JP2012058066A - Device and method for detecting rotation of sphere - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a rotation measurement device of a sphere by which rotation speed and a rotation direction of the sphere which flies with rotation are estimated by simple structure without being affected by acceleration due to centrifugal force.SOLUTION: A ball 1 is thrown, and triaxial acceleration signals detected from a triaxial acceleration sensor 3 provided at the center of gravity of the ball 1 are transmitted by radio. The acceleration signals in the triaxial direction during when the ball 1 is flying are extracted in an arithmetic processing part 9 from acceleration data obtained by performing A/D conversion of the acceleration signals received by a signal processor 8, and after preprocessing for removing an offset portion from a synthetic acceleration signal of the triaxial acceleration signals is performed, the rotation speed of the sphere and its time variation are estimated from time variation of a frequency amplitude value obtained by performing continuous wavelet conversion, and the rotation direction centering around a rotational axis of the sphere is estimated from time variation of an amplitude ratio of the extracted acceleration signals in the triaxial direction to be displayed on a display device 10.

Description

  The present invention relates to a sphere rotation detection apparatus and method for calculating and displaying an estimated rotation speed and direction of a sphere flying with rotation.

  In ball games such as baseball, softball, volleyball, soccer, and tennis, the rotation of the ball is an important factor in scientifically analyzing the quality of the competition. For example, in baseball, the role of the pitcher is large, and it is known that the result of the pitcher greatly depends on the victory or defeat.

  When evaluating a pitcher regardless of amateur or professional, the evaluation is often based on the so-called ball speed, ball control, goodness of ball breakage, etc., but the ball breakage is not quantitatively grasped. This ball breakage is considered to depend on the number of rotations (rotation speed) per unit time of the ball at the time of pitching and the direction of rotation. Also, from a sports medical standpoint, data on the number of rotations and rotation direction per unit time according to the type of ball when throwing in the correct form without injury, and data when throwing in an unreasonable form By comparing, it is also desirable for directors and coaches to explain the need to correct the load on the pitcher's shoulders and elbows.

As a method for measuring the number of revolutions per unit time, there is a method of measuring the number of revolutions by imaging a ball with a high-speed camera. However, the apparatus becomes large and costs and time are required for image processing.
In addition, a rotational speed measuring device that detects the rotational speed by attaching a mark having a different reflectance to the surface of the golf ball and detecting the amount of reflected light of the golf ball launched into the air has been proposed (Patent Document). 1).
Also proposed is a rotation speed detection device that is mounted on a rotating body that rotates without the rotation axis being in the direction of gravity and detects the angular velocity and the rotation speed of the rotating body by detecting the rotational tangential acceleration of the rotating body. (See Patent Document 2).
Alternatively, in order to determine the ball type, a wireless tag circuit element is built in the apex of the virtual regular tetrahedron inside the ball, and the virtual positive detected by the azimuth antenna provided outside the field of the baseball field. The coordinates of the center of gravity are calculated from the vertex coordinates of the tetrahedron. These data are sampled from when the ball is thrown up until it is replenished, stored in the memory, and posture analysis and motion analysis are performed to determine the type of ball (see Patent Document 3). ).

Japanese Patent Laid-Open No. 9-68539 JP 2009-42196 A JP 2007-80102 A

However, in the method of optically detecting the number of rotations of the ball as in Patent Document 1, it is necessary to detect reflected light obtained by irradiating the ball with light from the light projecting unit. In addition, when the light projection area is limited, depending on the type of the ball, there is a case where the ball hardly rotates in the light projection area, and therefore it is assumed that the number of rotations per unit time cannot be measured.
Further, as in Patent Document 2, it is also possible to measure the tangential acceleration of the rotating body with an acceleration sensor and detect the number of rotations from the principle of measurement. However, the ball thrown by the pitcher includes, for example, a straight high-speed ball type that rotates 40 times per second, and a low-speed rotation ball type that hardly rotates such as a fork ball or a knuckle ball. Therefore, even if the position of the acceleration sensor is slightly shifted, a variation in gravitational acceleration acts greatly, so that a measurement error is likely to occur.
Further, it is difficult to incorporate the RFID circuit element at the apex of the virtual tetrahedron in the ball as in Patent Document 3. In addition, since the amount of data detected by the RFID circuit element is large and complicated calculation processing is required to perform posture analysis and motion analysis, there is a problem that the apparatus cost increases.

  A gyro sensor is used to measure the angular velocity of the rotating body. Therefore, it is presumed that the rotational speed can be measured by mounting a gyro sensor in the ball. However, for example, since the rotation speed of a ball thrown by a professional baseball player may reach 40 rpm, there is no gyro sensor for measuring such high-speed rotation.

When the pitcher throws the ball toward the catcher, acceleration acting on the ball after the throw includes acceleration a _air due to air resistance and acceleration a _mag due to the Magnus effect. Although gravitational acceleration is not taken into account, the gravitational acceleration cannot be measured while the ball is flying due to the characteristics of the acceleration sensor. The Magnus effect is a phenomenon in which a pressure difference occurs around the ball as it moves while rotating in a viscous fluid. For example, in the case of a straight longitudinally rotating ball, It receives vertical force against it.

