The importance of being elastic: Deflection of a badminton racket during a stroke

Abstract

The deflection profiles of a badminton racket during strokes performed by elite and world-class badminton players were recorded by strain gauges and subsequently analysed to determine the role of shaft stiffness in racket performance. Deflection behaviour was consistent in all strokes across all players, suggesting a controlled use of racket elasticity. In addition, all impacts occurred within 100 ms of each other, a duration in which deflection velocity provides an increase in racket velocity, indicating that the players were able to use racket elasticity to their advantage. Since deflection behaviour is a product of the racket–player interaction, further work is required to determine the effects of different racket properties and player techniques on the elastic response of rackets during strokes.     

Using dual Euler angles for the analysis of arm movement during the badminton smash

Camera techniques are typically used in the study of human movement. However, as the number of joints and markers involved in a study increases, data extraction and calculation become increasingly tedious and complicated. To overcome this challenge, we propose a method of study that simplifies data extraction and calculation by using an electrogoniometer and dual Euler angles. The contribution of the rotation of each arm segment to produce a racket head’s speed was identified in the context of a badminton smash. The contribution of each segment rotation was computed using dual velocity analysis. A set of orthogonal Cartesian frames was established for computing the anatomical rotational velocities for each of the three segments of the upper arm. Electrogoniometers were attached to the subjects during the execution of the smash to obtain measurements of joint angles throughout the motion. To test the algorithm, the calculated velocity of the racket head was compared to the measured velocity. The calculated velocity was derived from an algorithm, while the measured velocity was obtained from a video image. The results are similar, indicating that the dual velocity method is suitable for determining segmental velocities in such kinematic situations.     

Investigation of high-speed badminton racket kinematics by motion capture

The kinematics of a badminton racket during a smash stroke was observed in this study with the purpose of investigating stroke dynamics and racket behaviour. Motion capture measurements of the racket during several smash strokes performed by three players of different skill levels indicated a clear increase in racket velocity at impact with increasing skill level. Variations between translational and rotational contributions to the impact speed could also be seen between the players. The advanced player produced a much higher peak angular velocity and also relied much less on translation, with a translational velocity of only 8% of the total velocity versus the 20% for the recreational player. It is proposed that, as an alternative to shuttlecock speeds, racket head speed measurements can be used as an indicator of performance, and can also provide some insight into the interaction between the racket and player.     

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.     

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.     

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.     

Effect of the racket mass and the rate of strokes on kinematics and kinetics in the table tennis topspin backhand

The purpose of this study was to investigate the effect of the racket mass and the rate of strokes on the kinematics and kinetics of the trunk and the racket arm in the table tennis topspin backhand. Eight male Division I collegiate table tennis players hit topspin backhands against topspin balls projected at 75 balls · min^?1 and 35 balls · min^?1 using three rackets varying in mass of 153.5, 176 and 201.5 g. A motion capture system was used to obtain trunk and racket arm motion data. The joint torques of the racket arm were determined using inverse dynamics. The racket mass did not significantly affect all the trunk and racket arm kinematics and kinetics examined except for the wrist dorsiflexion torque, which was significantly larger for the large mass racket than for the small mass racket. The racket speed at impact was significantly lower for the high ball frequency than for the low ball frequency. This was probably because pelvis and upper trunk axial rotations tended to be more restricted for the high ball frequency. The result highlights one of the advantages of playing close to the table and making the rally speed fast.     

The effects of player grip on the dynamic behaviour of a tennis racket

The aim of this article is to characterise the extent to which the dynamic behaviour of a tennis racket is dependent on its mechanical characteristics and the modulation of the player’s grip force. This problem is addressed through steps involving both experiment and modelling. The first step was a free boundary condition modal analysis on five commercial rackets. Operational modal analyses were carried out under “slight”, “medium” and “strong” grip force conditions. Modal frequencies and damping factors were then obtained using a high-resolution method. Results indicated that the dynamic behaviour of a racket is not only determined by its mechanical characteristics, but is also highly dependent on the player’s grip force. Depending on the grip force intensity, the first two bending modes and the first torsional mode frequencies respectively decreased and increased while damping factors increased. The second step considered the design of a phenomenological hand-gripped racket model. This model is fruitful in that it easily predicts the potential variations in a racket’s dynamic behaviour according to the player’s grip force. These results provide a new perspective on the player/racket interaction optimisation by revealing how grip force can drive racket dynamic behaviour, and hence underlining the necessity of taking the player into account in the racket design process.     

