Lower-limb joint kinetics and their contribution to attacking arm hand velocity during the aerial phase of the volleyball jump serve

Abstract

Background

In volleyball, the jump serve is a fundamental and widely employed serving technique. A high attacking arm’s hand velocity is a critical determinant for the effective execution of this technique. While previous studies have highlighted the importance of trunk and upper limb movements in influencing hand velocity during the aerial spiking phase, the contribution of lower-limb kinetics remains insufficiently understood. The present study characterised lower-limb kinetics (attacking and non-attacking legs) during the aerial spiking phase of the jump serve and examined the associations between relevant kinematic and kinetic variables and the hand velocity.

Methods

Seventeen male professional volleyball players participated in this study. Three-dimensional coordinate data were collected using a motion capture system (200 Hz). Kinetic and kinematic variables from take-off (TO) to ball contact (BC) were calculated, and Pearson product–moment correlation and stepwise linear regression were employed to identify factors associated with the hand velocity at BC.

Results

During the aerial spiking phase, the peak forward inclination angular velocity of the pelvis was significantly correlated with the attacking arm’s hand velocity at BC. The peak hip flexion moment and positive joint power of the non-attacking leg were also significantly correlated with the hand velocity at BC. The peak knee extension moments and positive joint power of both legs demonstrated additional significant correlations. A stepwise regression model (adjusted R² = 0.532, p = 0.002) included two significant predictors of hand velocity: peak pelvic forward inclination angular velocity and peak hip flexion moment of the non-attacking leg.

Conclusion

The findings suggest that enhancing forward pelvic tilt through contraction of the non-attacking leg’s hip flexor is essential for achieving high attacking hand velocity at BC. Additionally, generating mechanical energy by exerting the knee extensors of both legs contributes to enhancing attacking hand velocity.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13102-025-01421-x.

Introduction

The serve is the initial offensive action in volleyball, executed independently of the opponent’s strategies, with the aim of either scoring directly or disrupting the opposing team’s tactical organization [1–3]. Among the various serving techniques, the jump serve has become the dominant choice in modern volleyball due to its high ball speed and the challenge it poses for receivers [1, 4]. A previous performance analysis found that jump serves accounted for 69% of all serves in top international matches, significantly exceeding the use of other serve types [5]. Given its widespread adoption and tactical relevance, elucidating the biomechanical principles underlying the jump serve is essential for refining technique and developing effective training strategies.

The spike and jump serve in volleyball are complex skills involving a sequence of movements, including the approach, take-off, and aerial spiking [6]. Previous research on the biomechanics of the lower limbs has primarily focused on the plant and take-off phase, which is the final step before take-off (see Fig. 1). Wagner et al. [7] reported that the range of motion in the attacking-leg knee joint (flexion–extension) was significantly associated with jump height. Fuchs et al. [8] further demonstrated that the peak angular velocity of attacking-leg knee extension is a key predictor of jump height. These findings suggest that a rapid knee extension after sufficient flexion enhances the upward velocity of the body’s centre of mass (CoM), contributing to greater jump height. Moreover, Makino et al. [9] found that peak moments of ankle plantarflexion, hip extension and hip adduction in the non-attacking leg are strongly associated with jump height. Their results indicate that the non-attacking leg plays an important role in converting horizontal CoM velocity into vertical velocity, contributing more to jump height than the attacking leg. Similarly, Sarvestan et al. [10] found that compared to the failed spike attempts, successful attempts exhibited greater extension angular velocities in the hip and knee joints of the non-attacking leg, emphasising its importance in jump height. While these studies have clarified the contributions of both the attacking and non-attacking legs during the jumping motion with a run-up, the role of lower-limb motion and muscle exertion during the aerial spiking phase remains unclear. Moreover, unlike the plant and take-off phase, the aerial spiking phase occurs entirely in the air, where the lower limbs experience no ground reaction forces other than gravity. In this distinct mechanical environment, it is essential to quantify lower-limb joint kinetics characteristics and examine their relationship with the attacking arm’s hand velocity at BC.

Fig. 1.

The two phases of the volleyball jump serve motion. In this study, the right leg is defined as the attacking leg, and the left leg as the non-attacking leg. ACG: attacking leg makes contact with the ground. TO: take-off. MSE: maximum shoulder external rotation. BC: ball contact. The plant and take-off phase is defined as the period from ACG to TO, and the aerial spiking phase is defined as the period from TO to BC

The aerial spiking motion of the jump serve follows the kinetic chain principle, in which angular momentum is sequentially transferred from the pelvis, trunk, upper arm, and forearm to the hand. This coordinated process accelerates the distal segments, resulting in a higher hand velocity at ball contact. A faster attacking hand velocity is therefore a critical determinant of spiking performance, as it directly transfers more momentum to the ball and leads to an increase in ball speed [8, 10–12]. Scientific research has confirmed that hand velocity is strongly correlated with ball speed and serves as a key factor influencing the aerial spike performance in jump serve [3]. Furthermore, analyses of movement patterns across different sports [13] have demonstrated that the tennis serve, handball throw, and volleyball aerial spiking all follow a proximal-to-distal sequence in generating peak angular velocities, where the pelvis initiates the rotation, followed by trunk rotation, and finally, the upper limb joints accelerate in succession. This coordinated activation ensures efficient angular momentum and energy transfer, enabling athletes to generate high-end velocity and execute powerful spikes or throws. While previous studies have extensively examined upper-body mechanics, the role of lower-limb kinetics during the aerial phase remains insufficiently explored.

