Kinematic Analysis of Para Table Tennis Players’ Movement Dynamics in Response to Alternating Directional Ball Feeds

Abstract

This study investigated the kinematic characteristics of center of mass (CoM) movement in elite standing para table tennis players during a controlled 20-ball displacement speed test, focusing on displacement, velocity, acceleration, and jerk as indicators of movement coordination and control. Twenty-one national-level athletes (classes 6–11) performed alternating forehand and backhand strokes while three-dimensional motion analysis captured CoM trajectories. The primary aim was to characterize directional CoM kinematics, and the secondary aim was to examine associations with functional ability, stroke accuracy, and expert-rated technical performance. Results indicated that the range of CoM displacement was largest in the medio-lateral direction, reflecting the sport-specific demands of side-to-side repositioning, while mean displacement did not differ significantly between the medio-lateral and antero-posterior axes. Similarly, velocity, acceleration, and jerk ranges were greatest laterally, highlighting the dynamic requirements of lateral movement. Correlation analyses revealed no statistically significant associations between CoM metrics and functional ability, stroke accuracy, or expert-rated performance after Bonferroni correction, though exploratory trends suggested that higher-functioning athletes may exhibit greater lateral displacement. Jerk, as a measure of movement smoothness, did not systematically differentiate performance or functional class. These findings underscore the predominance of lateral CoM control in para table tennis and provide a biomechanical basis for training interventions aimed at improving lateral stability, coordination, and functional efficiency.

1. Introduction

Table tennis is a Paralympic sport that requires athletes with a wide range of physical impairments to respond to rapid changes in ball direction, spin, and speed, while simultaneously maintaining postural stability and executing technically precise strokes [1]. Differences in functional classification among standing athletes (Classes 6–10) and players with intellectual impairment (Class 11) are associated with distinct movement strategies, coordination patterns, and biomechanical constraints [2]. These adaptations underscore the significance of comprehending movement dynamics and balance control within the context of sport-specific functional limitations.

In racket sports, the movement of the body’s center of mass (CoM) has been increasingly recognized as a key determinant of movement efficiency, technical execution, and overall performance [3]. Efficient CoM control facilitates energy transfer through the kinetic chain, enhances stroke precision, and supports rapid repositioning between strokes [4,5]. Such findings are consistent with broader evidence emphasizing motor coordination and control as central components of technical proficiency in sport [6].

In tennis, for example, Talaat and Attaallah [7] demonstrated that CoM trajectory during the serve closely mirrored the motion of the striking limb, underscoring the coordination between whole-body dynamics and upper-limb actions. Similarly, Wang et al. [8] reported significant differences in CoM displacement patterns between expert and novice badminton players, suggesting that refined CoM control reflects superior technical proficiency and movement economy.

In table tennis, previous kinematic studies have primarily examined joint angles, racket velocity, and plantar pressure distribution [9,10]. However, research quantifying whole-body CoM behaviour is extremely limited in both able-bodied and para table tennis, and evidence specific to para athletes is almost nonexistent [1,11,12,13]. Recent reviews of Paralympic biomechanics similarly emphasize the absence of CoM-focused analyses in para table tennis, despite their importance for balance, movement efficiency, and trunk-limb coordination [14,15,16,17]. Wong et al. [10] noted that although forehand and backhand mechanics have been described, a CoM-level analysis remains a critical knowledge gap, particularly among standing para-athletes whose trunk and limb impairments may alter dynamic stability. Because the present study includes only standing players (Classes 6–11), the interpretation of CoM control is restricted to this population; wheelchair-specific differences are not relevant to the current dataset and are therefore not considered in this study [1,10,11,12,18].

A particularly informative, yet underexplored, parameter in kinematic analyses is jerk, defined as the rate of change of acceleration (m·s⁻³). Jerk reflects the smoothness and coordination of movement and is often used as an indicator of motor control efficiency [19]. Lower jerk values are typically associated with smoother and more coordinated motion, whereas higher jerk indicates abrupt, less controlled changes in acceleration—often interpreted as reduced movement fluency [20,21]. Studies in rehabilitation and motor control contexts have shown that jerk-based measures can effectively differentiate between movement strategies in individuals with motor impairments [22].

In para table tennis, particularly among standing athletes with varying degrees of trunk and upper-limb impairment, jerk provides a sensitive indicator of how functional limitations affect movement smoothness and control, i.e., functional efficiency. It is therefore expected that athletes with higher functional ability (lower impairment) will exhibit lower jerk and more efficient CoM regulation, reflecting better functional efficiency, especially during medio-lateral actions required by alternating forehand–backhand strokes. Accordingly, the present study is designed to characterize CoM displacement, velocity, acceleration, and jerk during a controlled 20-ball displacement speed test and to determine how these variables differ across functional classes and stroke directions among standing para table tennis athletes (Classes 6–11).

Based on previous findings and biomechanical reasoning, the following hypotheses are proposed: (1) CoM kinematic variables (displacement, velocity, acceleration, jerk) will show greater magnitude in the medio-lateral direction than in the antero-posterior or vertical directions; (2) athletes in higher functional classes (lower impairment) will exhibit smoother CoM movement (lower jerk) and superior performance (e.g., number of successful returns, Gómez scale); (3) more efficient CoM dynamics (lower jerk and more consistent displacement patterns) will be positively associated with performance during the displacement speed test.

