In this study, we used G Power 3.1.9.2 to calculate the required sample size with an effect size of 0.75. Under the conditions of α = 0.05 and a statistical power of 95%, 12 participants were needed (Kang, 2021). This study recruited 12 high-level Tai Chi athletes from Wuhan Sports University, aged between 16 and 28 years. Among them, there were 6 national master-level athletes, 2 first-level athletes, and 4 second-level athletes. Their average age was 18.83 ± 3.32 years, average height was 173.08 ± 5.58 cm, average weight was 63.33 ± 6.56 kg, and average years of martial arts experience was 9.08 ± 4.78 years. All participants had good physical fitness and athletic ability, with no history of injuries or diseases in the past year. Before the experiment, they thoroughly read the experimental plan, understood the purpose, methods, testing procedures, and potential risks of the study, and signed informed consent forms. This study was approved by the Medical Ethics Committee of Wuhan Sports University (Approval number: 2024048). Confirming that all experiments were performed in accordance with relevant guidelines and regulations.

The experiment was conducted at the Key Laboratory of Sports Engineering, General Administration of Sports, Wuhan Sports University. A Vicon motion capture system (T40, Vicon, UK, with a sampling frequency of 200 Hz), a Kistler 3D force platform (9260AA6, Switzerland, with a sampling frequency of 1500 Hz), and a Noraxon surface electromyography (EMG) system were used to synchronously collect motion capture data, force data, and surface EMG data of Tai Chi Leg Stirrup Movements.

A modified version of the Visual 3D default full-body model with 38 marker points was used. The specific marker placement was as follows: left and right forehead (LHAD, RHAD), left and right rear head (LFAD, RFAD), clavicle (CLAV), seventh cervical vertebra (C7), sternum (STRN), 10th thoracic vertebra (T10), left and right anterior superior iliac spines (LASIS, RASIS), left and right iliac crests (LICST, RICST), left and right posterior superior iliac spines (LPSIS, RPSIS), left and right greater trochanters (LTROC, RTROC), left and right thigh tracking points (LTH1, LTH2, RTH1, RTH2), left and right knee medial and lateral epicondyles (LMEP, RMEP, LLEP, RLEP), left and right shank tracking points (LSK1, LSK2, RSK1, RSK2), left and right ankle medial and lateral malleoli (LMME, RMME, LLME, RLME), left and right heels (LHEEL, RHEEL), left and right first metatarsals (LHM1, RHM1), and left and right fifth metatarsals (LHM5, RHM5).

Since the leg push is mainly designed to extend the flexion and extension of the hip, knee and ankle joints, this study selected 12 muscles of the left and right legs: rectus femoris (RF), lateralis femoris (VL), tibialis anterior (TA), biceps femoris (BF), medial head of gastrocnemius (MG) and gluteus maximus (GMAX). The knee extensor includes the rectus femoris and the lateral femoris, which are mainly responsible for knee extension, and the knee flexor includes the biceps femoris. The ankle plantar flexor group includes the medial head of gastrocnemius muscle, and the ankle dorsiflexor group includes the tibialis anterior muscle. The hip flexor group includes the gluteus maximus.

The experimental procedure and precautions were explained to the subjects, ensuring that they signed the informed consent form after full understanding. The subjects’ basic information was recorded, and key morphological indicators, such as trunk, upper arm, forearm, thigh, shank, and foot lengths, were measured. Based on the Visual 3D full-body model, 38 marker points were securely attached to the subjects’ bodies. To reduce errors, the subjects wore lab-specific tight clothing, and the same tester placed the markers each time. After placement, each sensor was checked for secure attachment and the sensors on the measured muscles were verified to be correctly connected to the corresponding channels. The skin surface of the measured muscles was cleaned with 75% alcohol swabs and shaved to ensure successful EMG signal collection.

Before the experiment began, static data were collected once, followed by a 5-min warm-up to prevent muscle strain during the test. During formal data collection, the entire process was videotaped. The testers guided the subjects to position themselves in the motion capture area with one foot on a force platform. The subjects performed the Tai Chi Leg Stirrup Movements based on the tester’s commands, repeating the action five times. A Tai Chi coach checked whether the subjects’ movements met standard requirements. The test scenario is shown in Figure 1.

Import the raw kinematic data from the Vicon motion capture system into Visual 3D for inverse dynamics calculations. Use the calculated center of mass displacement to further compute the velocity of the center of gravity (VCG) using Matlab R2022a, as shown in Equation 1: V C G = d t i + 1   ‐   d t i t i + 1 ‐ t i (1) where d t i + 1 represents the displacement at time point t i + 1 , d t i represents the displacement at time point t i , t i represents the current time point, and t i + 1 represents the subsequent time point.

