## 2 Simulation of Bowden Cable-Fabric Force Transfer and Analysis of Lower Limb Motion
### Angle and Torque Fitting of Knee Joint  
To simulate the knee joint and lower leg movement of human walking on the experimental platform, the dynamic capture of an adult walking was carried out. The scene in this article is set as a human body walking on flat land, using a three-dimensional motion capture system (PhaseSpace, San Leandro, CA, USA), which is equipped with a high-resolution digital camera. The data on human joint motion and foot pressure were collected by the force measuring table system (Bertec FIT, Columbus, OH, USA). Figure 3 shows the motion capture of walking joints and the collection of plantar force measurements. The beginning of the gait cycle is usually defined by the maximum extension angle of the hip joint. The percentages of gait in the following graphs of the joint angles and joint torque are divided by the maximum hip joint angle, and the beginning of the gait cycle is assisted when the hip joint angle reaches the maximum. In the process of testing the walking human body, the data collected by the 3D motion capture system and the force measuring table system were input into the OpenSim V4.0 software, the musculoskeletal model was constructed, and the joint torque was calculated using the inverse dynamic  
Figure 1: Model of flexible lower extremity assisting device; 1, back strap; 2, waist strap; 3, thigh strap; 4, lower leg strap; 5, foot strap; 6, fabric; 7, fixture; 8, Bowden cable; 9, electric control box. Figure 2: In vitro experimental platform. method. In order to more clearly see the movement angle and moment of human lower limb joints in a single gait cycle, the movement of lower limb joints in a gait cycle was analyzed, and the data curve was smoothened. Figure 4 shows the curve of knee joint angle and torque change during a gait cycle. This curve is very similar to the sine function, so the next choice was to use the sine function to fit the force curve. The Cftool in MATLAB 2018b software was used to fit the knee joint angle curve, and different function types, such as the exponential function approximation, Gaussian function approximation, polynomial function approximation, and sine function approximation, were used to fit, etc. Finally, it was found that the general model Sin3 had a higher degree of fitting. Therefore, the function between the knee joint angle and time is as follows:  
\[\theta_{k}(t)=a_{1}\sin(b_{1}t+c_{1})+a_{2}\sin(b_{2}t+c_{2})+a_{3}\sin(b_{3}t+ c_{3}) \tag{1}\]  
The specific values of parameters in Formula (1) are shown in Table 1. The fitting curve of this function is shown in Figure 5. To simulate the angle of the human body during walking, a fixed knee joint motion curve and gait time was generated in the form of a leg model driven by a motor. Figure 4: Angle and torque of knee joint. (**a**) Knee angle; (**b**) knee torque. Figure 3: 3D Motion capture system and force measuring table system. Figure 4b shows that the maximum torque was at the 20% gait period, and the torque is positive between 10% and 30%. Therefore, the expected force should be maximum at the 20% gait period. The goal is to provide force only between 10% and 30%, preventing interference with the wearer's movement. A unimodal force curve starting at 10% and ending at 30% was fitted according to the torque of the knee joint. The simulation of knee joint torque converted the lower limb knee joint torque during walking to the experimental platform. Since this experiment was an in vitro experiment, the test torque on the experimental platform was set as 10% of the actual knee joint torque after consideration of factors such as the lower leg mass of the experimental platform and the actual knee joint torque. And the auxiliary efficiencies of 40%, 50%, and 60% were used to set the expected force curve. We used Formula (2) to decompose the peak force of knee torque in Figure 4b into two independent parametric sinusoids, and they represent a portion of the simplified biological knee force.