Theoretical Modeling of Grip Firmness during Ball-Racket Impact

Abstract

This study was undertaken to establish theoretical bases for the experimental results reported by Baker and Putnam (1979), and Walanabe, Ikegami and Miyashita (1979), concerning grip firmness on a tennis racket and its effect on the ratio of post- to pre-impact ball velocity. The model predicted that, for central impacts, there was no change in the ball velocity ratio when a regular tennis racket was tightly clamped at the grip or allowed to freely stand on its butt. To validate the model further, alterations were made to two parameters of the racket—a tennis racket was modified to increase the stiffness, and a racketball racket was used to simulate a shortened tennis racket. Multiple exposure photographs were taken of balls striking the center of the rackets under the two extremes of grip firmness. Measurements were taken from enlargements of these photographs in order to calculate the horizontal component of post- to pre-impact ball velocity. It was found that shortening the length and greatly increasing the stiffness was required before the effect of grip firmness was noticeable.     

Comparison of a finite element model of a tennis racket to experimental data

Modern tennis rackets are manufactured from composite materials with high stiffness-to-weight ratios. In this paper, a finite element (FE) model was constructed to simulate an impact of a tennis ball on a freely suspended racket. The FE model was in good agreement with experimental data collected in a laboratory. The model showed racket stiffness to have no influence on the rebound characteristics of the ball, when simulating oblique spinning impacts at the geometric stringbed centre. The rebound velocity and topspin of the ball increased with the resultant impact velocity. It is likely that the maximum speed at which a player can swing a racket will increase as the moment of inertia (swingweight) decreases. Therefore, a player has the capacity to hit the ball faster, and with more topspin, when using a racket with a low swingweight.     

乒乓球拍微结构对乒乓球与球拍碰撞过程的研究

利用商用有限元软件MSC．MARC,通过对乒乓球与球拍碰撞过程的数值模拟,着重研究由传统木材和碳纤维复合材料板叠合而成的乒乓球拍的微结构对碰撞后乒乓球运动规律的影响,为优化设计新型球拍提供理论依据。     

Dynamic strain profile of the ice hockey stick: comparisons of player calibre and stick shaft stiffness

The goal of this research was to develop a method to quantify the dynamic strain profile (DSP) of an ice hockey stick shaft and assess the potential influence of player skill and stick shaft stiffness on DSP during slap (SS) and wrist shots (WS). Seventeen adult males performed shots with two different stick stiffness’ on synthetic ice. Subjects were subdivided as high (HC) and low calibre (LC). Dependent measures included strain measures from five strain gauge pairs along the shaft length recorded at 10 kHz. In general, this approach was sufficiently sensitive to clearly distinguish between shot types (strains SS > WS), player calibre (strains HC > LC) and stick models (strain flex77 > flex102) as well as to identify within stick deflection differences along the shaft. This strain based analysis has a time and spatial resolution undetected by common motion capture based systems.     

Effect of tennis racket parameters on a simulated groundstroke

Composite materials have given manufacturers the freedom to develop a broad range of tennis rackets, allowing them to change key parameters such as the structural stiffness, mass, and position of the balance point. The aim of this research was to determine how changing these parameters could affect ball resultant rebound velocity and spin for a simulated groundstroke. A finite element model of a freely suspended racket and strings was used to determine the effect of racket parameters for oblique spinning impacts at a range of locations on the stringbed. The finite element simulations were conducted in the laboratory frame of reference, where the ball is projected onto an initially stationary racket. The mean rebound velocity of the ball was 9% higher for a structurally stiff racket, 37% higher for a heavy racket, and 32% higher for a head-heavy racket. In addition, the mean rebound topspin of the ball was 23% higher for a heavy racket and 21% higher for a head-heavy racket. Therefore, in relation to a groundstroke with an impact location away from the node, the rebound velocity of the ball is likely to increase with the structural stiffness of a racket. The effect of changing the mass and position of the balance point is more complex, as it is dependent on the relationship between the transverse moment of inertia and maximum pre-impact swing velocity.     

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.     

A computer simulation model of tennis racket/ball impacts

A forward dynamics computer simulation for replicating tennis racket/ball impacts is described consisting of two rigid segments coupled with two degrees of rotational freedom for the racket frame, nine equally spaced point masses connected by 24 visco-elastic springs for the string-bed and a point mass visco-elastic ball model. The first and second modal responses both in and perpendicular to the racket string-bed plane have been reproduced for two contrasting racket frames, each strung at a high and a low tension. Ball/string-bed normal impact simulations of real impacts at nine locations on each string-bed and six different initial ball velocities resulted in <3% RMS error in rebound velocity (over the 16–27 m/s range observed). The RMS difference between simulated and measured oblique impact rebound angles across nine impact locations was 1°. Thus, careful measurement of ball and racket characteristics to configure the model parameters enables researchers to accurately introduce ball impact at different locations and subsequent modal response of the tennis racket to rigid body simulations of tennis strokes without punitive computational cost.     

