The kinematic differences between accurate and inaccurate squash forehand drives for athletes of different skill levels

ABSTRACT

To maintain the accuracy of squash shots under varying conditions, such as the oncoming ball’s velocity and trajectory, players must adjust their technique. Although differences in technique between skilled and less-skilled players have been studied, it is not yet understood how players vary their technique in a functional manner to maintain accuracy under varying conditions. This study compared 3-dimensional joint and racket kinematics and their variability between accurate and inaccurate squash forehand drives of 9 highly skilled and 9 less-skilled male athletes. During inaccurate shots, less-skilled players hit the ball with a more open racket, demonstrating a difference in this task-relevant parameter. No joint kinematic differences were found for accuracy for either group. Coordinated joint rotations at the elbow and wrist both displayed a “zeroing-in” effect, whereby movement variability was reduced from the initiation of propulsive joint rotation to a higher consistency at ball-impact; potentially highlighting the “functionality” of the variability prior to the impact that enabled consistent task-relevant parameters (racket orientation and velocity) under varying conditions. Further, highly skilled players demonstrated greater consistency of task-relevant parameters at impact than less-skilled players. These findings highlight the superior ability of highly skilled players to adjust their technique to achieve consistent task-relevant parameters and a successful shot.

KEYWORDS:

• Biomechanics
• motor control
• squash
• racquet
• forehand drive

Introduction

Successful performance within a squash match requires the ball to be hit accurately, to strategically advantageous areas of the court, thereby making it difficult for an opponent to successfully return the ball to their advantage. Racket angle and racket velocity at impact are 2 of the critical factors that determine the speed and direction of a hit ball (Kwon et al., 2017). These critical factors are controlled by an athlete’s swing mechanics, with linear and angular movements of the trunk and upper-limb segments playing a crucial role in effective stroke production (Elliott et al., 1997). Accordingly, there have been a number of studies of the kinematics of squash strokes (Ariff et al., 2012; Chapman, 1986; Elliott et al., 1996; Williams et al., 2020; Woo & Chapman, 1992). However, the accuracy component of the shot and the kinematic technique differences that might distinguish accurate from inaccurate shots in squash have not been investigated to date. Given the unavoidably variable nature of the “initial task conditions” (approaching ball speed, height and direction) and therefore the resulting variable racket-ball impact location, consistent swing kinematics may not necessarily lead to accurate shots. It is therefore important to consider how the kinematic variables of a stroke are adjusted to ensure accuracy.

An inaccurate shot may provide an opponent with an opportunity to hit a winning return, or alternatively, could result in an “unforced error” and the loss of a point. It has been proposed that skill level could influence the number of unforced errors hit, and consequently points lost, within a match (Brody, 2006). In light of this, it is surprising that there has been a lack of research to investigate the mechanics that may distinguish accurate from inaccurate squash shots. In contrast, there have been a number of investigations into the stroke and racket kinematics that constitute an accurate or successful shot in other racket sports such as tennis (Kwon et al., 2017; J. Landlinger et al., 2012). Landlinger et al. (2012) found a difference between athletes of different skill levels in the speed with which accurate tennis forehand strokes were hit. The highly skilled elite group hit the ball faster, while maintaining their accuracy, than less-skilled high-performance youth players; however, there was no investigation into how players adjusted their kinematics prior to impact.

The idea that variability should not necessarily be considered as noise or error, based on dynamical systems theory (Davids et al., 2003), has also been explored to provide supplementary information on movement skill performance (Mullineaux & Uhl, 2010; Whiteside et al., 2015). Joint coordination and movement variability may play an important functional role that allows adaptations to the initial task conditions, potentially reduces injury risk, and could facilitate the necessary coordination changes to optimise a successful performance outcome (Bartlett et al., 2007). Skilled athletes may exhibit “functional” variability, such that accuracy is maintained despite the varying initial conditions of the task (Davids et al., 2003). In contrast, less-skilled athletes may be less able than skilled athletes to adjust to variations in initial conditions of the task.

Variability has been studied within different sporting skills (basketball free-throw shooting: Button et al. (2003), Mullineaux and Uhl (2010), table tennis forehand drive stroke: Bootsma and Van Wieringen (1990), long jump approach phase: Scott et al. (1997), under-arm throwing: Dupuy et al. (2000)). Despite kinematic disparity between the movements, their key endpoint parameters, otherwise referred to as "task-relevant parameters" (Hamacher et al., 2017), showed small variability and allowed a successful movement pattern to emerge. It has been proposed that the contributing joints may have a “covariance” which reduces the variability of the task-relevant variables to tolerable limits such that performance error is minimised (Müller & Sternad, 2004). This implies that highly skilled athletes are able to vary their kinematics between shots to “zero-in” to the desired values of the task-relevant parameters at impact to reduce variability that is detrimental to performance (Langdown et al., 2012).

