Hindawi Applied Bionics and Biomechanics Volume 2020, Article ID 8413948, 10 pages https://doi.org/10.1155/2020/8413948 Research Article Using Wearable Inertial Sensors to Estimate Kinematic Parameters and Variability in the Table Tennis Topspin Forehand Stroke 1 2 Ziemowit Bańkosz and Sławomir Winiarski Department of Sports Didactics, Faculty of Sports, University School of Physical Education in Wrocław, Wrocław, Poland Division of Biomechanics, Faculty of Physical Education, University School of Physical Education in Wrocław, Wrocław, Poland Correspondence should be addressed to Ziemowit Bańkosz; firstname.lastname@example.org Received 21 December 2019; Accepted 28 April 2020; Published 11 May 2020 Academic Editor: Juri Taborri Copyright © 2020 Ziemowit Bańkosz and Sławomir Winiarski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The study examined kinematic parameters and their inter- and intrasubject variability in the topspin forehand of seven top-level table tennis players. A wireless inertial measurement unit (IMU) system measured the movement of the playing hand to analyze the Ready position, Backswing, and Forward events, and a racket-mounted piezoelectric sensor captured the racket-ball Contact. In a four-phase cycle (Backswing, Hitting, Followthrough, and Back to Ready position), body sensors recorded the cycle and phase duration; angles in the sagittal plane at the shoulder, elbow, and wrist of the playing hand and at the knee joints; and acceleration of the playing hand at the moment of racket-ball contact. The coeﬃcient of variation (CV) was calculated to determine the variability of kinematic parameters within and between players. The observed variability in stroke time duration was low (CV < 20%) indicating constancy. The small-to-medium intraindividual variability of angles (CV < 40%) indicates that each player used a broadly repeatable technique. The large intraindividual variability in movement was probably functional (i.e., motor adjustment and injury avoidance). Interindividual and intraindividual variability of knee and elbow angles was low; wrist extension was the most variable parameter (CV > 40%) for all tasks, and shoulder joint variability was medium-to-large. Variability in hand acceleration was low (CV < 20%). Individual players achieved relatively constant hand acceleration at the moment of contact, possibly because angular changes at one joint (e.g., shoulder) could be compensated for by changes at another (e.g., wrist). These ﬁndings can help to guide the teaching-learning process and to individualize the training process. to determine tactical potential and likelihood of achieving 1. Introduction champion status . Table tennis is a very fast, varied, and complex game, requir- There is evidence that the topspin forehand is among the ing an immediate response to changing stimuli. The diﬃculty most frequently used strokes in modern table tennis, in both of the game is increased by the high speed and variety of ball the ﬁrst attack and its continuation or counter-attack [7–9]. rotation [1, 2]. Multiple factors aﬀect performance in this In this stroke, the velocity of the racket at the moment of con- sporting discipline, including the level of technical prepara- tact with the ball reaches 20 m/s; following impact, the ball tion, tactical thinking, motor skills, mental preparation, and reaches a velocity of up to 45 m/s, rotating at up to 140 revo- physiological determinants . At an elite level, competition lutions per second [1, 10, 11]. Theoreticians and practitioners (match) outcomes are often determined by very small diﬀer- regard the topspin forehand as a complex stroke, involving a kinematic chain of proximal-to-distal sequences or a stretch- ences and sometimes by moments of excellent performance, and many table tennis coaches and professionals have identi- shortening cycle. The speed at which the racket hits the ball is ﬁed comprehensive and perfect technique as a prerequisite