## 2 Methods
### Data Collection and Analysis
#### 2.5.3 Musculoskeletal Model  
A Kistler three-dimensional force platform was used to synchronously collect the ground reaction force (GRF) at a frequency of 1000 Hz, and kinetic data reduction was carried out using Visual 3D software. The musculoskeletal modeling in OpenSim (Simtk.org) software was used to generate the motion files and meet the subject scaling requirements. A general musculoskeletal model with 23 degrees of freedom (DOF) driven by 92 Hill-type muscle-tendon units was constructed, and it was scaled according to the anthropometric data of each subject to make the model highly match the physical characteristics of the  
Figure 4: Schematic diagram of the classification of joint coordination.  
Figure 3: Data collection workflow diagram.  
subjects. The model was optimized using the Residual Reduction Algorithm (RRA), and its mass properties and kinematic parameters were finely adjusted. The Computed Muscle Control (CMC) algorithm was used to determine muscle excitation, and a forward dynamic simulation of the participants' landing kinematics was carried out. Joint reaction force (JRF) analysis was carried out in OpenSim to obtain the net knee joint JRFs. Finally, the muscle forces and knee joint JRFs obtained were input into the sagittal plane knee joint model developed by [PERSON] and [PERSON] to accurately calculate the ACL force (\(F_{ACL}\)).  
The specific process is as follows (Figure 5) [19]:  
1. Calculation of Tibiofemoral Contact Force (\(F_{tf}\)) \[F_{\parallel}=F_{tf}\cdot\cos\varphi_{tf}-F_{pat}\cdot\cos\varphi_{pat}-F_{ham} \cdot\cos\varphi_{ham}-F_{gas}\]  
Parameter Explanation:  
\(F_{\parallel}\): Net axial force.  
\(F_{tf}\): Tibiofemoral contact force, which is the solution target of this formula.  
\(\varphi_{tf}\): Tibial posterior slope angle. According to previous literature, it is set to 8.5\({}^{\circ}\).  
\(F_{pat}\): The sum of all quadriceps muscle strength estimates.  
\(\varphi_{pat}\): The tendon angle of the patellar tendon force (quadriceps) depending on the knee flexion angle.  
\(F_{ham}\): The sum of all hamstring muscle strength estimates.  
\(\varphi_{ham}\): The tendon angle of the hamstring depending on the knee flexion angle.  
\(F_{gas}\): The sum of the medial and lateral gastrocnemius muscle strength estimates.  
2. Calculation of the Anterior-Posterior Shear Force on the Knee Ligament (\(F_{ligament}\)) \[F_{AP}=F_{tf}\cdot\sin\varphi_{tf}+F_{pat}\cdot\sin\varphi_{pat}-F_{ham} \cdot\sin\varphi_{ham}+F_{ligament}\]  
Parameter Explanation:  
\(F_{AP}\): Net anterior-posterior (AP) shear force.  
Figure 5: Sagittal plane knee model angles.  
\(F_{ligament}\): The anterior-posterior shear force on the knee ligament, which is the solution target of this formula.
3. Calculation of ACL Force (\(F_{ACL}\)) \[F_{ACL}=N(F_{100N}+F_{0}(\theta_{Rnee}))\] Parameter Explanation: \(N\): Proportional coefficient. \(F_{100N}\): The ACL force reported when a 100 N anterior tibial force is applied and the corresponding knee joint angle is \(\theta_{Rnee}\). \(F_{0}\): The ACL force reported when no anterior tibial force is applied and the corresponding knee joint angle is \(\theta_{Rnee}\). \(\theta_{Rnee}\): Knee joint angle.