湯川 治敏

<p>Shock attenuation property of sports surfaces is especially important not only for the athlete's performance but also for injury prevention. To evaluate the properties of the sports surfaces, some sports governing bodies often adopt friction tests and shock attenuation tests to determine the horizontal and vertical characteristics, respectively. Although the diagonal impacts are often observed in athletic sports, shock attenuation test treats only the vertical impact test. Therefore, we developed a two-dimensional impact test device for examining the two-dimensional cushioning characteristics of sports surfaces in previous studies. To produce a simultaneous two-dimensional force against a test specimen, we incorporated a parallelogram linkage in the measuring system. The weight is dropped onto the upper side of the parallelogram linkage with various height and various initial angles. Initial angle controls the ratio of vertical/horizontal impact forces. In previous studies, FR (Force Reduction) values are calculated from experimental un-cushioned and cushioned forces for evaluating the shock attenuation properties. Additionally, to evaluate the maximum deformation during the impact, a biaxial accelerometer is attached to the sensor unit. Although FR values are simple and easy to calculate from the experimental data, it needs a vast cost because there are huge number of combinations of impact angles, magnitude of impacts and impact durations if the tests should be covered for various human activities. Therefore, in previous studies, we proposed the vertical viscoelastic model which can represent the behavior of sports surfaces during the impact for evaluating the shock attenuation properties. In this study, we propose the two-dimensional viscoelastic model of sport surfaces for evaluating the two-dimensional cushioning properties. Finally, proposed model can be used for estimating the impact forces from the experimental data.</p>

Shock attenuation property of sports surfaces is especially important not only for the athlete’s performance but also for injury prevention. To evaluate the properties of the sports surfaces, some sports governing bodies often adopt friction tests and shock attenuation tests to determine the horizontal and vertical characteristics, respectively. Although the diagonal impacts are often observed in athletic sports, shock attenuation test only treats the vertical impact test. Therefore we developed a two-dimensional impact test device for examining the two-dimensional cushioning characteristics of sports surfaces in this studies. To produce a simultaneous two-dimensional force against a test specimen, we incorporated a parallelogram linkage in the measuring system. The impact force generated was measured by the load cell. And an accelerometer was attached and the acceleration was also calculated. And experiments were performed to three kinds of different samples. In order to confirm the characteristics of the surface, the relationship between vertical and horizontal maximum force and displacement was confirmed. As the results, Hysteresis property in the vertical direction was found to depend on the hardness of the sports surfaces. However, it was found that the property in the horizontal direction is more complex than the vertical direction.

<p>Shock attenuation property of sports surfaces is especially important not only for the athlete's performance but also for injury prevention. To evaluate the properties of the sports surfaces, some sports governing bodies often adopt friction tests and shock attenuation tests to determine the horizontal and vertical characteristics, respectively. Although the diagonal impacts are often observed in athletic sports, shock attenuation test only treats the vertical impact test. Therefore we developed a two-dimensional impact test device for examining the two-dimensional cushioning characteristics of sports surfaces in previous studies. To produce a simultaneous two-dimensional force against a test specimen, we incorporated a parallelogram linkage in the measuring system. In previous study, it was examined for hysteresis for three types of hardness samples. In this study, we improved the two dimensional impact test device and experiments were performed to three kinds of different samples. To evaluate the hysteresis properties of sports surfaces, the energy loss of each impact was calculated. As the results, Hysteresis property in the vertical direction was found to depend on the hardness of the sports surfaces. However, it was found that the hysteresis property in the horizontal direction is more complex than the vertical direction.</p>