It has been suggested that low variability in the task-relevant parameters is critical to success in tasks involving projectiles (Whiteside et al., 2013). For racket sports such as squash, these parameters are racket face orientation angle and velocity at ball impact (Kwon et al., 2017). Therefore, the regulation and stabilisation of these task-relevant parameters depends on the mechanical adjustments of the corresponding joint mechanics (Bootsma & Van Wieringen, 1990; Whiteside et al., 2015).

Examining the variability of joint movements and the racket kinematics within accurate and inaccurate squash drives may provide useful information on how shot accuracy is maintained and how the joint kinematics differ between skill levels. Consequently, the purpose of this study is to identify differences in the trunk, dominant upper-limb and racket kinematics of accurate (successful) and inaccurate (unsuccessful) squash forehand drive shots between highly skilled and less-skilled players.

Methods

Participants

Eighteen male squash players from a national sports academy volunteered to participate in the study and were allocated into 2 groups; highly skilled (n = 9, age 22.7 ± 6.6 years, height 1.76 ± 0.07 m, weight 69.9 ± 10.2 kg) and less-skilled (n = 9, age 14.7 ± 1.7 years, height 1.68 ± 0.08 m, weight 60.5 ± 11.0 kg). Group allocation was determined objectively, with participants ranked using the “Hunt Squash Accuracy Test” (HSAT) (the HSAT was used for the protocol of this study, explained below, and has been validated against tournament performance (Williams et al., 2018)) and then separated into 2 groups using a score of >60% for the highly skilled group (mean score: 73 ± 7%) and <60% for the less-skilled (mean score: 51 ± 6%). Group allocation was affirmed by 3 expert coach opinions whereby the coaches independently divided participants into 2 skill groups based on stroke technique. The results of both group assignment methods agreed. At the time of testing, all participants were injury free and players under the age of 19 held a top 5 national ranking for their respective age groups, while players over the age of 19 had been playing professionally for a minimum of 4 years. There were 2 left-handed participants, with the remaining 16 being right-handed. All participants gave written informed consent before participating in the study, which was approved by the ADLQ Institutional Review Board (E2017000216).

Equipment set-up and testing protocol

A 15-camera optical motion capture system (Vicon Motion Systems, UK) operating at 200 Hz was used to collect 3-dimensional motion analysis data. Cameras were positioned around each of the 4 glass walls of a court (ASB ShowGlassCourt, Czech Republic) to allow a capture volume of approximately 6 m x 6 m to be established around the centre “T” area of the court. A global coordinate system was defined as per Figure 1. The ability of the motion analysis system to accurately collect data through the glass walls of the squash court was previously investigated, with the mean absolute error for distance and angle reported to be 0.3 mm and 0.1° (Williams et al., 2020).

Prior to the start of the data collection, participants performed a self-selected warm-up that included warming the ball to be “match ready”. The testing protocol was based on the HSAT, which required hitting the ball to a designated target area. The HSAT has been shown to have large correlations to winning shot percentage during a match as well as total shot success within a tournament (Williams et al., 2018). All participants had prior experience of the test having completed it a number of times previously (average 7.7 ± 4.1 times) as part of their normal training programmes.

A horizontal target area that measured 0.5 m either side of the half court line and extended from the back wall to 2.61 m towards the front wall (Figure 1) was marked on the court. Participants hit approximately 25 drive shots continuously to themselves (the initial shot did not count) and were required to hit the ball after the first bounce, without letting the ball hit the back wall. Participants were not limited to a particular grip or technique and were requested to perform each shot at a speed similar to that within a game. Shots that landed within the designated target area were analysed as successful shots, whilst shots that landed outside the target area were analysed as unsuccessful shots. The 5 successful and 5 unsuccessful shots that were preceded by a successful shot (to ensure a certain amount of consistency in the approaching ball speed and trajectory) with the least number of broken reconstructed DLT traces were chosen for analysis.

Figure 1. Equipment set-up: the target area marked on the floor of the court, camera positions around the glass walls of the squash court and global coordinate system. Shots landing within the target area were scored as accurate.

