Current research predominantly focuses on exploring soccer ball velocity, particularly its relationship with lower limb biomechanical characteristics (1–3). The key to increasing ball velocity lies in optimizing limb movement patterns and enhancing the efficiency of velocity transfer from the foot to the ball (4). The kicking motion exhibits a typical proximal-distal timing characteristic: the thigh (the proximal segment) initiates the forward swing first, driving the delayed explosive movement of the lower leg and foot (the distal segments) (4). The knee joint, serving as the core hub of this kinetic chain, plays a crucial role in power transmission and velocity generation (5). Naito et al. developed a 3-D dynamical model of the multi-joint kinetic chain in instep kicking to quantify the contributions of key dynamical factors to maximizing knee extension angular velocity (6). Their findings highlighted that the leg structure (knee angle) is important for effective instep kicking. Moreover, Sinclair et al. reported that sagittal plane knee extension angular velocity is significantly related to foot linear velocity for instep kicking (7). However, existing research mainly focuses on the biomechanics of the kicking leg during the swing before and after ball contact (8). The kicking action is a complex, multi-phase movement that requires the coordination of both lower limbs. The complete kicking process includes three key phases: the approach run, the positioning of the supporting foot, and the final phase of leg swing and ball contact. The effectiveness of the kicking action is dependent on the coordination of each phase (9). Therefore, although knee angle and velocity have been proven to be important parameters affecting kicking performance (5), their specific roles at various phases of the movement have not been fully studied. Understanding these roles is crucial not only for maximizing ball velocity, but also for other performance metrics.

Indeed, while ball velocity is critical, the ability to execute long-range kicks represents another dimension of kicking performance with significant tactical value. Players can break through the opponent's offside trap and disrupt the defensive formation with long-range passes, creating defensive gaps. However, few biomechanical studies have focused on the distance of the kick. The majority of current studies have been conducted in laboratory settings, where the kicking target is placed only 1.6–4 m from the kicking point (8, 10, 11). In terms of research techniques, current studies usually conduct kinematic analysis using optical or image-based motion capture technologies, both of which have issues such as light interference, object occlusion, and limited applicability in field settings (12). These limitations have posed challenges for the comprehensive analysis of soccer technique research. With the innovative development of inertial navigation technology and micro-electromechanical systems, Inertial Measurement Units (IMUs) offer more possibilities for field research in soccer. OpenSim modeling analysis based on IMU data has been shown to yield knee angles that are consistent with those from optical motion capture, with a root mean square difference of 3–6 degrees (13).

Therefore, this study aims to analyze the correlation between kinematic parameters of the knee joint and kicking distances in soccer players across different phases of the kicking motion, by utilizing IMUs and OpenSim modeling.

The results indicate that the average kicking distance for soccer players was 35.49 ± 7.18 m. Table 1 presents the kinematic parameters of the knee joint during the kicking process, including the extremum angle, ROM, and average angular velocity at different time points during the approach, support, and swing phases. Table 2 and Figure 4 present the results of the correlation analysis between the kinematic parameters of the knee joint and the kicking distance. During the approach phase, the extremum angle of the second knee flexion (r = 0.152, p = 0.041; Figure 4A), as well as the ROM of the second knee extension (r = 0.169, p = 0.023; Figure 4B) and the average angular velocity of the second knee extension (r = 0.185, p = 0.013; Figure 4C), were positively correlated with the kicking distance. During the swing phase, the extremum angle (r = 0.178, p = 0.016; Figure 4D) and the average angular velocity (r = 0.283, p < 0.001; Figure 4E) of knee extension were positively correlated with the kicking distance.

The present study examined the relationship between players’ knee joint kinematics and kicking distance. It was found that during the approach phase, the maximum angle of the second knee flexion, as well as the ROM and average angular velocity of the second knee extension, were positively correlated with the kicking distance. The approach phase is the technical action process that is completed in the form of running. Players use this phase to generate more momentum, which is then transferred to the football, aiding in better control of the ball's velocity and direction, and increasing the power of passes or shots (6). During this phase, the second knee flexion occurs during the touchdown process at the end of the approach. The knee joint buffers the ground reaction force through flexion and utilizes the stretch-shortening cycle mechanism. The quadriceps undergo eccentric contraction to store elastic potential energy for the subsequent extension (20). This also promotes an increase in the ROM and average angular velocity of the second knee extension. The rapid and full extension of the knee effectively enhances the horizontal propulsion force away from the ground. This force is ultimately converted into the overall kinetic energy of the kicking motion, thereby helping players kick the football to a greater flying distance (21). Previous studies have shown that approaching the football with a faster running velocity increases the ball's exit velocity (22, 23), which is consistent with the findings of this study.

