## 4 Results and Discussion
### Gait Characteristics  
The effect of MCPSS on the gait characteristics are investigated in this section. The gait characteristics include the stride period, the stride length, the average horizontal speed, and the duty factor in this study. The relation of every gait characteristic with MCPSS is analyzed at the low, medium, and high horizontal speeds, respectively. The stride period is the duration of a complete period. It can be obtained by calculating the time difference between two continuous periods at the Poincare section, as shown in Figure 6a. When the horizontal speed is low, the stride period gets shorter first until \(\lambda=0.4\) and then increases, and the changes remain small. When the horizontal speed is medium and high, the shorter distance between MCPSS and hip joint causes a monotonic increase of stride period, and this trend gets very obviously when MCPSS is near the hip joint. For example, the stride period as MCPSS being at the hip joint is 44%, 28%, and 15% than that as MCPSS being at the geometric center of spinal segment at the high, medium, and low horizontal speeds, respectively. These so longer stride periods are more beneficial to leg-orientation control for the following step. The stride length can be calculated by the horizontal movement distance of the spinal joint in a whole period. It can be seen from Figure 6b that the stride length keeps increasing as MCPSS moves from the spinal joint towards the hip joint, and the increasing trend gets more obviously gradually. In particular, the effect of MCPSS on the stride length becomes more significant as speed increases. For example, stride length corresponding to MCPSS being at the hip joint is 14.8%, 36.24%, and 50.32% than that with MCPSS being at the spinal joint at the low, medium, and high speeds, respectively. The  
Figure 6: Relations between MCPSS with gait characteristics including the stride period (**a**), the stride length (**b**), the average horizontal speed (**c**), and the duty factor (**d**). The red circle, green triangle, and blue quadrilateral correspond to the low, medium, and high horizontal speeds, respectively. stride length corresponding to MCPSS being at the hip joint is 1%, 6%, and 8.5% than that with MCPSS being at the spinal joint at the low, medium and high speeds, respectively. Adjusting MCPSS towards the hip joint is favorable for faster quadruped bounding. The average horizontal speed can be obtained easily by dividing stride length and stride period, as shown in Figure 6c. It can be found that the average horizontal speed maintains a small increase as MCPSS moves from the spinal joint towards the hip joint at all speeds. The average horizontal speed corresponding to MCPSS being at the hip joint is about 7.2%, 2.7%, and 1.2% higher than that corresponding to MCPSS being at the spinal joint at the low, medium and high speeds, respectively. Although the stride length increases obviously, but the increasing amount of the average horizontal speed is always small on the whole, which is probably due to the obviously increased stride period. These findings indicate that the effect has a light influence on the average horizontal speed of quadruped bounding at all speeds. The duty factor is defined as the ratio of the duration of leg contacting with the ground to the whole stride period. The smaller duty factor is more beneficial to faster motion and better acceleration performance. Figure 6d shows the effect of MCPSS on the duty factor of leg at the low, medium, and high horizontal speeds, respectively. The anterior and posterior legs are found to have the same duty factor due to the asymmetric structure of the quadruped robot. So, only the effect of MCPSS on the anterior leg is presented. It can be seen that the duty factor with respect to different MCPSS show a single peak at all speeds. MCPSS being at peaks of duty factor are all near the geometric center of spinal segment.