G R F X , G R F Y , and G R F Z represent the ground reaction forces in the coronal, sagittal, and vertical axes respectively. B W represents the normalized body weight, and N D P represents the number of frames.

MATLAB R2022a was used to preprocess the surface EMG data and extract the muscle synergy patterns. Non-negative Matrix Factorization (NNMF) was employed to decompose the surface EMG signal envelope matrix (M) into a linear combination of a weight matrix ( W i , synergy structure) and a muscle activation coefficient matrix ( C i , activation coefficients) (Kim et al., 2017; Lee and Seung, 1999; Rabbi et al., 2020). As shown in Equations 2, 3. M = ∑ i = 1 N W i C i + e     W i ≥ 0 ,   C i ≥ 0 (2) M ′ = ∑ i = 1 N W i C i   W i ≥ 0 ,   C i ≥ 0 (3)

M represents the original surface EMG signal envelope matrix with dimensions m × n, where m is the number of measured muscles, and n is the length of the time series of samples (i.e., the number of sampling points). N is the number of muscle synergies, W i represents the muscle synergy structure matrix with dimensions m × N, and Ci represents the muscle synergy activation coefficient matrix with dimensions N × n. e is the residual, and M ′ is the reconstructed EMG matrix obtained by multiplying W i and C i .

In muscle synergy extraction based on Non-negative Matrix Factorization, the number of muscles m and time series length n is known, but the number of muscle synergies N is unknown. Different values of N result in varying accuracies of the reconstructed EMG matrix M ′ , which is measured by the variability accounted for (VAF).

To determine the final number of synergies n during extraction, the Variance Accounted For (VAF) was used to evaluate the reconstruction accuracy of matrix M ′ relative to the original matrix M , as shown in Equation 4: V A F = 1 − ∑ i = 1 m ∑ j = 1 n M i , j ‐ M ′ i , j 2 ∑ i = 1 m ∑ j = 1 n M i , j 2 (4)

M is the original matrix and M′ is the reconstructed matrix. The VAF ranges from 0 to 1, with higher values indicating a higher reconstruction accuracy (i.e., M and M′ are closer).

The variance threshold method is used to determine the number of muscle synergies. Starting with N = 1, N increases incrementally during matrix decomposition. If the current number of synergies yielded an average VAF above all, the subjects’ synergy patterns were classified using k-means clustering analysis. The number of clusters k was determined by testing values from 1 to 10 and calculating the sum of squared errors (sumD) for each k. The process continued until sumD was minimally affected by the random initial centers of the k-means algorithm. Thus, the final number of clusters, k, in this study was set to four. a fixed value, the calculation stops and the number of muscle synergies is set to N. The synergy patterns of all subjects were classified using k-means clustering analysis. The number of clusters k was determined by testing values from 1 to 10, calculating the sum of squared errors (sumD) for each k. The process continued until the sumD was minimally affected by the random initial centers of the k-means algorithm. Thus, the final number of clusters, k, in this study was set to four. All synergy patterns were named Synergy 1-4, abbreviated as SYN1-4. According to the researchers’ studies, the active muscles in the synergistic module are defined as those with spatial component values exceeding 0.3 (Kubota et al., 2020; Milosevic et al., 2017). In this study, the activation curves for the leg thrusting action during each phase are divided into early, mid, and late phases based on time averaging.

Subsequently, Pearson’s correlation analysis was used to examine the relationship between the velocity of center of gravity and muscle synergies at each phase. Statistical significance was defined as p < 0.05, with “*” indicating p < 0.05 and “**” indicating p < 0.01. r > 0.7 is a strong positive correlation, 0.5 < r < 0.7 is a moderate positive correlation, and 0.3 < r < 0.5 is a weak positive correlation. r < −0.7 is a strong negative correlation, −0.5 > r > −0.7 is a moderate negative correlation, and −0.3 > r > −0.5 is a weak negative correlation. We selected the muscle synergies with the strongest correlation with the dynamic stability index at each stage as the best muscle synergies (r > 0.7 or r < −0.7).

Preparation Moment: The moment the athlete’s left toe leaves the ground; Maximum Knee Flexion Moment: the moment the athlete’s left knee joint reaches maximum flexion; Maximum Extension Moment: the moment the lifted leg reaches maximum extension; Ground Contact Moment: the moment the athlete’s left toe touches the ground. Knee lift phase: This phase starts when the force line of the supporting leg on the force platform begins to decrease and ends when the knee joint of the supporting leg reaches maximum flexion. Extension phase: This phase starts when the knee joint of the stirrup leg reaches maximum flexion and ends when it reaches maximum extension. Recovery phase: The stirrup leg slowly flexes the knee and adducts the hip joint to land beside the supporting foot, with the heel touching the ground. The phase started when the knee joint of the stirrup leg reached its maximum extension and ended when the force line on the force platform returned to its initial value. As shown in Figure 2.