Data collection and analysis

A total of 14 spherical reflective markers (14 mm diameter) were attached to specific anatomical landmarks of each participant on their dominant upper-limb as per Table 1 (Vicon upper-limb model marker set). The marker set comprised anatomical, single technical, and triad clusters of technical markers. This upper-limb model has been validated previously (Cutti et al., 2005; Murray, 1999) and used to investigate shoulder and humerus rotations in volleyball (Seminati et al., 2015), overarm throwing technique (Taylor et al., 2015) and water polo shot technique (Taylor et al., 2014). Three additional reflective markers were attached to the mid-sides and top of the head of a racket, such that racket orientation angles could be calculated. Racket kinematic data were collected at the same time as the upper-limb model via a rigid body model that was input into Nexus software (Nexus 2.2, Vicon Motion Systems, UK). All data were collected via Nexus software.

Table 1. Trunk and dominant upper-limb anatomical marker placement.

Marker	Anatomical placement
C-7	Spinous process of 7th cervical vertebra
T-10	Spinous process of 10th thoracic vertebra
Clavicle	Jugular notch: where the clavicles meet the sternum
Sternum	Xiphoid process of sternum
Shoulder	Acromioclavicular joint
Upper arm A	Lateral upper arm
Upper arm B	Lateral upper arm, beneath “upper arm A”
Upper arm C	Lateral upper arm, beneath “upper arm B”
Elbow	Lateral epicondyle approximating the elbow joint axis
Medial epicondyle^a	Humerus medial epicondyle
Forearm	Mid-forearm
Wrist A	At the thumb side of the right radial styloid attached symmetrically with a wristband on the posterior of the right wrist, as close to the wrist joint centre as possible
Wrist B	At the little finger side of the right ulnar styloid attached symmetrically with a wristband on the posterior of the right wrist, as close to the wrist joint centre as possible
Finger	Below the third metacarpus

^aMarker used only during static acquisition.

The 3-dimensional coordinates of the automatically digitised markers were reconstructed and labelled according to the respective models using Nexus software. Any broken trajectories were filled using cubic spline interpolation. A second-order polynomial extrapolation estimated marker trajectories at impact in order to avoid over-smoothing (Reid et al., 2012). Data were filtered using a Woltring filter (Woltring, 1986), with an optimal mean square error of 25 prior to joint positions being calculated according to their respective models (Davis et al., 1991; Murray, 1999; Murray & Johnson, 2004).

An Euler xzy sequence was used to calculate joint kinematics, except at the shoulder where, in accordance with the International Society of Biomechanics recommendations (Seminati et al., 2015; Wu et al., 2005), an Euler decomposition of “plane of elevation”, “elevation”, and “axial rotation” was used. Racket head projection angles relative to the global reference frame were produced (whereby 0° racket face angle (in the y-z plane) indicated a fully “closed” racket face (face down and parallel to the floor) and 90° racket face angle indicated an “open” racket face perpendicular to the floor (parallel to the front wall)) (Kwon et al., 2017). Linear racket head velocity was produced from the midpoint between the racket markers on the sides of the racket head (Elliott et al., 1996). To provide consistency within the statistical analysis, the 2 left-handed players’ kinematics were inverted where appropriate, to allow the data from all players to be considered right-hand dominant (Whiteside et al., 2013).

The task-relevant parameters were determined based on previous studies of racket sports in which parameters important for accurate/successful performance were identified (Chapman, 1986; Kwon et al., 2017; Marshall & Elliott, 2000; Whiteside et al., 2013; Williams et al., 2020). The task-relevant parameters chosen were racket parameters calculated at impact: racket face projection angles (relative to the global reference frame) onto the x-y plane (horizontal swing angle), x-z plane (racket head elevation angle) and y-z plane (racket face angle); and racket head linear velocities in the global x, y and z directions.

The joint kinematics selected for analysis were chosen because they were considered to have a functional influence on the task-relevant parameters and were based upon previous research as well as discussions with international squash coaches (Elliott et al., 1996; Whiteside et al., 2013; Williams et al., 2020; Woo & Chapman, 1992). Thus, orientation angles at the “top of the backswing” (the instant before the racket top marker moves in the positive forward (y) direction) and at ball impact, as well as peak angular velocities were calculated and used for analysis of: trunk rotation (relative to the global coordinate system); shoulder plane of elevation; shoulder angle of elevation; shoulder internal/external rotation; elbow flexion/extension; forearm pronation/supination; and wrist flexion/extension.