According to the kinetic chain concept, the lower limbs serve as the primary generators of mechanical energy. In most throwing or striking movements, this energy is transmitted via the pelvic and trunk (proximal segments) and sequentially delivered to the distal segments of the upper extremities—from the upper arm to the forearm and finally to the hand. For example, in baseball pitching, de Swart et al. [14] analyzed joint power flow through the lower extremities and found that the leading leg primarily functions to transfer energy in a distal to proximal sequence from the ankle through the knee and hip to the pelvic, while the trailing leg, particularly at the hip, generates substantial power that contributes to trunk rotation and upper limb acceleration. Similarly, Iino [15] reported that during the table tennis topspin forehand, extension and external rotation moments at the playing-side hip facilitate rapid pelvic rotation, resulting in increased racket velocity. These studies underscore that optimizing lower limb joint moment production and power output to enhance kinetic chain efficiency is crucial for maximizing end segment velocity in throwing and striking movements. However, during the aerial striking phase of the jump serve, the body remains fully airborne and is subjected solely to gravitational forces. A volleyball textbook [12] describes a coordinated movement pattern in which, as the arm cocking begins, the hip joints extend while the knees flex, followed by hip flexion and knee extension as the arm accelerates toward ball contact. This movement suggests that the lower limbs generate angular momentum in the opposite direction to that of the upper body, counteracting its motion to maintain whole-body angular momentum conservation and balance. While this description provides a fundamental kinematic perspective on lower-limb movement, the characteristics of lower-limb kinetics remain unclear. It is also worth noting that previous research using three-dimensional (3D) motion capture and lower limb joint kinetics analysis in volleyball spiking motion has predominantly concentrated on the plant and take-off phase, when the lower limbs are in contact with the ground and generate forces through ground reaction forces. In contrast, during the aerial spiking phase, the lower limbs operate without ground contact, so joint kinetic patterns are governed solely by gravitational forces and internal segmental interactions. In this unique mechanical environment, quantifying the influence of lower-limb joint kinetics on hand velocity offers novel insights into volleyball performance, both from a practical application perspective and a research approach. To our knowledge, no previous study has examined these relationships during the aerial phase in volleyball or other striking sports. Consequently, it is imperative to delineate the force and power output characteristics of the lower limbs during the aerial spiking phase and to examine their relationship with the hand velocity at BC.

The pelvis plays a pivotal role in the kinetic chain by anatomically connecting the lower limbs to the trunk and mediating the transfer of mechanical energy or angular momentum across body segments. Previous studies on table tennis strokes [15] have shown that the pelvic angular velocity is significantly correlated with racket velocity, indicating that rapid pelvic rotation facilitates the transfer of mechanical energy from the lower limbs to the trunk, ultimately accelerating racket velocity. Volleyball researchers and coaches have emphasized that during spike motion, angular momentum is transmitted sequentially from the pelvis through the trunk, upper arm, and forearm to the hand. This sequential transfer is essential for achieving high spiking velocity [8, 10, 12, 13, 16]. However, the relationship between pelvic rotational kinematics and the hand velocity of the attacking arm remains unclear. Gaining insight into the biomechanical factors associated with hand velocity may assist coaches in developing targeted training strategies to improve jump serve performance. Therefore, the purpose of this study was to determine the lower-limb joint kinetics during the aerial spiking phase of the jump serve and to investigate the relationship between the relevant kinematic and kinetic variables and the attacking arm’s hand velocity at BC. Building on prior biomechanical findings from baseball pitching and table tennis forehand strokes, we hypothesized that the peak pelvic angular velocities, as well as the peak joint moment and joint power of the attacking and non-attacking legs, would be correlated with the hand velocity at BC.

Methods

Participants

A total of 17 right-handed male professional volleyball players participated in this study. The participants were recruited from local professional volleyball institutions and had extensive experience in national-level professional leagues, qualifying them as advanced athletes. The average age, height, weight, and playing experience were 20.65 ± 4.57 years, 1.95 ± 0.06 m, 83.65 ± 11.84 kg, and 7.88 ± 2.55 years, respectively. All players regularly practiced and executed the jump serve technique fluidly in both training and competition. No participant had sustained a severe neuromuscular or skeletal injury within three months prior to data collection. We performed a post hoc power analysis for both the correlation and regression tests using G*Power (version 3.1.9.7). For the variables that showed significant correlations (see Tables 1 and 2), most achieved a statistical power (1–β) exceeding 0.80. For the regression model (adjusted R² = 0.532), the statistical power (1–β) also exceeded 0.80. The experiment was conducted in accordance with the Declaration of Helsinki, and all procedures were approved by the Shanghai Research Institute of Sports Science (Shanghai Anti-Doping Agency) Ethics Committee.

Table 1.

Correlations between peak pelvic angular velocities and attacking arm’s hand velocity at ball contact (BC)

Variables	Mean ± SD	r	p	95% CI
Pelvic angular veloctiy (rad/s)
Pelvic inclination backward (-) peak	−3.02 ± 1.30	−0.319	0.212	−0.693 to 0.191
Pelvic inclination forward (+) peak	3.93 ± 1.06	0.596	0.012*	0.162 to 0.837
Pelvic rotation forward (+) peak	6.56 ± 2.00	−0.180	0.488	−0.608 to 0.329

*p < 0.05

Table 2.

