JP2019037409A - Analysis apparatus of behavior of hitting tool - Google Patents

Abstract

To provide an analysis apparatus capable of analyzing deformation of a hitting tool during swinging with higher accuracy.SOLUTION: An analysis apparatus is provided for analyzing behavior of a hitting tool having nature of deforming during swinging. The analysis apparatus includes an acquisition unit for acquiring measurement data measuring the swinging behavior of a first region included in the hitting tool, a central calculation unit for calculating a rotation center in the hitting tool during swinging based on the measurement data, and an analysis unit for analyzing deformation of the hitting tool during swinging based on the measurement data and the rotation center.SELECTED DRAWING: Figure 11

Description

  The present invention relates to an analysis apparatus, method, and program for analyzing the behavior of a hitting tool having a property of deforming during a swing.

  2. Description of the Related Art Conventionally, a technique for analyzing the behavior of a hitting tool having a property of deforming during a swing is known (for example, see Non-Patent Document 1). Non-Patent Document 1 discloses a technique for simulating a bending deformation during a swing of each minute element constituting a shaft of a golf club according to an analysis model based on a finite element method.

Kenta Matsumoto and 5 others, “Influence of club head inertia on shaft behavior”, Sports Engineering / Human Dynamics 2015 Proceedings, B-34 (USB memory), October 2015

Japanese Unexamined Patent Publication No. 2017-023690 JP, 2006-034483, A Japanese Patent Laid-Open No. 2005-292061 JP 2011-122972 A

  By the way, simulation is performed by approximately modeling a system to be analyzed, and it is difficult to completely reproduce an actual system. Therefore, a technique for improving the accuracy of the simulation is always required particularly in a scene where a complicated system such as a hitting tool that is deformed during a swing is analyzed.

  An object of the present invention is to provide an analysis apparatus, method, and program capable of analyzing deformation of a hitting tool during a swing with higher accuracy.

  An analysis apparatus according to a first aspect is an analysis apparatus that analyzes a behavior of a hitting tool having a property of being deformed during a swing, and includes measurement data obtained by measuring a behavior during a swing of a first part included in the hitting tool. An acquisition unit to acquire, a center calculation unit for calculating a rotation center of the hitting tool during a swing based on the measurement data, and a deformation of the hitting tool during the swing based on the measurement data and the rotation center. An analysis unit for analysis.

  An analysis apparatus according to a second aspect is the analysis apparatus according to the first aspect, wherein the analysis unit corrects the measurement data based on the rotation center, and swings based on the corrected measurement data. The deformation of the hitting tool inside is analyzed.

  An analysis apparatus according to a third aspect is the analysis apparatus according to the first aspect or the second aspect, wherein the acquisition unit acquires first measurement data that is the measurement data at a first timing, and 2nd measurement data which is the said measurement data in the timing of 2 is acquired. The center calculation unit calculates the rotation center based on the first measurement data. The analysis unit analyzes deformation of the hitting tool during a swing based on the second measurement data and the rotation center.

  An analysis device according to a fourth aspect is the analysis device according to any one of the first to third aspects, wherein the center calculation unit is data included in the measurement data and is a user of the hitting tool The measurement data of the behavior of the first part when the waggle performs a waggle operation, and the hitting tool is intended to give only a rotary motion without giving a translational motion to the hitting tool. The center of rotation is calculated based on at least one of data obtained by measuring the behavior of the first part when a tool is operated.

  An analysis device according to a fifth aspect is the analysis device according to any one of the first to fourth aspects, wherein the center calculation unit minimizes movement in the hitting tool based on the measurement data. The position is calculated as the rotation center.

  An analysis device according to a sixth aspect is the analysis device according to any one of the first to fifth aspects, wherein the user of the hitting tool grasps the hitting tool based on the measurement data. A determination unit that determines the strength is further provided. The analysis unit analyzes the deformation of the hitting tool during a swing based further on the strength of the gripping force.

  An analysis device according to a seventh aspect is the analysis device according to the sixth aspect, wherein the determination unit specifies the magnitude of a predetermined frequency component included in the measurement data, and the magnitude of the predetermined frequency component In response to this, the strength of the gripping force is determined.

  An analysis device according to an eighth aspect is the analysis device according to any one of the first to seventh aspects, wherein the acquisition unit is measured by an inertial sensor attached to the first part as the measurement data. Get the data.

  An analysis device according to a ninth aspect is the analysis device according to any one of the first to eighth aspects, wherein the analysis unit is included in the first tool based on deformation of the tool. The behavior of the second part different from the part is derived.

  An analysis apparatus according to a tenth aspect is the analysis apparatus according to the ninth aspect, wherein the hitting tool is a golf club, the first part is a grip or a shaft, and the second part is a head. is there.