primarily inﬂuenced by hip joint and body rotation, ﬂexion for high-level success [4, 5]. In general, technique is thought and adduction at the shoulder joint, and ﬂexion at the elbow 2 Applied Bionics and Biomechanics they characterized as “compensatory variability.” In a study joint [12, 13]. During a game, the player must react to diﬀer- ent situations and associated changes in ball parameters such of racket kinematics and direction during the forehand drive as speed, rotation, ﬂight trajectory, point of contact with the stroke across diﬀerent levels of expertise, Shepard and Lee also found that movement variation was reduced at the time table, and height of rebound. In deciding on the type of stroke, the player adjusts their movements, the angle of the of racket-ball contact . They described this phenomenon racket, the force applied, and the direction of racket move- as “funneling” and again noted the speed-accuracy trade-oﬀ. ment. For example, a player attacking with topspin against It seems, then, that the mechanisms of movement vari- a backspin shot and hitting the ball below the line (surface) ability in table tennis warrant more detailed investigation. In particular, it seems interesting to investigate the best table of the table must “open” the racket, hitting the ball close to its central line and directing the movement from the bottom tennis players’ use of the topspin forehand, which is the most upward. In contrast, when returning a topspin ball ﬂying commonly used stroke in the game. To guide the teaching- above the net line, they must close the racket, hitting the learning process and to individualize the training process, it upper part of the ball and directing movement strongly for- seems useful to explore movement variability and the condi- tions and limits of its occurrence. This may assist in the ward. Deciding on the type of stroke may also involve other changes—for example, from a rotational to a direct hit—- process of monitoring and correcting technique and in devel- resulting in further alteration of motion parameters. oping improvement plans for individual players. This complexity means that players must choose from a To that end, the present study employed inertial mea- range of options while maintaining high movement accuracy. surement unit (IMU) sensors from the myoMotion System to measure selected kinematic parameters of the topspin It is therefore interesting to explore variations in table tennis players’ movements and the limits of this variation. Within forehand stroke and the intra- and interindividual variability the rich literature on movement variation, some researchers of these parameters among advanced male table tennis have approached this as a problem of movement “noise”—- players. Speciﬁcally, we hypothesized that measurement of that is, as nontargeted variability resulting from a complex key kinematic parameters of the topspin forehand stroke (duration of the cycle and its phases and knee, shoulder, multijoint movement . However, it is increasingly sug- gested that this variability (both inter- and intraindividual) elbow, and wrist joint angles) would explain any variability may be a functional and purposeful response to diﬀerent sit- in these strokes. We further assumed that the values of some of these parameters would vary more (CV > 40%) uations and requirements of the task, such as parameters of —espe- the ﬂying ball or avoiding injury . Others have empha- cially in the Ready position and Backswing phases—and that sized the need for consistency and repeatability; for example, some would be less variable (CV < 20%), especially the Whiteside et al. suggested that a consistent projection angle moment of contact and elbow and wrist joint angles, in light during service is critical for successful tennis performance of the principle of “funneling” described in the literature. . Small diﬀerences in movement parameters may also indicate a compensation mechanism, as for example when a 2. Materials and Methods change in the range of motion at one joint is compensated by a change at another [16–20]. According to some The study participants were seven top adult male players researchers, human movement variability facilitates motor from Poland’s national team, with a mean body height of learning through active nervous system regulation [21, 22]. 