Correlations between peak lower-limb joint variables and attacking arm’s hand velocity at ball contact (BC)

Variables	Mean ± SD	r	p	95% CI
Joint moment (Nm/kg)
Attacking leg hip flexion (+) 1st	0.92 ± 0.32	0.202	0.437	−0.309 to 0.622
Attacking leg hip flexion (+) 2nd	1.20 ± 0.49	0.216	0.406	−0.296 to 0.631
Attacking leg hip adduction (+)	1.06 ± 0.37	0.077	0.768	−0.419 to 0.538
Attacking leg knee extension (−)	−0.92 ± 0.34	−0.499	0.041*	−0.790 to −0.024
Non-attacking leg hip flexion (+)	1.74 ± 0.46	0.595	0.012*	0.160 to 0.836
Non-attacking leg hip adduction (−)	−0.93 ± 0.35#	−0.260	0.313	−0.658 to 0.252
Non-attacking leg knee extension (−)	−0.90 ± 0.38	−0.585	0.014*	−0.832 to −0.145
Joint power (W/kg)
Attacking leg hip flexion/extension positive (+)	6.26 ± 3.77	0.188	0.470	−0.322 to 0.613
Attacking leg hip abduction/adduction positive (+)	4.28 ± 2.78	0.218	0.400	−0.293 to 0.633
Attacking leg knee flexion/extension negative (−)	−4.24 ± 2.13	−0.416	0.097	−0.747 to 0.081
Attacking leg knee flexion/extension positive (+)	7.05 ± 3.63	0.532	0.028*	0.069 to 0.806
Non-attacking leg hip flexion/extension negative (−)	−4.33 ± 1.91	−0.163	0.532	−0.597 to 0.345
Non-attacking leg hip flexion/extension positive (+)	9.84 ± 3.06	0.576	0.016*	0.132 to 0.827
Non-attacking leg hip abduction/adduction negative (−)	−2.37 ± 1.63#	−0.059	0.824	−0.525 to 0.434
Non-attacking leg knee flexion/extension negative (−)	−3.19 ± 1.56	−0.551	0.022*	−0.816 to −0.095
Non-attacking leg knee flexion/extension positive (+)	6.07 ± 3.73	0.594	0.012*	0.159 to 0.836

*p < 0.05

Experimental setup and procedure

The experiment was conducted on a standard volleyball court measuring 18 m in length and 9 m in width, with the net set at a height of 2.43 m (Fig. 2). A designated area (1.2 m × 1 m), consisting of four force plates (FP 600 × 500 × 50, Kistler Group, Winterthur, Switzerland), was positioned just behind the court’s end line to detect the moment of take-off. To ensure a consistent ground height during the approach phase, a hard plastic runway measuring 6 m × 1 m × 0.05 m was placed behind the force plates.

Fig. 2.

Measurement environment

Before data collection, participants performed their usual warm-up routine, which included activities such as stretching, running, and jumping. Following the warm-up session, participants performed practice jump serves to familiarize themselves with the testing conditions. Each participant executed jump serves directed at a target zone (6 m × 3 m) with maximal effort. During the final stride before take-off, participants were instructed to position both feet on the force plate area. The ball toss and run-up were performed along the runway before take-off. However, if a participant stepped off the runway with their leg during the run-up due to a poorly executed ball toss, or exhibited severe movement distortion during the execution of the spiking action that resulted in a loss of balance in the air, the trial was deemed unsuccessful, even if the ball successfully crossed the net and landed within the target zone.

The volleyball jump serve is a complex movement involving the ball toss, approach, take-off, and aerial spiking, making it difficult even for high-level athletes to maintain consistent performance across multiple trials. Therefore, we adopted the dual-selection method described by Liu et al. [4], in which the trial selected for analysis was based on both self-assessments from the participants and objective measure (ball speed). After each trial, participants rated their performance on a five-point Likert scale, with scores of 5 and 4 indicating excellent and good trials, respectively. Participants continued serving until at least three successful trials with a score of 4 or 5 in each direction were achieved. To minimize the effects of fatigue and ensure optimal performance, sufficient rest time was provided between trials. The rest period was self-determined by each participant based on their perceived fatigue status. The trial with the highest ball speed was selected for subsequent movement analysis to characterize each participant’s jump serve performance.

Data collection

Participants wore snug-fitting clothing, a swim cap, and their personal athletic shoes. A total of 47 retro-reflective markers (14 mm in diameter) were attached to the participants’ bodies. Marker placement locations (Fig. 3) were consistent with those described in Liu et al. [11]. All markers were placed by the same experienced research assistant to ensure consistency. A 12-camera motion capture system (Qualisys Track Manager, Qualisys, Sweden) recorded the three-dimensional coordinates of the markers during jump serves at 200 Hz. Before each data collection session, the cameras were positioned as shown in Fig. 2 and aligned to ensure full coverage of the capture volume based on the global coordinate system defined by the L-frame. The system was then calibrated using the manufacturer-recommended wand calibration procedure, with an average calibration error for the 12-camera system was approximately 1.6 mm. Following system calibration, each participant performed a static T-pose trial, which was captured to establish their anatomical reference frames. Ground reaction force data were recorded using four force plates (FP 600 × 500 × 50; Kistler Group, Winterthur, Switzerland) at a sampling rate of 200 Hz, synchronized with the motion data. Ball speed was measured using a portable volleyball radar device (Smart Coach, Pocket Radar Inc., Santa Rosa, USA). In accordance with Lima et al. [3], the radar gun was securely positioned behind the target zone and aligned directly with the server to minimize potential measurement error.

