This study recruited 3–5 years old children from a private kindergarten in Renqiu City who met the test criteria and voluntarily participated in the experiment. With the assistance of teachers, detailed information about the subjects was obtained, including socioeconomic background, physical activity levels, and any potential confounding factors that might affect gait development, such as parental education level, and frequency of physical activity. Children with limited mobility, limb or organ diseases, or unstable health conditions were excluded. In total, 56 children completed the infrared data measurement. Before the infrared data measurement, markers were applied to the subjects according to the method shown in Table 1. The subjects were then asked to walk normally across the force plate to collect infrared data. During data processing, data with marker displacement and abnormal values were excluded. Their basic information is shown in Table 2. This study was approved by the Ethics Committee of the Faculty of Psychology at Beijing Normal University, with the approval number: 201910210061. During the study, informed consent forms were distributed to the parents of the participants, and the testing procedures were explained in detail to the teachers.

This study used Python 3 for data processing and standardized the dynamic data of muscle strength and joint moments for all participants by weight to eliminate the impact of individual weight differences on the results. In the analysis of significant differences in muscle strength among children of different ages, normally distributed data were analyzed using one-way ANOVA, while non-normally distributed data were analyzed using the Kruskal-Wallis H test. The number of coordination patterns for joint angles and joint moments was determined through PCA, using the cumulative variance index to decide on the coordination patterns, defining the optimal number of patterns as when the cumulative variance reaches over 95%.

The analysis of the Lyapunov exponent for joint angles indicated unique dynamic stability characteristics among children of different age groups (Table 6). This transition from joint angle coordination to Lyapunov exponent analysis highlights the shift from kinematic coordination to dynamic stability, showing how movement coordination evolves into dynamic stability control as children age. In 3-year-olds, hip abduction showed very high stability (−0.003), while hip flexion (0.210) and external rotation (0.120) had weaker stability. Knee flexion (0.130) and ankle plantar flexion (0.063) showed good stability, but Sub Talar Eversion was weaker (0.186). For 4-year-olds, hip abduction (−0.229), flexion (0.007), and external rotation (−0.114) showed higher stability, while knee flexion (0.086), ankle plantar flexion (−0.090), and Sub Talar Eversion (0.081) also had good stability. In 5-year-olds, hip abduction (0.081) had moderate stability, while hip flexion (−0.134) had higher stability. Hip external rotation (0.298) showed poorer stability. Knee flexion (0.199), ankle plantar flexion (−0.049), and Sub Talar Eversion (0.024) demonstrated moderate to high stability.

In the analysis of the Lyapunov exponent for joint moments (Table 6), significant differences in dynamic stability were also observed among children of different age groups. This transition from joint moment coordination to Lyapunov analysis emphasizes the increasing complexity of dynamic control in older children, showing how joint torque coordination evolves into more stable and complex dynamic behaviors. In 3-year-olds, hip abduction (−0.062), flexion (−0.056), and external rotation (−0.078) had high stability. Knee flexion (−0.039), ankle plantar flexion (0.061), and Sub Talar Eversion (0.030) showed good stability. In 4-year-olds, hip abduction (−0.046) and flexion (−0.043) showed strong stability. Hip external rotation (0.015) had moderate stability, while knee flexion (0.031), ankle plantarflexion (−0.037), and Sub Talar Eversion (−0.069) showed variable stability. For 5-year-olds, hip abduction (−0.019), flexion (0.009), and external rotation (0.002) showed higher stability. Knee flexion (−0.058) and ankle plantarflexion (0.050) demonstrated high stability, while Sub Talar Eversion (−0.206) showed very high stability. As children age, their joint torque stability improves. The fluctuations in 5-year-olds’ indices suggest more complex gait control, balancing short-term stability with flexibility, reflecting gait maturation.

Gait requires coordinated joint actions to handle movement complexity (10, 11). The central nervous system simplifies motor processes, improving control efficiency (26–28). The neuromuscular system plays a key role in coordinating joints and muscles (29). This study uses PCA to analyze the kinematic and torque patterns in the lower limbs of children aged 3–5 during the gait support phase, uncovering gait characteristics and developmental patterns.