177 ± 3:5cm and mean body mass of 76 ± 8:5kg. Each par- Functional variability of movement is also thought to change ticipant was informed about the purpose and nature of the and develop with player age and experience . There is research and signed an informed consent form. The study also evidence that variability decreases when movement is protocol was approved by the Institutional Ethics Board accompanied by increased mental focus on a particular (Senate’s Research Bioethics Commission at the University aspect of activity . School of Physical Education in Wrocław). All the players As well as works investigating the kinematics of table ten- ranked among the top ten Polish senior athletes. Six of the nis strokes [10, 12, 25], a number of studies on stroke kine- players were right-handed, and one was left-handed. Partici- matics have examined the relationships between movement pants were asked to perform the topspin forehand stroke and work done or force generated, between force and racket with submaximal or maximal force on a specially prepared speed, and between the kinetics of the upper limbs and other stand (see Figure 1), and individual kinematic parameters body segments [13, 26, 27]. To the best of our knowledge, of the players were measured using the MR3 myoMuscle however, the issue of movement variability in table tennis Master Edition system (myoMOTION™, Noraxon, USA). kinematics has not yet been intensively explored. Among To record acceleration, wireless IMU sensors were attached existing studies, Bootsma and van Wieringen  referred (as per the myoMotion protocol described in the manual) to movement variability in the accuracy and time of move- to the following body segments: head, left and right arms, left ment of ﬁve table tennis players during a drive stroke (which and right forearms, left and right hands, left and right thighs, can be described for present purposes as “light topspin”). left and right foot, shanks, and body trunk (see Figure 2). The They found that when forced to play accurately—that is, to myoMotion system includes a set of 1 to 16 inertial sensors; hit a speciﬁed target—the spatial and temporal accuracy of using so-called fusion algorithms, a 3D accelerometer, gyro- players’ movement was reduced in attempting to hit the tar- scope, and magnetometer measure the 3D rotation of each get. At the same time, variability at the moment of contact sensor in absolute space in terms of yaw, pitch, and roll (also between racket and ball was also reduced—a phenomenon known as orientation or navigation angles). To record and Applied Bionics and Biomechanics 3 the sagittal plane following the swing); and Forward (the moment at which the racket changes direction from forward to backward in the sagittal plane after the stroke). The fourth event in the cycle—the moment of ball-racket contact—was captured by the racket-mounted sensor. Each click on the racket (i.e., contact of racket and ball) transmitted a signal from the sensor to the system software. The moment at which this signal was registered was treated as the moment of racket-ball contact. By capturing these events, it was possible to determine the duration of individual phases of the stroke: Backswing (Ph1); Hitting (Ph2); Followthrough (Ph3); and Back to Ready position (Ph4). It is also worth noting that the study conﬁrms the utility of Noraxon’s IMU as an alternative to optical motion capture systems for movement analysis. Dur- ing dynamic trials, the root mean square error (RMSE) for Figure 1: Research stand. myoMotion (as compared to Vicon) was 0.50 deg, with a cor- relation coeﬃcient