Shock attenuation property of sports surfaces is especially important not only for the athlete's performance but also for injury prevention. To evaluate the properties of the sports surfaces, some sports governing bodies often adopt friction tests and shock attenuation tests to determine the horizontal and vertical characteristics, respectively. Although the diagonal impacts are often observed in athletic sports, shock attenuation test only treats the vertical impact test. Therefore we developed a two-dimensional impact test device for examining the two-dimensional cushioning characteristics of sports surfaces in previous studies. To produce a simultaneous two-dimensional force against a test specimen, we incorporated a parallelogram linkage in the measuring system. In previous study, three different hardness of surfaces were examined for calculating the FR (Force Reduction) values not only the vertical component but also the horizontal component. As the results, Vertical FR values were increased with increasing the initial angle and impact intensity in all surfaces. And the different patterns of horizontal FR values were observed in these surfaces. In this study, we evaluated vertical and horizontal displacement by two-dimensional impact tests with high-speed video analysis. And we evaluated hysteresis properties of sports surfaces. As the results, horizontal properties of sports surfaces might depend on not only the material but also the structure of the specimen.

The purpose of this study is to investigate the shock attenuation properties of long pile synthetic turf by modeling and simulation method. Three types of specimens which have different hardness were used for comparing the shock attenuation properties. The hardness was controlled by the composite ratio of infill material, i.e. normal type specimen was formed by mixing the sand and the rubber chip for volume ratio at 1:1, 2:1 for hard and 1:2 for soft. And five types of test feet were used for incorporating the area parameter to the model. To identify the model parameters, multi-intensity multi-area impact tests were performed in various impact intensities and various impact areas. Because of the structure of long pile synthetic turf, the acquired data from the impact tests were unstable. Therefore, ten trials were performed in each condition for reducing the variation of measurements. As a result, the impact forces could be reproduced by the model and the shock attenuation properties of long pile synthetic turf in various conditions were estimated by simulation. However, it may be necessary to rebuild the model for improving the accuracy.

The purpose of this study is to compare the differences of running styles, Rear-foot strike (RFS) and Fore-foot strike (FFS), concerning the parameters of the vertical mathematical model and propose effective running style. The ground reaction forces are measured by force platform under two types of running style with various velocities ranged from 2.23 m/s to 4.46 m/s. A unique set of parameters of the model for each trial is computed by nonlinear programming to minimize the sum of the relative standard error of ground reaction force and the relative error of rebound velocity. The differences of the running styles were considered by using results from parameters of multi-degree of freedom model. The results of this study indicate that although the FFS needs much energy than that of RFS in low speed running, the FFS needs less energy than that of RFS in high speed running because of the impulse as the internal forces that is calculated by a set of parameters of multi-degree of freedom model.

The purpose of this study is to investigate the shock attenuation properties of long pile synthetic turf filling unit. Two different types of specimens (turf in infill, volume ratio; sand : rubber = 5:5 and 7:3), one type specimen (no turf in infill, volume ratio; sand : rubber = 5:5) and five different areas of test foot were prepared. Multi-intensity multi-area impact tests (20 impact trials with different intensity are performed for each 5 different impact areas) were performed for considering the parameter identification and shock absorbing properties with simulation. As the results, we could not measure in no turf because test foot was buried in infill. But, Stable data were obtained in turf. Adaptation of exponential type nonlinear Voigt model is also possible for the sample of this study. However, identification accuracy was same as the previous study.

Shock attenuation property of sports surfaces is especially important not only for the athlete's performance but also for injury prevention. To evaluate the properties of the sports surfaces, some sports governing bodies often adopt friction tests and shock attenuation tests to determine the horizontal and vertical characteristics, respectively. Although the diagonal impacts are often observed in athletic sports, shock attenuation test treats only the vertical impact test. Therefore we developed a two-dimensional impact test device for examining the two-dimensional cushioning characteristics of sports surfaces in previous studies. To produce a simultaneous two-dimensional force against a test specimen, we incorporated a parallelogram linkage in the measuring system. In this study, two kinds of cushioned and an non-cushioned impact tests were examined to calculate the FR(Force Reduction) values not only in vertical but also in horizontal impact force. And the maximum deformations of impact tests were also acquired by the high-speed video analysis. As the results, both of vertical and horizontal impact forces which varied with initial impact angle and drop height were well represented by quadratic surface. Therefore vertical and horizontal FR value of two kinds of surface were calculated from the experimental maximum force and estimated impact force with the same height and initial angle. Futhermore, the horizontal maximum deformations are strongly related to the initial angle of the impact force because the horizontal impact force increases sharply with increasing the initial angle of the impact.

