Effect of endpoint conditions on position and velocity near impact in tennis

Smoothing to obtain accurate position and velocity data near impacts in sport biomechanics studies is complicated by the accelerations of impact, endpoint effects and the smoothing technique used. Wrist goniometric data with two levels of random noise added were used to examine three endpoint modelling conditions for obtaining accurate position and velocity data at impact in the tennis forehand. The common approach of smoothing through impact created distortions of the position signal up to 100 ms before impact and resulted in consistent underestimations (-3.2%) of wrist angle and angular velocity (-67.9%) at impact. New linear and polynomial extrapolation conditions smoothed with all techniques provided lower root mean squared errors than the smoothing-through-impact condition, with discrete wrist positions at impact within 1.1% of the criterion data. Both the new linear and polynomial conditions can be used to make more accurate angular position and velocity estimates for tennis impacts, whereas the smoothing-through-impact condition creates spurious decreases in speed before impact that in the past have been assumed to be aspects of skilful movement.     

An investigation into the power point in tennis

This paper investigates the nature of the power point in tennis. A series of static racket impacts and a polynomial fit were used to simulate four different racket shots with increasing amounts of angular velocity—identifying the true ‘power point’ for each shot. A rigid body model was used to define the ‘ideal point’ for each shot—the impact point which theoretically yields maximum outbound ball velocity. Comparing theory with experiment revealed that the ‘ideal point’ is most accurate for impacts around the racket’s node point (the rigid body model does not account for frame vibration). Previous research has shown that tennis players aim to strike the node point of the racket. The concept of the ideal point has potential in tuning the weight distribution of a racket to a player’s shot type. If the ‘ideal point’ exists at the racket node point for a player’s typical forehand shot, then outbound ball velocities can be maximised.     

The effect of ball impact location on racket and forearm joint angle changes for one-handed tennis backhand groundstrokes

Recreational tennis players tend to have higher incidence of tennis elbow, and this has been hypothesised to be related to one-handed backhand technique and off-centre ball impacts on the racket face. This study aimed to investigate for a range of participants the effect of off-longitudinal axis and off-lateral axis ball–racket impact locations on racket and forearm joint angle changes immediately following impact in one-handed tennis backhand groundstrokes. Three-dimensional racket and wrist angular kinematic data were recorded for 14 university tennis players each performing 30 “flat” one-handed backhand groundstrokes. Off-longitudinal axis ball–racket impact locations explained over 70% of the variation in racket rotation about the longitudinal axis and wrist flexion/extension angles during the 30 ms immediately following impact. Off-lateral axis ball–racket impact locations had a less clear cut influence on racket and forearm rotations. Specifically off-longitudinal impacts below the longitudinal axis forced the wrist into flexion for all participants with there being between 11° and 32° of forced wrist flexion for an off-longitudinal axis impact that was 1 ball diameter away from the midline. This study has confirmed that off-longitudinal impacts below the longitudinal axis contribute to forced wrist flexion and eccentric stretch of the wrist extensors and there can be large differences in the amount of forced wrist flexion from individual to individual and between strokes with different impact locations.     

Contributions of upper limb rotations to racket velocity in table tennis backhands against topspin and backspin

The purpose of this study was to assess the contributions of racket arm joint rotations to the racket tip velocity at ball impact in table tennis topspin backhands against topspin and backspin using the method of Sprigings et al. (1994). Two cine cameras were used to determine three-dimensional motions of the racket arm and racket, and the contributions of the rotations for 11 male advanced table tennis players. The racket upward velocity at impact was significantly higher in the backhand against backspin than against topspin, while the forward velocity was not significantly different between the two types of backhands. The negative contribution of elbow extension to the upward velocity was significantly less against backspin than against topspin. The contribution of wrist dorsiflexion to the upward velocity was significantly greater against backspin than against topspin. The magnitudes of the angular velocities of elbow extension and wrist dorsiflexion at impact were both similar between the two types of backhands. Our results suggest that the differences in contributions of elbow extension and wrist dorsiflexion to the upward velocity were associated with the difference in upper limb configuration rather than in magnitudes of their angular velocities.     