FIG. 16 shows the acceleration acting on the ball when the ball advances in the X ′ direction while rotating vertically. In FIG. 16, an XY coordinate indicates a motion coordinate system (sensor axis), and an X′-Y ′ coordinate indicates an absolute coordinate system.
The acceleration a _air due to the air resistance acts in the opposite direction to the traveling direction, and the acceleration a _mag due to the Magnus effect acts vertically upward with respect to the traveling direction. This is because a pressure difference is generated between the upper side and the lower side with respect to the rotation direction of the ball. When the resultant acceleration is obtained by an acceleration sensor (XY motion coordinate system) mounted on the ball, the direction changes in synchronization with the rotation of the ball, so that a sine wave signal is obtained. Furthermore, the acceleration of the centrifugal force due to the rotation of the ball is added as an offset.
The acceleration measured by the acceleration sensor becomes a sine wave signal having an offset and can be expressed by the following equation.
a = a _air + a _mag + (dω / dt) × r + ω × (ω × r)
The acceleration acting on the ball is measured by an acceleration sensor in an absolute coordinate system in which the moving direction of the ball is the X-axis and the Y-axis is the vertical direction, and the resultant acceleration in the X′-Y ′ direction is obtained to synchronize with the rotation of the ball. Since the direction of acceleration also changes, it is measured as a sine wave signal as shown in FIG. At this time, acceleration (a constant value) due to centrifugal force resulting from the assembly of the acceleration sensor at a position shifted from the center of gravity of the ball is superimposed. When the mounting radius of the acceleration sensor is large as described above, the value of the offset signal becomes large, so that it is necessary to use an acceleration sensor with a large measurement range. However, since the amplitude of the sine wave signal to be originally measured is relatively smaller than the value of the offset signal, the amplitude is buried as noise and is difficult to measure.

  The purpose of the means for solving the problems described below is to rotate the sphere that can estimate the rotational speed and direction of the sphere flying with a simple structure without being affected by the acceleration due to the centrifugal force. It is to provide a measuring apparatus and method.

A typical means for solving the above-described problems has the following configuration.
A sphere that flies with rotation, an acceleration detection unit that detects acceleration in the three-axis directions of the X axis, the Y axis, and the Z axis that are provided at or near the center of gravity of the sphere, and 3 detected by the acceleration detection unit An acceleration detection device having a transmitter that amplifies an axial acceleration signal and wirelessly transmits the signal, and an acceleration signal that is transmitted wirelessly from the transmitter and that acts on the flying sphere is received by an analog receiver. -A receiving circuit for digital conversion and outputting as acceleration data; storing acceleration data output from the receiving circuit; and extracting an acceleration signal in three axis directions while the sphere is flying; From the time change of the frequency amplitude value at a predetermined time interval of the acceleration signal in the triaxial direction obtained by performing the continuous wavelet transform process after performing the pre-processing for removing the offset, the sphere An arithmetic processing unit that estimates a rotation speed and calculates a rotation axis position estimated from an amplitude ratio of the extracted acceleration signals in the three-axis directions, and a signal processing device that is calculated by the arithmetic processing unit And a display device that displays an estimated value of the rotation speed of the sphere and a rotation direction about the estimated rotation axis on the screen.
The vicinity of the center of gravity described above indicates a minute radius area centered on the center of gravity. In other words, since the acceleration sensor itself in the X, Y, and Z axis directions of the acceleration detecting unit cannot be placed on the center of the substrate in reality, it is placed at the error of the sensor itself or the center of gravity of the sphere. This takes into account the fact that errors due to assembly are actually occurring.

  In addition, the arithmetic processing unit extracts acceleration components in the X, Y, and Z-axis directions obtained by removing the average value of each data from acceleration data within a predetermined time from the start of flight to the end of flight of the sphere, and the combined acceleration By subtracting the least-square approximation from the pre-processing to remove the offset, and then performing the continuous wavelet transform process, the rotational speed of the sphere and its temporal change are obtained from the temporal change in the frequency amplitude of the resultant acceleration. It is characterized by that.

In addition, the calculation processing unit is characterized in that a rotation direction centered on a rotation axis of a sphere is estimated from a temporal change in an amplitude ratio of the extracted acceleration data in the three-axis direction.
In addition, the arithmetic processing unit estimates an air resistance force by performing an arithmetic process of estimating a Magnus force from the estimated value of the rotational speed of the sphere and subtracting it from the amplitude value of the combined acceleration in the three-axis direction, The ball speed and its time change are estimated from force.

  Other device configurations include a sphere that flies with rotation, an acceleration detection unit that is provided at or near the center of gravity of the sphere, and detects accelerations in the X-axis, Y-axis, and Z-axis directions, and the acceleration An acceleration detection device comprising: a storage unit that stores acceleration signals in the three-axis directions detected between the start of flight and the end of flight by the detection unit; and an analog that takes in the acceleration signal stored in the storage unit -A signal converter for digital conversion and output as acceleration data; storing acceleration data output from the signal converter; and extracting acceleration signals in the three axis directions during the flight of the sphere; Time change of frequency amplitude value at a predetermined time interval of acceleration signals in three axes obtained by performing continuous wavelet transform after pre-processing to remove offset from acceleration A signal processing device comprising: an arithmetic processing unit that estimates a rotational speed of the sphere and its temporal change, and calculates a rotational axis position estimated from an amplitude ratio of the extracted acceleration signals in the three-axis directions; And a display device that displays an estimated value of the rotation speed of the sphere calculated by the arithmetic processing unit and a rotation direction centered on the estimated rotation axis on a screen.