The study shows that 3-year-olds use complex multi-joint coordination in gait, but their strategies are immature, leading to instability. In joint angle coordination pattern 1, hip and knee flexion show high synergy, while the ankle contributes to gait movement. This indicates that children use hip and knee movements along with the ankle to propel forward, a pattern also important for 4- and 5-year-olds (Figure 4). Research suggests ankle maturation occurs around age 4 (9). The key transition at age 4 is reflected in the increasing involvement of the ankle joint in coordination patterns, suggesting that this age marks the shift toward the ankle assuming a more independent role in gait.

In the gait support phase, 3-year-olds show high synergy in knee and hip flexion in joint angle coordination pattern 1, while hip flexion and knee extension dominate in torque patterns 1 and 3 (Figure 4). This suggests that 3-year-olds may need counteracting torques at the knee to maintain balance during gait, indicating they have not mastered joint angle and torque coordination fully. However, at age 4, there is a notable shift in the coordination between the hip and knee joints, marking a transition from reliance on compensatory strategies to more integrated joint control.

In joint angle coordination pattern 2, there is a significant synergy between hip extension and knee flexion (Figure 4). Sub Talar joint eversion enhances stability and cushioning during gait, but its significant eversion (−0.423) may lead to instability due to insufficient coordination with other movements. This synergy also shows similarities in the joint coordination patterns of 4- and 5-year-olds. At age 4, this synergy between the hip and knee joints begins to stabilize, indicating that gait control is gradually shifting toward more coordinated and stable strategies.

In joint angle coordination pattern 3, ankle plantar flexion is dominant for 3-year-olds. This matches findings that ankle maturation occurs around age 4, while hip and knee maturation occurs around age 7 (9). Joint torque pattern 2 for 3-year-olds shows significant negative participation from hip flexion, potentially leading to uneven torque distribution and affecting gait stability (Figure 4). The negative involvement of hip flexor torque at age 3 suggests this is a characteristic of early gait control, with uneven torque distribution possibly leading to instability in gait. The negative participation of the hip joint during dynamic center of mass transfer may be a typical feature of early gait control in children, with uneven torque distribution possibly leading to instability in gait control.

In 4- and 5-year-olds, torque coordination characteristics gradually decrease with age. Observations of joint angle coordination patterns across ages show similarities in gait actions, especially in pattern 2. The transition at age 4 is further emphasized by the increased coordination between the hip and knee joints, especially with the involvement of ankle plantarflexion, marking a shift toward more balanced gait control. In 4-year-olds, hip flexion (0.797) dominates pattern 2, coordinating with Sub Talar Eversion and ankle plantar flexion. This suggests that 4-year-olds still rely on the hip joint heavily and have insufficient multi-joint coordination in complex gait tasks, primarily using the hip joint to drive movement (Figure 4). This reliance on the hip joint at age 4 illustrates the critical transitional nature of this stage, where children are still working on integrating distal joints into a more balanced coordination strategy.

In 5-year-olds, joint coordination pattern 2 shows hip extension (−0.751) dominating, with knee flexion, ankle plantar flexion, and Sub Talar inversion (−0.355) working together. This indicates a more complex gait control strategy, allowing better handling of complex movements (Figure 4). By age 5, this transition is reflected in a more coordinated joint control strategy, where children begin to integrate the full lower limb into their motor control system. In joint coordination pattern 3, children’s coordination becomes more efficient with age. Coordination in this pattern is generally similar across all three age groups. However, while 3- and 4-year-olds have ankle plantar flexion dominating, 5-year-olds show more efficient coordination. This pattern shows clear joint angle coordination with ankle plantar flexion, knee extension, and Sub Talar Eversion forming joint angle pattern 3. While the other two age groups also have dominant ankle plantar flexion, the involvement of other joints varies, complicating their coordination.

