Validated dynamic analysis of real sports equipment using finite element; a case study using tennis rackets

Allen, Thomas B.; Hart, John; Spurr, James; Haake, Steve; Goodwill, Simon

doi:10.1016/j.proeng.2010.04.144

Cited by 13 publications

(7 citation statements)

References 14 publications

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“…For this purpose, we chose to represent the player's effect as a cylindrically shaped massspring system connected to the end of the racket, where the springs reveal both hand and forearm stiffnesses. Obviously, our goal was not to accurately model the racket, since more suitable numerical models have already been proposed (Allen, Hart, Spurr, Haake, & Goodwill, 2010;Kawazoe & Yoshinari, 2010), but to design an easily understandable and usable tool for estimating how the modal frequencies of a racket will be affected when held by a player under different grip force conditions. Constraining a racket to a simple three degrees of freedom system, the beam equivalent parameters estimated for each racket are of the expected order of magnitude but not accurately estimated (e.g., about 30% error for I r ).…”

Section: Discussionmentioning

confidence: 99%

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

Chadefaux

Rao

Carrou

et al. 2016

Journal of Sports Sciences

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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.

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Section: Discussionmentioning

confidence: 99%

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

Chadefaux

Rao

Carrou

et al. 2016

Journal of Sports Sciences

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“…Researchers could use the mean shapes in Fig 3 as a basis for initial inputs when modelling rackets from different eras, with the aligned silhouette outlines used to inform further investigations into less common designs. Such analyses could cover both the frequency and shape of vibration modes [ 20 ] and the impact with the ball [ 17 – 19 ], with a view to improving our understanding of the effect of racket shape on both performance and injury risk. As well as modelling, commercial sensors are now available for analysing tennis strokes [ 10 , 39 ].…”

Section: Discussionmentioning

confidence: 99%

“…Finite element models can faithfully capture the shape of an object [ 2 , 17 – 23 ], with the potential to systematically investigate possible associations between tennis racket design, performance, and injury risk. However, developing geometrically faithful finite element models of tennis rackets is time-consuming, so it is inefficient and impractical to apply this technique to many samples.…”

Section: Introductionmentioning

confidence: 99%

Morphometrics for sports mechanics: Showcasing tennis racket shape diversity

2022

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Tennis racket design has changed from its conception in 1874. While we know that modern tennis rackets are lighter and have larger heads than their wooden predecessors, it is unknown how their gross shape has changed specifically. It is also unknown how racket shape is related to factors that influence performance, like the Transverse and Polar moments of inertia. The aim of this study was to quantify how tennis racket shape has changed over time, with a view to furthering our understanding of how such developments have influenced the game. Two-dimensional morphometric analysis was applied to silhouettes extracted from photographs of 514 rackets dating from 1874 to 2017. A principal component analysis was conducted on silhouette outlines, to allow racket shape to be summarised. The rackets were grouped by age and material for further analysis. Principal Component 1 accounted for 87% of the variation in racket shape. A pairwise Pearson’s correlation test indicated that head width and length were both strongly correlated to Principal Component 1 (r = 0.916 & r = 0.801, p-values<0.001). Principal Component 1 was also correlated to the Polar (r = 0.862, p<0.001) and Transverse (r = -0.506, p<0.001) moments of inertia. Racket age and material had a medium (p<0.001, η2p = 0.074) and small (p = 0.015, η2p = 0.017) effect on Principal Component 1, respectively. Mean racket shapes were also generated from the morphometric analyses for the material and age groupings, and we consider how these shape changes may have influenced performance and injury risk. These mean shape groupings could support the development of models, such as finite element analysis, for predicting how historical developments in tennis equipment have affected performance and injury risk.

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“…Another highly applicable field for these materials is sports sciences. Other applications of the hyper-elastic material include their vast usage in sports' instruments like clothing [38][39][40], basketball, baseball and golf balls [41,42] and sports tracks [43] as well as injuries due to impact of the ball and other hyper-elastic materials to the human body in sports matches [44][45][46][47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

A framework for model base hyper-elastic material simulation

2020

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In this research, a framework for modelling and simulation of hyper-elastic materials is proposed. The framework explains how to employ strain energy functions as a constitutive model, standard loading test data, and a powerful optimisation method to determine a mathematical function for explaining the mechanical behaviour of a hyper-elastic material using minimum types of loading test data. In the first part, a survey on hyper-elastic constitutive models is presented. Fifty models are collected and classified into six categories. Thereafter, five types of standard loading tests including uniaxial, biaxial, equi-biaxial, pure shear, and simple shear are introduced. It is shown that depending on the loading type, physical parameters, Cauchy, and nominal stress tensors, each constitutive model possesses a particular function. The genetic algorithm as a powerful optimisation method is used to determine the most accurate function for each type of loading test data. It is presented that based on the selected constitutive model and regardless of a number of existing loading types test data, a unique function can be determined for expressing and simulating the mechanical behaviour of the considered hyper-elastic material.

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Validated dynamic analysis of real sports equipment using finite element; a case study using tennis rackets

Cited by 13 publications

References 14 publications

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

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

Morphometrics for sports mechanics: Showcasing tennis racket shape diversity

A framework for model base hyper-elastic material simulation

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