The support phase is equally critical to the performance of kicking technique. Upon landing, the supporting leg cushions the horizontal velocity acquired from the approach, converting it into vertical velocity for the body's upward motion, while simultaneously withstanding ground reaction forces equivalent to 2–3 times the player's body weight (24, 25). However, the results of this study reveal that there is no correlation between the kinematic characteristics of the knee joint during the support phase and the kicking distance. We speculate that this could be due to two factors: firstly, the high level of athleticism exhibited by all players, who executed this phase of the movement adequately; secondly, the study's protocol required players to perform the kicking technique with only a single step approach, being a short distance and may not fully reveal the impact of the support phase on kicking distance. Previous research has indicated that extending the approach distance can lead to a further acceleration in the ball velocity during a kick (26). Nevertheless, it remains uncertain whether this enhancement is linked to the kinematics of the knee joint. Therefore, future research should incorporate a larger sample size to further investigate the relationship between the kinematic characteristics of the knee joint during the support phase and kicking distance across varying approach distances.

The swing phase refers to the swinging motion of the kicking leg as it completes the striking motion, primarily achieved through the flexion and extension of lower limb joints. This study found that soccer players with a faster extension velocity of the swinging knee tend to achieve a longer kicking distance. This finding is consistent with previous research, indicating that knee extension ability is an important factor in kicking performance (1). Related electromyographic studies suggest that, although the specific muscle tissues have not been clearly identified, the knee extensor muscles play a likely crucial role in enhancing foot velocity during the striking motion (27). However, other research has indicated that the hamstrings undergo eccentric contraction during the forward swing, reach their maximum length, thereby increasing the risk of injury (28, 29). Additionally, the results of this study show that players who achieve a longer kicking distance have a greater degree of knee flexion at the final stage of extension (in this study, a fully extended knee joint is defined as 0°). This may be due to the posterior thigh muscles being passively stretched and then contracting before the ball strike as the lower leg accelerates forward, to control the knee joint angle, thereby improving the accuracy of ball contact.

This study provides valuable insights for optimizing training methods by clearly identifying key knee joint kinematic features associated with longer kicking distances. Coaches and strength and conditioning specialists can utilize these findings to design more targeted training programs. Specifically, it is essential to enhance lower limb stability, enabling greater knee flexion angles during ground contact in the approach phase while maintaining safe and efficient absorption of ground reaction forces. Furthermore, the role of knee extension during both the push-off phase of the approach and the swing-kick motion highlights the importance of incorporating knee extension-focused exercises into explosive strength training. Additionally, complementary flexibility and coordination exercises should be integrated to maximize leg movement velocity and optimal kicking angles.

This study still has some limitations that need to be addressed. This study was conducted on an outdoor football field, which ensured some ecological validity. However, we limited the analysis to single-step approaches, although this limitation also existed in previous studies (30). Nevertheless, in most cases, players tend to use multi-step approaches, which means the ecological validity of this study is somewhat lacking at this level. Additionally, this study did not assess the movement variability of the players, focusing only on the average kinematic characteristics of the movements. While this helps identify common patterns in technical execution, it may overlook individual differences in their ability to adapt through variability in dynamic environments (31). Future research could quantify the variability in players’ kicking techniques to gain a more comprehensive understanding of the adaptive mechanisms underlying their movement control. Furthermore, although previous studies have validated the effectiveness of the IMU combined with OpenSim method against a gold standard (13), there is a lack of data specifically from kicking movements. Future research could conduct confirmatory studies in this regard and include more football-specific technical scenarios to support the application of this method in football science research. Future studies could also further reveal the biomechanical mechanisms influencing kicking distance and accuracy by including a wider range of sample sizes, measuring additional joints, or focusing on parameters related to ball contact quality.

This study, which utilized IMUs and OpenSim modeling, analyzed the correlation between knee joint kinematics in soccer players and their kicking distances. The study found that a larger flexion angle during the ground contact phase of the approach, a faster extension velocity and a greater range of motion during the push-off phase, as well as a faster extension velocity and a greater final flexion angle during the swing phase, were associated with longer kick distances.