Joint torque coordination patterns show greater variability with age compared to coordination patterns. According to Figure 5, we find that 3-year-olds use three main joint torque patterns to complete actions, while 4- and 5-year-olds use two. This suggests that as children age, their ability to coordinate joint torques improves. Interestingly, the three patterns seen in 3-year-olds can be encompassed by the two patterns in 5-year-olds. In contrast, 4-year-olds show more variability in their joint torque patterns compared to the other age groups. This variability at age 4 reflects the transitional nature of motor control during this period, where children are refining their strategies but still exhibit a range of movement patterns.

In joint torque pattern 1, 3-year-olds show a hip flexion-dominant pattern. This is similar to the pattern in 5-year-olds, but 5-year-olds also coordinate hip flexion with knee extension and ankle plantar flexion, showing more complex and mature coordination. In joint torque pattern 2, hip extension dominates for 4-year-olds, with greater ankle joint participation compared to 3-year-olds. This suggests that 4-year-olds are starting to focus on coordinating the ankle and hip joints. In joint torque patterns 2 and 3 for 3-year-olds, actions mainly involve hip adduction and knee extension. These patterns suggest that their overall coordination ability is relatively singular, making it hard to compensate for deficiencies in other joints, resulting in less stability. From Figure 5, we observe that in joint torque pattern 1 for 4-year-olds, ankle plantar flexion torque significantly increases, and torque distribution becomes more balanced between hip and knee joints, indicating greater reliance on ankle strength. In gait progression, the use of distal lower limb strength becomes clearer, allowing better management of center of gravity changes during gait, which enhances stability and efficiency. In joint torque pattern 2, 5-year-olds show increased hip abduction torque, with a balanced distribution between knee and hip joint torques. Minimal contribution from other joints indicates effective use of distal lower limb strength while maintaining stability.

Overall, from ages 3–5, children show more complex and diverse joint coordination strategies in gait. 3-year-olds have a more singular pattern, primarily relying on hip and knee flexion for gait. Meanwhile, 4-year-olds show greater variability in coordination patterns, indicating a critical stage in motor development. The key transition at age 4 is marked by the increasing integration of distal joints, and the shift toward more balanced coordination strategies. By age 5, children effectively coordinate multiple joint strengths during gait and demonstrate flexible strategies for different tasks. This aligns with Blandine Bril’s research, which suggests that 5- to 6-year-olds can maintain balance using only their leg muscles during walking (30). Despite improvements in gait control, their immaturity and dependency indicate that further development and refinement in motor skills are needed.

This section analyzes the differences in the dynamics of the ankle, knee, and hip joints and related muscle strength in 3, 4, and 5-year-olds during gait. The aim is to explore the characteristic differences in motor control strategies across different age groups. Previous studies have shown that joint dynamics during gait are crucial for gait completion. For example, Salam M’s research indicates that hip extension torque significantly influences the ground reaction force during the early phase of gait (31).

In 3-year-olds, hip abduction power is low (0.02 W/Kg), possibly due to insufficient strength in the abductor muscles (e.g., GMe and Gmi) (Tables 3, 4). This low power reflects a lack of control ability in hip abduction during gait in 3-year-olds. They mainly rely on high energy absorption (energy absorption ratio of −0.93) to maintain gait stability (Table 5). This reliance on energy absorption rather than propulsion highlights the developmental stage at age 3, where stability is achieved through passive mechanisms, marking it as a foundational phase of motor development. By age 4, hip abduction power further decreases to 0.01, although this power reduction occurs. However, children may partially compensate for the lack of abductor strength by enhancing GMe strength (Tables 3, 4). This shows transitional characteristics in gait control. This shift in muscle strength suggests a transitional phase at age 4, where children begin to rely more on active muscle control rather than passive mechanisms. By age 5, hip abduction power rises to 0.02 W/Kg, and the relative stability of GMe strength indicates that their gait control strategies have matured. Through more efficient muscle coordination, they achieve more stable hip abduction movements and propulsion in gait (Tables 3, 4). Previous research also indicates that increased hip abductor strength contributes to enhanced gait speed (32).