2. Materials and Methods

2.1. Participants’ Characteristics

A total of twenty-one para table tennis athletes (17 men and 4 women) participated in the study (

Table 1. Distribution of functional classes in standing para table tennis athletes.

Sport Class	Description	Men (n)	Women (n)	Total (n)
Class 6	Severe lower-limb or playing arm/hand limitation	2	1	3
Class 7	Severe lower-limb and arm/hand limitation	4	0	4
Class 8	Moderate impairment of one or both lower limbs/arm	5	1	6
Class 9	Mild–moderate limitation of one lower limb or arm	3	1	4
Class 10	Mild lower-limb or arm/hand limitation	1	0	1
Class 11	Intellectual impairment	2	1	3

). All athletes competed in standing categories, corresponding to classes 6 to 11 in the International Table Tennis Federation (ITTF) Para Table Tennis classification system [23]. These classes encompass athletes with varying degrees of physical impairment who can play in a standing position, ranging from more severe functional limitations (Class 6) to minimal impairments (Class 10), as well as athletes with intellectual impairments (Class 11). Most participants played using the right arm (n = 19), whereas only one woman and one man were left-handed.

All participants (

Table 2. Demographic, performance characteristics and functional class of para table tennis athletes (mean ± standard deviation).

Participants	Age [Years]	Body Mass [kg]	Body Height [cm]	Points on Gomez Scale
Women (n = 4)	26.25 ± 10.21	55.1 ± 3.81	159.5 ± 9	4.00 ± 1.41
Men (n = 17)	17.76 ± 5.97	52.58 ± 15.08	162.59 ± 13.03	3.41 ± 1.80
All	19.38 ± 7.47	53.06 ± 13.6	162 ± 12.23	3.52 ± 1.72

) were members of the Polish Para Table Tennis National Team, with an average of 12.78 ± 7.27 years of training experience and a training frequency of five to ten sessions per week. Therefore, no formal sample size calculation was conducted; therefore, the study may be underpowered to detect small-to-moderate effects, and results should be interpreted with this limitation in mind. None of the athletes reported injuries, pain, or musculoskeletal disorders during the twelve months preceding the measurements.

The inclusion criteria for the study were as follows: written informed consent from the athletes’ parents or legal guardians; confirmed membership in the Polish national para table tennis team; possession of a valid license issued by the Polish Table Tennis Association, which includes accident insurance (NNW); a minimum of two years of systematic training experience; a year of birth corresponding to the targeted or specialized training stage (to be specified); and a health condition allowing for the safe execution of all physical performance tests. Additionally, only athletes whose playing style involved the use of smooth rubbers or short pips were included. Players using atypical rubbers such as anti-spin or long pips were excluded, due to the distinct stroke mechanics these rubbers promote, which differ from the topspin techniques required in the displacement speed test.

The Gómez Performance Scale was used as an expert-based measure of technical proficiency, movement coordination, and motor control. The scale ranges from 1 to 5 points, where 1 denotes very poor performance with unstable or uncoordinated motion, and 5 represents very good or exemplary performance characterized by fluid, precise, and well-coordinated movements (

Table 3. The Gómez Scale—Description and Interpretation.

Points on Gomez Scale (1–5)	Description of Performance Quality	Movement Characteristics
1—Very poor	Task execution unsuccessful or highly unstable	Numerous errors, lack of movement control, poor coordination
2—Poor	Low effectiveness and difficulty completing the task	High instability, limited smoothness, disrupted rhythm
3—Average	Acceptable performance but inconsistent or imprecise	Movement with visible compensations or asymmetries
4—Good	Stable, smooth, and precise execution	Good control, minor technical inaccuracies
5—Very good/exemplary	Smooth, well-coordinated, and technically correct movement	High precision and excellent motor control

). The scale has been previously validated and adapted for athletes with impairments in para table tennis, demonstrating adequate reliability and construct validity [24,25]. This assessment tool, originally developed for use in Paralympic sports, has been applied to evaluate qualitative aspects of movement execution in para table tennis, boccia, and other precision-based disciplines [23,26].

Gómez’s performance scores ranged from 1 to 5, indicating substantial variability in movement quality and technical control. Among male players, the distribution of Gómez scores was as follows: score 1—five players, score 2—one player, score 3—one player, score 4—three players, and score 5—seven players. Among female players, the distribution was: score 2—one athlete, score 4—one athlete, and score 5—three athletes. On average, male players achieved a Gómez score of 3.41 ± 1.80, and female players 4.00 ± 1.41. A general trend was observed in which athletes from higher functional classes tended to obtain higher Gómez scores, suggesting that individuals with fewer functional limitations may demonstrate better technical execution and motor control. However, this observation was not statistically tested and should be interpreted cautiously.

The rating scale was adopted from able-bodied athletes solely for illustrative purposes to indicate the level relative to sex. However, it is more meaningful to analyse performance in terms of the number of successful hits of a ball delivered at 80 balls/min over 15 s (maximum 20), rather than referring exclusively to the scale itself, since it was constructed for able-bodied individuals, with sex-based norms, and does not account for variables such as age, stage of training, training experience, training frequency, or the 11 sport classes in which athletes with impairments compete.