  Further, in the rotation measurement method of the sphere, the acceleration generated in the sphere from the start to the end of the flight of the sphere that flies with the rotation is expressed by the X axis, Y axis, Detecting by the Z axis triaxial acceleration detection unit, amplifying the triaxial acceleration signal and wirelessly transmitting from the transmitter, and receiving the triaxial acceleration signal by the receiver The step of storing the acceleration data in the three-axis direction obtained by analog-digital conversion in the signal processing device, and the arithmetic processing unit of the signal processing device are configured so that the sphere is flying from the acceleration data in the three-axis direction. A predetermined time interval of acceleration signals in the three-axis direction obtained by extracting the acceleration component in the axial direction and performing the pre-processing for removing the offset from the combined acceleration in the three-axis direction and then performing the continuous wavelet transform process. Estimating the rotational speed of the sphere and its temporal change from the time change of the frequency amplitude value in it, calculating the rotational axis position estimated from the amplitude ratio of the extracted acceleration signals in the three-axis directions, Displaying the estimated rotational speed of the sphere estimated from the time change of the frequency amplitude value and the rotational direction centered on the rotational axis estimated from the amplitude ratio of the extracted acceleration signals in the three-axis direction on a display device; It is characterized by including.

  As another method, the acceleration generated in the sphere from the start of flight to the end of flight of the sphere flying with rotation can be determined by using the X-axis, Y-axis, and Z-axis provided at or near the center of gravity of the sphere. A step of storing in the storage unit the detected acceleration signal in the three-axis direction detected by the acceleration detection unit in the axial direction, and an analog signal obtained by fetching the acceleration signal in the three-axis direction stored in the storage unit into the signal processing device -Digital conversion is performed, and the arithmetic processing unit extracts the acceleration component in the three-axis direction during the flight of the sphere from the acceleration data in the three-axis direction, and performs pre-processing to remove the offset from the combined acceleration in the three-axis direction. The rotation speed of the sphere and its time change are estimated from the time change of the frequency amplitude value at a predetermined time interval of the acceleration signal in the triaxial direction obtained by performing the continuous wavelet transform process later, and the extracted A step of calculating a rotational axis position estimated from an amplitude ratio of the acceleration signal in the axial direction, an estimated rotational speed of the sphere estimated from a time change of the frequency amplitude value of the acceleration signal, and an amplitude ratio of the acceleration data in the three axial directions And a step of displaying on a display device a rotation direction centered on the rotation axis estimated from the above.

According to the sphere rotation measuring apparatus and method, since the acceleration detecting unit is provided at or near the center of gravity of the sphere, when the sphere flies with rotation, three axes of X axis, Y axis, and Z axis Direction acceleration data is detected by the acceleration detector, and the detected acceleration data is wirelessly transmitted from the transmitter. In this acceleration data, it is possible to collect acceleration data exclusively detected by the air resistance force or the Magnus force while minimizing the influence of the acceleration due to the centrifugal force. The acceleration detector is preferably arranged at the center of gravity of the sphere, but in order to avoid the influence of centrifugal force, it is necessary to provide it in a minute radius area near the center of gravity in consideration of sensor errors and assembly errors. .
In addition, the arithmetic processing unit extracts the acceleration signal in the three-axis direction during the flight of the sphere from the acceleration data, performs pre-processing to remove the offset from the combined acceleration signal of the acceleration signal in the three-axis direction, and then performs the continuous wavelet. The rotational speed of the sphere and its time change are estimated from the time change of the frequency amplitude value obtained by performing the conversion process, and the rotation axis position is estimated from the amplitude ratio of the extracted acceleration signals in the three-axis directions. Thereby, the rotation speed and rotation direction of the sphere due to the air resistance force or the Magnus force can be estimated by a simple method.
Further, since the display device displays the estimated value of the rotation speed of the sphere calculated by the arithmetic processing unit and the rotation direction centered on the estimated rotation axis on the screen, the goodness of the sphere is quantitatively and visually confirmed. Can grasp.

The arithmetic processing unit increases the measurement accuracy by taking out the acceleration data within the hover time from the start of flight to the end of flight and excluding the flight start and flight end when the acceleration value becomes extremely large By extracting acceleration components in the X, Y, and Z axis directions excluding the average value of each data, the influence of offset can be reduced.
In addition, by performing continuous wavelet transform processing following the pre-processing for removing the offset, the time change of the frequency amplitude value within a predetermined time of the acceleration component in the three-axis direction is obtained, and the rotational speed of the sphere and its time change Can be estimated with a finer analysis.
In addition, since the arithmetic processing unit estimates the rotation direction around the rotation axis of the sphere from the time change of the amplitude ratio of the extracted acceleration data in the three-axis direction, the rotation direction according to the sphere type together with the rotation speed of the sphere Can be verified by checking the rotation characteristics and the goodness of the sphere.

