## 2 Materials and Methods
### Research Tools and Assessments  
#### 2.3.1 The Range of Motion in the Lower Limb Joints During Layups Take-Off  
This study utilized high-resolution video recording equipment (Model: Sony Alpha 7R IV, resolution: 3840 \(\times\) 2160 pixels (4K), frame rate: 100 Hz) to capture athletes' layup take-off movements. The camera was positioned at the athlete's side, 5 m away, at a height of 1.2 m, and angled at 90 degrees to the ground to ensure the complete capture of the layup take-off movement [28]. During the recording process, an LED synchronization signal was used to align the timeline of the video camera with the force plate (PASCO PS-3230) to ensure data consistency [29]. During the image analysis phase, key frame images were extracted from the lowest posture before jumping, and image processing and analysis were performed using ImageJ software (Version: 1.53t). ImageJ is an open-source image processing software developed by the National Institutes of Health (NIH) [30]. The study utilized its angle measurement tool to measure the flexion angles of the hip, knee, and ankle joints (sagittal plane) and calculated their ranges of motion. The reliability and validity of the ImageJ software, according to [PERSON] et al., were evaluated in a study. The research found that ImageJ's measurement of stretch distance and movement angles exhibited high test-retest reliability [31].  
3.2 Assessment of Lower Limb Explosive Performance During Layup Take-Offs with PASCO PS-3230 Force Plate  
This study used the PASCO PS-3230 wireless dual-axis force plate (manufactured in Roseville, CA, USA) to evaluate the explosive strength of the lower limbs during take-off for a layup. The equipment was a high-precision voltage-sensing force plate equipped with four force sensors, each with a measurement range of \(\pm\)1100N and a maximum vertical resultant force capacity of 4400N [32]. Each force sensor was equipped with an overload protection capacity of 1700N, with a total vertical overload protection capacity of up to 6600N, ensuring the stability and safety of the equipment during high-intensity tests. The force plate's sampling frequency was set to 1000 Hz, generating 1000 measurements per second to capture the subtle kinetic variations at the moment of take-off during a layup. The reliability and validity of the PASCO PS-3230 wireless dual-axis force plate, according to [PERSON] et al., were evaluated in a study. The research found that the PASCO PS-3230 force plate effectively detected ground reaction forces during take-off and demonstrated excellent performance characteristics, confirming its strong reliability and validity [33].  
The participants simulated basketball layup movements on a basketball court with a solid flooring surface, stepping on a force plate to perform jump tests. The tests were repeated multiple times to ensure data accuracy. This study utilized the device to measure the following parameters: take-off time, ground reaction force (GRF), rate of force development (RFD), hang time, and jump height. To ensure data accuracy, the force plate  
\begin{table}
\begin{tabular}{c c} \hline
**Content** & **Intensity/Repetitions** \\ \hline Double-Leg Squat Jumps & Intensity: 75–80\%, repeated 8–10 times \\ \hline \multirow{8}{*}{Stretching} & 1. Hamstring stretch: bent forward and tried to touch the \\  & toes of the extended leg, holding the position for 20–30 s. \\  & 2. Hip flexor stretch: adopted a half-kneeling position with \\ \cline{1-1}  & one leg in front and one leg behind. Pushed the hips \\ \cline{1-1}  & forward and held the position for 20–30 s. \\ \cline{1-1}  & 3. Calf muscle stretch: placed hands against a wall with one \\ \cline{1-1}  & leg in front and one leg behind. Pressed the heel of the back \\ \cline{1-1}  & leg towards the ground, holding the position for 20–30 s. \\ \hline \end{tabular}
\end{table}
Table 1: _Cont._was calibrated before each test and synchronized with the timeline of the video recording equipment to integrate kinetic data.