In 3-year-olds, hip flexion power is low (0.06 W/Kg), mainly relying on high energy absorption to maintain gait stability (Tables 4, 5). This characteristic may lead to insufficient hip flexion strength, affecting propulsion and rhythm in gait. This increase in hip flexion power at age 4 marks the onset of a critical transition in motor control, where the ability to generate propulsion becomes more pronounced. As they age, hip flexion power in 4-year-olds significantly increases to 0.19 W/Kg, indicating enhanced propulsion strength. At this stage, gait control is transitional, displaying some gait fluctuations. By age 5 (Tables 3–5), hip flexion power slightly declines to 0.07 W/Kg, but the strength of the RF increases. This indicates that 5-year-olds can achieve stable and efficient hip flexion movements through more effective muscle coordination and energy utilization.

The study finds that hip external rotation power remains at low levels across all age groups (Tables 3–5). This indicates that the main function of hip external rotation in gait is to maintain stability rather than produce propulsion. For 3-year-olds, hip external rotation strength mainly relies on the GMe. Although hip external rotation power increases at age 4, energy utilization at this age tends to balance out. By age 5, the strength of the GMe and GMi stabilizes. The energy absorption ratio of hip external rotation indicates that gait control strategies are gradually maturing. This gradual improvement, particularly noticeable by age 4, underscores the importance of this age as a transition point where stability and muscle coordination begin to show clear improvements.

The knee joint plays a crucial role in generating propulsion during gait. Previous studies show that the knee extensors control the knee during the support phase of gait, generating necessary propulsion (33, 34). Decreased knee flexor strength may lead to shorter stride length at self-selected walking speeds (35). This study finds that knee flexion power significantly increases at age 4, closely related to the significant strengthening of the BF and SED (Tables 3–5). This indicates that children in this age group rely more on knee flexion movements for gait propulsion. However, 3-year-olds show low knee flexion power, indicating insufficient propulsion in gait. In 5-year-olds, knee flexion power slightly declines, but improved coordination of knee muscles enhances energy absorption ratios. This indicates the gradual maturation and stability of gait control strategies.

The ankle joint plays a more significant role in generating propulsion. Research shows that ankle dorsiflexion and plantar flexion directly affect gait balance and speed (36). Contraction of the ankle flexors can produce forward propulsion and the propulsion generated accounts for approximately 67% of the total joint power during the stance phase of gait (37–39). This study finds that with age, the dynamics of the ankle joint during gait varies: As age increases, ankle plantar flexion power gradually increases, indicating a growing demand for propulsion during gait. The GAT strength in 3-year-olds is relatively high, but it slightly decreases in 5-year-olds as they age (Table 3). However, through stable output from the SL, energy absorption ratios improve, indicating that energy utilization in ankle plantar flexion becomes increasingly effective (Tables 3–5). The output of gait propulsion becomes more stable and mature. In contrast, Sub Talar joint eversion shows negative power across all age groups, indicating its primary role in stability rather than propulsion during gait. Overall, children exhibit a high energy absorption ratio at this joint, indicating its greater role in stability during gait. This is especially crucial in regulating stability during unsteady gait.

This chapter primarily reveals the differences in the dynamics of the hip, knee, and ankle joints and muscle strength among 3, 4, and 5-year-olds during gait. The results indicate that the gait stability of 3-year-olds mainly relies on high energy absorption. Four-year-old show transitional characteristics in gait control, with significant increases in knee flexion power and muscle strength. These transitional characteristics are particularly indicative of the developmental milestone at age 4, where the ability to generate propulsion and improve joint coordination becomes more apparent. By age 5, gait control matures, achieving stable propulsion through more efficient muscle coordination. Especially, 4-year-olds are in a critical period of motor development, with notable transitional gait characteristics.

To further analyze the differences in gait control strategies among children of different ages, this study incorporates the Lyapunov index of joint angles and torques as a measure of dynamic stability in gait. The Lyapunov index reflects the sensitivity of movements to small disturbances, with higher values indicating greater instability.

