## 4 Discussion  
This study examines the characteristics of lower-limb muscle synergies during the open-stance forehand stroke in tennis players of different skill levels. It also compares the muscle activation patterns of elite and amateur players at various movement phases. The results indicate significant differences in muscle synergy between the two groups. Elite players demonstrate a more stable and optimized activation pattern, whereas amateurs exhibit greater variability in activation timing, intensity, and muscle group distribution. During the BS phase, the activation patterns of Syn1 and Syn2 in elite players are superior to those of amateurs. Notably, Syn2 activation is significantly higher in the mid-BS phase (56.2-60.4%) (\(p\) < 0.05). This suggests that elite players utilize their lower limb muscles more effectively for stable support and power preparation, enhancing stroke efficiency. In Syn1, elite players primarily rely on small distal muscles (LTA) for stability control while adjusting lower-limb posture through RBF. In contrast, amateurs exhibit a more dispersed activation pattern, relying more on core muscles (LES, RES) and larger muscle groups (LGMAX). This indicates that amateur players may require additional muscle adjustments to maintain movement continuity. In Syn2, elite players exhibit stronger quadriceps and gluteus maximus synergy (higher RRF, RGMAX, and RBF activation with lower LTA and LES activation, \(p\) < 0.05), whereas amateurs rely more on the lower-leg muscles (LTA) for compensation. This optimized synergy in elite players may reflect precise neuromuscular control of pre-activation within the kinetic chain. According to the \"muscle synergy hierarchical control theory\" [19], elite players enhance the coupling between the gluteus maximus and quadriceps (RGMAX/RRF contribution \(\Delta\) = +34%), pre-establishing hip-knee stiffness matching and reducing energy loss during subsequent push-off phases [15]. In contrast, amateurs excessively rely on core muscles in Syn1 (LES/RES activation intensity \(\Delta\) = +22%) and lower-leg compensation (LTA activation \(\Delta\) = +18%), aligning with the \"compensatory synergy hypothesis\" [20], which describes excessive activation of non-dominant muscle groups. While this strategy helps maintain movement continuity to some extent, it reduces overall energy transfer efficiency, compromising stroke explosiveness and stability. During the FS phase, the activation pattern of Syn3 differs significantly between elite and amateur players. The elite group exhibits higher activation levels of the rectus femoris (RRF), tibialis anterior (RTA), and gluteus maximus (RGMAX), while activation of the lumbar erector spinase (LES) and rectus abdominis (RES) is lower (\(p\) < 0.05). This suggests that elite players primarily rely on coordinated activation of the rectus femorisand gluteus maximus to generate stroke power while minimizing excessive core muscle engagement, thereby improving energy transfer efficiency. This pattern aligns with the \"proximal-to-distal sequencing\" principle, where hip-driven momentum transfer optimizes kinetic energy conversion in the stroke [16]. The elite group's selective activation of RGMAX/RRF (\(\Delta=+41\%\), \(p<0.01\)) facilitates smoother energy transfer between the hip and knee joints, while significantly reducing core muscle activation (LES/RES activation \(\Delta=-37\%\)). This neuromuscular strategy likely enhances intersegmental force transmission along the kinetic chain, as suggested in previous studies on multi-joint coordination during tennis strokes [12; 13; 46]. Moreover, such a proximal-driven activation pattern has been shown to reduce upper-limb loading and improve stroke repeatability [5; 16], which may explain the more stable and efficient stroke mechanics observed in elite players. In contrast, the amateur group exhibits a distinct activation pattern, characterized by greater LES and RES activation but lower RRF and RGMAX contributions.