It is a block block diagram of the rotation measurement apparatus of a ball. 1 is a cross-sectional view of a soft baseball. It is a complex Morlet wavelet waveform diagram. It is sectional drawing of the volleyball which incorporated the gyro sensor and the acceleration sensor. It is a graph which shows the total acceleration data detected by the acceleration sensor which throws a volleyball and acts on the ball | bowl from pitching to catching. It is a graph which shows the total acceleration data detected by the gyro sensor which pitches a volleyball and acts on the ball | bowl from pitching to catching. It is a graph before and after the pre-processing which removes an offset part from X-axis acceleration data. It is a graph figure after carrying out the fast Fourier transformation process of the pre-processed X-axis acceleration data from an acceleration sensor. FIG. 7 is a graph after fast Fourier transform processing is performed on preprocessed X-axis acceleration data from the gyro sensor. It is a graph figure after carrying out the continuous wavelet transform process of the pre-processed X-axis acceleration data from an acceleration sensor. It is a graph figure after carrying out the continuous wavelet transform process of the pre-processed X-axis acceleration data from a gyro sensor. It is a graph which shows the total acceleration data detected by the acceleration sensor which pitches a soft-type baseball and acts on the ball | bowl from pitching to catching. FIG. 6 is a graph after fast Fourier transform processing is performed on preprocessed X-axis acceleration data. It is a graph figure after carrying out the continuous wavelet transform process of the pre-processed X-axis acceleration data. It is a graph which shows the time change of the amplitude value of the synthetic | combination acceleration data of a triaxial direction after a continuous wavelet transformation process. It is a mechanical analysis diagram of the rotation direction of the ball and the acceleration acting on the ball. It is waveform explanatory drawing which shows the synthetic | combination acceleration of the X'-Y 'coordinate system which generate | occur | produces on a ball | bowl.

First, the block configuration of the sphere rotation measuring device will be described.
In the following, the ball 1 for soft baseball will be described as an example of a sphere, and the number of rotations or the rotation speed and direction of rotation of the ball 1 per unit time until the pitcher throws the ball 1 and the catcher catches the ball. The case of measuring will be described.

In FIG. 1, an acceleration detection device (sensor circuit unit) 2 includes a ball 1 (see FIG. 2) flying with rotation, and an X axis, a Y axis, and a Z axis provided at or near the center of gravity O of the ball 1. A three-axis acceleration sensor (acceleration detection unit) 3 that detects the acceleration in the three-axis direction, an amplifier circuit that amplifies the acceleration signal in the three-axis direction detected by the three-axis acceleration sensor 3, and the amplified acceleration signal wirelessly A transmitter 4 for transmission is provided.
Note that the vicinity of the center of gravity indicates a minute radius area centered on the center of gravity O. That is, since the three-axis acceleration sensor 3 is not always mounted at the center of the substrate, an error in the sensor itself or an error due to assembly when the ball 1 is placed at the center of gravity O is actually generated. Consider that.

  In FIG. 2, a ball 1 is formed into a sphere by laminating different rubber materials 1a and 1b in two layers. A foam 1c is embedded in the hollow portion of the ball 1, and the center of gravity O is cut out to embed a triaxial acceleration sensor 3. The ball 1 is assumed to be a soft baseball ball 1 as an example, but the structure of the ball may be different if the competition is different, such as volleyball.

  The receiving circuit unit 5 receives the acceleration signal applied to the flying ball 1 wirelessly transmitted from the transmitter 4 and analog-to-digital conversion of the acceleration signal (analog signal) received by the receiver 6. An A / D converter 7 for outputting as acceleration data is provided.

The signal processing device 8 stores the acceleration data output from the A / D converter 7 in a storage medium (memory, hard disk, etc.). As the signal processing device 8, a personal computer (PC) or a DSP (Digital Signal Processor) is used.
The signal processing device 8 includes an arithmetic processing unit 9 (for example, a CPU, an MPU, etc.), and the arithmetic processing unit 9 extracts an acceleration signal in the three-axis direction during the flight of the ball 1 from the acceleration data, and calculates from the combined acceleration in the three-axis direction. The rotational speed of the sphere and its time change are estimated from the time change of the frequency amplitude value at a predetermined time interval of the triaxial acceleration signal obtained by performing the frequency analysis process after performing the preprocessing for removing the offset, The rotational axis position is estimated from the amplitude ratio of the extracted acceleration signals in the three-axis directions.

  The display device 10 displays on the screen the estimated number of rotations or rotation speed of the ball 1 calculated by the arithmetic processing unit 9 of the signal processing device 8 and the rotation direction around the rotation axis. The display device 10 is a liquid crystal display connected to a personal computer (PC). The receiving circuit unit 5 may be externally connected to the signal processing device 8, but may be configured to be received in the signal processing device 8 by an antenna.

Further, since the arithmetic processing unit 9 takes out the acceleration data within a predetermined flight time from when the ball 1 starts throwing (flying start) to when it is caught (flying end) and performs signal processing, the acceleration value is remarkably high. The accuracy of measurement can be improved by excluding the time when the flight starts to increase and the time when the flight ends, and the influence of offset can be obtained by extracting acceleration components in the X, Y, and Z axis directions excluding the average value of each data. Can be reduced.
The arithmetic processing unit 9 performs a continuous wavelet transform (CWT) process on the acceleration data from which the offset has been removed, and observes temporal changes in frequency amplitude values within a predetermined time interval of acceleration components in the three-axis directions. Thus, the rotation speed (the number of rotations per unit time) of the ball 1 and its change with time are estimated more finely.

