## 2 Materials and Methods
### Design of the Semi-Active Prosthetic Knee  
The active and passive structures of the prosthetic knee are shown in Figure 3. The thigh connector is connected to thigh socket in the upper side. The lower side is connected with the four-bar linkage. The upper piston rod is connected with the four-bar linkage by a drive link. For the variable damping control, the provided hydraulic system (Figure 3b) had one fan rotation valve, namely designed throttle valve, to generate joint resistance for the flexion and the extension movement. The position of the fan valve plate was controlled by the motor 1. The flow resistance could be continuously adjusted from low to high values by the rotation of the fan valve plate. When the piston rod moved down during knee flexion, the oil flowed through the throttle valve and one-way valve 1a in the flexion channel. The oil could not flow through the extension channel due to the unidirectional cutoff characteristic of the one-way valve 1b. The knee flexion damping could be regulated by the position change of the fan valve plate. The steel spring was stretched during knee flexion by the displacement of the upper piston. For the knee extension, the piston rod moved up and the oil flowed through the throttle valve and one-way valve 1b in the extension channel. The oil could not flow through the flexion channel due to the unidirectional cutoff characteristic of the one-way valve 1a. The knee extension damping was also adjusted by the position change of the fan valve plate. The energy stored by stretch of steel spring was released. This could provide assistance for knee extension. For the powered mode, the throttle valve is completely open. This means the passive hydraulic damping is free. The lower piston rod is driven by the ball screw. The vertical displacement of the ball screw is controlled by the synchronous belt connected to the motor 2. When the lower piston moved up, the upper piston was pushed up and the active knee torque was provided by the four-bar linkage. A hole exists on the lower piston rod to ensure that the oil flow is not affected by the up and down motion of the lower piston rod. The detailed structure of the hydraulic system and the prototype are shown in Figure 4.  
Figure 3: The active and passive structures of the prosthetic knee. **(a)** The 3D model of the prosthetic knee; **(b)** The active and passive working principle.  
The work scheme of the semi-active prosthetic knee is shown in Figure 5. At the beginning of stance in the human gait, the heel touches the ground. The calf quadriceps need to concentric contraction to increase the center of gravity and prevent the lateral foot in the swing phase from touching the ground. The knee joint provides positive work. We connect the motor 2 with the synchronous belt to output the active torque and transfer it to the ball screw. The transmitted torque of the ball screw is controlled by adjusting the speed of the motor 2. Therefore, the torque needed by the human body to do positive work is outputted by the motor 2. When the knee joint enters the swing flexion phase, the side leg touches the ground and the hip joint begins to flex. At this time, the hydraulic damping cylinder works. The pressure between the upper and lower oil chambers of the hydraulic cylinder is changed by the position change of the fan valve plate. The real-time damping torque was provided by this operation. During the swing extension phase, the extension damping torque was provided to slow the foot movement to the initial velocity of contact with the ground. Due to the fact that the prototype is currently in the processing state, the sensor system is not completely determined. In terms of control, the design mentioned in this paper will mainly use angle sensor, IMU, and force sensor to identify the gait cycle and control the position of the rotating valve. The sensor system can consider our previous work [24].  
Figure 4: The detailed structure of the semi-active system and the prototype.