of 0.99 between Vicon and myoMotion analyze the moment of racket-ball contact, a piezoelectric for dynamic trials . sensor (7BB-20-6L0, Murata Manufacturing Co., Ltd., USA) Using basic descriptive statistics (means, standard devia- compatible with the myoMotion system was attached to the tions, and variances) for all kinematic parameters, their var- racket. The max sampling rate was 100 Hz per sensor for iability was measured as coeﬃcients of variation . For the whole 16-sensor set, and this was adjusted to the speed the purposes of this study, low variability was deﬁned as of registration by the piezoelectric sensor (1500 Hz). The CV < 20; medium variability was deﬁned as 20–40; and high maximum test range of the 3-axis digital accelerometer is variability was deﬁned as CV > 40. Statistical calculations ±16g (g =9:8 m/s ) with 10000g high shock survivability. were performed using the Statistica software (Statistica 12.5, Prior to testing, the athletes completed the standardized StatSoft Inc., Tulsa, USA). general (15 minutes) and sport-speciﬁc (20 minutes) warm- up procedures. Each then performed a topspin forehand with 3. Results and Discussion maximum or submaximal force. Each task comprised 15 pre- sented strokes, and the player was required to hit the marked Intraindividual and interindividual variability in the topspin area (30 × 30 cm) at the corner of the table. Every successful forehand stroke was measured by coeﬃcients of variation shot (i.e., “on table” and played diagonally) was recorded (CV), based on IMU values for the following kinematic for further analysis. Any balls missed, hit out of bounds, or parameters. hit into the net were excluded. Balls were delivered according to speciﬁed parameters (see Table 1) by a dedicated table ten- 3.1. Time Duration. The results for temporal parameters are nis robot (Newgy Robo Pong Robot 2050, Newgy Industries, shown in Tables 2 and 3. Tennessee, USA; see Figure 1). There was little variation in overall cycle duration across All movement parameters were recorded and calculated participants (Table 2). Of the four distinct phases, the Hitting using a standard protocol and report of the myoMotion soft- phase (Ph2) was shortest in duration. Variability in the dura- ware. Focusing on the topspin forehand technique, assess- tion of individual hitting phases was small (CV < 20%)or ment of variability was conﬁned to joints on the playing medium (20–40%). Values in Ph4 (return to the Ready posi- side (shoulder, elbow, and wrist) and the knee joints, which tion) diﬀered for every player and returned the most cases of have been identiﬁed as decisive for performance of the top- CV > 40%. Among individual players, variability in duration spin forehand [12, 30, 31]. We chose to discuss only selected of the entire cycle and its individual phases (Table 3) was movements in sagittal plane where the ROM is greatest and small (total time TT), with CV values for all players ranging the speed of movement has probably the greatest impact on from 0.8% to 6.7% (Table 3). Low variability cases included the spin of ball. In order to show the magnitude of variation, Ph1 (one player), Ph2 (four players), and Ph3 (six players). we chose only selected parameters. The sensors attached to The remaining cases in these three phases were characterized the athlete’s body and to the racket recorded the values of by medium variability. Based on these results, the large the following parameters for further analysis: angles of play- number of cases of low variability (low CV values) in indi- ing hand, extension of the wrist, shoulder ﬂexion, elbow ﬂex- vidual athletes for the entire duration of the stroke (TT) ion, and knee ﬂexion (both sides), and acceleration of the and for most phases (mainly Hitting and Followthrough) playing hand at the moment of racket-ball contact. Move- indicates that variation in these parameters is small and ment of the playing hand was measured to assess the follow- that stroke