All participants, and for those under 18 years of age, their parents, provided written informed consent after being fully informed about the study aims and procedures. The experimental protocol was approved by the Senate Bioethics Committee of the Józef Piłsudski University of Physical Education in Warsaw, Poland (decision no. SKE.0030.41.2025, approval date 13 May 2025). The study was conducted in accordance with the principles of the Declaration of Helsinki.

2.2. Protocol

Participants completed one trial from the Table Tennis Specific Test Battery [24,27]. A familiarization session was conducted for all athletes before the measurements to ensure proper understanding of the testing procedures and to minimize learning effects. The Table Tennis Specific Test Battery comprises seven standardized tests designed to assess the technical, physical, and coordination-related abilities of para table tennis players. These include assessments of (1) displacement speed, (2) lateral footwork agility, (3) stroke accuracy, (4) reaction time, (5) rally endurance, (6) power generation during the forehand topspin, and (7) serve precision.

The Displacement Speed Test evaluates an athlete’s ability to rapidly coordinate trunk and upper-limb movements while alternating forehand and backhand topspin strokes across a designated target area on the opponent’s side of the table, with the number of successful hits recorded over a fixed time interval. The Lateral Footwork Agility Test measures the speed, coordination, and accuracy of side-to-side stepping movements between predefined positions on the court. The Stroke Accuracy Test evaluates the precision of forehand and backhand topspin strokes aimed at specific target zones, with scoring based on the number of accurate placements. The Reaction Time Test assesses an athlete’s ability to respond quickly to a visual stimulus by executing the appropriate stroke, with reaction time measured from stimulus presentation to successful ball contact. The Rally Endurance Test examines the ability to maintain continuous, controlled strokes over a sustained period at a fixed rhythm, assessing both technical consistency and physical endurance. The Power Stroke Test evaluates the maximum-speed execution of forehand topspin strokes, measuring the athlete’s ability to generate force while maintaining proper technique. Finally, the Serve Precision Test measures the accuracy and placement of standardized serves into designated target areas, assessing technical control and consistency under game-like conditions.

In the present study, only the Displacement Speed Test was employed, as this test specifically evaluates an athlete’s ability to coordinate rapid trunk and upper-limb movements while maintaining balance and stroke precision, key determinants of technical performance in para table tennis [28,29]. Valid hits were verified by two observers, who counted successful contacts in real time during each trial, and all attempts were subsequently re-checked frame-by-frame using video recordings.

During the task, athletes alternated forehand and backhand topspin strokes played cross-court into a designated rectangular target area (135 × 76 cm) on the opponent’s half of the table. Only successful cross-court hits were recorded as valid attempts. Ball delivery was standardized using a Tibhar Robo Pro Junior robot (Tibhar, Saarbrücken, Germany) positioned at the center of the table. The robot’s throwing roller generated a fixed 45° trajectory while its body remained stationary, ensuring consistent ball placement and spin. The robot was operated remotely, and identical settings were applied across all trials: speed = 6, spin = 0 (topspin), frequency = 6, resulting in approximately 80 balls·min⁻¹. Each trial lasted 15 s, corresponding to 20 ball feeds. The dispersion control (scale 1–3) was set to 3, directing balls toward the table corner while maintaining the 45° trajectory. Similar robotic devices have been used in previous studies to ensure repeatability and precision in ball projection, including Newgy Robo Pong 2050 (Hendersonville, TN, USA) [12], Tibhar Robo Pro Master (Tibhar, Germany) [30], and Newgy Robo Pong 1040 (Hendersonville, TN, USA) [28,29,31].

All tests were performed on ITTF-certified tables adapted for athletes with disabilities, using Tibhar 3-star plastic balls (Tibhar, Saarbrücken, Germany). Reaction times and trial durations were verified using a CASIO HS-80TW-1EF electronic stopwatch (Casio, Tokyo, Japan). Kinematic data were recorded using an eight-camera motion capture system (Simi Motion 3D v10.2; Simi Reality Motion Systems GmbH, Unterschleißheim, Germany) operating at 160 Hz. Before testing, a 3D spatial calibration was performed, with the origin defined at the table’s center. The global coordinate system was oriented such that X = medio-lateral (left–right relative to the table), Y = antero-posterior (from player to opponent), and Z = vertical (upward from the table surface). Athlete movements were reconstructed in 3D using Simi Shape 3D v5.0.1, which employs a markerless silhouette-based tracking method. Background subtraction was used to isolate the athlete’s silhouette from a reference image of the empty scene, followed by alignment of a 3D digital body model to the silhouette using the Iterative Closest Point (ICP) algorithm. Although markerless motion capture can introduce measurement errors, validation studies of the Simi Shape 3D system in dynamic tennis tasks have shown standard deviations of approximately 2–3 cm for segment CoM and joint centre positions, with strong correlations for key joint angles compared to traditional marker-based systems [32,33]. These results support the accuracy of the system for capturing dynamic sport-specific movements.