Internal rotation of the upper-arm and forearm, along with wrist flexion, have been shown previously to play important roles in the development of racket head velocity and orientation (Elliott et al., 1996; Marshall & Elliott, 2000). Couplings between these joint movements may display compensatory effects that could influence the task-relevant parameters and ultimately the accuracy of a shot. As such, the variability of the relative motion between shoulder rotation and forearm rotation, as well as between forearm rotation and wrist flexion/extension, were assessed during the forward swing phase (from the top of backswing to ball impact) using a vector coding technique which quantifies the motion of one joint relative to another (Tepavac & Field-Fote, 2001). The coding technique produces a coefficient of correspondence (CoC) which quantifies the magnitude of variability between motions of joint pairs, using values between 0 (maximum variability) and 1 (no variability). This method is advantageous in that it considers both the vector direction and magnitude (Wheat & Glazier, 2006) and may therefore provide insights into the compensations (functional variability) that might occur in order to maintain low variability within the task-relevant parameters.

The CoC was calculated for the entire swing phase and at specific events of interest during the swing phase: “backswing” (top of the backswing), “propulsion initiation” (the instant the proximal limb of the joint coupling began to rotate towards: shoulder internal rotation for the shoulder-forearm coupling; and forearm pronation for the forearm-wrist coupling) and “ball impact”. The variability of an event was represented by the CoC value at that time point. Further, the variability of the task-relevant parameters, racket orientation and racket velocity at impact, were calculated as the standard deviation (SD) of each participant’s trials.

Statistical analysis

Means and standard deviations were calculated for descriptive statistics. SPSS Statistics software (IBM, version 22) was used to analyse all kinematic data. A 2-way mixed analysis of variance (ANOVA) with the main effects of accuracy (within participants: accurate and inaccurate) and skill level (between participants: highly skilled and less-skilled) were used to test for statistical differences, interactions and effects in the kinematic variables, variability of the task-relevant parameters and the mean swing phase CoC. With a total of 180 shots being analysed across the different conditions, an a priori power analysis (G*power, 3.0.10) for an effect size of 0.25 revealed a statistical power of 0.85 (Faul et al., 2007). The differences between the variability (CoC) at the points of interest within the forward swing phase were tested for statistical differences, interactions and effects using a 3-way mixed ANOVA with the main effects of phase (differences between CoC points of interest), accuracy (within participants: accurate and inaccurate) and skill (between participants: highly skilled and less-skilled). The 0.05 alpha level was adopted to test significance. When a significant main effect or interaction was observed, a Bonferroni post-hoc test was performed to find the source of the difference and interaction. Effect sizes (partial eta squared ƞ²) were considered as small (>0.01), medium (>0.06) and large (>0.14) (Cohen, 1988).

Results

Kinematic variables

There was a significant group effect found for shoulder plane of elevation at backswing and impact, indicating that the highly skilled group had approximately 16° and 9° greater shoulder plane of elevation than the less-skilled group, respectively (Table 2). Wrist extension angle at impact was also found to significantly differ between groups, with the highly skilled group having approximately 15° more wrist extension than the less-skilled group. There were no other significant group main effects found for any of the peak trunk or upper-limb angular rotations. Further, there were no significant main effects for accuracy found between any of the variables at backswing, peak velocity, or ball impact.

Table 2. Mean (±SD) values for the discrete kinematic variables of highly skilled and less-skilled accurate and inaccurate shots.

