*2.1. Participants*

Fifteen male collegiate badminton players (age: 21.1 ± 2.2 years; height: 1.81 ± 0.04 m; weight: 72.5 ± 8.4 kg; years of badminton training: 8.9 ± 3.5 years) were recruited for the study. All participants were free from any injuries within the previous 3 months and did not take part in any high-intensity training or competitions during the two days prior to the experiment. All participants were informed of the procedures and requirements of the test, and written informed consent was obtained from each participant. In addition, a questionnaire about anthropometrics, health status, injury history, and physical activity level was completed. To minimize the potential e ffect of footwear, participants wore badminton shoes and socks of the same brand and series. The study was approved by the ethics committee of Beihang University (No. BM201900077).

#### *2.2. Experimental Protocol*

The test was conducted on a simulated badminton court of the biomechanics laboratory. Prior to the test, participants performed a familiarization of the forehand forward lunge and the study protocol, which included 10 min warm-up; tests of heart rate (HR), blood lactate (BL), and Borg 6–20 rating of perceived exertion (RPE); and a fatigue protocol. Considering the dependency of fatigue on the task being undertaken [23,24] and the aim of this study, repeating the forehand forward lunge until participants reached the state of exhaustion was proposed as the fatigue protocol [16]. More specifically, a forehand forward lunge cycle was defined as lunging from the starting position using the dominate limb with a sliding step, landing on the force plate positioned at the right front, hitting one shuttlecock, and then moving backward to the starting position. The degree of fatigue was estimated by values of HR [15], BL, and RPE [25], which were measured before (pre) and immediately after (post) the fatigue protocol.

A system of 9 optoelectronic cameras (Oqus 300+ Series, Qualisys AB®, Gothenburg, Sweden) and a Kistler mobile multi-component force plate (Type 9286A, Kistler, Kistler Instrument AG, Winterthur, Switzerland), integrated into the walkway, were used to record the marker position and ground reaction forces, and synchronized at 200 and 1000 Hz, respectively. According to the color atlas of skeletal (CAST) landmark definitions of the lower leg [26], twenty-eight reflective markers (diameter: 18 mm) were attached to the lower extremity for dynamic motion capture. The locations included anterior superior iliac spines, posterior superior iliac spines, thigh (markers cluster), shank (markers cluster), calcaneus, hallux, and 2nd and 5th metatarsal head of the left and right lower extremity. The markers on calcaneus, hallux, and 2nd and 5th metatarsal head were placed on the corresponding anatomical location of the badminton shoes.

#### *2.3. Data Analysis*

The kinematic and force data were obtained by the optical motion-capture system and then exported and saved as c3d files. Then, the hip, knee, and ankle joint angles, moments, power, and ground reaction force (GRF) were calculated using visual 3D software (V5, C-Motion, Bethesda, MD, USA). The raw kinematic data were filtered with a low-pass (Butterworth) filter with frequency of 20 Hz [10]. The threshold of the vertical ground reaction force (vGRF) data was set as 10 N.

The stance phase, from initial contact (heel strike) to final lift-off from the force-plate by the dominant limb, was determined by the vGRF value. During this phase, there were three vGRF peaks, namely, the initial impact peak (PF1) for heel strike transient, the secondary impact peak (PF2) for impact loading, and the third impact peak (PF3) for drive-off. Based on the classification of previous studies [10,20,21], five periods can be clearly identified in the stance phase: (I) initial contact (from heel strike to PF1); (II) impact loading (from PF1 to PF2); (III) weight acceptance (from PF2 to peak knee joint flexion angle (PAK)); (IV) pre drive-off (from PAK to PF3); and (V) drive-off (from PF3 to lift-off from ground). In addition, the fatiguing process was divided into four stages according to the slope of the HR–time curve. Six continuous lunging motions were assessed at the end of each stage, and the kinematic and kinetic data of three lunge motions were then averaged and normalized for further statistical analysis.

During the stance phase, the motion of lower extremity joints, particularly the knee, occurs primarily in the sagittal plane. This contributes to the major knee joint biomechanical characteristics in badminton research [10,21]. Based on the previous literature linked to the lunge in badminton [10,17–21,27], we analyzed the impact peak; duration of five sub-stance phases; hip, knee, and ankle joint initial contact angles; durations to peak angle; ranges of motion (RoM); peak angles; moments; and power in the sagittal plane.

#### *2.4. Statistical Analysis*

All variables of the fatiguing process were calculated during four sub-stages. The kinetic data were normalized by body weight. All discrete variables were reported as mean ± standard deviation (SD), and examined for normality using a Shapiro–Wilk test prior to statistical analysis. One-way repeated measures ANOVA was used for the analysis of the influence of fatigue on the related parameters and discrete biomechanical data. Paired *t*-tests were performed to identify the differences. All statistical procedures were performed with SPSS 25 (IBM SPSS Statistics for Window, IBM Corp., NY, USA). Additionally, the waveform data of joint angles, moments, and power in the sagittal plane were analyzed (paired *t*-test) and plotted using one-dimensional statistical parametric mapping (SPM (1D) (https://spm1d.org/)) in MATLAB (R2014b, Mathworks, Inc., Natick, MA, USA). In addition, prior to statistical analysis, normality tests were performed for the waveform data with SPM (1D). The statistical significance level was set at 0.05.
