increasing the height of the leg center of mass can enhance the performance of the optimized mechanism.