  The arithmetic processing unit 9 calculates the direction of the rotation axis vector estimated from the amplitude ratio of the extracted acceleration data in the three axis directions, and estimates the rotation direction around the rotation axis vector. Thereby, the data analysis including the rotation direction according to the ball type together with the rotation speed or the rotation speed can be performed, and the rotation characteristics according to the ball type and the goodness of the sphere can be verified.

ここで、ａはスケールパラメータであり、マザーウェーブレットφ（ｔ）の拡大縮小の比率を決定する正の実数である。また、ｂはシフトパラメータでありマザーウェーブレットφ（ｔ）の時間方向へのシフト量を示す正の実数である。また、１／ａ^{（１/２）}は正規化するための係数である。本実施形態では、マザーウェーブレットφ（ｔ）として（数式２）に示す複素Ｍｏｒｌｅｔウェーブレットを使用した。
（数式２）

ここでｆ_ｂは中心周波数、ｆｃは帯域幅である。複素Ｍｏｒｌｅｔウェーブレットの外形を図３に示す。 Here, an outline of the difference between the Fourier transform and the wavelet transform will be described. In Fourier transform, a stationary signal is decomposed into sinusoidal waves of various frequencies, and only the frequency of the signal is analyzed, but the temporal change of the frequency cannot be known. On the other hand, in the wavelet transform, it is possible to analyze the signal in both time and frequency by scaling up and down a basic function called mother wavelet. Therefore, this is an effective analysis method when analyzing an unsteady signal whose frequency changes with time. Since the rotation speed of the flying ball is not constant and is considered to fluctuate due to the influence of air resistance force or Magnus force, the wavelet transform is considered to be an effective analysis method. The continuous wavelet transform is defined by the equation shown in (Equation 1) by the signal f (t) to be analyzed and the mother wavelet φ (t).
(Formula 1)

Here, a is a scale parameter, which is a positive real number that determines the scaling ratio of the mother wavelet φ (t). Further, b is a shift parameter, which is a positive real number indicating the shift amount of the mother wavelet φ (t) in the time direction. 1 / a ^(1/2) is a coefficient for normalization. In this embodiment, the complex Morlet wavelet shown in (Formula 2) is used as the mother wavelet φ (t).
(Formula 2)

Here _{f b} is the center frequency, fc is the bandwidth. The outline of the complex Morlet wavelet is shown in FIG.

Hereinafter, experimental results of measuring the number of rotations (rotational speed) of the ball 1 using the sphere rotation measuring apparatus and method of the present embodiment will be described with reference to FIGS. 4 to 15.
In the experiment, due to the necessity of comparing the true value with the data from the acceleration sensor, the acceleration sensor and the gyro sensor were embedded in the vicinity of the center of the volleyball 1 as shown in FIG.
Volleyball used a No. 5 test ball manufactured by Molten Co., Ltd., and the acceleration sensor and the gyro sensor used an 8-channel wireless 6-axis motion recorder and a high-capacity 3-axis gyro sensor manufactured by Microstone in a wireless manner. The 8ch wireless 6-axis motion recorder has three built-in three-axis acceleration sensor and transmitter 1e and three-axis gyro sensor 1f, but the built-in gyro sensor has a narrow angular velocity detection range and meets the requirements required in this experiment. There wasn't. Therefore, the built-in gyro sensor was not used, and the high-capacity three-axis gyro sensor 1f was used by being externally connected to the motion recorder. Then, the acceleration signal and the angular velocity signal were wirelessly transmitted to a personal computer with a sampling time of 5 [msec]. As shown in FIG. 4, in addition to the sensor and the ball, the experimental apparatus is composed of a foam material 1c and a plastic case 1d of 100 × 70 × 40 [mm], and the foamed polystyrene is packed in the ball cut in half. A plastic case 1d containing two sensors was fixed.

The pitching experiment was conducted with a distance of about 7 m between the pitcher and the catcher. The pitch was made with the straight shown in FIG. 15 in mind. FIG. 5 shows the acceleration signal at this time, and FIG. 6 shows the angular velocity signal of the gyro sensor.
The X and Y axis acceleration signals shown in FIG. 5 are measured as sinusoidal signals having a certain offset. Further, since the Z-axis acceleration signal hardly vibrates, it is considered that the Z-axis acceleration signal has rotated around the Z-axis. This can be seen in FIG. 6 because the Z-axis angular velocity is larger than the X and Y-axis angular velocities.

Next, in order to perform frequency analysis, data in which the ball is in the air is extracted from these acceleration signal data. It can be seen that the acceleration changes abruptly immediately before throwing and immediately after catching. From this, the differential value of acceleration was used to discriminate between the start of pitching and immediately after catching. First, the measurement data is divided into the first half and the second half. Next, in the first half, the time at which the differential value of acceleration is maximum and minimum is obtained for each of the X, Y, and Z-axis accelerations, and the latest time is set as the time of pitching disclosure. In the second half, the time of catching is specified in the same way.
Next, data after 50 [ms] at the time of throwing and before 50 [ms] at the time of catching were extracted, and frequency analysis was performed using the data of 170 points in total.