				Highly-skilled						Less-skilled
	Significance			Accurate			Inaccurate			Accurate			Inaccurate			Accuracy effect			Group effect
Variable	Acc	Grp	Int	Mean		SD	Mean		SD	Mean		SD	Mean		SD	F	p	ƞ^2	F	p	ƞ^2
Backswing
Trunk rotation θ (°)				−96.8	±	12.9	−96.1	±	14.8	−106.6	±	17.6	−104.0	±	17.2	1.52	0.24	0.09	1.45	0.25	0.08
Sh plane of elev θ (°)		*		26.6	±	12.7	27.7	±	13.8	10.4	±	10.4	11.2	±	7.3	1.10	0.31	0.06	9.69	0.01	0.38
Sh elev θ (°)				61.3	±	14.5	61.7	±	14.4	63.0	±	9.7	61.4	±	9.7	0.84	0.37	0.05	0.02	0.90	0.00
Sh internal rot θ (°)				−71.3	±	9.6	−72.0	±	9.7	−68.3	±	11.5	−68.7	±	10.5	0.89	0.36	0.05	0.41	0.53	0.03
Elb flexion θ (°)				87.8	±	9.5	88.4	±	9.5	95.1	±	12.4	94.7	±	12.2	0.03	0.87	0.00	1.76	0.20	0.10
Propulsion
Peak trunk rot ⍵ (° s⁻^1)				234.0	±	51.8	228.8	±	48.0	254.3	±	73.9	256.8	±	78.7	0.04	0.85	0.00	0.67	0.43	0.04
Peak Sh plane of elev ⍵ (° s⁻^1)				356.0	±	77.6	347.7	±	89.8	376.3	±	48.3	392.1	±	41.0	0.14	0.71	0.01	1.16	0.30	0.07
Peak Sh internal rot ⍵ (° s⁻^1)				860.7	±	311.0	859.6	±	321.3	961.4	±	345.5	978.5	±	343.0	0.05	0.82	0.00	0.52	0.48	0.03
Peak Elb extension ⍵ (° s⁻^1)				854.4	±	243.6	853.7	±	240.6	821.5	±	220.4	807.4	±	235.9	0.50	0.49	0.03	0.13	0.73	0.01
Peak Forearm pro ⍵ (° s⁻^1)				815.7	±	261.3	814.2	±	240.8	728.1	±	301.5	708.5	±	289.3	0.30	0.60	0.02	0.57	0.46	0.04
Peak Wrist flexion ⍵ (° s⁻^1)				658.0	±	119.5	661.7	±	124.7	708.1	±	87.8	747.6	±	120.5	0.91	0.35	0.05	1.94	0.18	0.11
Impact
Trunk rot θ (°)				−64.8	±	9.8	−65.4	±	9.5	−65.0	±	9.8	−63.9	±	8.9	0.03	0.87	0.00	0.02	0.89	0.00
Sh plane of elev θ (°)		*		76.6	±	8.0	76.1	±	7.5	67.8	±	10.6	66.8	±	10.5	0.37	0.55	0.02	4.66	0.05	0.23
Sh internal rot θ (°)				−90.2	±	13.4	−88.7	±	14.0	−84.7	±	15.4	−83.8	±	13.0	0.84	0.37	0.05	0.66	0.43	0.04
Elb flexion θ (°)				32.8	±	7.5	33.1	±	8.1	35.9	±	7.2	36.6	±	7.9	0.44	0.51	0.03	0.86	0.37	0.05
Elb internal rot θ (°)				126.6	±	10.3	127.2	±	9.8	115.7	±	20.6	113.5	±	18.2	0.99	0.34	0.06	2.90	0.11	0.15
Wrist extension θ (°)		*		46.1	±	8.7	45.6	±	7.8	31.1	±	12.2	29.7	±	13.1	1.25	0.28	0.07	9.70	0.01	0.38
Racket X-Y plane θ (°)		*		−19.2	±	3.5	−19.3	±	2.5	−13.1	±	2.6	−12.8	±	2.5	0.03	0.88	0.00	29.11	0.00	0.65
Racket X-Z plane θ (°)		*	#	−19.2	±	6.1	−16.7	±	5.9	−24.2	±	8.7	−27.4	±	6.1	0.09	0.77	0.01	7.03	0.02	0.31
Racket Y-Z plane θ (°)		*	#	119.3	±	2.2	118.3	±	1.3	123.2	±	4.2	125.2	±	4.7	0.76	0.40	0.05	12.68	0.00	0.44
Racket X velocity (m · s^−1)				4.6	±	4.0	4.7	±	4.0	3.1	±	3.9	2.9	±	3.8	0.03	0.86	0.00	0.79	0.39	0.05
Racket Y velocity (m · s^−1)		*		25.4	±	1.9	25.3	±	2.0	23.6	±	2.0	23.3	±	1.7	0.63	0.44	0.04	4.74	0.05	0.23
Racket Z velocity (m · s^−1)				−1.7	±	1.9	−1.6	±	1.4	−0.6	±	0.8	−0.6	±	1.1	0.14	0.71	0.01	2.95	0.11	0.16

*Significant group effect, #significant interaction, θ = angle, ⍵ = angular velocity, Acc = Accuracy, Grp = Group, Int = interaction between accuracy and group, Sh = shoulder, Elb = elbow, elev = elevation, rot = rotation, in = internal, ext = external, pro = pronation, sup = supination, flex = flexion.

There was, however, a significant interaction between the effects of accuracy and skill level for racket angle in the x-z plane (racket head elevation angle) at impact (F = 5.86, p = 0.03, ƞ² = 0.27). The interaction indicated a significant difference between groups for inaccurate shots (p < 0.00) and that the highly skilled group decreased their racket head elevation angle slightly during inaccurate shots, while the less-skilled group increased their racket head elevation angle slightly; although neither change was substantial enough to be shown by within-group contrasts (p = 0.15 and p = 0.07, respectively). A significant interaction effect for racket angle in the y-z plane (racket face angle) at impact (F = 6.96, p = 0.02, ƞ² = 0.30) was also found, indicating that the highly skilled had a lower angle than the less-skilled group for both accurate (p = 0.03) and inaccurate (p < 0.00) shots, and that the less-skilled group had a significantly greater racket face angle during inaccurate shots compared to accurate shots (p = 0.02) (Table 2).

