## 1 Introduction  
Badminton is one of the most globally practiced racket sports, with over 200 million participants worldwide [1]. Its inclusion in the 1992 Olympic Games significantly elevated its competitive profile, contributing to a steady rise in both amateur and professional players [2]. As a physically demanding sport, badminton is characterized by rapid multidirectional movements, explosive jumps, and frequent direction changes, all of which place substantial stress on the lower extremities [3]. Epidemiological studies indicate that 58-92.3% of injuries in badminton occur in the lower limbs, primarily affecting the knee and ankle joints [4]. The sport's high physical demands, with peak heart rates reaching 190.5 beats/min and an average of 173.5 beats/min over a 28 min match duration, further emphasize the need for effective injury prevention strategies [5]. Given the intense nature of badminton footwork, footwear design must optimize shock absorption, energy return, and stability to reduce excessive loading on the lower limbs and mitigate injury risk. [PERSON] et al. [6] divide the development of sport shoes into three stages: the past, the present, and the future. Research on some sports, including badminton, only began to emerge during the later part of the present stage. With the development of sports science and the broad use of and research on shoes in sport field, badminton shoes gradually became attractive to sport scientists, especially movement scientists [6; 7]. Proper footwear is particularly crucial for competitive badminton players, who rely on precise foot placement, dynamic balance, and efficient movement execution to reach the shuttlecock and maintain stability during rapid exchanges [8; 9]. While rigorous training plays a fundamental role in performance, appropriate shoe design enhances biomechanical efficiency, supporting foot stability while reducing excessive joint loading. Research has established that footwear design parameters influence lower-limb biomechanics, affecting joint stability, energy transfer efficiency, and injury susceptibility [7]. Key features such as forefoot bending stiffness (resistance to metatarsophalangeal joint flexion), torsional rigidity (a shoe's resistance to longitudinal axis rotation, critical for ankle stability during multidirectional movements), lateral-wedge hardness (stiffness of the midsole's lateral margin), midsole hardness, and heel curvature are known to modulate shock attenuation, movement coordination, and ground reaction forces (GRFs) [10; 11; 12]. For instance, increased forefoot bending stiffness has been shown to reduce foot torsional motion and knee adduction, potentially lowering the risk of medial knee loading injuries [10]. Similarly, moderate torsional stiffness optimizes ankle stability, reducing knee abduction angles during sidestep cutting, which is crucial for anterior cruciate ligament (ACL) injury prevention [11]. Despite extensive research on footwear biomechanics in sports such as running and basketball, badminton-specific shoe modifications remain relatively underexplored. [PERSON] [13] identified key functionalities of general court shoes, including pronation control, adequate cushioning, and optimal traction. However, badminton shoes require additional optimizations to accommodate the sport's unique demands, such as rapid directional changes, high-impact landings, and explosive acceleration [2]. These requirements indicate that badminton footwear must be further specialized beyond traditional court shoe designs to provide enhanced stability, injury protection, and energy return. Additionally, the interactions between different shoe design elements, such as midsole thickness and forefoot bending stiffness, are still not fully understood, emphasizing the need for further biomechanical research [14]. Gender-specific differences in badminton footwear requirements also warrant greater attention.