A three-dimensional analysis of the contributions of upper limb joint movements to horizontal racket head velocity at ball impact during tennis serving

In this study, we examined the relationship between upper limb joint movements and horizontal racket head velocity to clarify joint movements for developing racket head speed during tennis serving. Sixty-six male tennis players were videotaped at 200 Hz using two high-speed video cameras while hitting high-speed serves. The contributions of each joint rotation to horizontal racket velocity were calculated using vector cross-products between the angular velocity vectors of each joint movement and relative position vectors from each joint to the racket head. Major contributors to horizontal racket head velocity at ball impact were shoulder internal rotation (41.1%) and wrist palmar flexion (31.7%). The contribution of internal rotation showed a significant positive correlation with horizontal racket head velocity at impact (r = 0.490, P < 0.001), while the contribution of palmar flexion showed a significant negative correlation (r = ? 0.431, P < 0.001). The joint movement producing the difference in horizontal racket head velocity between fast and slow servers was shoulder internal rotation, and angular velocity of shoulder internal rotation must be developed to produce a high racket speed.     

String vibration dampers do not reduce racket frame vibration transfer to the forearm

In this study, we examined the effect of string vibration damping devices on reducing racket frame vibration transfer to the forearm. Twenty participants volunteered to hold a tennis racket stationary in a forehand and backhand stroking position while tennis balls were fired at 20 m x s(-1) towards two impact locations, the node of vibration and the dead spot. A three-way analysis of variance with repeated measures on damping condition, impact location and stroke condition was performed on the data. The resonant frequency of the hand-held racket was found to be approximately 120 Hz. No significant differences in amplitude of vibration at the resonant frequency were found for the wrist or the elbow when damped and non-damped impacts were compared. Impacts at the dead spot produced greater amplitudes of vibration (P < 0.01) but no interaction between impact location and string dampers was evident. The string dampers had no effect on the grip force used or the muscle electrical activity in the forearm after impact. In conclusion, we found that string dampers do not reduce the amount of racket frame vibration received at the forearm. We suggest that string dampers remain a popular accessory among tennis players because of their acoustic effects and psychological support rather than any mechanical advantage.     

A three-dimensional analysis of the contributions of upper limb joint movements to horizontal racket head velocity at ball impact during tennis serving

In this study, we examined the relationship between upper limb joint movements and horizontal racket head velocity to clarify joint movements for developing racket head speed during tennis serving. Sixty-six male tennis players were videotaped at 200 Hz using two high-speed video cameras while hitting high-speed serves. The contributions of each joint rotation to horizontal racket velocity were calculated using vector cross-products between the angular velocity vectors of each joint movement and relative position vectors from each joint to the racket head. Major contributors to horizontal racket head velocity at ball impact were shoulder internal rotation (41.1%) and wrist palmar flexion (31.7%). The contribution of internal rotation showed a significant positive correlation with horizontal racket head velocity at impact (r = 0.490, P < 0.001), while the contribution of palmar flexion showed a significant negative correlation (r = - 0.431, P < 0.001). The joint movement producing the difference in horizontal racket head velocity between fast and slow servers was shoulder internal rotation, and angular velocity of shoulder internal rotation must be developed to produce a high racket speed.     