The kicking action is characterized by four muscle synergy patterns across three phases. In the knee-lift phase, the primary activated muscles in SYN1 are the right rectus femoris, right vastus lateralis, and right medial gastrocnemius, with the knee extensor muscles of the swing leg and the ankle plantar flexor muscles as the main activated muscle groups. These muscles are activated during the mid-to-late phase. In SYN2, the primary activated muscles are the right rectus femoris, right vastus lateralis, and right biceps femoris, with the knee extensor muscles of the swing leg and the stabilizing muscles of the stance leg as the main muscle groups, showing activity in both the early and late phases. SYN3 is dominated by the right rectus femoris, right vastus lateralis, and right tibialis anterior, with additional activation of the right biceps femoris. The knee extensor muscles of the swing leg are the main muscle group, with activation in the early-to-mid phase. SYN4’s primary activated muscle is the left medial gastrocnemius, with the plantar flexor muscles of the stance leg’s ankle joint being the main muscle group activated, showing activity in both the early and late phases. As shown in Figure 3.

During the extension phase, the main activated muscles in SYN1 are the right vastus lateralis and right medial gastrocnemius, primarily activating the knee extensor muscles of the swing leg, with activity in the early and late phases. In SYN3, the main activated muscles are the right rectus femoris and right biceps femoris, along with some activation of the left rectus femoris and left tibialis anterior, primarily activating the knee extensor muscles of the swing leg, with activity in the mid-to-late phase. SYN2 and SYN4 do not show significant activation of any major muscle groups during this phase. As shown in Figure 3.

In the recovery phase, the main activated muscle in SYN1 is the right rectus femoris, primarily activating the knee extensor muscles of the swing leg, with activity in the early and mid-to-late phases. SYN2’s main activated muscles are the right rectus femoris, right vastus lateralis, and right medial gastrocnemius, primarily activating the knee extensor muscles of the swing leg, with overall activity throughout the phase. In SYN3, the main activated muscles are the right rectus femoris, right vastus lateralis, right medial gastrocnemius, and left gluteus maximus, primarily activating the knee extensor muscles of the swing leg and the hip extensors of the stance leg, with activity in the mid-to-late phase. SYN4’s main activated muscles are the right vastus lateralis and right medial gastrocnemius, primarily activating the knee flexor muscles of the swing leg, with activity in the early phase. As shown in Figure 3.

During the knee lift phase, SYN1 showed a strong positive correlation with the VCG (r = 0.785**, p < 0.01), indicating that SYN1 provides good knee lift speed and stability, reducing wobble, and aiding smooth transitions. SYN2 showed a non-significant correlation with the VCG (r = 0.077, p > 0.05), indicating that SYN2 had little impact on dynamic and trunk stability at this phase. SYN3 and SYN4 showed moderate negative correlations with the VCG (r = −0.350**, p < 0.01; r = −0.551**, p < 0.01). This negative correlation may be related to improper muscle control or a lack of coordination between the hip and leg muscles. Improving the coordination of these muscles and techniques can reduce their negative impact on stability, enhance knee movement stability, and reduce body sway. As shown in Table 1.

During the extension phase, SYN1 showed a moderate negative correlation with the VCG (r = −0.508**, p < 0.01), indicating that excessive force or lack of coordination during extension may negatively impact dynamic and overall stability. SYN2 showed a strong positive correlation with the VCG (r = 0.663**, p < 0.01), indicating that the knee extensor muscle group positively affects the dynamic stability and stability of the Stirrup leg. Good SYN2 training helps stabilize extension movements and enhances the overall strength output stability. SYN3 and SYN4 showed negative correlations with the VCG (r = −0.104*, p < 0.01; r = −0.439**, p < 0.01). These negative correlations may be related to other control factors of the legs and hips, reflecting coordination or muscle imbalance. Improving muscle coordination related to these indicators can reduce wobble and instability caused by lack of coordination, ensuring stability during extension movements. As shown in Table 1.

During the recovery phase, SYN1 showed a weak negative correlation with the VCG (r = −0.129**, p < 0.01), indicating a weak but significant association between muscle activity recovery and VCG. This suggests that SYN1 has a certain inhibitory effect on VCG during the recovery process after knee lift. SYN2 showed a strong positive correlation with the VCG (r = 0.642**, p < 0.01), indicating that as VCG increases, SYN2 exhibits good muscle coordination during the recovery phase, reducing tremors and instability. SYN3 showed a moderate negative correlation with the VCG (r = −0.407**, p < 0.01), and SYN4 showed a strong negative correlation with VCG (r = −0.794**, p < 0.01). This indicates that SYN3 and SYN4 significantly contributed to instability during the recovery phase, suggesting the need to improve muscle endurance and posture control. As shown in Table 1.