Fig. 3.

Location of the reflective markers. The reflective marker positions were as follows: vertex of the head, tragus, suprasternal notch, xiphoid process, 5th cervical vertebra, 10th thoracic vertebra, anterior and posterior shoulders, acromions, lateral costal borders (10th rib), medial and lateral elbow joints, medial and lateral wrist joints, 3rd metacarpals of the hands, greater trochanters, anterior and posterior superior iliac spines, medial and lateral knee joints, medial and lateral ankle joints, 1 st and 5th metatarsals, calcaneal tuberosities, and toes

Data analysis

Data were processed using MATLAB 2016a (MathWorks Inc., Natick, MA, USA). Marker trajectory data were filtered using a low-pass Butterworth filter with a 15 Hz cutoff frequency [11, 17]. The ground reaction force data were only used to identify the moment of take-off and were not filtered. The X, Y, and Z axes of the global coordinate system were defined as rightward–leftward, forward–backward, and vertically upward directions, respectively.

Each participant’s lower limbs were modeled using a seven-segment lower-limb model, comprising the left/right feet, shanks, thighs, and the pelvic, following the method described by Ae et al. [18] in their study on lower-limb kinetics in baseball. The right leg (comprising the right thigh, shank, and foot) was defined as the attacking leg, while the left leg (left thigh, shank, and foot) was defined as the non-attacking leg. The attacking arm’s hand (right hand) was modeled as a rigid body. The centre of mass (CoM) and inertia parameters for each segment were estimated using the anthropometric data from Ae et al. [19].

Variables computation

The hand velocity of the attacking arm was determined as the square root of the CoM velocity of the hand at ball contact (BC), following the method adopted in previous studies [4, 11].

The pelvic inclination angle was defined as the angle between the line connecting the mid-hip and mid-rib markers along the Z-axis in the YZ plane. The pelvic rotation angle was defined as the angle between the line connecting the right and left anterior superior iliac spine markers and the X-axis of the global coordinate system (see Fig. 4 for details). Angular velocity for each angle was calculated through numerical differentiation. Positive and negative values corresponded to the forward (serving) and backward (opposite serving) directions, respectively.

Fig. 4.

Mean (standard deviation) time-series data for pelvic angular velocity in inclination (top) and rotation (bottom). The black line depicts the mean values, and the grey shaded area represents the standard deviation values. TO: take-off; MSE: maximum shoulder external rotation; BC: ball contact. The aerial spiking phase has been time-normalised to 100%, with 0% corresponding to TO and 100% to BC. The vertical dotted line in the figure indicates the normalised time point for the MSE. The stick pictures on the right correspond to the pelvic inclination angle (a) and pelvic rotation angle (b), which are defined according to the global coordinate system. The arrow in the figure suggest that the extracted peak kinematic variable is significantly correlated with the attacking arm’s hand velocity at BC. The number beside each arrow shows the correlation coefficient (r), and the significance marker (*) indicates p < 0.05

Joint angular velocity was calculated by subtracting the angular velocity of the proximal segment from that of the distal segment. Joint moments at the lower limb joints were calculated using the bottom-up inverse dynamics method with the Newton-Euler equation [20]. The joint moment (JM) was calculated using the following equation:

Where is the inertia matrix for the segment i. The _i and are the angular acceleration and angular velocity of segment i, respectively. The and are the position vectors from the junction to the CoM of the proximal and distal segments, respectively. The and are the joint forces applied to segment i by the adjacent proximal and distal segments, respectively. is the joint moment acting on segment i from the adjacent distal segment. The joint angular velocities and moments were then transformed into the joint coordinate system (JCS). The JCS for each lower limb was defined according to the method described by Ae et al. [18]. To account for individual differences in body weight and facilitate statistical analysis, joint moments were normalised to body mass (kg) and expressed in Nm/kg. The sign convention for joint angular velocities and joint moments was as follows: positive (+) values correspond to flexion, adduction, and internal rotation, while negative (−) values correspond to extension, abduction, and external rotation. Note that angular velocity and joint moment of the ankle joints were excluded from the analysis due to negligible movement or moment during the aerial spiking phase.

Joint power was calculated as the product of each joint moment and the corresponding joint angular velocity, with results expressed in W/kg. Additionally, when interpreting joint power, both the magnitude and direction of the joint moment and angular velocity at a given time must be considered [20, 21]. For example, if a positive hip flexion moment (+) occurs along with a positive flexion angular velocity (+), the joint power will be positive, indicating that the flexor muscle group is generating mechanical energy through concentric contraction—referred to as power generation. Conversely, if the moment is positive (flexion) but the angular velocity is negative (extension), the joint power will be negative, indicating that the flexor muscle group is absorbing mechanical energy through eccentric contraction—referred to as power absorption.

Aerial spiking phase

The aerial spiking phase of the jump serve spans from take-off (TO) to BC. TO was defined as the moment when both feet left the ground, confirmed by a vertical ground reaction force of less than 5 N. Regarding the identification of ball contact (BC), when the hand makes contact with the ball, it experiences a reaction force that causes a deceleration in its forward (spike-direction) acceleration. We adopted of approach of Liu et al. [4] and Zhang et al. [22], BC was defined as the frame immediately preceding (0.005 s) the first detectable deceleration in the anterior positive horizontal acceleration (Y-axis) of the attacking arm’s hand CoM (Fig. 2). All variables were normalised to 100% of the aerial spiking phase, from TO to BC. For peak extraction, all kinetic and kinematic variables were examined during the aerial spiking phase. If two same-direction peaks occurred within this phase (e.g., two peak hip flexion moment, see Table 2), both were extracted and labeled “(1st)” and “(2nd)” according to their temporal order. If only one peak was present, it was extracted without labelling.