Kinematics used by world class tennis players to produce high-velocity serves

The purpose of this study was to quantify ranges and speeds of movement, from shoulder external rotation to ball impact, in the tennis service actions of world class players. Two electronically synchronised 200 Hz video cameras were used to record 20 tennis players during singles competition at the Sydney 2000 Olympic games. Three-dimensional motion of 20 landmarks on each player and racquet were manually digitized. Based upon the mean values for this group, the elbow flexed to 104 degrees and the upper arm rotated into 172 degrees of shoulder external rotation as the front knee extended. From this cocked position, there was a rapid sequence of segment rotations. The order of maximum angular velocities was trunk tilt (280 degrees/s), upper torso rotation (870 degrees/s), pelvis rotation (440 degrees/s), elbow extension (1510 degrees/s), wrist flexion (1950 degrees/s), and shoulder internal rotation. Shoulder internal rotation was greater for males (2420 degrees/s) than females (1370 degrees/s), which may be related to the faster ball velocity produced by the males (50.8 m/s) than the females (41.5 m/s). Although both genders produced segment rotations in the same order, maximum upper torso velocity occurred earlier for females (0.075 s before impact) than for males (0.058 s). At impact, the trunk was tilted 48 degrees above horizontal, the arm was abducted 101 degrees and the elbow, wrist, and lead knee were slightly flexed. Male and female players should be trained to develop the kinematics measured in this study in order to produce effective high-velocity serves.     

String vibration dampers do not reduce racket frame vibration transfer to the forearm

In this study, we examined the effect of string vibration damping devices on reducing racket frame vibration transfer to the forearm. Twenty participants volunteered to hold a tennis racket stationary in a forehand and backhand stroking position while tennis balls were fired at 20 m?·?s^?1 towards two impact locations, the node of vibration and the dead spot. A three-way analysis of variance with repeated measures on damping condition, impact location and stroke condition was performed on the data. The resonant frequency of the hand-held racket was found to be ～120 Hz. No significant differences in amplitude of vibration at the resonant frequency were found for the wrist or the elbow when damped and non-damped impacts were compared. Impacts at the dead spot produced greater amplitudes of vibration (P <?0.01) but no interaction between impact location and string dampers was evident. The string dampers had no effect on the grip force used or the muscle electrical activity in the forearm after impact. In conclusion, we found that string dampers do not reduce the amount of racket frame vibration received at the forearm. We suggest that string dampers remain a popular accessory among tennis players because of their acoustic effects and psychological support rather than any mechanical advantage.     

Tennis forehand kinematics change as post-impact ball speed is altered

Peak joint angles and joint angular velocities were evaluated for varying speed forehands in an attempt to better understand what kinematic variables are most closely related to increases in post-impact ball velocity above 50% of maximal effort. High-speed video was used to measure three-dimensional motion for 12 highly skilled tennis players who performed forehands at three different post-impact ball speeds: fast (42.7 +/- 3.8 m/s), medium (32.1 +/- 2.9 m/s), and slow (21.4 +/- 2.0 m/s). Several dominant-side peak joint angles (prior to ball impact) increased as post-impact ball speed increased from slow to fast: wrist extension (16%), trunk rotation (28%), hip flexion (38%), knee flexion (27%), and dorsiflexion (5%). Between the aforementioned peak joint angles and ball impact, dominant-side peak angular velocities increased as ball speed increased from slow to fast: peak wrist flexion (118%), elbow flexion (176%), trunk rotation (99%), hip extension (143%), knee extension (56%), and plantarflexion (87%). Most kinematic variables changed as forehand ball speed changed; however, some variables changed more than others, indicating that range of motion and angular velocity for some joints may be more closely related to post-impact ball speed than for other joints.     

Tennis racket stiffness,string tension and impact velocity effects on post-impact ball angular velocity

There has been significant technological advancement in the game of tennis over the past two decades. In particular, tennis rackets have changed in size, shape and material composition. The effects of these changes on ball rebound speed have been well documented, but few studies have considered the effects on ball angular velocity. The purpose of this study was to investigate the effects of three factors on post-impact ball spin. Tennis balls were projected at three velocities toward a clamped racket simulating three levels of stiffness and strung at three string tensions. The angular velocity of each tennis ball was measured from stroboscopic images during an oblique impact with the racket. A three-way factorial ANOVA revealed significant (P < 0.01) differences in the post-impact angular velocity for string tension, racket stiffness and impact velocity, as well as two-way interactions between string tension and impact velocity, and between racket stiffness and impact velocity. The possibility of tangential elastic strain energy being stored in the racket and ball was evident in low impact velocity trials. These displayed a post-impact angular velocity where the circumference of the ball was translating faster than the relative velocity between the ball’s centre of mass and the string surface. It was concluded that increasing the relative impact velocity between the racket and ball was the best means of increasing the post-impact angular velocity of the tennis ball.     