characteristics are fairly constant, conﬁrming ing speciﬁc events in the cycle: Ready position (racket not the ﬁndings of previous studies [11, 13]. For each player, moving after previous stroke, before swing, forward- the greatest variation was observed in duration of Ph4 backward acceleration =0); Backswing (the moment at which (Back to Ready position). The beginning of the Ready the racket changes direction from backward to forward in position phase (Ph4) was deﬁned as the point at which 4 Applied Bionics and Biomechanics Head Upper arm Forearm Hand Thigh Shank Foot Figure 2: Sensor locations. Table 1: Table tennis robot parameters. Table 2: Time duration of particular phases during topspin forehand in the entire group of players (n =7)—means, standard Robot parameter Value deviations (SD), variations (V), and coeﬃcients of variation (CV). Rotation (direction of spin) Topspin Topspin forehand Variable Speed (determines both speed and spin, where 0 18 Ph1 Ph2 Ph3 Ph4 TT is the minimum and 30 is the maximum) Mean (s) 0.5 0.1 0.2 0.4 1.5 Left position (left most position to which the SD (s) 0.1 0.0 0.0 0.1 0.0 ball is delivered) V 0.0 0.0 0.0 0.0 0.0 Wing (robot’s head angle indicator) 8.5 ∗∗ ∗∗ ∗ ∗∗ CV (%) 18.3 46.2 18.2 25.7 1.4 Frequency (time interval between balls thrown) 1.4 Ph1: Backswing; Ph2: Hitting; Ph3: Followthrough; Ph4: Back to Ready ∗ ∗∗ position; TT: total time of the cycle. Average variability. Small variability. Not marked CV: high and very high variability. the player held the racket stationary before the next action (forward − back acceleration = 0) while waiting for the robot to deliver the ball. As this moment was freely deter- mined by each participant, the duration of this phase varied 3.2. Angles. The myoMotion system was also used to measure more. Interestingly, the results across the entire group indi- angles at joints known to be important for speciﬁc events cate small or medium variation in duration for most phases during table tennis performance (see Tables 3 and 4). In the analysis of results for the entire group (intervariability), knee (Table 3) other than Ph4 (from Forward to Ready position), where variability exceeded 40%. This indicates that players’ and elbow joints accounted for the highest number of cases of performance of the tasks was similar in terms of duration small variability (low CV value) (see Table 4). There were 8 of the stroke and its individual phases. cases of high or very high variability and 12 cases of small Applied Bionics and Biomechanics 5 the entire group and for individual players (Table 6). It is Table 3: Variability (CV in %) of time duration of particular phases during topspin forehand in particular players (1-7). important to mention that the speciﬁed task required partic- ipants to use submaximal force. At the moment of contact, Topspin forehand several players exhibited high or very high variability of Player Ph1 Ph2 Ph3 Ph4 TT angles, especially in extension at the wrist joint. There was ∗∗ ∗∗ ∗ ∗∗ 31.6 10.0 21.4 2.3 1 107.8 also medium and high variability of the shoulder joint in ∗ ∗ ∗∗ ∗∗ 22.1 36.8 3.1 1.1 many cases, but the variability of acceleration values 2 65.9 remained low, perhaps because changes at the shoulder and ∗ ∗ ∗∗ ∗∗ 3 25.3 36.0 1.6 79.9 5.0 wrist joints are mutually dependent—in other words, ∗ ∗∗ ∗∗ ∗∗ 21.6 13.8 5.2 0.8 4 64.4 changes at one joint are compensated for by changes at the ∗∗ ∗∗ ∗∗ ∗∗ 15.9 15.5 2.8 0.9 5 63.7 other. This kind of compensation mechanism has been ∗ ∗ ∗∗ ∗∗ observed in other studies and in other sports; for example, 22.2 30.8 8.9 6.3 6 65.2 Button, MacLeod, Sanders, and Coleman evaluated move- ∗ ∗∗ ∗∗ ∗∗ 7 28.4 9.2 6.7 80.1 6.7 ment variability in basketball players performing free throws Ph1: Backswing; Ph2: Hitting; Ph3: Followthrough; Ph4; Back to Ready  and found that players compensated for mutual changes ∗ ∗∗ position; TT: total time of the cycle; Average variability. Small of angle at the elbow