Golf is the sports that have been enjoyed by the people of a wide age group. The many golfers aim to get the high score and hope to getting the longer distance and raising the ball speed by the golf club (Driver). The improvement of the golf club head has been accomplished. In 2008, the upper limit of the coefficient of restitution of the golf club head was regulated. Therefore, the study of the golf club shaft comes to attract more attention. Therefore, in the previous study, the golf swing simulation has already been proposed by the authors. In this simulation, considering the motion and torsion of the grip of the golfer, the golf swing was simulated. Also, this swing simulation consists of the finite element approach using the grip motion obtained by the swing image. In this study, the accuracy of the proposed swing simulation is discussed.

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Golf is the sports that have been enjoyed by the people of a wide age group. The many golfers aim to get the high score and hope to getting the longer distance and to raising the ball speed with the golf club (Driver). And the improvement of the golf club head has been accomplished. In 2008, the upper limit of the coefficient of restitution of the golf club head was regulated. Therefore, the study of the golf club shaft comes to attract more attention. The authors already proposed the swing simulation referring the swing image of the golf swing robot. In the proposed swing simulation, the finite element model of golf club which consists of the golf club head and the laminated composite shaft is used. In this study, using the proposed swing simulation, the effect of the swing speed to the behavior of the swinging golf club shaft is clarified.

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The effect of the shaft length on the head speed in golf swing is investigated in order to obtain a longer distance of driving shot. Seven driving clubs, which have almost the same specifications except the shaft length, were manufactured for the experiments. Using these clubs, the head speed at the impact was measured during the swing by fifteen experienced golfers of both sexes in comparison with that by a golf robot. Results showed that the increase in the length of the club shaft created an increase in the head speed at the impact on all the subjects. The rate of the speed increase on the professional golfer was almost the same as that of the robot, and those on the male golfers were larger than the robot. On the other hand, it was smaller on the female golfers. By the consideration on the relation between the head speed and the ball speed at the impact, the total effect on the increase of driving distance is expected by the increase in the head speed using a longer shaft in spite of the reduction of the head weight.

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This paper considers the following important problems to be clarified or solved for making evaluation, selection and design of golf shafts systematically on the basis of their static characteristics.
1) Expression of the deflection characteristics
2) Method for measuring the above expressing parameters and the flexural rigidity (EI-value)
3) Development of the apparatus for measuring the parameters and EI-value
As to the item 1), two parameters, curvature 1/ρ(x) and newly introduced parameter λ are proposed; the curvature expressing the figure of deflection of a shaft in microscopic measurement and the parameter in macroscopic measurement. Also it is shown λ is geometrically related to 1/ρ(x). As to the item 2), a calculation algorithm of the parameters and EI-value using an approximate polynomial fitted to the measured deflection data is discussed. As to the item 3), the basic construction and functions of the trially-constructed apparatus for measuring the deflection characteristics and EI-value and the experimental results are reported.

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Glass fiber reinforced plastics (GFRP) have been used in a wide range of industrial fields due to the high strength and failure strain of glass fibers; their mechanical properties and price are well balanced as well. To investigate the effect of the glass fiber tex (i.e., mass measured in grams per 1000 m of bundle) on the torsional properties of GFRP shafts, five kinds of glass fiber rovings (280, 800, 1150, 2220, and 2300 tex) were used as reinforcement, and GFRP shafts were fabricated by the filament winding method. As a result, it was determined that high strength GFRP shafts with excellent surface properties could be fabricated using glass fiber rovings with lower tex values. Furthermore, the shear strengths of GFRP shafts using 280, 800, and 1150 tex glass fiber rovings were higher than that of the GFRP shaft using HME-glass fiber (high strength glass fiber) roving for filament winding.

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A measuring apparatus of the torsional rigidity distribution of a shaft has been trially constructed which is applicable to the measurement for golf shafts. The structure, measuring principle and accuracy evaluation are reported.