Subject-specific computer simulation model for determining elbow loading in one-handed tennis backhand groundstrokes

A subject-specific angle-driven computer model of a tennis player, combined with a forward dynamics, equipment-specific computer model of tennis ball-racket impacts, was developed to determine the effect of ball-racket impacts on loading at the elbow for one-handed backhand groundstrokes. Matching subject-specific computer simulations of a typical topspin/slice one-handed backhand groundstroke performed by an elite tennis player were done with root mean square differences between performance and matching simulations of < 0.5 degrees over a 50 ms period starting from ball impact. Simulation results suggest that for similar ball-racket impact conditions, the difference in elbow loading for a topspin and slice one-handed backhand groundstroke is relatively small. In this study, the relatively small differences in elbow loading may be due to comparable angle-time histories at the wrist and elbow joints with the major kinematic differences occurring at the shoulder. Using a subject-specific angle-driven computer model combined with a forward dynamics, equipment-specific computer model of tennis ball-racket impacts allows peak internal loading, net impulse, and shock due to ball-racket impact to be calculated which would not otherwise be possible without impractical invasive techniques. This study provides a basis for further investigation of the factors that may increase elbow loading during tennis strokes.     

The influence of elbow joint kinematics on wrist speed in cricket fast bowling

This modelling study sought to describe the relationships between elbow joint kinematics and wrist joint linear velocity in cricket fast bowlers, and to assess the sensitivity of wrist velocity to systematic manipulations of empirical joint kinematic profiles. A 12-camera Vicon motion analysis system operating at 250 Hz recorded the bowling actions of 12 high performance fast bowlers. Empirical elbow joint kinematic data were entered into a cricket bowling specific “Forward Kinematic Model” and then subsequently underwent fixed angle, angular offset and angle amplification manipulations. A combination of 20° flexion and 20° abduction at the elbow was shown to maximise wrist velocity within the experimental limits. An increased elbow flexion offset manipulation elicited an increase in wrist velocity. Amplification of elbow joint flexion–extension angular displacement indicated that, contrary to previous research, elbow extension range of motion and angular velocity at the time of ball release were negatively related to wrist velocity. Some relationships between manipulated joint angular waveforms and wrist velocity were non-linear, supporting the use of a model that accounts for the non-linear relationships between execution and outcome variables in assessing the relationships between elbow joint kinematics and wrist joint velocity in cricket fast bowlers.     

Assessment of model-based image-matching for future reconstruction of unhelmeted sport head impact kinematics

Player-to-player contact inherent in many unhelmeted sports means that head impacts are a frequent occurrence. Model-Based Image-Matching (MBIM) provides a technique for the assessment of three-dimensional linear and rotational motion patterns from multiple camera views of a head impact event, but the accuracy is unknown for this application. The goal of this study is to assess the accuracy of the MBIM method relative to reflective marker-based motion analysis data for estimating six degree of freedom head displacements and velocities in a staged pedestrian impact scenario at 40 km/h. Results showed RMS error was under 20 mm for all linear head displacements and 0.01–0.04 rad for head rotations. For velocities, the MBIM method yielded RMS errors between 0.42 and 1.29 m/s for head linear velocities and 3.53–5.38 rad/s for angular velocities. This method is thus beneficial as a tool to directly measure six degree of freedom head positional data from video of sporting head impacts, but velocity data is less reliable. MBIM data, combined in future with velocity/acceleration data from wearable sensors could be used to provide input conditions and evaluate the outputs of multibody and finite element head models for brain injury assessment of sporting head impacts.     