and wrist joints. They further reported variability. Not marked CV: high and very high variability. that variability at the elbow and wrist joints tended to increase toward the end of the throwing action. In a study of cueing actions in billiards (assessing parameters such as velocity, or average variability. In terms of intraindividual variability, acceleration, height, and angle of the cue), Kornfeind et al. the analysis indicates that individual variability of movement  observed signiﬁcant variability in stroke movement was low in 82 of 140 cases and medium in 19 cases (Table 5). despite very similar outcome values. Regarding individual events, there were some cases of high Many researchers have emphasized functional variabi- variability for all joints, most of which related to angles in lity—that is, ﬂexible changes in movement parameters in the Ready position (6 of 35 cases) and at the moment of con- response to the changing requirements of the game or com- tact (14 of 35 cases) (see Table 4). High variability most often petition [14, 19, 36]. In the present case, the observed accel- related to the position of the hand at the wrist joint on adopt- eration values may indicate similar functional variability ing the Ready position (2 of 7 cases), completion of the move- and compensation mechanisms in table tennis. While ment (Forward, 6 of 7 cases), and the position of the arm at angular variability at the joints was often low or medium in the shoulder joint at the moment of Backswing (3 of 7 cases). individual athletes, the frequency of high variability cases The analysis of angle variations in the four selected top- indicates that table tennis players’ technique is not entirely spin forehand events (Ready position, Backswing, Contact, repetitive. In contrast, there was very little diﬀerence in hand and Forward) focused on the CV values of the angles. acceleration at the time of contact, with CV values well below Intraindividual variability was more often small or medium 10%. Despite some angular variation in subsequent events, rather than large, indicating that the participating players individual players (and the entire group) exhibited relatively each used a repeatable technique. As in other sports, how- constant hand acceleration at the moment of contact between ever, it is impossible to state unequivocally that any given racket and ball, indicating compensatory changes in angular player repeated the same task with the same movement pat- parameters (e.g., shoulder/wrist) as observed in many other tern. For example, in their review of research on interindivid- sports [16–19, 37, 38]. ual and intraindividual variation in track and ﬁeld throwing In sporting contexts, there is some evidence of the need events, basketball throws, and gait during human locomo- for constancy and repeatability in the range of speciﬁc tion, Bartlett et al. demonstrated that the large variation in parameters ; in the present case, one such constant ele- movement is probably functional in character, as athletes ment was acceleration value at the moment of contact, with make motor adjustments or seek to avoid injury . They small CV values across the entire group. A similar phenom- also noted that even the best athletes (with similar results) fail enon has been documented in billiards , golf , basket- to perfectly reproduce the same movement (in terms of ball , and by other authors . The low CV values for parameters, range of motion, and coordination). Bartlett acceleration at so important a point as racket-ball contact et al. further argued that these factors should be considered support the ﬁndings of Bootsma and Wieringen  and when preparing an individualized training plan for each Shepard and Lee and Xie  regarding acceleration and athlete, taking into account their unique capabilities. In reduced variability at critical moments. the present context, that might include addressing the var- Among the limitations of the present study, the