Statistical analysis

All statistical analyses were conducted using JASP software (https://jasp-stats.org/). Descriptive statistics were presented as mean ± standard deviation. Data normality was assessed using the Shapiro–Wilk test. Pearson product–moment correlation coefficients were calculated to evaluate the relationships between peak pelvic kinematics, peak joint moments, peak joint power, and the attacking arm’s hand velocity at BC. If normality assumptions were violated, Spearman’s rank correlation test was applied. Statistical significance was set at P < 0.05.

Stepwise multiple regression analysis was performed to identify key predictors of hand velocity. Since hand velocity represents the cumulative output of the kinetic chain from the trunk to the upper limbs, and the hand directly contacts the ball during impact, it plays a decisive role in determining the ball’s post-contact flight speed, as described in the introduction. Peak pelvic angular velocity, joint moment, and joint power variables that showed significant correlations were entered as independent variables. To assess multicollinearity, variance inflation factor (VIF) and tolerance values were computed, with VIF values above 10 or tolerance values below 0.1 indicating multicollinearity concerns [23]. Statistical significance for regression coefficients was also set at P < 0.05.

Results

Attacking arm’s hand velocity

The attacking arm’s hand velocity at ball contact (BC) was 15.67 ± 1.77 m/s, and the values were normally distributed.

Pelvic angular velocity

Figure 4 presents the time series of changes in angular velocity for pelvic motion. From take-off (TO), the pelvis tilted backward (−). At approximately 40% of the aerial spiking phase, the pelvis rapidly tilted forward (+), reaching a peak near maximum shoulder external rotation (MSE) (a). Simultaneously, the pelvis rotated rapidly forward (+), with a peak occurring at approximately 70% of the phase (b). The peak forward angular velocity (+) of pelvic inclination (3.93 ± 1.06 rad/s) was significantly correlated with the hand velocity at BC (r = 0.596, p = 0.012) (Table 1).

Attacking leg joint kinetics

Figure 5 presents the time series of changes in joint angular velocity, joint moment, and joint power for the attacking leg. In the flexion and extension directions, from approximately 70% of the aerial phase, the hip joint flexed (a) rapidly, generating a larger flexion moment (b), which resulted in higher positive power (c). For adduction and abduction, from around 40% of the motion to MSE, the hip joint began to adduct (d) while exerting a larger adduction moment (e), which led to positive power (f). Regarding internal and external rotations, starting from TO, the hip joint initially rotated internally and then rotated externally (g), with the joint moment (h) approaching zero, resulting in zero power (i). No kinetic variable of the hip joint was significantly correlated with the hand velocity at BC (Table 2).

Fig. 5.

Mean (standard deviation) time-series data for joint angular velocity (top), joint moment (middle), and joint power (bottom) of the attacking leg. The black line depicts the mean values, and the grey shaded area represents the standard deviation values. TO: take-off; MSE: maximum shoulder external rotation; BC: ball contact. The aerial spiking phase has been time-normalised to 100%, with 0% corresponding to TO and 100% to BC. The vertical dotted line in the figure indicates the normalised time point for the MSE. The arrows in the figures suggest that the extracted peak kinetic variables are significantly correlated with the attacking arm’s hand velocity at BC. The number beside each arrow shows the correlation coefficient (r), and the significance marker (*) indicates p < 0.05

In the flexion and extension directions, the knee joint angular velocity increased in flexion from TO and then rapidly extended from approximately 40% of the aerial phase (j). The joint moment showed an extension moment from TO to just before MSE (k). Accordingly, the knee joint produced negative power from TO to around 40% of the aerial phase, followed by positive power (l). The peak knee extension moment (− 0.92 ± 0.34 Nm/kg) and positive power (7.05 ± 3.63 W/kg) were significantly correlated with the hand velocity at BC (r = − 0.499, p = 0.041; r = 0.532, p = 0.028) (Table 2), respectively.

Non-attacking leg joint kinetics

Figure 6 presents the time series of changes in joint angular velocity, joint moment, and joint power for the non-attacking leg. In the flexion and extension directions, the hip joint angular velocity increased in extension from TO to approximately 50% of the aerial phase, followed by rapid flexion (a). The joint moment exhibited a large flexion moment throughout the aerial spiking phase (b), resulting in small negative power from approximately 30% to 60% of the aerial spiking phase, followed by large positive power (c). The peak hip flexion moment (1.74 ± 0.46 Nm/kg) and positive power (9.84 ± 3.06 W/kg) were significantly correlated with the hand velocity at BC (r = 0.595, p = 0.012; r = 0.576, p = 0.016) (Table 2).

Fig. 6.