At the start of each trial, athletes adopted a standardized ready position with a slight forward lean and flexed elbows to facilitate model alignment. Participants wore tight-fitting, dark-colored clothing to optimize silhouette contrast and ensure reliable motion detection from all camera perspectives. The captured kinematic data were time-normalized and processed using the Simi Motion and Simi Shape software suite. A second-order low-pass Butterworth filter (cut-off frequency = 7 Hz) was applied to remove high-frequency noise. This cut-off was selected based on prior biomechanical research and established signal-analysis principles, which indicate that the majority of meaningful human-movement kinematic power is concentrated below approximately 7 Hz, with residual analysis commonly supporting cut-off frequencies in this range [34]. Furthermore, similar low-pass filtering parameters have been used in previous racket-sport kinematic studies, including table tennis, to effectively suppress noise while preserving functionally relevant movement information [10].

2.3. Kinematic Variables and Signal Processing Procedures

The kinematic analysis focused on the displacement of the center of mass (CoM) in three orthogonal directions: medio-lateral (X), antero-posterior (Y), and vertical (Z). Based on the CoM trajectories, linear velocity, acceleration, and jerk were computed using numerical differentiation in MatLab R2021a (MathWorks Inc., Natick, MA, USA). Linear velocity was obtained as the first derivative of CoM displacement with respect to time. Linear acceleration, calculated as the derivative of velocity, described the rate of change of body motion and provided insight into the control of movement initiation and transitions between strokes.

To minimize artefacts introduced by numerical differentiation, especially for acceleration and jerk, which are highly sensitive to high-frequency noise, a second-order low-pass Butterworth filter (cut-off frequency = 7 Hz) was applied to the displacement data and to the velocity signal prior to differentiation. Applying the filter before each differentiation step reduces noise amplification associated with calculating higher-order derivatives. The choice of a 7 Hz cut-off was based on biomechanical signal-processing principles, indicating that most human-movement kinematic power lies below ~6–8 Hz, as well as validation studies of the Simi markerless system in dynamic racket-sport tasks, which support filtering within this range to preserve meaningful motion while suppressing artefacts [35,36].

Jerk, defined as the time derivative of acceleration (the third derivative of displacement), quantifies the smoothness of movement and serves as an indicator of movement coordination and control [37,38]. Lower jerk values were interpreted as smoother and more coordinated motion patterns, while higher values indicated increased variability and abrupt changes in movement dynamics.

In the present study, non-normalized jerk values were used because (i) trial duration (15 s) and stroke frequency were standardized across athletes in the Displacement Speed Test, reducing variability due to movement timing; (ii) the aim was to capture natural inter-individual differences in whole-body movement smoothness rather than impose amplitude- or duration-based scaling; and (iii) no established amplitude normalization exists for whole-body CoM trajectories. It is acknowledged that jerk is sensitive to displacement magnitude, and therefore comparisons should be interpreted as reflecting naturally occurring coordination differences between athletes. In future research, normalized or log-dimensionless jerk metrics may be incorporated to facilitate comparisons across tasks and populations.

All kinematic signals (CoM displacement, velocity, acceleration, and jerk) were subsequently time-normalized to ensure equal trial length across participants. Each 15-s trial, originally sampled at 160 Hz, was resampled to a fixed length of 1600 samples using cubic interpolation. Time-normalization was applied across the full trial duration without alignment to discrete events (e.g., ball contact), as the test involves continuous alternating topspin strokes and reliable event identification was not feasible across participants. Mean, range, and root mean square (RMS) values were then calculated from the time-normalized curves to ensure comparability across participants.

2.4. Statistical Analysis

For each athlete, the mean, range, and RMS values of the CoM displacement, velocity, acceleration, and jerk in the X, Y, and Z directions were computed across the 20-ball Displacement Speed Test trial. Before RMS calculation, all signals were demeaned (i.e., their mean value was subtracted) to ensure that RMS reflected variability around the mean rather than absolute displacement.

The distribution of all CoM-derived variables was assessed using the Shapiro–Wilk test, which indicated that several parameters deviated from normality. Consequently, non-parametric statistical methods were applied throughout the analyses. Differences across movement directions for each CoM parameter were examined using the Friedman ANOVA. Effect sizes for the Friedman tests were calculated as Kendall’s W, which quantifies the degree of association between ranks across repeated measures, ranging from 0 (no agreement) to 1 (perfect agreement) [39]. Dunn–Bonferroni post hoc tests were applied to identify specific pairwise differences. Effect size interpretation followed standard thresholds for Kendall’s W: small (0.1 ≤ W < 0.3), moderate (0.3 ≤ W < 0.5), and large (W ≥ 0.5) [40].

To investigate associations between CoM kinematics and functional and performance outcomes, Spearman’s rank correlation coefficients (ρ) were calculated between CoM-derived parameters (mean, range, RMS) and three key outcome measures: Functional Class, Number of Hits [x/20] (as a measure of stroke accuracy), and Points on the Gómez Scale (reflecting expert evaluation of technical performance). Effect sizes for correlations were derived from the t-statistic using the formula:

$$t=\rho \sqrt{{\displaystyle \frac{n-2}{1-{\rho }^2}}}$$

where n is the sample size. This allowed estimation of the practical magnitude of correlations alongside their statistical significance. Correlation effect sizes were interpreted using standard benchmarks: weak (|ρ| < 0.30), moderate (0.30 ≤ |ρ| < 0.50), and strong (|ρ| ≥ 0.50) [41].