  An analysis device according to an eleventh aspect is the analysis device according to any one of the first to ninth aspects, wherein the hitting tool is a golf club.

  An analysis device according to a twelfth aspect is the analysis device according to any of the first to eleventh aspects, wherein the analysis unit calculates an inertial force acting on the hitting tool based on the measurement data. Based on the inertial force, the deformation amount of the hitting tool is calculated by a finite element method model.

The analysis program according to the thirteenth aspect is an analysis program for analyzing the behavior of a hitting tool having a property of deforming during a swing, and causes a computer to execute the following steps.
A step of acquiring measurement data obtained by measuring a behavior of the first part included in the hitting tool during the swing, a step of calculating a rotation center of the hitting tool during the swing based on the measurement data, the measurement data, and Analyzing the deformation of the hitting tool during a swing based on the center of rotation;

The analysis method according to the fourteenth aspect is an analysis method for analyzing the behavior of a hitting tool having a property of deforming during a swing, and includes the following steps.
A step of acquiring measurement data obtained by measuring a behavior of the first part included in the hitting tool during the swing, a step of calculating a rotation center of the hitting tool during the swing based on the measurement data, the measurement data, and Analyzing the deformation of the hitting tool during a swing based on the center of rotation;

  An analysis device according to a fifteenth aspect is an analysis device that analyzes a behavior of a hitting tool having a property of deforming during a swing, and includes measurement data obtained by measuring a behavior during a swing of a first portion included in the hitting tool. Based on the acquisition unit to be acquired, the determination unit that determines the strength of the gripping force with which the user of the hitting tool grips the hitting tool based on the measurement data, the measurement data, and the strength of the gripping force And an analysis unit for analyzing the deformation of the hitting tool during the swing.

  In many cases, the user of the hitting tool swings the hitting tool by grasping the end of the hitting tool. Therefore, conventionally, in the simulation model for analyzing the behavior of the hitting tool during the swing, it is assumed that the hitting tool rotates around its end as in Patent Documents 1 and 2. In practice, however, the center of rotation of the hitting tool is often not near the end of the hitting tool but in the vicinity of the position that the player has just grasped. Conventionally, the true rotation center of such a hitting tool has not been considered, but grasping this can contribute to a more accurate simulation.

  In this regard, according to the first aspect of the present invention, the rotation center of the hitting tool is calculated based on the measurement data obtained by measuring the behavior of the first part included in the hitting tool during the swing. That is, the true rotation center of the hitting tool is calculated, and the deformation of the hitting tool during the swing is analyzed based on this. As a result, the deformation of the hitting tool during the swing can be analyzed with higher accuracy.

  Also, the gripping force with which the user grips the hitting tool can affect the behavior of the hitting tool. Therefore, in the scene where the behavior of the hitting tool is analyzed, it is important to grasp the gripping state of the hitting tool. In this regard, Patent Documents 3 and 4 disclose that a pressure sensor is attached to the grip of a golf club and the pressure when the player grips the grip is measured. However, the pressure sensors as disclosed in Patent Documents 3 and 4 sometimes lack versatility.

  In this regard, according to the fifteenth aspect of the present invention, the strength of the gripping force with which the user grips the hitting tool is determined based on the measurement data obtained by measuring the behavior during the swing of the first part included in the hitting tool. Is done. Therefore, the strength of the gripping force is specified without directly measuring the gripping force, and based on this, the deformation of the hitting tool during the swing is analyzed. As a result, the deformation of the hitting tool during the swing can be analyzed with higher accuracy.

The figure which shows the whole structure of the swing analysis system containing the analyzer which concerns on one Embodiment of this invention. The functional block diagram of a swing analysis system. The perspective view of a golf club. (A) The figure which shows an address state. (B) The figure which shows a top state. (C) The figure which shows an impact state. (D) The figure which shows a finish state. The figure explaining the exercise | movement of the golf club at the time of a waggle operation | movement. The figure which modeled the golf club according to the finite element method. The figure which modeled the golf club at the time of a deformation | transformation. A graph of angular velocity during a golf swing by a golfer with strong gripping force. The graph of the angular velocity at the time of the golf swing by the golfer with a weak gripping force. FIG. 8A is a graph of the frequency spectrum of the angular velocity in FIG. 8A. FIG. 8B is a graph of the frequency spectrum of the angular velocity in FIG. 8B. A graph of the frequency spectrum of angular velocity when a golfer intentionally holds a golf club and swings it. FIG. 10B is a graph of a frequency spectrum of angular velocity when a golf club is intentionally held weakly and swung by the same golf player as FIG. 10A. The flowchart which shows the flow of an analysis process. The graph of the locus | trajectory of the grip end based on the sensor data before correction | amendment and after correction | amendment. The figure which shows the simulation result of the track | orbit of a golf club seen from the front side of the golfer which concerns on a reference example and an Example. The figure which shows the simulation result of the track | orbit of a golf club seen from the golfer's right side which concerns on a reference example and an Example. The figure which shows the analysis result of the head speed which concerns on a reference example and an Example. The figure which shows the analysis result of the face angle which concerns on a reference example and an Example. The figure which shows the analysis result of the approach angle which concerns on a reference example and an Example. The figure which shows the analysis result of the blow angle which concerns on a reference example and an Example.