Variability

The variability of the racket angles at impact and racket velocity at impact all showed a significant main effect for group (Table 3), indicating the less-skilled group had significantly more variability than the highly skilled group. There was no significant main effect for accuracy in the variability of any of the racket angles at impact; however, there was a large effect size (ƞ² = 0.18, p = 0.08) in the variability of the racket angle in the y-z plane (racket face angle), suggesting a possible trend towards a difference between accurate and inaccurate shots (Table 3). No significant main effect for accuracy was found in racket velocity variability at impact in any of the directions.

Table 3. Mean (±SD) values for the variability measures of highly skilled and less-skilled accurate and inaccurate shots.

				Highly-skilled						Less-skilled
	Significance			Accurate			Inaccurate			Accurate			Inaccurate			Accuracy effect			Group effect
Variable	Acc	Grp	Int	Mean		SD	Mean		SD	Mean		SD	Mean		SD	F	p	ƞ^2	F	p	ƞ^2
Impact Variability
Racket X-Y plane		*		3.24	±	1.12	3.70	±	1.32	4.36	±	1.60	4.96	±	1.13	1.98	0.18	0.11	5.96	0.03	0.27
Racket X-Z plane		*		5.18	±	2.29	5.99	±	1.31	9.69	±	4.35	8.85	±	4.70	0.00	0.99	0.00	6.51	0.02	0.29
Racket Y-Z plane		*		2.01	±	0.51	1.95	±	1.06	3.00	±	1.31	4.75	±	1.88	3.61	0.08	0.18	21.17	0.00	0.57
Racket X velocity		*		1.14	±	0.34	1.30	±	0.46	1.92	±	0.95	2.15	±	1.08	0.44	0.51	0.03	234.82	0.00	0.94
Racket Y velocity		*		1.06	±	0.66	1.01	±	0.31	1.43	±	0.65	2.32	±	1.57	2.13	0.16	0.12	79.25	0.00	0.83
Racket Z velocity		*		1.07	±	0.44	0.97	±	0.45	1.35	±	0.46	1.35	±	0.66	0.19	0.67	0.01	130.71	0.00	0.89
CoC – Forward swing phase
Sh rotation – Forearm rotation		*		0.80	±	0.06	0.81	±	0.10	0.76	±	0.06	0.73	±	0.06	0.16	0.69	0.01	6.87	0.02	0.30
Forearm rotation – Wrist flex/ext		*		0.75	±	0.07	0.75	±	0.08	0.68	±	0.04	0.68	±	0.08	0.03	0.87	0.00	8.84	0.01	0.36

*Significant group effect, Acc = Accuracy, Grp = Group, Int = interaction between accuracy and group, Sh = shoulder, flex = flexion, ext = extension.

The mean group variability (CoC) of the joint couplings during the swing phase is shown in Figure 2. There was no significant main effect for accuracy in either joint coupling for swing phase CoC (Table 3). However, a significant main effect for group was found for both shoulder rotation-forearm rotation and forearm rotation-wrist flexion/extension for swing phase CoC, indicating that the highly skilled group had a lower mean variability (values closer to 1) throughout the swing phase than the less-skilled group (Figure 2).

Analysis of the variability of the relative movement of shoulder rotation-forearm rotation at the swing points of interest revealed no main effect for accuracy. However, a main effect for phase was found (F = 64.45, p < 0.01, ƞ² = 0.80), indicating that there was more variability at the time of propulsion initiation than there was at both backswing and impact (Figure 2). There was also a main effect for group (F = 6.03, p = 0.03, ƞ² = 0.27), with no interaction between group/phase, therefore indicating the highly skilled group had less variability than the less-skilled at each of the temporal events of interest. The relative movement of forearm rotation-wrist flexion/extension at the swing points of interest showed no significant main effects for accuracy or group; however, a main effect was observed for phase (F = 16.82, p < 0.01, ƞ² = 0.51), indicating that ball impact exhibited less variability than both backswing and propulsion initiation for both groups (Figure 2).

Figure 2. Mean coefficient of correspondence of shoulder rotation–forearm rotation curves (a) and forearm rotation–wrist flexion/extension curves throughout the swing phase (b).

Discussion

The purpose of this study was to compare the trunk, dominant upper-limb and racket kinematics between accurate and inaccurate squash forehand drive shots, as well as to identify differences between highly skilled and less-skilled players. Determining the potential mechanical sources of inaccurate drive shots could help players become more skilful, therefore reducing the number of unforced errors hit and potential points lost within a match. Additionally, understanding the joint kinematics that are varied functionally to minimise errors in the parameters related to success, i.e. the “task-relevant parameters”, could further aid the development of efficient, successful swing mechanics.