  In addition, if the acceleration data includes an offset signal, frequency analysis becomes difficult due to the influence of the low frequency due to the offset. Therefore, preprocessing for removing the offset is performed. As this preprocessing, the acceleration data of the ball in the air is approximated by least squares, and the offset signal is removed by subtracting the approximate data from the original acceleration data. Further, a signal passing through a secondary low-pass filter having a cutoff frequency of 100 [Hz] is obtained. FIG. 7 shows data obtained by performing the above preprocessing on the X-axis acceleration. In FIG. 7, the broken line waveform is the X-axis acceleration, the black solid line is the X-axis acceleration approximated to the least square, and the black solid line waveform is the X-axis acceleration after offset removal.

  Next, a fast Fourier transform (FFT) process and a continuous wavelet transform (CWT) process are performed on the acceleration signal that has been preprocessed to obtain a rotational speed, and compared with the rotational speed obtained from the gyro sensor. Validity is verified. Here, the rotational speed obtained from the gyro sensor means a rotational speed around the rotational axis obtained by synthesizing the X, Y, and Z-axis rotational speeds of the gyro sensor.

First, a fast Fourier transform (FFT) process is performed to obtain a rotation speed. Since the number of data when performing the fast Fourier transform processing needs to be a power of two, 86 points are added after 170 points of data, and FFT is applied to data of a total of 256 points (2 ⁸ ). . The result of applying FFT to the X-axis acceleration signal is shown in FIG. The FFT processing was performed on the pulsating acceleration signal excluding the average value of the acceleration signal in order to reduce the influence of the offset signal, and the window processing using the Hamming window was performed.
The rotational speed obtained from the spectrum peak value in FIG. 8 and the rotational speed obtained from the gyro sensor are shown in FIG. From FIG. 9, it can be confirmed that an almost correct rotation speed of the ball is obtained by FFT.
However, there is a slight deviation. The cause of this deviation may be that the frequency resolution is low because the data to be analyzed is less than one second. On the other hand, the rotational speed obtained from the gyro sensor slightly decreases from around 0.4 [s] while vibrating. Since time information is lost in the fast Fourier transform, the rotational speed shows a constant value regardless of the time, and it is difficult to estimate the rotational speed change.

  Next, the rotation speed is obtained by continuous wavelet transform processing. The CWT command of MATLAB's Wavelet Tool Box of MathWorks was used for the estimation of rotation speed by offline processing. The result of applying CWT to the X-axis acceleration signal is shown in FIG. Here, the horizontal axis represents time [s], the vertical axis represents the rotation speed [rps], and the color shading represents the intensity of the spectrum value. It can be seen from FIG. 10 that the spectrum value increases in the vicinity of about 7 [rps]. FIG. 11 shows the rotational speed obtained from the peak value of the spectrum in FIG. 10 and the rotational speed obtained from the gyro sensor. As shown in FIG. 11, it can be confirmed that the rotational speed of the ball is also obtained in continuous wavelet transform (CWT). In addition, since time frequency analysis is possible with CWT, a time change in frequency that was not obtained with FFT is also obtained. In FIG. 10, it can be seen that a slight change (decrease) in the rotational speed is required although it is somewhat vibrational. Therefore, it becomes possible to estimate the rotation speed of the ball more precisely with time. In addition, the average value of the rotation speed of the ball can be displayed by CWT conversion, and the initial speed immediately after the start of pitching and the final speed immediately before the catch can be displayed.

Next, a baseball ball was equipped with an acceleration sensor and a pitching experiment was conducted to estimate the rotational speed.
As the ball 1, a soft baseball class B mars ball (manufactured by Daiwa Mares Co., Ltd.) was used, and as the triaxial acceleration sensor 3, a wireless triaxial acceleration sensor manufactured by Wireless Technology was used. As shown in FIG. 2, the triaxial acceleration sensor 3 divides the ball 1 into two parts and fills the hollow portion with the foam material 1 c and incorporates it in the vicinity of the center of gravity O. From the sensor circuit unit 2, sampling is performed at intervals of 5 [ms], and an acceleration signal is transmitted to the signal processing device 8. In the pitching experiment, the pitcher and the catcher pitched at a distance of about 10 [m]. At this time, the ball type of the ball 1 was thrown in consideration of straightness. FIG. 12 shows acceleration data in the three-axis directions of the X, Y, and Z axes measured at this time.
Furthermore, acceleration signal data in the air is extracted in the same manner as in a pitching experiment using volleyball, and fast Fourier transform (FFT) processing and continuous wavelet transform (CWT) are performed on the acceleration signal that has been preprocessed to remove the offset. Each process was performed to estimate the rotational speed.

  FIG. 13 shows the rotational speed obtained by continuous wavelet transform (CWT) of the X-axis acceleration signal. Furthermore, the rotational speed obtained from the maximum value of the spectrum of FIG. 13 and the rotational speed obtained by fast Fourier transform (FFT) are shown in FIG. FIG. 14 shows that the ball is rotating at a rotational speed of about 13 [rps].