  Hereinafter, an embodiment in which the analysis device, method, and program according to the present invention are applied to analysis of the behavior of a golf club during a swing will be described with reference to the drawings.

<1. Overview of swing analysis system>
1 and 2 show an overall configuration diagram of a swing analysis system 100 including an analysis apparatus 1 according to an embodiment of the present invention. The swing analysis system 100 is configured to analyze the behavior of the golf club 5 during a swing by the golfer 7. A portion of the golf club 5, particularly the shaft 52, has a property of being deformed during the swing. The analysis device 1 analyzes the deformation of the grip 51 and the shaft 52 of the golf club 5 based on the measurement data obtained by measuring the behavior of the grip end 51a of the golf club 5 during the swing, 53 behavior is analyzed. The above measurement is performed by the measurement device 2, and the measurement device 2 constitutes the swing analysis system 100 together with the analysis device 1. The analysis result by the analysis device 1 is used for various purposes such as fitting of the golf club 5 suitable for the golfer 7, improvement of the form of the golfer 7, and development of golf equipment.

  Hereinafter, after describing the configuration of each part of the swing analysis system 100, an analysis method by the swing analysis system 100 will be described.

<2. Details of each part>
<2-1. Measuring device>
The measuring device 2 according to the present embodiment includes an inertial sensor unit 4 and a distance image sensor 21. Hereinafter, it demonstrates in order.

<2-1-1. Inertial sensor unit>
As shown in FIG. 1, the inertial sensor unit 4 is attached to a grip end 51 a that is the end of the golf club 5 opposite to the head 53 in the grip 51, and measures the behavior of the grip end 51 a. As shown in FIG. 3, the golf club 5 is a general golf club, and includes a shaft 52, a head 53 provided at one end of the shaft 52, and a grip 51 provided at the other end of the shaft 52. The The inertial sensor unit 4 is configured to be small and light so as not to hinder the swing operation.

  As shown in FIG. 2, an acceleration sensor 41, an angular velocity sensor 42, and a geomagnetic sensor 43 are mounted on the inertial sensor unit 4 according to the present embodiment. The inertial sensor unit 4 is also equipped with a communication device 40 for transmitting sensor data output from these sensors 41 to 43 to an external device such as the analysis device 1 via the communication line 17. . In the present embodiment, the communication device 40 is wireless so as not to hinder the swing operation, but may be connected to the analysis device 1 in a wired manner via a cable.

The acceleration sensor 41, the angular velocity sensor 42, and the geomagnetic sensor 43 respectively measure acceleration, angular velocity, and geomagnetism in the xyz local coordinate system. More specifically, the acceleration sensor 41 measures accelerations a _x , a _y , and a _z of the grip end 51a in the x-axis, y-axis, and z-axis directions. The angular velocity sensor 42 measures angular velocities ω _x , ω _y , and ω _z of the grip end 51a around the x axis, the y axis, and the z axis. Geomagnetic sensor 43 measures the x-axis at the handle end 51a, y-axis and z-axis direction terrestrial magnetism m _x, m _y, a m _z. Sensor data (measurement data) related to acceleration, angular velocity, and geomagnetism is acquired as time-series data having a predetermined short sampling period. The xyz local coordinate system is a three-axis orthogonal coordinate system defined as shown in FIG. That is, the z axis coincides with the direction in which the shaft 52 extends, and the direction from the head 53 toward the grip 51 is the positive z axis direction. The y-axis is oriented so as to be as close as possible to the flying direction of the golf club 5 at the time of addressing, that is, generally along the face-back direction, and the direction from the back side toward the face side is the y-axis positive direction. . The x-axis is oriented so as to be orthogonal to the y-axis and the z-axis, that is, substantially along the toe-heel direction, and the direction from the heel side to the toe side is the x-axis positive direction. The origin of the xyz local coordinate system is the grip end 51a.