Mean (standard deviation) time-series data for joint angular velocity (top), joint moment (middle), and joint power (bottom) of the non-attacking leg. The black line depicts the mean values, and the grey shaded area represents the standard deviation values. TO: take-off; MSE: maximum shoulder external rotation; BC: ball contact. The aerial spiking phase has been time-normalised to 100%, with 0% corresponding to TO and 100% to BC. The vertical dotted line in the figure indicates the normalised time point for the MSE. The arrows in the figures suggest that the extracted peak kinetic variables are significantly correlated with the attacking arm’s hand velocity at BC. The number beside each arrow shows the correlation coefficient (r), and the significance marker (*) indicates p < 0.05

In the adduction and abduction directions, from approximately 30% of the aerial phase to MSE, the hip joint angular velocity rapidly increased in abduction (d). The joint moment (e) showed an abduction moment from TO to around 50% of the aerial phase, followed by an adduction moment. As a result, the joint power (f) remained close to zero. Regarding internal and external rotations, starting from TO, the hip angular velocity demonstrated steep internal rotation (g), while the joint moment (h) remained near zero. Consequently, the joint power was also close to zero (i). No kinetic variable of the hip joint in the adduction–abduction and internal–external rotation directions was significantly correlated with the hand velocity at BC (Table 2).

In the flexion and extension directions, the knee joint angular velocity increased in flexion from TO and rapidly extended from approximately 40% of the aerial phase (j). The joint moment (k) showed an extension moment from around 40% to 60% of the aerial phase. The knee joint generated negative power from approximately 20% to 40% of the aerial phase, followed by large positive power (l). The peak knee extension moment (− 0.90 ± 0.38 Nm/kg), negative power (− 3.19 ± 1.56 W/kg), and positive power (6.07 ± 3.73 W/kg) were significantly correlated with the hand velocity at BC (r = − 0.585, p = 0.014; r = − 0.551, p = 0.022; r = 0.594, p = 0.012) (Table 2).

The regression model included peak pelvic forward inclination angular velocity and peak hip flexion moment of the non-attacking leg as predictors of the hand velocity at BC. This model explained 53.2% of the variance in hand velocity (R² = 0.591, adjusted R² = 0.532) and demonstrated a statistically significant fit (F(2, 14) = 10.097, p = 0.002). The predictive equation is as follows: hand velocity = 9.113 + 0.830 × (peak pelvic forward inclination angular velocity) + 1.892 × (peak non-attacking leg hip flexion moment).

Discussion

This study aimed to determine the lower-limb joint kinetics during the aerial spiking phase of the jump serve and to explore their relationship with the attacking arm’s hand velocity at ball contact (BC). The main findings were that the peak forward pelvic inclination angular velocity was significantly correlated with the hand velocity at BC. Additionally, the peak hip flexion moment and peak positive power of the non-attacking leg, as well as the peak knee extension moments and positive power in both legs, also exhibited significant correlations with hand velocity. Regression analysis, incorporating peak pelvic forward inclination angular velocity and peak hip flexion moment of the non-attacking leg as independent variables, accounted for 53.2% of the variance in the hand velocity at BC, which supports the hypothesis. However, it should be noted that most previous studies on lower-limb kinetics in volleyball have focused on the plant and take-off phase, with limited investigation during the aerial phase of the jump serve. Furthermore, in the aerial spiking motion, the athlete is in the air, with no external forces acting on the body except gravity. This condition differs significantly from ground-supported movements, making it difficult to apply existing literature and biomechanical theories to this context. Therefore, an exploratory stepwise regression approach was used to identify the effect of potentially relevant lower-limb kinetic variables on attacking hand velocity during the aerial spiking phase. While the results provide insights with possible training implications, caution should be exercised in their interpretation due to the data-driven nature of the analysis.

The peak pelvic forward (spike-ball direction) inclination angular velocity was significantly correlated with the hand velocity at BC, whereas the peak pelvic forward rotation angular velocity was not (Table 1). A volleyball textbook [12] and several volleyball studies [7, 8, 10, 16] suggest that during the aerial spiking motion, body parts follow a proximal-to-distal sequencing order, with the angular velocity peaks of the pelvis, trunk, and shoulder increasing in sequence to optimise spike velocity. These studies emphasise pelvic rotation as the initiating segment of this sequence, contributing to the transfer of angular momentum to the subsequent distal segments. However, our statistical findings did not fully support this argument, as pelvic inclination forward angular velocity, rather than pelvic forward rotation angular velocity, was significantly linked to hand velocity. Studies on tennis serving [24–26] have reported that elite players do not always follow a strict proximal-to-distal sequence and rely more on the forward inclination of the trunk. This is because of the trunk rapidly tilting forward generates angular momentum that directly contributes to the forward (stroke-direction direction) linear velocity generation of the shoulder and racket during the acceleration phase. Our results support this perspective, as the pelvis links the trunk and its rapid forward tilt, which may drive the entire trunk tilting together, enabling more effective momentum transfer to the upper limb and ultimately enhancing hand velocity. These findings emphasise the importance of optimising pelvic forward inclination to generate greater hand velocity.

The current study found no contribution of pelvic rotation; however, it revealed a significant correlation between the peak hip flexion moment in the non-attacking leg and the hand velocity at BC. In contrast, the peak hip flexion moment in the attacking leg was not significantly correlated. Previous research in sports biomechanics has suggested that pelvic motion is influenced by the moments and forces at the hip and lumbar joints bilaterally [15, 27]. In the aerial phase, where ground reaction forces are absent, pelvic motion arise from internal segmental interactions, primarily coupled hip actions. For example, Wagner et al. [28] reported that, during handball jump throws, hip flexion of the non-attacking leg is associated with increased pelvic motion via pelvis–hip coupling. Our results showed that the pelvis rapidly tilted forward, beginning at approximately 40% of the phase (Fig. 4a). Simultaneously, the hip flexion angular velocity (Fig. 6a) and moment (Fig. 6b) of the non-attacking leg increased until the end of the motion phase. In addition, regression analysis indicated that a 1 m/s increase in hand velocity corresponded to an increase of approximately 0.5 Nm/kg in peak hip flexion moment and 1.2 rad/s in peak pelvic forward-inclination angular velocity. Based on these results, we considered that the exertion of the greater hip flexion moment of the non-attacking leg may facilitate a faster forward pelvic inclination through pelvis–hip coupling, thereby directly enhancing the hand velocity.