To evaluate the properties of the sports surfaces, friction tests and shock attenuation tests have been generally adopted to determine the horizontal and vertical characteristics, respectively. Although the diagonal impacts are often observed in athletic sports, shock attenuation test treats only the vertical impact test. Therefore we developed a two-dimensional impact test device for examining the two-dimensional cushioning characteristics of sports surfaces in previous study. To produce a simultaneous two-dimensional force against a test specimen, we incorporated a parallelogram linkage in the measuring system. In this study, the various cushioned and non-cushioned impact tests were examined to calculate the FR(Force Reduction) values not only in vertical but also in horizontal impact force. As the results, horizontal shock attenuation characteristic was different from that of the vertical one in terms of initial angles. Additionally, the differences of relationship between the horizontal and the vertical shock attenuation were observed in specimens. This result indicates that HFR should be considered for preventing the injuries and providing the equality in regulation.

vThe purpose of this study is to investigate an applicability of multi-intensity multi-area impact test and the viscoelastic model proposed in previous studies to a long pile synthetic turf. The multi-intensity multi-area impact tests and the parameter identification method of the exponential function type nonlinear Voigt model with impact area were performed to one of the long pile synthetic turf. To identify the parameters of the viscoelastic model, 20 impact trials with different intensity are preformed for each 8 different impact areas. Then the elastic parameters were calculated by least squares method prior to the viscous parameters as the primary identification. After the primary identification, the parameter searching was performed to minimize the relative standard error between the experimental forces and the estimated forces as a secondary identification. Finally, a unique set of parameters including area parameters were identified for 160 trials. Although the identification accuracy of some trials were not so high, the proposed model and the identification method can be applicable to the long pile synthetic turf because the low accuracy trials should be improved by the testing conditions, such as the uniformity of surface conditions.

Various patterns of impact forces, impact durations, impact speeds and impact areas were observed in athlete's activities on the sport surfaces. Therefore, the study of shock absorption of the sport surfaces for evaluating the response property against the impact produced by the athlete activities is very important To evaluate these properties, the computer simulation method is very useful because it would be applicable to various conditions of impact, such as various impact area and impact shape. This study proposes the method for construction of Finite Element model to evaluate shock absorption properties in various conditions with multi-impact area and multi-shape contact surface. Parameters of physical property characterizing behavior of sport surface, a loss coefficient and an elastic coefficient in complex stillness model, are calculated from the experiment of steady excitation. We analyze and compare with multi intensity and multi impact area test by using Finite Element model.

The purpose of this study is to compare the differences of running styles, Rear-foot strike (RFS) and Fore-foot strike (FFS), concerning the parameters of the vertical mathematical model. The grand reaction forces are measured by force platform under two types of running style with various velocities ranged from 2.23 m/s to 3.21 m/s. A unique set of parameters of the model for each trial is computed by nonlinear programming to minimize the sum of the relative standard error of grand reaction force and the relative error of rebound velocity. The differences of the running styles were considered by using results from parameters of multi-degree of freedom model and motion analysis. The results of this study indicate that the FFS needs less energy than that of RFS because of its contact style and the impulse as the internal forces and the horizontal ground reaction force.

The purpose of this study is to propose a nonlinear viscoelastic model for sports surfaces and an identification method of this model. Although various models have been proposed to represent the behavior of rubber materials, some models represent only the material's elastic behavior, while other models deal with viscoelastic behavior but have problems in the computer simulation of that behavior. The model proposed in this study can represent viscoelastic behavior well and also has stability of computer simulation. In the identification methods, four types of drop weights, which have different mass and damping material for producing a wide range of impact durations and impact intensities, are used for impact tests. The impact force, velocity and deformation are measured in each impact test, the parameters of the elastic element of the model are calculated by the least squares method and then the parameters of the viscous element of the model are calculated from the experimental force and the estimated force produced by the elastic element. The model proposed in this study has high identification accuracy and stability of simulation compared to previous models.