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Application of CFRP tubes for torque transmission shafts is expected to improve driving performance and natural frequency as well as fuel efficiency. CFRP tubes manufactured by modified simultaneous multi ply winding method have less voids and fiber waviness compared with conventional CFRP tubes manufactured by filament winding method, and the modified CFRP tubes showed 20% improvement of the static torsional strength. We investigated the fracture mechanisms of CFRP tubes by modified simultaneous multi ply winding method. As a result, a delamination from the prepreg end occurred at the innermost layer and it progressed through ±45° interlayer just before the failure of the specimen. In order to apply CFRP tubes to torque transmission shafts, it is expected to design the stacking sequence appropriately for preventing the delamination from the prepreg end in terms of long-time reliability. Thus in this study, we investigated an influence of the stacking sequence of CFRP tubes on their torsional strength. According to static torsional tests, it was revealed that the specimen with less lamination angle differences caused less delamination due to relaxation of interlaminar shear stress. Moreover, torsional strength was improved moderately mainly because the small lamination angle differences delayed the initiation of the delamination.

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An FEM eigenvalue analysis program for such sheet winding products as CFRP golf club shafts is developed. A new cylindrical beam element is formulated considering the coupling effect between tension and torsion for anisotropic materials. In order to verify the coupling effect of the presented method, composite cylindrical cantilevers are analyzed. And the non dimensional torsion by the axial tension of the beam element model is compared with a shell element model. And the influence of coupling effect on the natural frequencies of CFRP golf club shafts is evaluated for various fiber angles by eigenvalue analyses.

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Composite materials have been employed in many sporting gears. Especially, laminated composite materials are used for the golf club shafts. The purpose of study is to present the two-dimensional swing simulation of the golf club refereeing the swing image of the golf swing robot to clarify the deflection of the swinging golf club shafts. Firstly, a finite element model of golf club which consists of the simplified golf club head and the laminated composite shaft is presented. And, it is proposed that the two-dimensional swing simulation of the golf clubs using the relationship between the time and the angular velocity of the grip of golf club estimated from the swing image of the golf swing robot. Next, from the results obtained by the proposed swing simulation, the validity of the grip position of the golf club is clarified. Finally, the effects of the stacking sequence of the golf club shaft and the swing speed to the deflection of the shaft during the swing are examined, respectively.

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A service choosing the best equipment for each player that is called 'Fitting' has received a lot of attention in golf market. However, Fitting is only conducted by experts called 'Fitters' who have special knowledge and experience. The one reason is that golf swing moitons are too complicated to systemize. Our objective is to reveal the complex swing motions and to establish a fitting system of golf shaft that can be used everybody who has not special knowledge. Firstly, we evaluated the validity of the calculated swing data using Design of Experiment and Response Surface Method to achieve our goal. It was found that the swing data were correct for 80% golfers their handicap is less than 40. Additionally, we developed a fitting system to choose the best golf shaft for each player and evaluated its accuracy. Using the shaft that the system recommended, 89 golfers of 103 improved their distance or direction or both.

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Ease-of-Swing of golf club deeply related to the speed of golf club head at impact. It is said at the golf industry, golf club weight and golf club balance are considered as the influential parameters for the speed of golf club head at impact. Also, moment of inertia of golf club around grip end is sometimes considered as the same. However, those considerations are not well grounded. In this study, the golfer's arm and club were modelled with the double pendulum model. And, the effects of club parameters for the speed of golf club head at impact were investigated with the theoretical modal analysis, numerical simulation, and experiment. It was found, as a result, that the moment of inertia around shoulder when the arm and golf club are on a straight line have more influential to the speed of golf club head than golf club weight, golf club balance, and moment of inertia of golf club around grip end.

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圧力の異なる二種の気体の圧力差を測定したり, 利用する機器では, 両気体の接触点にはゴムの薄膜を置き, シリンダー内のピストンを作動させ, その動きによって圧力差などをとり出すことが多い. この薄膜はベローズとダイヤフラムの中間的な機能を持ち, 絶えず変形している. この薄膜の挙動を解析するに当たり, 引張り, 圧縮, 曲げなどの変形に際して, 体積は変わらないと考えて, 伸縮を表す量を計算し, これを伸縮関数と名付けた. 最近よく使われている薄膜を例に採り, 作動中の各部の伸縮関数を採ってみると興味ある結果が得られた. 薄膜の挙動と耐久性を知るための基本的な取り扱い方として, 若干の線図とともに報告する.