The hip power of the non-attacking leg exhibited substantial positive generation during the later part of the aerial spiking phase (Fig. 6c) and the peak positive power was significantly correlated with the hand velocity at BC (Table 2). Some tennis serve studies [29–31] indicate that the lower limb drive provides the initial energy input to the kinetic chain. This energy is transmitted through the pelvis and trunk to the accelerating segments of the upper limb, which is crucial for increasing racket velocity. Lertwonghattakul et al. [32] studied energy flow in the tennis serve and demonstrated that hip power significantly contributes to the kinetic chain during the acceleration phase (aerial phase). Therefore, we propose that the spike motion in jump serves parallels the tennis serve. In both, the contraction of the hip flexors in the non-attacking leg generates considerable mechanical energy. This energy is transmitted to the attacking arm through the pelvis and trunk, ultimately increasing hand velocity (Fig. 7).

Fig. 7.

Contribution of joint powers from each joint of the attacking and non-attacking legs to hand velocity during approximately 60% of the aerial spiking phase

The knee joints of both the attacking and non-attacking legs exhibited similar patterns in angular velocity, joint moment, and power. From TO to MSE, both knees generated substantial extension moments (Figs. 5k and 6k). The peak values of these moments were significantly correlated with the hand velocity at BC (Table 2). During this period, knee joint angular velocity followed a flexion–extension pattern (Figs. 5j and 6j), resulting in an initial phase of negative power, followed by a larger positive power phase (Figs. 5l and 6l). Our statistical results revealed that the peak negative power of the knee joint of the non-attacking leg and the peak positive power of both knee joints were significantly associated with the hand velocity (Table 2). Previous studies on volleyball spikes [7, 8, 10, 16] show that during the plant and take-off phase (see Fig. 1), the knee joint first flexes, using the stretch-shortening cycle (SSC) to produce negative power through eccentric contraction, thereby absorbing mechanical energy, then rapidly extends concentrically to generate positive power and release the stored mechanical energy. Within the SSC framework, the eccentric contraction phase (negative power) not only absorbs but also stores elastic energy in the muscle–tendon complex, which is subsequently released during concentric contraction to augment energy generation [30, 33, 34]. This transition from negative to positive power, similar to a counter-movement jump [35, 36], increases the mechanical energy available to the body, thereby enhancing jump height and preparing for subsequent actions. Forthomme et al. [37] demonstrated that counter-movement jump ability (jump height) was significantly associated with ball speed, underscoring the importance of lower-limb explosive capacity in enhancing volleyball spike velocity.

Our results show that a similar eccentric–concentric sequence also occurs during the aerial spiking phase (Figs. 5l and 6l). This occurs because, as the athlete ascends through the air, part of the body’s linear kinetic energy is gradually converted into potential energy based on the principle of conservation of energy [20], which reduces the kinetic energy directly available for building the kinetic chain from trunk to attacking arm. In this context, the knee extensors function through the SSC by first eccentrically absorbing mechanical energy (negative power) and then concentrically releasing it (positive power). We consider that this compensatory mechanism can preserve whole-body kinetic energy and support efficient energy transfer along the kinetic chain from the lower limbs to the trunk and attacking arm, ultimately contributing to greater hand velocity at BC. It should be noted that although peak knee joint powers in both legs showed significant bivariate correlations with hand velocity (Table 2), they were not retained in the final stepwise regression model. This is because the method selects predictors based on their explanatory contribution after accounting for variables already included. In our analysis, the combination of peak pelvic forward inclination angular velocity and peak non-attacking leg hip flexion moment was identified as the optimal predictors. The inclusion of peak knee joint powers reduced the variance explained in hand velocity (adjusted R² = 0.532). This reduction in explanatory power was due to their high correlations with other predictors, which introduced multicollinearity. Therefore, peak knee joint powers were excluded according to the stepwise regression criteria, rather than due to a lack of biomechanical relevance.

Additionally, during the aerial spiking phase of the jump serve, the athlete’s body is subject to the principle of conservation of angular momentum, as no significant external torques act upon it. According to this principle, any increase in angular momentum in one body segment must be counterbalanced by an equal and opposite angular momentum in other segments to maintain overall body equilibrium [6, 20]. Liu et al. [11] reported that during the arm acceleration phase, the attacking arm and trunk undergo rapid rotation toward the spike-ball direction, generating considerable angular momentum and inducing a rotational tendency of the whole body. Simultaneously, the attacking and non-attacking legs generate angular momentum in the opposite direction. This has been interpreted as a compensatory mechanism aimed at stabilizing the body and minimizing excessive axial rotation. Building upon this, we propose that during the aerial spiking phase, the extension moments and angular velocities produced by both knee joints contribute to the regulation of aerial posture via angular momentum compensation. These kinetic patterns serve a critical role in maintaining balance in the air and may indirectly contribute to increased hand velocity.