sample ious ways of coordinating topspin movement and perhaps was small (n =7), and all of the participants were male, mak- compensating for a small range of motion in one joint by ing it diﬃcult to generalize the ﬁndings. Additionally, while ensuring a larger range of motion in another. Crucially, this study examined only the topspin forehand with use of any coaching to shape and improve stroke technique should submaximum or maximum force, our recent work reports be ﬂexible. similar ﬁndings for other variants of this stroke . A ﬁnal limitation is that the present study was laboratory-based, and 3.3. Acceleration and Compensatory Mechanism. The vari- examination of variability in kinematic parameters under game condition might yield diﬀerent outcomes. ability of acceleration values was small in all cases, both for 6 Applied Bionics and Biomechanics Table 4: Values of angles at joints in chosen events during topspin forehand in the entire group of players (n =7)—means, standard deviations (SD), variations (V), and coeﬃcients of variation (CV). Ready position Backswing Contact Forward ShF ElF WrE RKnF LKnF ShF ElF WrE RKnF LKnF ShF ElF WrE RKnF LKnF ShF ElF WrE RKnF LKnF Mean (deg) 13.2 66.1 44.7 43.3 41.4 8.7 47.6 25.4 51.9 58.0 26.4 43.7 47.7 47.6 52.7 90.8 87.0 -3.0 51.1 49.7 SD (deg) 9.2 6.6 41.5 10.6 5.3 8.6 20.9 11.8 14.3 8.9 11.8 15.3 39.3 12.7 9.3 18.2 21.5 25.2 10.8 10.1 V 84.3 43.9 1727.8 111.5 28.1 74.9 435.0 139.3 203.6 78.7 139.1 232.8 1542.5 162.4 87.3 330.9 464.1 636.2 117.2 102.7 ∗∗ ∗ ∗∗ ∗ ∗∗ ∗ ∗ ∗∗ ∗ ∗ ∗ ∗ CV (%) 69.6 10.0 92.4 24.4 12.8 99.2 43.8 46.5 27.5 15.3 44.6 34.9 82.3 26.8 17.7 20.0 24.7 851.0 21.2 20.4 ∗ ∗∗ ShF: shoulder ﬂexion; ElF: elbow ﬂexion; WrE: wrist extension; RKnF: right knee ﬂexion; LKnF: left knee ﬂexion. Average variability. Small variability. Not marked CV: high and very high variability. Applied Bionics and Biomechanics 7 Table 5: Values of angles at joints in chosen events during topspin forehand of particular players (1-7)—means, standard deviations (SD), variations (V), and coeﬃcients of variation (CV). Ready position Backswing Contact Forward Variable ShF ElF WrE RKnF LKnF ShF ElF WrE RKnF LKnF ShF ElF WrE RKnF LKnF ShF ElF WrE RKnF LKnF Mean (deg) 10.8 62.2 82.2 44.7 42.1 36.1 75.8 6.0 74.8 65.8 34.9 56.7 88.5 71.7 59.6 82.1 108.5 40.2 66.9 57.6 SD (deg) 11.6 11.9 33.9 16.6 13.2 32.7 6.2 43.2 3.4 6.9 15.8 26.1 39.9 30.8 27.6 24.2 19.6 74.3 10.9 9.3 V 135.1 141.2 1148.4 276.5 173.6 1067.2 38.6 1862.9 11.3 48.3 251.1 681.1 1593.4 947.4 759.6 586.3 383.7 5521.9 118.9 86.5 ∗∗ ∗ ∗ ∗∗ ∗∗ ∗∗ ∗ ∗∗ ∗∗ ∗∗ 19.0 33.4 28.1 8.4 4.5 10.7 32.3 18.4 16.9 16.5 CV (%) 147.7 49.1 138.3 185.9 55.7 55.4 54.8 54.3 55.3 308.3 Mean (deg) 18.5 80.3 40.0 59.5 40.2 0.6 58.1 31.6 70.6 71.6 17.2 61.0 62.1 64.3 70.4 70.2 72.2 -8.4 50.5 61.8 SD (deg) 19.6 3.6 10.1 3.8 7.3 30.5 19.2 23.7 7.2 6.0 22.6 21.5 16.0 2.7 4.1 36.7 2.7 11.5 4.7 5.2 V 386.0 12.6 103.0 14.2 53.1 930.5 370.3 563.8 52.0 35.6 509.8 463.6 255.5 7.3 16.7 1344.6 7.4 132.5 21.9 27.0 ∗∗ ∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗ ∗∗ ∗ ∗∗ ∗∗ ∗∗ 4.4 23.1 6.4 17.7 10.4 8.4 24.1 4.2 5.8 3.8 9.0 8.4 CV (%) 144.6 931.5 35.04 88.0 181.5 41.5 48.5 131.3 Mean (deg) 17.2 68.8 33.9 38.1 50.0 11.5 67.5 40.4 47.9 57.7 -1.4 43.9 5.9 42.4 61.3 75.9 104.5 11.9 58.6 47.8 SD (deg) 3.5 7.6 8.1 4.5 4.7 2.4 2.4 8.3 3.6 5.1 3.4 22.2 4.4 21.2 29.5 2.3 8.9 6.6 5.7 7.7 V 12.2 57.1 65.5 20.0 22.2 5.6 5.7 68.9 12.6 26.4 11.6 493.9 19.6 450.0 871.6 5.2 78.9 43.9 32.6 58.5 ∗ ∗∗ ∗ ∗∗ ∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ 20.8 CV (%) 11.1 24.2 11.3 9.3 19.2 3.5 19.1 7.6 8.9 147.0 66.4 78.0 66.6 65.7 3.0 8.3 48.5 9.8 15.7 Mean (deg) 14.6 67.3 -1.5 48.1 36.1 12.8 13.9 23.4 48.6 50.0 19.1 18.6 24.2 45.6 43.0 87.8 60.9 12.1 52.2 37.0 SD (deg) 6.0 17.7 2.7 10.0 6.4 7.6 7.0 3.0 16.7 6.7 6.0 7.2 6.8 17.3 12.9 3.9 3.5 6.1 16.8 4.9 V 35.4 311.6 7.1 100.6 40.4 57.8 49.4 8.9 277.9 45.2 36.4 52.3 45.7 297.8 165.7 15.2 12.0 37.6 281.6 23.9 ∗ ∗ ∗∗ ∗∗ ∗ ∗∗ ∗ ∗ ∗ ∗∗ ∗∗ ∗ ∗∗ 27.8 22.5 16.6 13.0 37.8 13.4 32.7 30.4 31.0 4.4 5.7 36.8 12.7 CV (%) 41.8 214.5 59.3 47.9 40.5 44.9 52.6 Mean (deg) 21.1 61.8 79.5 46.1 40.4 6.0 48.3 30.3 49.8 55.2 10.3 62.3 54.9 49.5 50.5 107.1 113.8 -48.3 56.6 57.5 SD (deg) 3.5 4.9 6.3 3.9 7.6 3.8 6.2 6.3 3.2 5.1 4.6 4.4 4.8 3.1 6.5 2.4 4.4 7.7 4.3 4.7 V 12.0 23.6 40.1 15.6 57.8 14.5 38.8 40.3 10.3 25.8 21.2 19.7 23.1 9.7 42.8 5.9 19.0 59.6 18.2 22.6 ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗ ∗∗ ∗∗ ∗∗ ∗∗ CV (%) 16.9 7.9 7.9 8.5 20.0 60.7 13.1 21.1 6.5 9.2 46.1 7.1 8.8 6.3 12.7 2.3 3.8 15.2 7.5 8.18 Mean (deg) 0.8 60.6 102.7 39.3 38.7 22.3 29.0 26.8 45.5 44.1 27.2 35.3 88.9 48.9 52.9 135.2 71.8 -27.7 52.2 49.7 SD (deg) 2.6 3.4 8.7 5.0 3.5 2.9 4.0 3.5 3.1 3.7 2.5 5.2 6.2 5.1 3.4 37.6 4.7 20.2 6.4 4.6 V 6.5 11.8 75.4 25.4 12.2 8.2 16.4 12.1 9.8 13.7 6.3 26.9 38.3 25.8 11.6 1412.7 22.5 408.1 41.4 21.3 ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗ ∗∗ ∗∗ ∗∗ 5.6 8.7 13.1 9.3 12.4 13.8 12.6 7.0 8.2 9.1 14.1 7.0 10.6 6.3 30.7 6.6 12.6 9.3 CV (%) 356.6 83.0 Mean (deg) 22.1 73.8 -6.5 26.7 33.2 -14.2 34.7 11.2 36.3 66.6 2.6 38.0 11.6 35.2 65.9 94.7 88.0 12.8 29.6 36.0 SD (deg) 9.7 4.6 5.2 6.2 4.6 4.6 5.6 5.8 1.1 3.1 3.4 5.9 4.8 1.4 2.6 4.6 5.0 6.9 3.4 3.7 V 94.4 20.8 27.5 38.4 20.7 21.3 30.9 33.2 1.2 9.8 11.4 34.3 23.2 1.8 6.6 21.0 25.3 47.5 11.4 14.0 ∗∗ ∗ ∗∗ ∗ ∗∗ ∗∗ ∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ CV (%) 43.7 6.7 76.3 22.9 13.8 35.1 15.1 48.4 3.0 4.7 121.2 14.7 42.0 3.9 3.9 4.8 5.8 57.3 11.3 10.4 ShF: shoulder ﬂexion; ElF: elbow ﬂexion; WrE: wrist extension; RKnF: right knee ﬂexion; LKnF: left knee ﬂexion; Average variability; ∗∗Small variability; not marked CV: high and very high variability. 8 Applied Bionics and Biomechanics Intraindividual variability of angles was most often low Table 6: Values of acceleration of “playing hand” in the moment of racquet’s contact with the ball—entire group and particular or medium, indicating repeatable technique among the par- players—means, standard deviations (SD), variations (V), and ticipating players. Nevertheless, it is impossible to state coeﬃcients of variation (CV). unequivocally that any player repeated the same task with the same movement pattern. As the literature suggests, the Variable Topspin forehand large variability in movement may be functional and Mean (m/s ) 149.2 compensatory in character, reﬂecting motor adjustment of SD (m/s ) 8.6 various parameters. Entire group (n =7) V 73.7 Inter- and intraindividual variability of joint angles was ∗∗ generally low for the knees and the elbow joint. The greatest 5.8 CV (%) observed variability was in extension at the wrist joint, with Players medium or large variability of the shoulder joint in many Mean (m/s ) 159.4 cases. It seems likely that the observed changes at the shoul- SD (m/s ) 3.1 der and wrist joints are mutually dependent (i.e., changes at one joint are compensated for by changes at the other). V 9.6 ∗∗ There was low variability in hand acceleration. Despite 2.0 CV (%) the variability of some angles in subsequent events, it can Mean (m/s ) 160.1 be concluded that individual players achieved relatively con- SD (m/s ) 14.3 stant hand acceleration at the moment of contact between racket and ball. This indicates compensatory changes in V 204.6 ∗∗ angular parameters at one joint to oﬀset changes at another. 9.2 CV (%) Mean (m/s ) 158.9 Data Availability SD (m/s ) 3.6 The raw data.xls data used to support the study ﬁndings V 12.9 ∗∗ are included in the supplementary information ﬁle (avail- 2.3 CV (%) able here). Mean (m/s ) 156.0 SD (m/s ) 6.8 Disclosure V 46.0 ∗∗ This research was performed as part of the authors’ employ- 4.3 CV (%) ment at the University School of Physical Education in Mean (m/s ) 138.4 Wrocław. No other parties were involved in writing, editing, SD (m/s ) 10.1 or approving the manuscript, or in the decision to publish. 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Published: May 11, 2020