Swing and racket kinematics

During inaccurate shots the less-skilled group impacted the ball with a significantly greater mean racket face angle, resulting in a more “open” racket face. The approximate 2° difference in angle between accurate and inaccurate shots at ball impact for this group could have caused deviations to the subsequent ball flight path, resulting in an unsuccessful shot (Brody, 2006). With no other significant differences found between accurate and inaccurate shots in any of the other racket parameters, it is possible that the more open racket face at impact could have resulted in the ball being hit higher. In a match situation, if the ball is hit higher on the front wall it could provide an advantage to an opponent by allowing them to “cut the ball off early” by hitting a volley shot before the ball bounces, which reduces the time an opponent has to react to the returned ball (Vučković et al., 2013).

The differences between accurate and inaccurate shots within each group did not reach statistical significance for any of the selected body kinematic variables. It therefore appears that no single measure of trunk or upper-limb movement during the forward swing phase had a direct influence on shot outcome for either the highly skilled or less-skilled group. These findings support previous assertions of an absence of singular mechanical sources of error in racket stroke technique (Kwon et al., 2017; Landlinger et al., 2012; Whiteside et al., 2013). This also highlights how complex the squash forehand drive swing is, with many degrees of freedom, and that no single discrete kinematic variable adequately reflects the errors in the emergent movement pattern.

There was a small number of between-group differences found in the upper-body kinematics during the forward swing. The less-skilled group demonstrated a significantly reduced plane of elevation angle at the top of their backswing compared to the highly skilled group, implying that their upper-arm was less horizontally abducted when they initiated the forward racket swing. Similarly, the less-skilled group displayed smaller shoulder plane of elevation and wrist angles at ball impact compared to the highly skilled group. It has been previously suggested that the smaller shoulder plane of elevation angle helps ensure the racket is square with the ball at impact due to the smaller wrist extension angle seen within the less-skilled players compared to skilled players (Williams et al., 2020).

In agreement with previous studies, it was found that the highly skilled group hit the ball with a higher horizontal linear racket velocity compared to the less-skilled group (Landlinger et al., 2010a; Nesbit et al., 2008; Williams et al., 2020). To potentially compensate for the slower racket velocity at impact, the less-skilled players hit the ball with a more open racket face (Williams et al., 2020). However, as previously noted, the more open the racket face angle at impact the more likely the ball could travel higher and, under the constraints of the protocol used in this study, result in task failure. It appears that the ability to hit the ball with a “flatter” racket at impact could be a limiting factor for the less-skilled players that ultimately resulted in more inaccurate shots than the highly skilled players (HSAT score: highly skilled 73%; less-skilled 51%).

Joint coordination and racket variability

Both of the analysed joint couplings (shoulder rotation-forearm rotation and forearm rotation-wrist flexion/extension) displayed a significant decrease in variability at the critical time point of ball impact compared to propulsion initiation for both groups regardless of shot outcome (Figure 2). The fact that variability significantly decreased between these time points highlights the functional importance of the initiation of the propulsive movement in the proximal joint. This was particularly the case for the relative shoulder rotation-forearm rotation joint coupling, that displayed an increase in variability from backswing to propulsion initiation, followed by a decrease in variability at impact. These findings support the notion of a “zeroing-in” process, whereby detrimental variability is reduced as the critical task-relevant parameters approach (Langdown et al., 2012) and is similar to previous findings in basketball free-throw shooting (Mullineaux & Uhl, 2010) and table tennis drive shots (Bootsma & Van Wieringen, 1990). However, these findings are in disaccord with those found during investigations into the tennis serve mechanics, where relative elbow-wrist joint rotations (Whiteside et al., 2013) and elbow joint movement coordination (Whiteside et al., 2015) were both shown to increase in variability at the critical endpoint. Nevertheless, as noted by Whiteside et al. (2015), neither increase in coordination variability negatively impacted their task outcome, and given the tennis serves dynamic full-body action, there may have been other compensatory mechanics that contributed to task success.

The high level of consistency at ball impact of the highly skilled group in the relative motion of shoulder rotation-forearm rotation suggests a higher degree of functional compensation and zeroing-in between propulsion initiation and impact. Furthermore, the highly skilled group displayed significantly more consistent relative movements of the limbs for both joint couplings over the duration of the swing phase than the less-skilled players. Sufficient compensation for the potential small margins of error of the task-relevant parameters in racket sports (Knudson & Blackwell, 2005) would require a well-evolved movement coordination system, which could be lacking in less-skilled athletes (Cortis et al., 2009; Whiteside et al., 2013). Further evidence of the differences between skill levels was apparent from the group differences in the variability of all the task-relevant parameters, whereby the less-skilled had higher variability than the highly skilled group. These results support previous findings in basketball free-throw shooting (Button et al., 2003) and the long-jump approach (Scott et al., 1997).