The present study has some practical implications. Our regression model suggests that each 1.2 rad/s increase in peak pelvic forward inclination angular velocity is associated with a 1.0 m/s increase in hand velocity. Similarly, a 0.5 Nm/kg increase in non-attacking leg hip flexion moment corresponds to a comparable gain in hand velocity. Notably, the hip flexion moment of the non-attacking leg showed a stronger effect (β = 1.892) than pelvic forward inclination angular velocity (β = 0.830). From a training standpoint, these findings suggest that coaches and athletes should focus on strengthening the hip flexors of the non-attacking leg to improving rapid pelvic forward tilt during the aerial phase to enhance arm swing velocity at BC. To achieve this, we recommend exercises, such as single-leg straight leg raise and Bulgarian split squats, to develop unilateral hip flexor strength and improve unilateral hip–pelvis coordination. Bulgarian split squats significantly increase the activation of rectus femoris and erector spinae, when performed with a forward trunk lean [38]. They also strengthen the unilateral hip flexor and enhance trunk stability, which indirectly supports unilateral hip–pelvis coordination and may facilitate a more rapid pelvic forward tilt. Additionally, plyometric drills, such as jump lunges, generate markedly higher activation of the quadriceps (rectus femoris, vastus lateralis, and vastus medialis) [39]. Further, Jönhagen et al. [40] showed that rectus femoris exhibits significant activation during the eccentric and concentric phases of a jumping lunge, indicating its involvement in rapid SSC actions. Therefore, jump lunges can directly enhance hip flexor and knee extensor function through SSC loading, improve explosive capacity, and enhance the dynamic coordination between the hip joint and pelvic control, simulating the neuromuscular demands of aerial spiking motion. Finally, rapid squat jumps can improve the knee extensors’ ability to produce rapid eccentric–concentric contractions, increasing whole-body kinetic energy through improved SSC function and possibly contributing indirectly to greater hand velocity. These exercises can be incorporated into volleyball-specific conditioning during the season, one–three times per week, performed with moderate sets and repetitions, and combined with jump serve practice to facilitate the transition to aerial spiking motion.

There are several limitations in the present study. First, the participants were high-level male volleyball players, which may limit the generalizability of the findings to athletes of different skill levels or to female athletes. Second, lower-limb joint moments were calculated using an inverse dynamics approach, which, although effective for estimating net joint moments, does not provide direct insight into the contributions of specific muscles to joint motion. Third, although our discussion suggests that hip flexion moments in the non-attacking leg contribute to forward pelvic tilt, this explanation does not fully capture the dynamic mechanisms underlying pelvic motion, as a substantial portion of pelvic movement is also influenced by forces and moments at the lumbar joint. Fourth, although we used stepwise regression to explore the relationship between lower-limb kinetic variables and attacking arm hand velocity, this method has well-documented limitations, including model instability, overfitting, and the risk of capitalizing on chance correlations within a given sample. Therefore, the statistical results should be interpreted with caution. To our knowledge, however, this is the first biomechanical study to examine the role of lower-limb dynamics in arm swing speed during execution of the jump serve technique. These findings provide valuable insights for coaching jump serve techniques and for designing strength training programs to enhance performance. Further studies should combine kinematic, kinetic, and electromyographic (EMG) data to examine individual muscle activation patterns and better identify key muscular contributors in the lower limb joints during the aerial spiking motion. Additionally, expanding the sample to include comparisons between elite and amateur players, as well as between male and female athletes, to increase our knowledge on biomechanics of the volleyball jump serve.

Conclusions

The results of this study suggest that increasing the hip flexion moment in the non-attacking leg facilitates a more rapid forward pelvic tilt, which can contribute to a higher attacking arm’s hand velocity at BC. Additionally, peak knee extension moments and power generation in both the attacking and non-attacking legs were correlated with hand velocity. These findings indicate that knee extensors play a crucial role in generating mechanical energy, maintaining whole-body balance, and establishing an effective kinetic chain that supports improvements in hand velocity. Overall, these findings underscore the importance of lower-limb movement during the aerial spiking phase of the jump serve.

This study was conducted with only male professional volleyball players. Future studies should include players at different levels (e.g., elite and amateur) and female players to improve the generalisability and practical applicability of the findings.

Abbreviations

ACG

Attacking leg makes contact with the ground

TO

Take-off

MSE

Maximum shoulder external rotation

BC

Ball contact

3D

Three dimensional

JSC

Joint coordinate system

CoM

Center of mass

VIF

Variance inflation factor

SSC

Stretch–shortening cycle

EMG

Electromyographic

Authors’ contributions

LL and ZC contributed to the conception and design of the study. LL and ZC were responsible for data acquisition. LL, ZC, and TP analyzed and interpreted the data. LL drafted the manuscript. ZC and TP substantively revised the manuscript. All authors read and approved the final manuscript. All authors read and approved the final manuscript.

Funding

This research was funded by Shanghai Sports Science and Technology Program (grant number: 25J007).

Data availability

In accordance with ethical guidelines, the data generated and/or analyzed during this study are not publicly accessible, but can be obtained from the corresponding author upon reasonable request.

Declarations

Ethics approval and consent to participate

All procedures were approved by the Ethics Committee of the Shanghai Research Institute of Sports Science (Shanghai Anti-Doping Agency) (Approval No. LLSC20230015). Informed consent was obtained from all participants after they were fully informed about the study.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.