  FIG. 15 shows the time change of the amplitude value of the combined acceleration of the triaxial acceleration signal after the continuous wavelet transform. The amplitude value of the acceleration signal is obtained by combining the air resistance force and the Magnus force due to the Magnus effect. There is a correlation that the Magnus force depends on the rotational speed of the sphere, and the air resistance force depends on the traveling direction speed (spherical speed) of the sphere. In FIG. 15, the amplitude value of the combined acceleration of the three-axis acceleration decreases with time, which is a result of the decrease in the air resistance force and the Magnus force. The Magnus force can be estimated from the rotational speed of the sphere, and when the force is subtracted from the amplitude value, it becomes an air resistance force. Since the air resistance corresponds to the ball speed, the ball speed can be estimated as a result. Furthermore, the time change of the amplitude value is also related to the time change of the ball speed, and if the force component due to the Magnus effect is corrected, the time change of the ball speed can be estimated. Therefore, while only an average ball speed value can be measured with a speed gun, the application of this method can estimate the ball speed and the temporal change of the ball speed from the amplitude value of the acceleration signal. Specifically, in the block configuration diagram of FIG. 1, the arithmetic processing unit 9 performs arithmetic processing to estimate the Magnus force from the estimated value of the rotational speed of the sphere and subtract it from the amplitude value of the resultant acceleration in the three-axis direction. The resistance force can be estimated, and the ball speed and its time change can be estimated from the estimated air resistance force.

As described above, when the sphere rotation measuring device and method described in the embodiment are used, when the sphere flies with rotation, acceleration signals in the X-axis, Y-axis, and Z-axis directions are detected by the acceleration detection device. (Sensor circuit unit) 2 is detected moment by moment, and the detected acceleration signal is wirelessly transmitted from the transmitter 4. In this acceleration data, it is possible to collect acceleration signals detected exclusively by the air resistance force or the Magnus force while minimizing the influence of the acceleration due to the centrifugal force.
Further, the acceleration data obtained by receiving the acceleration signal by the signal processing device 8 and A / D converting the acceleration data in the three-axis direction during the flight of the ball 1 by the arithmetic processing unit 9 and extracting the three-axis direction acceleration signal. From the time change of the frequency amplitude value obtained by performing the continuous wavelet transform process after performing the pre-processing for removing the offset from the synthesized acceleration signal of the acceleration signal, the rotation speed of the ball 1 (the number of rotations per unit time) and The time change is estimated, and the rotation axis position is estimated from the amplitude ratio of the extracted acceleration signals in the three-axis directions. Thus, by using continuous wavelet transform rather than fast Fourier transform (FFT) as a frequency analysis for the frequency change of acceleration acting on the ball 1 due to air resistance force or Magnus force, the rotational speed of the ball 1 and its Time change can be estimated.
In addition, the arithmetic processing unit 9 estimates the rotation direction around the rotation axis from the amplitude ratio of the extracted acceleration data in the three-axis direction and displays the rotation direction on the display device 10. Data analysis including the rotation direction according to the sphere type can be performed to verify the rotation characteristics and the goodness of the sphere according to the sphere type.

Next, another example of the sphere rotation measuring apparatus and method will be described.
The schematic configuration of the rotation measuring device is the same as the above-described device configuration, and different points will be mainly described. A data storage device (storage unit) is built in the ball 1, and acceleration signals in the three-axis directions detected from the start of flight to the end of flight by the acceleration sensor 3 are stored in the data storage device. Good. For example, a flash memory or the like is used as the data storage device. The data stored in the data storage device may be amplified and collectively transmitted to the signal processing device 8 by the transmitter 4 or may be taken into the signal processing device 8 by wire transmission by providing a connection terminal. Good. In the case of wired communication, it is possible to measure the rotation of a flying sphere at an arbitrary distance without being limited to the range in which the transmitter 4 and the receiver 6 can perform wireless communication.

  The triaxial acceleration data obtained by taking the triaxial acceleration signal stored in the data storage device and performing analog-digital conversion in the signal conversion unit is stored in the signal processing device 8. In addition, the arithmetic processing unit 9 of the signal processing device 8 extracts the acceleration component in the three-axis direction during the flight of the ball 1 from the acceleration data in the three-axis direction, and removes the offset from the combined acceleration in the three-axis direction. To estimate the rotational speed of the sphere and its time change from the time change of the frequency amplitude value at a predetermined time interval of the triaxial acceleration signal obtained by performing frequency analysis processing (continuous wavelet transform processing) after The point that the rotation direction centering on the rotation axis estimated from the amplitude ratio of the extracted combined acceleration signal in the three-axis direction is displayed on the display device is the same as in the above-described embodiment.

  Although the above embodiment explained rotation measurement of a volleyball and a soft baseball, it applies to rotation measurement of a sphere used for other ball games, such as an official baseball, a softball, a soccer ball, and a tennis ball. Is also possible.

DESCRIPTION OF SYMBOLS 1 Ball 1a, 1b Rubber material 1c Foam material 1d Plastic case 1e 3-axis acceleration sensor and transmitter 1f 3-axis gyro sensor 2 Acceleration detection apparatus (sensor circuit part)
DESCRIPTION OF SYMBOLS 3 3-axis acceleration sensor 4 Transmitter 5 Reception circuit part 6 Receiver 7 A / D converter 8 Signal processing apparatus 9 Arithmetic processing part 10 Display apparatus

Claims (7)