Machine-learning-based head impact subtyping based on the spectral densities of the measurable head kinematics

BackgroundTraumatic brain injury can be caused by head impacts, but many brain injury risk estimation models are not equally accurate across the variety of impacts that patients may undergo, and the characteristics of different types of impacts are not well studied. We investigated the spectral characteristics of different head impact types with kinematics classification.MethodsData were analyzed from 3262 head impacts from lab reconstruction, American football, mixed martial arts, and publicly available car crash data. A random forest classifier with spectral densities of linear acceleration and angular velocity was built to classify head impact types (e.g., football, car crash, mixed martial arts). To test the classifier robustness, another 271 lab-reconstructed impacts were obtained from 5 other instrumented mouthguards. Finally, with the classifier, type-specific, nearest-neighbor regression models were built for brain strain.ResultsThe classifier reached a median accuracy of 96% over 1000 random partitions of training and test sets. The most important features in the classification included both low- and high-frequency features, both linear acceleration features and angular velocity features. Different head impact types had different distributions of spectral densities in low- and high-frequency ranges (e.g., the spectral densities of mixed martial arts impacts were higher in the high-frequency range than in the low-frequency range). The type-specific regression showed a generally higher R² value than baseline models without classification.ConclusionThe machine-learning-based classifier enables a better understanding of the impact kinematics spectral density in different sports, and it can be applied to evaluate the quality of impact-simulation systems and on-field data augmentation.     

Criterion validity of an isokinetic dynamometer to assess shoulder function in tennis players

Isokinetic dynamometry is used in the assessment and rehabilitation of shoulder function in tennis players. The aim of this study was to validate a newly installed Biodex III Isokinetic Dynamometer for internal and external shoulder rotation. A non-injured male performed this movement which replicates an integral section of the tennis service action (Cohen et al., 1994). Three maximal trials were performed at six randomly assigned angular velocities (0.52, 1.05, 1.57, 2.09, 2.62 and 3.14 rad x s(-1)) with 90 s rest between each set. Trials were recorded using an on-line motion analysis system and kinematic data were obtained. Kinematic angular displacement of the lever arm was slightly greater (> or = 0.01 rad x s(-1)) than for the isokinetic dynamometer at all test angular velocities. Mean angular velocities from the kinematic data were almost identical to those from the isokinetic dynamometer but less than the target values, and this difference (e.g. 2.55 rad x s(-1) at 3.14 rad x s(-1)) was greater at higher angular velocities owing to the greater acceleration phases required. Peak angular velocity was similar on the isokinetic dynamometer to the target values, but substantially less than those from the kinematic data (e.g. 0.68 rad x s(-1) at 0.52 rad x s(-1)). This suggests that the isokinetic data are over-smoothed and may mask important information. In summary, criterion validity of this isokinetic dynamometer is supported for displacement and mean angular velocity, but not for peak angular velocity. Shoulder rotations in tennis are often at angular velocities greater than the Biodex can reproduce, but for the purpose of monitoring the shoulder strength and range of motion of tennis players and providing safe functional rehabilitation, the use of slower angular velocities is acceptable.     

优秀青年男子运动员不同距离原地投篮命中率的出手参数影响因素分析

定距离原地投篮的弧线轨迹主要取决于出手速度和出手角度。为了探究优秀青年男子运动员不同距离原地投篮命中率的各影响因素,采用平面定机高速摄影和运动技术解析法,采集12名U16中国国家男子篮球运动员罚篮、中投和三分投球中篮过程投篮手臂的腕、肘、肩、膝等相关关节的线速度和角速度等参数,运用关联度和回归分析(Matlab2018a)探究规律。发现8项因素对原地投篮对命中率有不同程度的影响,其中,球初始高度、球离手高度、腕关节速度和膝关节速度4项因素,通过投篮角度和投篮速度对不同距离投篮中命中率的影响最大。     

