## 4 Displacement Analysis of Bowden Cable-Fabric Transmission
### Experimental Verification and Result Analysis  
In order to verify the effectiveness and accuracy of the Bowden cable-fabric force transfer control based on friction/displacement compensation, experiments were conducted according to the experimental platform shown in Figure 2. In the experiment, a 48 V DC power supply (Mingwei, LRS-400-48) was used to power the servo motor (Pulse Tower Intelligence, RD-X6). A 24 V DC power supply (Mingwei, LRS-800-24) supplied power to the DC brushless motor (Times Superstar 57 BL, 75S10-230) at the knee joint. The servo motor is directly controlled by the Single Chip Micyoco (Wildfire, Sunny STM32F407 IG7); the DC brushless motor is controlled by the SCM and a brushless motor drive board (ZM-6505A). In addition, the DC brushless motor is connected to the reducer (Times Superstar, PX6-57-1:20) to more accurately simulate knee joint movement. The servo motor outputs the auxiliary force through the Bowden cable and fabric to the lower leg. In the process of force transmission, there are internal friction losses of the Bowden cable and friction losses between the fabric and the clothing at the knee joint. The tension sensor (constant distance sensor, HYLY-019) collects the force signal and inputs it into the SCM through the analog-to-digital conversion module (Wildfire, AD7192 PC). The PC is connected to the SCM through the serial port as the upper computer, displaying the data collected by the tension sensor and processed by the SCM. The compliance and accuracy of the control are judged by the data of the start and end force sensors. The end force sensor data are only used as reference information to verify the following effect of the control system and do not directly participate in the system as a feedback quantity. The tension information of the end of the control system is calculated by injecting the tension value of the start force sensor and the joint angle value into the force transfer model. The actual motion displacement of the Bowden cable-fabric is returned by the motor encoder output value. The in vitro Bowden cable-fabric force transfer experimental platform is shown in Figure 14, in which Figure 14 is the overall picture of the experimental platform, Figure 14b is the range of lower leg model movement, and Figure 14c is the schematic diagram of friction at the knee  
Figure 13: The control effect of the impedance control. joint model. Figure 14b shows that the lower leg can be rotated 90\({}^{\circ}\). In this experiment, there is only one lower leg model, and it is at the position of 0\({}^{\circ}\); another leg model is added to indicate the limit position. Figure 14c simulates the friction of clothing and fabric during movement at the knee joint. The tension curve with a peak value of 40 N was selected to conduct the experiment. The information of the end force sensor was recorded for verification and compared with the simulation. The results are shown in Figure 15.  
Figure 14: In vitro Bowden cable–fabric force transfer experimental platform. (**a**) The whole of the experimental platform; (**b**) the range of lower leg model movement; (**c**) schematic diagram of friction at knee joint model. Figure 15: Comparison of actual and simulated output with a peak value of 40 N. (**a**) Comparison of output forces; (**b**) comparison of force errors. By comparing the simulation and experiment when the peak value was 40 N, it was found that the internal friction causes a small error when the motor starts loading; Because the force transfer model is related to acceleration and strain rate, the force will produce a small sudden change at the peak. Because the end force sensor is cantilever-mounted, taking into account the weight of itself and the wire rope, the output tension will remain in the range of less than 1 N jitter when the expected tension is zero. In order to test the force tracking effect of the force transmission system under different force peak values, experiments with peaks of 50 N and 60 N were selected at the same time.