The X-Factor: An evaluation of common methods used to analyse major inter-segment kinematics during the golf swing

Abstract

A common biomechanical feature of a golf swing, described in various ways in the literature, is the interaction between the thorax and pelvis, often termed the X-Factor. There is no consistent method used within golf biomechanics literature however to calculate these segment interactions. The purpose of this study was to examine X-factor data calculated using three reported methods in order to determine the similarity or otherwise of the data calculated using each method. A twelve-camera three-dimensional motion capture system was used to capture the driver swings of 19 participants and a subject specific three-dimensional biomechanical model was created with the position and orientation of each model estimated using a global optimisation algorithm. Comparison of the X-Factor methods showed significant differences for events during the swing (P < 0.05). Data for each kinematic measure were derived as a times series for all three methods and regression analysis of these data showed that whilst one method could be successfully mapped to another, the mappings between methods are subject dependent (P <0.05). Findings suggest that a consistent methodology considering the X-Factor from a joint angle approach is most insightful in describing a golf swing.     

太极柔力球拍头向下绕翻技术的运动学分析

太极柔力球柔力球作为一项结合了太极拳和球类运动特点的全民健身体育项目,在全民健身计划的推动下,正朝着竞技化、规范化的趋势发展,并在不断摸索、创新科学的训练手段和方法。文章为迎合项目的这一发展趋势,借鉴运动生物力学等其他学科的先进成果和方法,在本项目中创新的使用了红外线录像分析,对太极柔力球核心难度之一的拍头向下绕翻技术进行运动学分析,以期建立规范的动作技术模型,使动作最佳化、合理化,进一步促进项目的规范性发展。研究结果显示：太极柔力球拍头向下绕翻技术离心阶段运动较向心阶段运动时间长,球拍运动速度较快,角速度变化幅度大,呈现出先加速后减速的趋势,翻拍动作在向心阶段完成;肩关节活动幅度小,肘关节角速度在向心运动绕翻动作时有明显的加大,腕关节变化幅度小;在动作的向心阶段,手指与腕部配合完成预捏拍动作,为下一周动作做积极准备。     

The Influence of Tennis Racket Flexibility and String Tension on Rebound Velocity Following a Dynamic Impact

Abstract

The effects of string tension and longitudinal racket flexibility on post-impact ball velocity were investigated in tennis. Six wooden rackets, two with flexible shafts, two with medium and two with stiff shafts were strung with synthetic gut at tensions of 245N (55 lb), 289N (65 lb) and 334N (75 lb).

A pneumatically driven racket-arm was triggered by a stimulus from a photo-electric cell positioned at the exit nozzle of a ball machine so that impact occurred with the racket perpendicular to the path of the ball. New tennis balls were fired to impact each racket at the geometric center of the strings and 5 cm above the geometric center. The average horizontal velocity of the ball, both before and after impact, was determined using stroboscope photography.

A significant interaction between racket stiffness and string tension was recorded for an inward ball velocity of 22.7 m/s and a racket velocity of approximately 6.8 m/s. String tension had no significant influence on rebound velocity for a stiff racket following impact with a moving racket. Medium and flexible rackets produced the highest coefficients of restitution when strung at 245N (55 lb) compared to 289N (65 lb) and 334N (75 lb).     

Hip joint kinetics in the table tennis topspin forehand: relationship to racket velocity

The purpose of this study was to determine hip joint kinetics during a table tennis topspin forehand, and to investigate the relationship between the relevant kinematic and kinetic variables and the racket horizontal and vertical velocities at ball impact. Eighteen male advanced table tennis players hit cross-court topspin forehands against backspin balls. The hip joint torque and force components around the pelvis coordinate system were determined using inverse dynamics. Furthermore, the work done on the pelvis by these components was also determined. The peak pelvis axial rotation velocity and the work done by the playing side hip pelvis axial rotation torque were positively related to the racket horizontal velocity at impact. The sum of the work done on the pelvis by the backward tilt torques and the upward joint forces was positively related to the racket vertical velocity at impact. The results suggest that the playing side hip pelvis axial rotation torque exertion is important for acquiring a high racket horizontal velocity at impact. The pelvis backward tilt torques and upward joint forces at both hip joints collectively contribute to the generation of the racket vertical velocity, and the mechanism for acquiring the vertical velocity may vary among players.     

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.