羽毛球与网球高球下压技术差异性的运动学分析

为了指明羽毛球和网球高压球技术动作的差异性,为羽毛球和网球教学和训练提供定量的科学依据,使用三维立体摄影解析法获取羽毛球和网球高压球技术动作的运动学参数,并对数据进行统计学处理。研究结果表明:在蹬地击球过程中,大腿、小腿和足的运动顺序为大关节带动小关节;在整个击打过程中,肩、肘、腕三关节移动速度基本保持同步,肩关节角速度峰值最先出现,肘关节和腕关节角速度峰值出现时间基本同步;网球采用"棍打"的击球用力方式为主击球,羽毛球采用"鞭打"的击球用力方式为主击球。     

The penalty throw in water polo: a cinematographic analysis

Three-dimensional (3-D) high-speed cinematography was used to record the penalty throw in water polo by six elite male (M) and six elite female (F) players. The direct linear transformation technique (DLT) was used in the 3-D space reconstruction from 2-D images recorded via laterally placed phase-locked cameras operating at 200 Hz. Five of the twelve subjects lifted the ball from underneath at the start of the throw whilst the remaining subjects opted for a rotation lift. As the ball was brought behind the head the females used very little hip and shoulder rotation compared to the male players so that four of the six female subjects were square on to the target at the rear point. At the completion of the backswing the wrist was flexed to a similar angle (M-162 degrees; F-158 degrees); the elbow angle showed significantly greater flexion for females (85 degrees) than males (107 degrees). During the forward swing, from rear point to release, the wrist joint of the female players flexed from a rear point angle of 158 degrees to 148 degrees at release. The wrist movement for male subjects was different from the females in that it flexed from 162 degrees to 147 degrees, 0.10 s prior to release and then extended to 159 degrees at palmar release before again flexing to 156 degrees at release. The amount of elbow extension during the forward swing was 48 degrees for both groups; however, the females actually released the ball with the forearm vertical (89 degrees) compared to the male forearm angle of 78 degrees. Maximum angular velocity of the wrist and elbow occurred at release for 9 of the 12 subjects. Both the wrist and elbow joints (F-148 degrees; M-156 degrees at wrist and F-126 degrees; M-148 degrees at elbow) demonstrated greater flexion at release in female subjects, compared with males. Maximum linear endpoint velocities for the forearm and hand segments occurred at ball release resulting in mean ball velocities of 19.1 m s-1 and 14.7 m s-1 for male and female subjects respectively.     

Contributions of joint rotations to racquet speed in the tennis serve

The purpose of this study was to measure the contributions of the motions of body segments and joints to racquet head speed during the tennis serve. Nine experienced male players were studied using three-dimensional film analysis. Upper arm twist orientations were calculated with two alternative methods using joint centres and skin-attached markers. The results showed that skin-attached markers could not be used to calculate accurate upper arm twist orientations due to skin movement, and that the use of joint centres produced errors of more than 20 degrees in the upper arm twist orientation when the computed elbow flexion/extension angle exceeded 135 degrees in the final 0.03 s before impact. When there were large errors in the upper arm twist orientation, it was impossible to obtain accurate data for shoulder or elbow joint rotations about any axis. Considering only the contributors that could be measured within our standards of acceptable error, the approximate sequential order of main contributors to racquet speed between maximum knee flexion and impact was: shoulder external rotation, wrist extension, twist rotation of the lower trunk, twist rotation of the upper trunk relative to the lower trunk, shoulder abduction, elbow extension, ulnar deviation rotation, a second twist rotation of the upper trunk relative to the lower trunk, and wrist flexion. The elbow extension and wrist flexion contributions were especially large. Forearm pronation made a brief negative contribution. Computed contributions of shoulder internal rotation, elbow extension and forearm pronation within the final 0.03 s before impact were questionable due to the large degree of elbow extension. Near impact, the combined contribution of shoulder flexion/extension and abduction/adduction rotations to racquet speed was negligible.