A sphere that flies with rotation, an acceleration detection unit that detects acceleration in the three axes of the X axis, the Y axis, and the Z axis that is provided at or near the center of gravity of the sphere, and the three axes that are detected by the acceleration detection unit An acceleration detection device comprising a transmitter for amplifying and wirelessly transmitting the acceleration signal of
A receiving circuit that receives the acceleration signal acting on the sphere in flight wirelessly transmitted from the transmitter, and converts the analog signal into analog data and outputs it as acceleration data;
Continuous wavelet transform after storing acceleration data output from the receiving circuit and extracting an acceleration signal in the three-axis direction during the flight of the sphere and removing an offset from the combined acceleration in the three-axis direction The rotational speed of the sphere is estimated from the time change of the frequency amplitude value at a predetermined time interval of the acceleration signal in the triaxial direction obtained by performing the processing, and is estimated from the amplitude ratio of the acceleration signal in the triaxial direction. A signal processing device comprising an arithmetic processing unit for calculating
An apparatus for measuring rotation of a sphere, comprising: a display device that displays an estimated value of the rotation speed of the sphere calculated by the arithmetic processing unit and a rotation direction centered on the estimated rotation axis.   The arithmetic processing unit extracts an acceleration component in the X, Y, and Z axis directions excluding an average value of each data from acceleration data within a predetermined time from the start of flight of the sphere to the end of flight, and minimizes it from the synthesized acceleration. A request to determine the rotational speed of the sphere and its time change from the time change of the frequency amplitude value of the synthesized acceleration by performing the pre-processing to remove the offset by subtracting the square approximation and performing the continuous wavelet transform process Item 1. A spherical rotation measuring device according to Item 1.   3. The sphere rotation measurement according to claim 1, wherein the arithmetic processing unit estimates a rotation direction around the rotation axis of the sphere from a temporal change in the amplitude ratio of the extracted acceleration data in the three-axis directions. apparatus.   The arithmetic processing unit estimates an air resistance force by performing an arithmetic process of estimating a Magnus force from an estimated value of a rotational speed of a sphere and subtracting it from an amplitude value of a combined acceleration in three axis directions. From the estimated air resistance force The sphere rotation measuring device according to any one of claims 1 to 3, which estimates a ball speed and a temporal change thereof. The acceleration generated in the three-axis direction of the X axis, the Y axis, and the Z axis provided at or near the center of gravity of the sphere from the start of flight to the end of flight of the sphere flying with rotation. Detecting at 3 and amplifying the acceleration signal in the three-axis direction and wirelessly transmitting from the transmitter;
Storing the triaxial acceleration data in a signal processor by receiving the triaxial acceleration signal by a receiver and performing analog-digital conversion;
The arithmetic processing unit of the signal processing device performs preprocessing for extracting an acceleration component in the three-axis direction during the flight of the sphere from the acceleration data in the three-axis direction, and removing an offset from the combined acceleration in the three-axis direction. After that, the rotational speed of the sphere and its time change are estimated from the time change of the frequency amplitude value at a predetermined time interval of the acceleration signal in the three axis direction obtained by performing the continuous wavelet transform process, and the extracted three axis direction Calculating the rotational axis position estimated from the amplitude ratio of the acceleration signal;
Displaying the estimated rotational speed of the sphere estimated from the frequency of the acceleration signal and the rotational direction centered on the rotational axis estimated from the amplitude ratio of the extracted acceleration signals in the three-axis directions on a display device; A method of measuring rotation of a sphere characterized by comprising. A sphere that flies with rotation, an acceleration detector that detects acceleration in the three axes of the X, Y, and Z axes provided at or near the center of gravity of the sphere, and the flight from the start of flight by the acceleration detector An acceleration detection device comprising: a storage unit that stores acceleration signals in the three-axis directions detected until the end;
A signal conversion unit that takes in an acceleration signal stored in the storage unit and converts it to analog-digital and outputs it as acceleration data; stores acceleration data output from the signal conversion unit; and three axes in which the sphere is flying Frequency amplitude value at a predetermined time interval of the triaxial acceleration signal obtained by extracting the acceleration signal in the direction and performing the pre-processing to remove the offset from the combined acceleration in the triaxial direction and then performing the continuous wavelet transform process A signal processing device comprising: an arithmetic processing unit that estimates a rotational speed of the sphere and a time change thereof from a time change of the sphere, and calculates a rotation axis position estimated from an amplitude ratio of the extracted acceleration signals in the three axis directions When,
An apparatus for measuring rotation of a sphere, comprising: a display device that displays an estimated value of the rotation speed of the sphere calculated by the arithmetic processing unit and a rotation direction centered on the estimated rotation axis. The acceleration generated in the three-axis direction of the X axis, the Y axis, and the Z axis provided at or near the center of gravity of the sphere from the start of flight to the end of flight of the sphere flying with rotation. And detecting the detected acceleration signals in the three-axis directions in the storage unit;
The triaxial acceleration signal stored in the storage unit is taken into a signal processing device and converted into analog to digital form, and the arithmetic processing unit uses the triaxial acceleration data as a triaxial acceleration component during the flight of the sphere. Is extracted from the time change of the frequency amplitude value in a predetermined time interval of the acceleration signal in the three-axis direction obtained by performing the continuous wavelet transform process after performing the pre-processing for removing the offset from the combined acceleration in the three-axis direction. Estimating a rotational speed of the sphere and its temporal change, and calculating a rotational axis position estimated from an amplitude ratio of the extracted acceleration signals in the three-axis directions;
Displaying on the display device the rotation direction centered on the rotation axis estimated from the estimated rotation speed of the sphere estimated from the frequency of the acceleration signal and the amplitude ratio of the acceleration data in the triaxial direction. A method for measuring rotation of a featured sphere.

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