Given the number of planned correlations (12 per movement direction: four CoM parameters × three outcome measures), a Bonferroni correction was applied to control for Type I error, resulting in an adjusted significance threshold of p_adj = 0.004. Statistical significance for individual tests was set at p = 0.05 before correction.

3. Results

3.1. Descriptive Statistics of Center of Mass Kinematics

Across all athletes (n = 21), the amplitude of CoM displacement, as reflected by the range, was largest in the medio-lateral (X) direction, highlighting the predominant side-to-side movements characteristic of table tennis footwork. Mean displacement values, which reflect position relative to the global reference frame, did not differ significantly between the X and Y directions (median −0.88 m vs. −0.96 m; p = 0.49, Kendall’s W = 0.02). In contrast, displacement range was substantially greater in X (0.74 m) compared with Y (0.25 m, p = 0.01, W = 0.35) and Z (0.19 m, p = 0.01, W = 0.38) (

Table 4. Descriptive statistics (median [Q1, Q3]) for mean, range, and RMS values, along with ANOVA Friedman results and effect sizes (Kendall’s W) for center of mass (CoM) kinematic parameters in the medio-lateral (X), antero-posterior (Y), and vertical (Z) directions during the 20-ball displacement speed test, p—level of statistical significance, p < 0.05.

Parameter	Direction	Mean	Range	RMS
Displacement [m]	X	−0.88 (−0.91; −0.81)	0.74 (0.67; 0.92)	0.9 (0.82; 0.93)
	Y	−0.96 (−1.01; −0.87)	0.25 (0.19; 0.28)	0.96 (0.87; 1.01)
	Z	0.07 (0.05; 0.12)	0.19 (0.15; 0.2)	0.08 (0.06; 0.13)
X vs. Y		X ≈ Y, p = 0.49/W = 0.02	X > Y, p = 0.01*/W = 0.35	X < Y, p ≈ 0.49/W = 0.02
X vs. Z		X < Z, p = 0.01*/W = 0.27	X > Z, p = 0.01*/W = 0.38	X > Z, p = 0.01*/W = 0.31
Y vs. Z		Y < Z, p = 0.01*/W = 0.32	Y ≈ Z, p = 0.49/W = 0.01	Y > Z, p = 0.01*/W = 0.34
Velocity [m·s−1]	X	−0.0004 (−0.009; 0.007)	4.35 (3.41; 5.78)	0.78 (0.57; 0.88)
	Y	0.0007 (−0.007; 0.004)	1.54 (1.29; 1.89)	0.16 (0.15; 0.2)
	Z	−0.001 (−0.001; 0.001)	2.25 (1.87; 3.08)	0.38 (0.29; 0.41)
X vs. Y		X < Y, p = 0.99/W < 0.01	X > Y, p = 0.01*/W = 0.41	X > Y, p = 0.01*/W = 0.39
X vs. Z		X < Z, p = 0.99/W < 0.01	X > Z, p = 0.01*/W = 0.42	X > Z, p = 0.01*/W = 0.37
Y vs. Z		Y > Z, p = 0.99/W < 0.01	Y < Z, p = 0.13/W = 0.14	Y < Z, p = 0.01*/W = 0.36
Acceleration [m·s−2]	X	0.09 (0.02; 0.15)	174.95 (94.76; 214.16)	9.51 (8.39; 12.7)
	Y	0.002 (−0.01; 0.02)	66.83 (46.96; 83.98)	6.17 (5.29; 7.54)
	Z	0.001 (−0.02; 0.04)	84.35 (59.34; 108.37)	7.29 (5.73; 8.85)
X vs. Y		X > Y, p = 0.02*/W = 0.21	X > Y, p = 0.01*/W = 0.36	X > Y, p = 0.01*/W = 0.33
X vs. Z		X > Z, p = 0.01*/W = 0.27	X > Z, p = 0.01*/W = 0.34	X > Z, p = 0.01*/W = 0.31
Y vs. Z		Y > Z, p = 0.99/W < 0.01	Y < Z, p = 0.65/W = 0.07	Y < Z, p = 0.01*/W = 0.28
Jerk [m·s−3]	X	10,376.06 (8327.87; 13,084.68)	190,672.346 (117,422.74; 286,867.76)	14,374.69 (12,020.25; 18,701.95)
	Y	14,374.69 (12,020.25; 18,701.95)	120,751.681 (84,062.26; 181,490.16)	8599.87 (7361.65; 10,321.56)
	Z	8599.87 (7361.65; 10,321.56)	117,453.533 (75,801.88; 195,201.82)	11,976.82 (9807.7; 15,203.42)
X vs. Y		X > Y, p = 0.01*/W = 0.39	X > Y, p = 0.01*/W = 0.39	X > Y, p = 0.01*/W = 0.36
X vs. Z		X > Z, p = 0.01*/W = 0.37	X > Z, p = 0.01*/W = 0.37	X > Z, p = 0.01*/W = 0.35
Y vs. Z		Y > Z, p = 0.06/W = 0.18	Y > Z, p = 0.86/W = 0.01	Y > Z, p = 0.01*/W = 0.28

* indicate statistically significant differences.

