## Materials and Methods
### 3D Motion Data Collection  
A comprehensive 3D motion analysis was conducted by employing a VICON MX40 motion capture system (Oxford Metrics Ltd., Oxford, UK) featuring a configuration of 10 cameras. The system was set at a sampling frequency of 200 frames per second to capture the smash movement patterns through accurately tracing 59 reflective markers (39 on the subject's body, 16 on the racket, 1 on the shuttlecock, and 3 on the net, respectively) [5; 29]. Calibration residuals were meticulously determined in strict adherence to the established guidelines provided by VICON, resulting in a precision level of within 1 mm. It is noteworthy to underscore that the intrinsic capabilities of motion capture technology afford substantial latitude of movement to the participants, thereby enabling the unimpeded execution of their inherent motor behaviors. Consequently, this measurement methodology exerts minimal perturbation on the participants' innate playing styles, thereby preserving the authenticity of their actions. This pivotal attribute of the motion capture methodology ensures that the participants' distinctive playing styles remain essentially unaltered throughout the experimental proceedings. The study's objective was to assess smash quality independently of return quality. Therefore, the utilization of half of a standard badminton court sufficed for the research purpose. Additionally, deploying ten cameras to focus on this reduced court area significantly enhanced the precision of 3D motion capture data. Consequently, a half-standard badminton court (6.7 m in length, 7.0 m in width, and 1.55 m in net height) was set up to mimic a real badminton play environment. The spatial dimensions of the effective 3D motion capture domain were configured to span 6.7 m in length, 6.0 m in width, and 4.0 m in height, aligning with the standard dimensions of a conventional playing field. To accurately emulate the playing environment, a net with a height of 1.55 m, adhering to the established standard net height, was meticulously positioned. The meticulous orchestration of these conditions collectively mirrored the characteristics of an actual playing milieu. In the course of the experimental trials, uniformity was maintained through the utilization of the YONEX ARCSABER 001 series racket, characterized by specific attributes including a weight range of 85 to 89 g, a length of 684 mm, and a composition primarily comprising graphite material. This choice of racket was consistently accompanied by a standard YONEX shuttlecock, exhibiting a weight span of 4.74 to 5.50 g. Ensuring methodological consistency, sixteen adhesive markers were affixed to the sporting equipment in a strategic configuration. The distribution encompassed twelve markers on the racket, distributed as a singular marker on the handle base, three markers affixed to the shaft, and eight markers allocated to the head of the racket. In a similar vein, a solitary marker was affixed to the shuttlecock, carefully placed upon the cork, while an additional three markers were positioned upon the net structure. Furthermore, each participant involved in the study was adorned with a constellation of thirty-nine spherical, reflective markers, each manifesting a diameter of 9 mm. The placement of these markers meticulously adhered to standard anatomical landmarks, a necessity in the establishment of a 15-segment (head, upper trunk, lower trunk, upper arms, lower arms, hands, thighs, shanks, and feet) biomechanical model for the smash quantification [5; 29].