The purpose of this study is to investigate an applicability of multi-intensity impact test and viscoelastic modeling proposed in previous studies to a long pile synthetic turf and considering the shock attenuation of the long pile synthetic turf by using simulation method. The multi-intensity impact tests and the parameter identification method of the exponential function type nonlinear Voigt model were performed to two kinds of long pile synthetic turfs with different hardness. The hardness of these two specimens were controlled by changing the ratio of filling materials, i.e. sand and rubber chip. After a parameter identification of the model, shock attenuation properties were considered with two kinds of synthetic turf and one of the popular polyurethane synthetic surface certified by IAAF. Although the identification accuracy of some trials were not so high, it is possible to apply the parameter identification method and the estimation of shock attenuation by using the simulation to the long pile synthetic turf. Because the low accuracy should be improved by modifying the testing conditions such as the impact area, the stability of test foot and the uniformity of surface condition of the synthetic turf.

The purpose of this study is to investigate a viscoelastic model which can generate two dimensional ground reaction force in steady pace running. In previous our studies, we had proposed 3 degrees of freedom viscoelastic model which could generate not only the vertical ground reaction force precisely but also the rebound velocity which is almost same as the rebound velocity in experiment. According to the angle of the ground reaction force calculated from the ratio of vertical and horizontal ground reaction force during contact period, the model should have a rotational control element because the rotational behavior of the model showed a complicated movement. Therefore, the nonlinear rotational elastic and viscous elements were incorporated to the model for governing the rotational behavior. And the parameters of the model were obtained with parameter searching. In conclusions, there were some significant error between the experimental data and the simulation conditions though, the two dimensional ground reaction force was reproduced with the proposed model.

In previous studies, we proposed a variety of models of material and methods for identifying the parameters of these models by multi-intensity impact test. In particular, the exponential model (Kobayashi & Yukawa, 1998) shows excellent accuracy in identifying the properties of material behavior. Although other papers reveal that this model is applicable in cases of varying impact duration and various temperatures, we have not yet discussed how the properties would change as the impact area changed. The purpose of this study is to propose an identification technique of nonlinear Voigt model with hysteresis and dependence on impact area by multi-intensity multi-area impact test. The nonlinear elastic element of this model is expressed by the exponential function based on displacement and impact area. And the nonlinear viscous element of the model is expressed by the product of the exponential function based on displacement and the exponential function based on velocity.

The purpose of this study is to investigate the relationship between the parameters of human running model and a cushioning efficiency in a vertical ground reaction force in human running with three different sports surfaces. Seven experimental running data were used for searching an each set of parameters for mathematical model of human running without sports surface. The mathematical running model with each parameter set was dropped on the mathematical sports surface model proposed by Kobayashi and Yukawa. In order to investigate the influence of parameters to the ground reaction force absorption, a sensitive test was adopted with ±3% range of parameter value with an analysis of runner-sports surface coupled system. In this paper, the relationship and the sensitiveness of each parameter and the cushioning characteristics in vertical ground reaction force was discussed.

Motion analysis of baseball pitching with some inertial sensors was executed. Three baseball pitchers who were put some sensors on upper limb and trunk pitched fast ball into net. The accelerations of upper limb and the angular velocities of trunk were measured with the sensors, and the angular velocities of the upper limb were calculated from those accelerations. Some characteristics of motion were understood from those kinematics measured and calculated.

The purpose of this study is to investigate the relationship between the parameters of human running model and a cushioning efficiency of passive load absorption in a vertical ground reaction force in human running with sports surfaces. Four experimental running data were used for searching an each set of parameters for mathematical model of human running without sports surface. The mathematical running model with each parameter set was dropped on the mathematical sports surface model proposed by Kobayashi and Yukawa. In order to investigate the influence of parameters to the passive load absorption, a sensitive test was adopted with +-3% range of parameter value with an analysis of runner-sports surface coupled system. In this paper, the relationship and the sensitiveness of each parameter and the cushioning characteristics of passive load in vertical ground reaction force was discussed.