). All post hoc comparisons were conducted using Bonferroni-corrected significance levels (p_adj = 0.004). Negative values represent direction along the respective axis within the global coordinate system. Displacement values are expressed in meters (m), and negative values indicate movement toward the negative axis. The magnitude reflects cumulative movement across the entire 20-ball protocol rather than a single-step change. Effect sizes for the Friedman ANOVA were included to evaluate the practical relevance of directional differences. The observed effect sizes (W ≈ 0.35–0.38) indicate moderate practical effects according to Cohen’s thresholds for Kendall’s W (small: 0.1, moderate: 0.3, large: 0.5) [41].

For velocity, the greatest range and RMS values were again observed in the medio-lateral direction (range 4.35 m·s⁻¹; RMS 0.78 m·s⁻¹). Post hoc tests indicated significant differences between X and Y (range: p = 0.01, W = 0.42; RMS: p = 0.01, W = 0.39) and between X and Z (range: p = 0.01, W = 0.41; RMS: p = 0.01, W = 0.37). These effect sizes indicate moderate-to-large practical differences, reinforcing that medio-lateral velocity is substantially higher than in the antero-posterior and vertical directions. Mean velocities did not differ significantly (p > 0.99, W < 0.01), consistent with a negligible effect size.

Acceleration measures followed a similar pattern, with the highest median range and RMS values in the X direction (174.95 m·s⁻² and 9.51 m·s⁻², respectively). These values were significantly greater than in Y (range: p = 0.01, W = 0.36; RMS: p = 0.01, W = 0.33) and Z (range: p = 0.01, W = 0.34; RMS: p = 0.01, W = 0.31). Mean acceleration values showed smaller but still significant differences for X vs. Y (p = 0.02, W = 0.21) and X vs. Z (p = 0.01, W = 0.27), corresponding to small-to-moderate effect sizes. These findings confirm that side-to-side motion imposes the largest acceleratory demands during alternating strokes.

For jerk, which reflects rapid changes in acceleration, the highest range and RMS values were again observed in the X direction (range 190,672.35 m·s⁻³; RMS 14,374.69 m·s⁻³). Significant directional effects were found for X > Y (range: p = 0.01, W = 0.39; RMS: p = 0.01, W = 0.36) and X > Z (range: p = 0.01, W = 0.37; RMS: p = 0.01, W = 0.35). Differences between Y and Z were not significant for mean jerk (p = 0.06, W = 0.18, small effect) or range (p = 0.86, W = 0.01, negligible effect).

Overall, the findings demonstrate that the amplitude (range) of CoM displacement is greatest in the medio-lateral direction. Mean CoM positions reflect only the coordinate reference frame rather than functional asymmetries. Together, these outcomes reinforce the biomechanical predominance of medio-lateral demands during alternating forehand and backhand strokes in para table tennis.

3.2. Relationships Between Functional Classification, Technical Performance, and Kinematic Variables

Spearman’s rank correlations (ρ) were calculated between Functional Class, Number of Hits, Gómez Scale scores, and all CoM kinematic parameters (displacement, velocity, acceleration, jerk) across X, Y, and Z directions.

Table A1. Spearman correlations (ρ), and Bonferroni-adjusted p-values between CoM kinematic parameters and performance measures in para table tennis athletes, reported for medio-lateral (X), antero-posterior (Y), and vertical (Z) directions.

Parameter	Outcome Variable	ρ and p-Values (for Parameter Mean Value)		ρ and p-Values (for Parameter Range Value)		ρ and p-Values (for Parameter RMS Value)
Displacement X	Number of Hits	0.0417	0.8575	0.0039	0.9866	−0.0130	0.9553
	Gómez Score	0.0222	0.9239	−0.0721	0.756	0.018	0.9382
	Functional Class	0.0947	0.6832	0.4329	0.0490	−0.0695	0.7647
Displacement Y	Number of Hits	−0.4133	0.0626	−0.0795	0.7318	0.4133	0.0626
	Gómez Score	−0.3142	0.1654	−0.2157	0.3477	0.3142	0.1654
	Functional Class	−0.2681	0.24	−0.0834	0.7193	0.2681	0.24
Displacement Z	Number of Hits	0.2542	0.2661	0.1121	0.6285	0.2673	0.2415
	Gómez Score	0.1547	0.5032	0.1013	0.6623	0.1595	0.4898
	Functional Class	−0.1648	0.4752	0.1853	0.4212	−0.1840	0.4246
Velocity X	Number of Hits	−0.0352	0.8796	0	1	0.1317	0.5694
	Gómez Score	−0.2337	0.3079	−0.0229	0.9216	0.061	0.7927
	Functional Class	−0.0020	0.9932	0.1867	0.4178	0.3965	0.0752
Velocity Y	Number of Hits	0.0169	0.9419	0.1265	0.5849	0.0469	0.8399
	Gómez Score	0.1366	0.5548	0.0603	0.795	−0.0728	0.7538
	Functional Class	0.0304	0.8958	−0.0973	0.6748	0.0649	0.78
Velocity Z	Number of Hits	−0.1864	0.4184	0.0522	0.8224	0.1199	0.6045
	Gómez Score	−0.1616	0.4841	0.0243	0.9168	0.0673	0.772
	Functional Class	0.004	0.9864	0.0391	0.8665	0.3409	0.1305
Acceleration X	Number of Hits	−0.0039	0.9866	−0.0261	0.9107	0.0143	0.9508
	Gómez Score	−0.0562	0.8089	−0.0250	0.9145	−0.0021	0.9929
	Functional Class	−0.0007	0.9977	0.0642	0.7822	−0.0126	0.9569
Acceleration Y	Number of Hits	−0.0574	0.8049	0.1343	0.5617	−0.0887	0.7023
	Gómez Score	0.0791	0.7334	0.102	0.6601	−0.1172	0.6129
	Functional Class	0.184	0.4246	−0.1006	0.6643	−0.0271	0.907
Acceleration Z	Number of Hits	0.133	0.5655	0.1226	0.5966	0.1917	0.4053
	Gómez Score	−0.0208	0.9287	0.1352	0.5589	0.113	0.6256
	Functional Class	−0.1364	0.5556	−0.1000	0.6664	0.2416	0.2914
Jerk X	Number of Hits	0.0939	0.6857	0.1434	0.5351	0.0913	0.694
	Gómez Score	0.1075	0.6428	0.1359	0.5569	0.1054	0.6493
	Functional Class	−0.0093	0.9682	−0.1218	0.5989	−0.1721	0.4557
Jerk Y	Number of Hits	0.1082	0.6406	0.1447	0.5314	0.0104	0.9642
	Gómez Score	0.0971	0.6754	0.1241	0.5919	−0.0208	0.9287
	Functional Class	0.0715	0.7581	−0.2568	0.2611	−0.0927	0.6895
Jerk Z	Number of Hits	0.09	0.6982	0.2894	0.2032	0.2282	0.3199
	Gómez Score	0.0548	0.8135	0.2753	0.227	0.1574	0.4955
	Functional Class	0.0675	0.7712	−0.0900	0.698	−0.0510	0.8263

