# Design and Analysis of a Planar Six-Bar Crank-Driven Leg Mechanism for Walking Robots
## 6 Results and Discussion  
The foot of a walking robot is the component that directly contacts the ground, as shown in Figure 6. With the crank's rotation, the foot follows a cyclical path relative to the walker's body, referred to as the locus. This locus is segmented into four phases: support, lift, return, and lower. During the support or stride phase, the foot maintains ground contact. In the lift phase, the foot attains its peak height above the ground while moving in the same direction with the walker's body. Finally, the foot descends and re-establishes contact with the ground. In Figure 6, the overlapping blue dots (MATLAB) and orange line (GIM) indicate a high level of agreement between the two methods. This trajectory is crucial for ensuring sufficient ground clearance during the swing phase to avoid obstacles, maintaining the robot's stability, and minimizing energy consumption by optimizing its path. Additionally, the smooth curve reduces impact forces during landing, ensuring consistent and controlled foot movements, which are vital for an efficient and reliable walking robot performance. The start and end of the stride are characterized by more pronounced curves, facilitating a controlled descent of the foot and preventing it from scraping against the ground during elevation. The smooth, continuous curve signifies harmonic motion, further emphasizing the precision required in the foot point's trajectory for the optimal walking performance of the robot. Figures 7 and 8 present the velocity and acceleration results of the foot point P in the \(x\) and \(y\) directions through a kinematic analysis of the proposed mechanism. Figure 6: Foot locus simulated using MATLAB and GIM software. In Figure 7, the velocity of the foot point P in the \(x\) direction (\(v_{px}\)) and the \(y\) direction (\(v_{py}\)) is shown. The results from the MATLAB and GIM simulations are closely aligned, with both showing similar trends across the range of \(\theta_{2}\) angles. The velocity in the \(x\) direction reaches a maximum of approximately 0.2 m/s, while in the \(y\) direction it peaks slightly above 0.2 m/s. This indicates a balanced motion in both the horizontal and vertical directions. Figure 8 depicts the acceleration of the foot point P in the \(x\) direction (\(a_{px}\)) and the \(y\) direction (\(a_{py}\)). The acceleration in the \(x\) direction reaches up to 0.25 m/s\({}^{2}\), while in the \(y\) direction it shows a significantly larger peak, going up to nearly 0.4 m/s\({}^{2}\). The alignment of the MATLAB and GIM results here again confirms the consistency and accuracy of the simulations. The maximum velocity observed from the simulations is approximately 0.2 m/s, and the acceleration range extends up to 0.4 m/s\({}^{2}\). These values suggest that the proposed mechanism can achieve moderate speeds and accelerations, which are beneficial in reducing drag forces when interacting with surfaces like water. For ground surfaces, assuming no slip, the velocity of the feet is effectively the same as the velocity of the robot, ensuring stable and consistent movement. Driving torque is a crucial design parameter that significantly impacts the locomotion performance of leg mechanisms, influencing the frequency of stroke steps and the shape of  
Figure 8: Acceleration of the foot point P in two directions: (**a**) ‘X’. (**b**) ‘Y’. Figure 7: Velocity of the foot point P in two directions: (**a**) ‘X’. (**b**) ‘Y’. strides. Analyzing the driving torque helps determine the optimized swing cycle of the leg mechanism, thereby reducing energy consumption. Figure 9 presents the torque analysis of the proposed mechanism, reflecting the maximum and minimum torque requirements of the drive cycle at the driving node. The torque ranges from approximately \(-0.12\) N\(\cdot\)m to \(0.07\) N\(\cdot\)m, indicating its energy consumption and mechanical efficiency during the motion cycle. The waveform shows that the peak torque is generated during the swing phase, particularly around the interval of 150 to 200 degrees.