On the overall cushioning characteristics of sport surface and sole, an interaction exists between the cushioning caused by viscoelastic deformation and the one caused by sliding friction. The characteristics has come investigation with the instrument that can be measured force and velocity under landing impact. But in general, quantitative comparison and overall effect on the cushioning operations are difficult to evaluate from only these data. In this paper, we suggested that the research by the time variation of cushioning energy on sport surface under landing impact with slip.

The purpose of this study is to propose a two dimensional shock test device for sports surfaces. There are some shock tests used for evaluating shock attenuation which seems to be heavily related to injuries and performances. However these tests are reproductive and the criteria for evaluation is very strict, this evaluation method may have an issue of particularity because material behavior would be changed when mechanical properties of dropping mass-spring are changed even if the impact force are almost same. One of the effective way to avoid this issue may be incorporating a model and simulation method. There are some viscoelastic models for sports surfaces which can represent material behavior well. Although these models are dealing with only vertical properties, horizontal properties are also important for preventing the injuries and making good performances. In most of current standards, horizontal properties are not considered but coefficient of dynamic friction. Because of this reason, a two dimensional shock test device are proposed (Kobayashi and Yukawa, 2007). In this study, modified two dimensional shock test device based on the previous study is proposed and is used for acquiring data. With the comparison between the data from sensor unit and the data from video analysis, acquired data from this device shows almost the same values from the video analysis.

Purpose of this study is to propose a method of evaluation of cushioning characteristics of sport surface under the various landing impacts during running by means of computer simulation. The sport surface is expressed by nonlinear Voict model identified by means of multiintensity impact test with various durations of impact pulse. And the landing impact is expressed by the mass-spring model with drop test. The computer simulation of the landing impact onto the sport surface is carried out by means of coupling the surface model with the landing impact model.

There are many examples which the transient response of rubber caused by shock is being used for such as playing surface and sport shoes. However, the rubber shows nonlinear viscoelasticity and hysteresis between shock and deformation, and strong dependence on temperature. Purpose of this study is to propose an indentification technique of nonlinear Voigt model with hysteresis and dependence on temperature by multiintensity impact test. The nonlinear elastic element of this model is expressed by the exponential function based on displacement, and temperature. And the nonlinear viscous element of the model is expressed by the product of the exponential function based on displacement and the exponential function based on velocity. Each exponent of these functions is composed of displacement, velocity and temperature.

Although a ball's rebound height decreases for every fall, a man's rebound height in running is kept constant by supplying the actuating force in a certain amount through the ground reaction force of landing. Purpose of this study is to propose an estimation method of the actuating force from the ground reaction force. In this paper, the mechanical model of running is represented by the mass-nonlinear Voigt model which is composed of the nonlinear spring element whose stiffness decreases with time because of the biomechanical properties of passive tension of muscle and the nonlinear damping element which is expressed by polynomial of viscous element and some elastic-viscous interactive elements. In this model, when the resultant reaction force of the viscous and interactive elements agrees with the velocity of mass center in direction, the force is estimated as the actuating force.

Although a ball's rebound height decreases for every fall, a man's rebound height in running is kept constant by supplying the actuating force in a certain amount through the ground reaction force of landing. Purpose of this study is to propose an estimation method of the actuating force from the ground reaction force. In this paper, the mechanical model of running is represented by the mass-nonlinear Voigt model which is composed of the nonlinear spring element whose stiffness decreases with time because of the biomechanical properties of passive tension of muscle and the nonlinear damping element which is expressed by polynomial of viscous element and some elastic-viscous interactive elements. In this model, when the resultant reaction force of the viscous and interactive elements agrees with the velocity of mass center in direction, the force is estimated as the actuating force.