provides a complete summary of all correlations for mean, range, and RMS values.

Across all outcomes, correlations were generally weak and did not reach statistical significance after Bonferroni correction. The only association approaching significance was between medio-lateral displacement range and Functional Class (ρ = 0.43, p = 0.049), which should be interpreted cautiously as it did not survive correction. All remaining correlations were small (|ρ| < 0.41) and non-significant.

For technical performance, the Number of Hits showed its largest trends with antero-posterior displacement (mean: ρ = –0.41, p = 0.063; RMS: ρ = 0.41, p = 0.063), but these remained non-significant. Gómez scores showed uniformly weak correlations with all CoM measures (|ρ| ≤ 0.29).

Across all descriptive metrics, jerk values were weakly related to both functional class and performance (|ρ| ≤ 0.26, p ≥ 0.20), indicating no systematic association between movement smoothness and performance outcomes.

Overall, no CoM kinematic measure demonstrated a significant relationship with functional classification or performance once corrected for multiple comparisons.

4. Discussion

The present study examined CoM kinematics, including displacement, velocity, acceleration, and jerk, in elite para table tennis players performing a 20-ball displacement speed test with alternating forehand and backhand strokes. Analyses focused on the medio-lateral (X), antero-posterior (Y), and vertical (Z) directions to characterize dominant movement patterns. Spearman correlations were used to investigate associations between CoM metrics and functional class, stroke accuracy (Number of Hits), and expert technical rating (Gómez scale).

4.1. Dominance of Medio-Lateral Dynamics

Consistent with the movement demands of table tennis (and especially para table tennis, where functional limitations may affect trunk and lower-limb contributions), the results demonstrated that CoM kinematics were dominated by the medio-lateral axis. Specifically, displacement, velocity range, and RMS, acceleration range/RMS, and jerk mean/range/RMS were all highest in the X-direction. This aligns with the expectation that alternating side-to-side movements (between forehand and backhand) impose greater demands on lateral body translation and repositioning. While similar lateral dominance has been reported in able-bodied racket sports (e.g., badminton, tennis) where rapid side-stepping or lateral reach is common [42,43,44], the magnitude and characteristics of these movements may differ in para athletes due to individual impairments, trunk control, and modified movement strategies affecting functional efficiency.

The elevated acceleration and jerk values in the X direction highlight that not only is lateral movement of greater magnitude, but the changes in movement dynamics (i.e., rapid acceleration and deceleration) are more pronounced laterally than in the forward-backward or vertical axes. This points to the biomechanical specificity of para table tennis footwork and trunk/upper-limb coordination: players must quickly shift the CoM laterally, decelerate, reaccelerate, and stabilise before returning to a ready position.

4.2. Jerk as an Indicator of Movement Smoothness and Motor Control

The inclusion of jerk (the time derivative of acceleration) provided insight into the “smoothness” of movement. It should be noted, however, that jerk is highly sensitive to high-frequency noise and numerical differentiation artifacts, particularly in markerless motion capture systems. In motor control literature, lower jerk is often associated with smoother, more coordinated movement execution, consistent with optimal control models such as the minimum-jerk hypothesis [45]. For example, skilled golfers exhibited significantly lower normalized jerk than unskilled golfers during the downswing, suggesting smoother whole-body coordination in experts [46]. In rehabilitation settings, jerk-based metrics have been used to differentiate between impaired and normal movement smoothness [47].