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A model that calculates the deflections of a golf shaft during the swing was developed. Applying static deflection to a shaft which is flexible and has varying bending stiffness, a differential equation for moment and curvature which characterize its behavior over the duration of the swing were generated. Incorporated into concentrated moment are moment of forces acting at the tip and grip end of the shaft. These loads were calculated using a inverse dynamics analysis of the motion of the golf club during the swing. A motion capture system was utilized to collect the necessary data. Solutions to the equations for the shaft deflection were calculated numerically. The results are presented as deflections along the shaft at each time. Bending deflections are determined in two-dimensional direction.

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'Optimal Design' and ‘Fitting’ have received a lot of attention in golf market. 'Optimal Design' is defined as tailor made design and ‘Fitting’ is defined as a service choosing the best equipment for each player. Both of them have a same problem that they are only conducted by experts called 'Fitters' who have special knowledge and experience. The one reason is golf swings are very complex motions because of motion adjustment depending on the difference of gears. Thus, fitters are required for fitting but there are not enough numbers of advanced skilled fitters. Our objective is to develop a method of optimal design considering to swing motion adjustment and to establish a fitting system of golf shaft that can be used everybody who has not special knowledge. Firstly, we evaluated the validity of the calculated swing data using Design of Experiment and Response Surface Method to achieve our goal. The accuracy rates were over 80% with 9 skilled subjects whose handy caps were less than 40 including 3 professional golfers. On the other hand, the rates of 3 beginners were under 50%. Therefore, we limited the targets of this method to skilled golfers. Additionally, we developed a fitting system to choose the best golf shaft for each player and evaluated the accuracy. As a result, 89 players in 103 ones improved their distance, direction or both, using the optimal shaft recommend by our system.

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Application of carbon fiber reinforced plastics (CFRP) pipes to torque transmission shafts makes it possible to improve automotive driving performance as well as fuel efficiency. A modified simultaneous multi ply winding method was developed as a new forming method for CFRP pipes using prepregs. The CFRP pipes formed by the method have fewer initial flaws, such as voids and fiber waviness. It resulted in 20 % increase in the static torsional strength than conventional CFRP pipes formed by a filament winding method. In this study, effects of stacking sequence on the torsional fatigue properties of the CFRP pipes formed by the modified method were investigated. Torsional fatigue tests were conducted under load control. All tests were conducted at the test frequency f=1 Hz, the maximum applied torque T_max=1.0 kNm and the stress ratio R=0.1. [90₂/-45/+45]₆ and [90/-45/90/+45]₆ pipes were formed to investigate effects of lamination angle difference between adjacent plies. Maximum lamination angle difference of the [90/-45/90/+45]₆ pipe is smaller than that of the [90₂/-45/+45]₆ pipe. When the CFRP pipes had smaller lamination angle difference, the initiation and growth of the delamination from the prepreg end in the innermost layer were delayed because interlaminar stress was reduced. Moreover, [(90/-45/90/+45)₆/90] pipes were formed to investigate effects of an application of a 90° layer on the innermost layer. As the result, the delamination hardly initiated since the shear stress on the prereg end was reduced. Consequently, the fatigue life of the [(90/-45/90/+45)₆/90] pipes increased seven-fold than that of the [90₂/-45/+45]₆ pipes due to improvement of delamination resistance under cyclic torsional loading.

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Taylor-made designs are required for golf clubs, in particularly for golf shafts, because the golf equipment have great effects on the performances of players. Our objective is to establish an optimal design method of golf shafts for each player depending on their swing motions. We measured the swing motions with a 6-axis sensor that inserted into the grip end not to prevent normal motions. We analyzed the head motions at the impact using FEM with the swing data, and we tried to figure out the best shaft spec for an optimal impact. The optimization algorithm was followed 4 skilled shaft designers, which means that we had optimized the 4 SPECs in turn as below; 1) Weight, 2) Torque, 3) Flex, 4) EI pattern. As a result, the distance of a subject, a female professional golfer of JLPGA, was improved 11yrd more with the optimized shaft, and she uses the optimized shaft for more than 2 years. Thus our method was proven to be efficacious for some typical players. On the other hand, we were not able to get desired results for another 2 subjects. We believe the causes of undesired results are that some players change their swing motions depending on the shaft spec. We ought to consider the motion adjustment depending on the shaft spec in order to design optimal golf shafts for each player in the near future.

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