During walking, hip external rotation (40) and abduction (41, 42) affect the kinematic and dynamic characteristics of the knee joint in normal gait. Based on the Lyapunov index (Table 6), it was found that as age increases, the Lyapunov indices for hip abduction and external rotation decrease during the transition from ages 3 to 4, indicating that the stability of these joints improves during this stage. This transition at age 4 corresponds to a key developmental stage, as evidenced by the significant reduction in angular variability and the improvement in joint coordination, marking the shift toward more coordinated and stable movements. By age 5, we observed an increase in the Lyapunov indices for both hip external rotation and abduction angles, as well as a rise in hip flexion torque, which seems contradictory to the conclusion of enhanced stability. However, by examining the coordination patterns of joint angles and torques, we found that 5-year-olds exhibit greater flexibility and complexity in movement adjustment, enabling them to cope with larger gait fluctuations without compromising overall stability (Figures 4, 5). Specifically, although the Lyapunov index is higher at age 5, they may maintain gait stability through enhanced neuromuscular coordination. Previous studies have shown that hip flexion plays an important role in completing the gait process (43, 44).

Based on Table 6, we found that the stability of hip flexion angle increases with age, indicating that the control capability of hip flexion improves as children grow, leading to more mature gait control. In the Lyapunov index changes for hip flexion torque, we found that it increases with age, suggesting a transition from rigid stability to more flexible, dynamic gait control strategies. The knee joint is an important driving joint in human walking, contributing to forward propulsion (33), adjusting stride length (35) and influencing lower limb coordination (45). Analyzing the Lyapunov index of knee flexion in different children, we found a significant drop from 3 to 4 years, indicating increased stability in 4-year-olds, though this also correlates with greater rigidity, which may reduce knee flexibility. This marked reduction in variability at age 4 further emphasizes the transition toward greater stability, aligning with the milestone of improved motor control. By age 5, the Lyapunov index for knee flexion angle shows a significant increase, reflecting greater dynamic variability as children adapt to more complex task demands in gait control. As children grow, their motor skills improve, and they may attempt more challenging movements or gait adjustments, leading to greater angular variability and flexibility. Observing the Lyapunov index for knee flexion torque, we noted a rise at age 4, followed by a decline at age 5, indicating fluctuations as children explore control strategies for applying torque (Table 6). By age 5, the decline in the torque Lyapunov index indicates enhanced stability in applying torque. As they age, children develop finer muscle control, allowing for more stable torque application; even with increased angular variability, their control over force becomes more precise, reducing excessive torque fluctuations. As one of the three major joints in gait, ankle dorsiflexion plays a crucial role in generating propulsion (37, 39) and controlling body posture (46, 47). In this study, the Lyapunov index for preschool children’s ankle dorsiflexion during gait cycles showed a decrease followed by a slight increase from ages 3–5, while the torque Lyapunov index initially dropped sharply and then slightly rose. This change indicates that children’s gait control abilities are gradually improving, particularly with significant stability at age 4. By age 5, although angular variability slightly increases, this may be due to children’s enhanced flexibility to adapt to more complex gait changes and movement demands. Simultaneously, torque control becomes more refined and stable, indicating their ability to effectively control the forces applied during gait, leading to gradual maturation. Previous research shows that the degree of pronation in the Sub Talar joint correlates with stability in gait (48). The Lyapunov index for Sub Talar pronation angle and torque control gradually decreases with age, indicating improved stability in gait control over the years (Table 6). Notably, at age 5, the angle Lyapunov index is very low (close to 0), while the torque Lyapunov index drops significantly into the negative range, indicating that children achieve high stability in movement control at this joint and exhibit refined and stable force control. Overall, the gait control system in children at this age is developing toward greater maturity and stability.

This study utilized a sample from a single preschool located in a specific geographic region, which may introduce regional biases into the findings. As the sample was drawn from one location, the results may not fully represent the gait development patterns of children from different regions, considering potential differences in cultural backgrounds, environmental factors, and educational resources. However, despite these limitations, the sample provides valuable insights into gait development within a particular context, offering a foundational basis for future research. To enhance the generalizability of the findings, future studies should consider incorporating a more diverse sample from various regions and types of early childhood education institutions, which would help validate and extend the current results.