In the present cohort of para table tennis athletes, jerk values were highest in the X direction (consistent with the largest dynamic demands). Nevertheless, due to the sensitivity of jerk to measurement noise and variability in movement strategies among athletes with different impairments, these values should be interpreted cautiously. Correlation analyses did not identify any statistically significant associations between jerk metrics and functional ability, stroke accuracy, or Gómez scale ratings after Bonferroni correction, highlighting that jerk alone may not fully capture functional efficiency in this population. While this might initially appear surprising, several possible explanations emerge. First, although higher functional classes might be expected to demonstrate smoother movement (lower jerk), it is possible that the variability of disability types, compensatory strategies, and wheelchair vs. standing status contributes to the absence of a clear linear relationship between jerk and classification or performance. Second, expert technical ratings (Gómez scale) likely reflect multiple factors beyond pure movement smoothness, such as tactical decision-making, stroke timing, spin control, and upper-limb kinetics, which may not map directly onto CoM jerk metrics. Third, the sensitivity of jerk to measurement noise, filtering, and differentiation (especially third derivatives) is well documented [48]. Without normalisation (e.g., for movement amplitude, duration) and careful signal processing, the interpretability of jerk values is constrained.

Thus, while jerk remains a promising biomechanical metric of movement coordination, in the specific context of the para table tennis displacement speed test, it is hypothesized that its standalone association with performance and functional measures may be limited.

4.3. Functional Class-Dependent Kinematic Trends

Beyond direction-specific findings, descriptive patterns suggested that athletes from higher classes (e.g., 9–11) tended to exhibit lower RMS acceleration and jerk (especially laterally), and somewhat higher lateral displacement range, indicating broader lateral movement with relatively stable transitions, reflecting higher functional efficiency. Conversely, lower-class athletes appeared to display higher acceleration and jerk variability, potentially reflecting more abrupt trunk/CoM shifts. These observations may reflect differences in movement strategies associated with functional impairment, but direct statistical group comparisons were not conducted to confirm these differences [49].

4.4. Implications for Coaching and Training

The findings offer several practical implications. First, training programs for para table tennis athletes should emphasise competent lateral CoM control, both in terms of magnitude (range) and dynamic transitions (acceleration/jerk). Exercises that improve trunk stability, lateral weight-shifting control, and rapid repositioning may enhance movement economy [50]. Specific strength and conditioning strategies targeting the musculature involved in lateral displacement, such as hip abductors/adductors and trunk stabilizers, could include resistance band drills (e.g., lateral band walks, band-resisted side steps), slide-board or lateral shuffle exercises, and flywheel or conical pulley-based lateral strength training aimed at improving force production and control in side-to-side movements [51,52,53].

Second, while jerk metrics did not correlate with technical or functional outcomes in this study, they may still serve as monitoring tools for movement smoothness in individual athletes (e.g., tracking changes over time, or pre-/post-interventions).

Third, functional classification and technical assessment (Gómez scale) appear to reflect movement coordination complexity beyond simple CoM dynamics, so multidimensional assessments remain valuable.

By integrating these practical, lateral-movement-focused exercises, coaches and practitioners can more directly translate biomechanical findings into targeted training interventions to enhance performance in para table tennis.

4.5. Limitations and Future Directions

Several limitations warrant consideration. The sample size was relatively small and comprised elite para table tennis athletes with heterogeneous impairments, which may limit the generalisability of the findings. No a priori sample size calculation or power analysis was conducted, and the relatively small sample combined with the large number of correlations limits statistical power; therefore, all correlation analyses should be interpreted as exploratory. Additionally, the markerless motion capture system, while validated in able-bodied and some dynamic sports contexts, may exhibit reduced accuracy in athletes with diverse impairments, potentially affecting CoM and derived kinematic measures. The displacement speed test, though sport-specific, was a controlled task using a robot-controlled, fixed-trajectory ball feed; actual match-play dynamics, including variable spin, ball placement, anticipatory movements, irregular timing, and longer displacements, may elicit different CoM strategies. Only a single trial per athlete was collected, which may affect the reliability of CoM metrics and the observed correlations. The jerk metric used here was raw (non-normalised) and is highly sensitive to sampling frequency, filtering, and noise amplification; future work might apply normalised or dimensionless jerk indices (e.g., log-dimensionless jerk), which are less sensitive to movement amplitude/time and more robust for smoothness analysis [19,20]. Moreover, the multi-trial reliability of jerk measures in this population is not yet established. Future research could examine interventions (e.g., trunk-core training) and track changes in CoM kinematics and jerk pre-/post-training. All findings regarding functional ability and CoM behaviour should be interpreted as exploratory, and CoM metrics should not be used to make classification decisions without further validation in larger and stratified cohorts.

5. Conclusions

In summary, the CoM kinematics of para table tennis players during a rapid displacement test are dominated by lateral dynamics. While displacement, velocity, and acceleration metrics indicated clear directional and functional ability trends, jerk metrics did not systematically relate to functional classification or performance outcomes. Nonetheless, jerk remains conceptually relevant as an indicator of movement smoothness and functional efficiency, warranting further investigation in adaptive sport settings with appropriate normalization and sample stratification. Understanding CoM behaviour in para table tennis provides a biomechanical basis for targeted training and classification-aware movement analysis. Understanding CoM behaviour in para table tennis provides a biomechanical basis for potential applications in targeted training and functional efficiency–oriented interventions, but findings should be interpreted cautiously and not as prescriptive for classification decisions.