There were no significant main effects for accuracy found for the variability of the task-relevant parameters or joint coordination variability measures. This suggests that each group had similar magnitudes of variability in their respective movement patterns irrespective of the task outcome. This is in contradiction to recent investigations into the tennis serve (Whiteside et al., 2013) and the basketball free-throw shot (Mullineaux & Uhl, 2010) in which there were differences in the endpoint variability of coordinated joints between successful and unsuccessful tasks at ball impact and ball release, respectively. The absence of significant accuracy differences in the current study may be the result of the size of the target area and the continuous nature of the shots used in the protocol of this study. It is possible that due to the relatively large size of the target area and the variable spatial ball impact location on the court, the subtle differences in the task-relevant parameters that potentially distinguish task outcome were undetected (Knudson & Blackwell, 2005).

As previously stated, due to the unavoidable variability of the approaching ball speed and direction as well as player location on the court, the spatial racket-ball impact location would have also varied. Therefore, an athlete’s swing mechanics could also have an equivalent degree of variance, to match the varying racket-ball impact location (Whiteside et al., 2013). The increased variability of the joint couplings found at propulsion initiation in both groups could have occurred as a result of the necessary perceptual feedback required to predict the interception of the racket-ball impact location (Button & Summers, 2002). It is possible that once the racket-ball location could be accurately predicted, the movements moved from variable and approximate (propulsion initiation) to precise and specific at the task-relevant ball impact point (Whiteside et al., 2013). This notion of perceptual feedback influencing the variability of the mechanics of interceptive actions is supported by previous work in table tennis (Bootsma & Van Wieringen, 1990) and tennis (Whiteside et al., 2013). It appears that, for the squash forehand drive, the required mechanical adjustments, i.e. functional variability, occur when the respective upper-limb joints begin to rotate in a propulsive direction. The proceeding zeroing-in and reduction of the relative joint coordination variability, in turn, allows for the key task-relevant parameters to have a very high consistency.

The method of group separation and the statistical analysis approach in the present study is akin to previous research in which data were analysed according to skill level groups, regardless of an age difference (Landlinger et al., 2010b; Lyons et al., 2013; Wagner et al., 2012). Due to the complex interaction between skill level and experience, age, height and weight, it is difficult to account for any 1 factor without potentially removing the effect of skill (Giniger et al., 1983; Malina et al., 2007). An analysis of the kinematics of the lower body was outside of the scope of the present study. While the kinematics of the lower limbs could potentially influence the initial trunk position, there were no significant group or accuracy main effects for trunk rotation angle at the top of backswing, suggesting that the participants were able to maintain a consistent trunk angle at the start of each shot. The present study also did not consider the effect of racket properties (balance, weight, string tension) on the resulting ball velocities, nor did it measure any ball mechanics (approaching or post-impact), limitations that should be considered when interpreting the results. Future work may be advisable in investigating the lower-limb kinematics between accurate and inaccurate squash shots and the effect different racket properties can have on the resulting ball mechanics and shot outcome.

Conclusion

There was a lack of any distinct upper-body kinematic variable that distinguished accuracy in this study. However, during inaccurate shots, the less skilled players hit the ball with a more open racket face, demonstrating an inconsistency in this important task-relevant parameter. Furthermore, the less-skilled players displayed greater variability in all the measured task-relevant racket parameters compared to the highly skilled players, highlighting the necessary consistency required to attain a high level of skill.

Moreover, the evaluated joint couplings, irrespective of skill group, displayed a zeroing-in effect whereby the variability at the time the proximal joint initiated rotation in a propulsive direction was progressively reduced during the period prior to the critical task-relevant point of ball impact. Highly skilled players showed a greater consistency of the relative joint coordination over the duration of the forward swing phase and particularly at ball impact.

In order to progress the skill level of the forehand drive, less-skilled players should focus on improving the consistency of their task-relevant parameters, particularly reducing racket face angle at ball impact. This appears to be obtainable via functional variability at the initiation of propulsion of the upper-limb joint rotations, thereby allowing an increased consistency of the critical task-relevant parameters.

Acknowledgments

The authors would like to thank the athletes who volunteered to participate in the study and squash Head Coach Stewart Boswell for his assistance with the data collection. The publication of this article was funded by the Qatar National Library.

Disclosure Statement

The authors report no conflict of interest.