); [EMAIL_ADDRESS] (D.S. ); [EMAIL_ADDRESS] (D.W.); [EMAIL_ADDRESS] (D.C.); [EMAIL_ADDRESS] (F.L. ); [EMAIL_ADDRESS] (Z.Z. ); [EMAIL_ADDRESS] (D.J.) [PERSON]  
1 Faculty of Sports Science, Ningbo University, Ningbo 315211, China; [EMAIL_ADDRESS] (Y.W. ); [EMAIL_ADDRESS] (D.S. ); [EMAIL_ADDRESS] (D.W.); [EMAIL_ADDRESS] (D.C.); [EMAIL_ADDRESS] (F.L. ); [EMAIL_ADDRESS] (Z.Z. ); [EMAIL_ADDRESS] (D.J.) [PERSON]  
2 [PERSON]  
1 Faculty of Sports Science, Ningbo University, Ningbo 315211, China; [EMAIL_ADDRESS] (Y.W. ); [EMAIL_ADDRESS] (D.S. ); [EMAIL_ADDRESS] (D.W.); [EMAIL_ADDRESS] (D.C.); [EMAIL_ADDRESS] (F.L. ); [EMAIL_ADDRESS] (Z.Z. ); [EMAIL_ADDRESS] (D.J.) [PERSON]  
1 Faculty of Sports Science, Ningbo University, Ningbo 315211, China; [EMAIL_ADDRESS] (Y.W. ); sundong@In competitive tennis, a player can execute over 1100 strokes in a single match [6]. Among these, the forehand open-stance stroke is widely utilized for its strategic advantage in facilitating swift transitions between offensive and defensive play [7]. Effective execution of this movement relies heavily on lower limb musculature [8]. The performance of a forehand open-stance stroke is primarily influenced by lower limb stability, explosive strength, and coordinated muscle activation [9; 10; 11]. These elements impose substantial demands on neuromuscular control strategies and energy transfer efficiency [12], both of which are crucial in determining shot precision and effectiveness [13]. Studies indicate that 70-75% of stroke energy originates from the coordinated motion of the lower limbs, primarily involving the ankle-knee-hip joints of the supporting leg to ensure efficient kinetic chain transmission [14]. If the activation timing of lower limb muscles during a forehand open-stance stroke is delayed by more than 60 ms, the peak ground reaction force decreases by 18-22%, directly impairing kinetic energy transfer efficiency [15]. Furthermore, electromyographic (EMG) analysis of professional tennis players reveals that a 50 ms delay in lower limb muscle activation results in a 15% reduction in hip joint angular velocity, significantly lowering stroke speed [16]. One of the key challenges in motor control research is deciphering how the central nervous system (CNS) regulates multi-muscle coordination and adapts neuromuscular strategies accordingly [17; 18]. Differences in neuromuscular control strategies reflect the biological foundation of athletic performance [19]. Studies show that elite athletes exhibit a more refined pre-activation mechanism during stroke preparation, establishing a coordinated contraction pattern between the lower limb and core muscles. Notably, the co-activation index (CIC) between the vastus medialis and transversus abdominis in elite players can reach 0.82, whereas it is only 0.51 in amateur players [20]. This timing advantage not only improves energy transmission efficiency (by 23%) but also reduces joint oscillation (by 37%), preserving the integrity of the kinetic chain [15]. However, most existing studies focus either on muscle activation levels or timing patterns individually [21; 22], failing to examine their synergistic interactions, which limits a comprehensive understanding of motor skill control mechanisms. In recent years, non-negative matrix factorization (NMF) has gained significant attention in sports science due to its strong physiological interpretability and stability [21; 23]. It is particularly effective in analyzing multi-muscle coordination during complex movement tasks by extracting a limited number of muscle synergy modules and reducing high-dimensional EMG data into a few representative muscle coordination patterns. The non-negativity constraint ensures that extracted synergy patterns align with muscle physiology, where muscle excitations remain non-negative, reflecting realistic activation mechanisms [24].