  A golf swing generally proceeds in the order of address, top, impact, and finish. The address means a stationary state in which the head 53 is disposed near the ball as shown in FIG. 4A, and the top means that the golf club 5 is taken back from the address as shown in FIG. This means that the head 53 is swung up most. As shown in FIG. 4 (C), the impact means a state at the moment when the golf club 5 is swung down from the top and the head 53 collides with the ball, and the finish is as shown in FIG. 4 (D). It means a state in which the golf club 5 is swung forward after impact. In general, the golfer 7 performs a waggle operation before the address. The waggle operation refers to a movement of swinging the golf club 5 to the left or right as if the head 53 is rotated around the position where the golfer 7 grips the grip 51 with the hand 71 in order to determine the address position ( (See FIG. 5). In the description of the present embodiment, a waggle operation is assumed to be included in a golf swing unless otherwise specified.

  In the present embodiment, sensor data from the acceleration sensor 41, the angular velocity sensor 42, and the geomagnetic sensor 43 are transmitted to the analysis device 1 in real time via the communication device 40. However, for example, sensor data may be stored in a storage device in the inertial sensor unit 4, and the sensor data may be taken out from the storage device after the swing operation is finished and transferred to the analysis device 1.

<2-1-2. Distance image sensor>
The distance image sensor 21 is a camera having a distance measuring function for shooting a golf player 7 as a two-dimensional image of trial hitting the golf club 5 and measuring a distance to a subject. Therefore, the distance image sensor 21 can output a time-series depth image together with a time-series two-dimensional image. Note that the two-dimensional image here is an image obtained by projecting an image of the photographing space onto a plane orthogonal to the optical axis of the camera. The depth image is an image in which data on the depth of the subject in the optical axis direction of the camera is assigned to pixels within substantially the same imaging range as the two-dimensional image. In the present embodiment, the distance image sensor 21 is installed in front of the golfer 7 so as to photograph the golfer 7 from the front side.

  The distance image sensor 21 used in the present embodiment captures a two-dimensional image as an infrared image (hereinafter referred to as an IR image). The depth image is obtained by a method such as a time-of-flight method using infrared rays or a dot pattern projection method. Therefore, as shown in FIG. 2, the distance image sensor 21 emits infrared rays toward the front, and an IR light emitting unit 21 a that receives the infrared rays that are irradiated from the IR light emitting unit 21 a and reflected back to the subject. And a light receiving portion 21b. The IR light receiving unit 21b is a camera having an optical system, an image sensor, and the like. The IR light emitting unit 21a and the IR light receiving unit 21b are accommodated in the same housing 21f and are disposed in front of the housing 21f.

  In addition to the CPU 21c that controls the entire operation of the distance image sensor 21, the distance image sensor 21 includes a memory 21d that stores at least temporarily image data (measurement data) of the captured IR image and depth image. . A control program for controlling the operation of the distance image sensor 21 is stored in the memory 21d. The distance image sensor 21 also includes a communication unit 21e. The communication unit 21e transmits captured image data to an external device such as the analysis apparatus 1 via a wired or wireless communication line 17. Can be output. In the present embodiment, the CPU 21c and the memory 21d are also housed in the housing 21f together with the IR light emitting unit 21a and the IR light receiving unit 21b. It is not always necessary to transfer the image data to the analysis device 1 via the communication unit 21e. For example, if the memory 21d is detachable, the image data is read out by the analysis device 1 by removing it from the housing 21f and inserting it into the reader of the analysis device 1 (corresponding to the communication unit 15 described later). Can do.

  In the present embodiment, infrared imaging is performed by the distance image sensor 21, and the behavior of the grip end 51a is analyzed based on the captured IR image. Accordingly, although not particularly shown in FIGS. 1 and 3, a reflective sheet that efficiently reflects infrared rays is provided on the grip end 51a so that the distance image sensor 21 can easily measure the behavior of the grip end 51a. It is affixed as. A similar infrared reflective sheet is also attached to the shaft 52 as a marker.

<2-2. Analyzer>
The analysis device 1 is a general-purpose computer as hardware, and is realized as, for example, a desktop computer, a notebook computer, a tablet computer, or a smartphone. As shown in FIG. 2, the analysis apparatus 1 is manufactured by installing an analysis program 6 in a general-purpose computer from a computer-readable recording medium 30 such as a CD-ROM or via a communication line such as the Internet. The The analysis program 6 is software for analyzing the behavior of the golf club 5 during the swing based on the measurement data sent from the measurement device 2, and causes the analysis device 1 to perform an operation described later. The analysis program 6 has a function of estimating the center of rotation C of the golf club 5 during the swing, and a function of estimating the strength of the gripping force with which the golfer 7 grips the grip 51.

  The analysis device 1 includes a display unit 11, an input unit 12, a storage unit 13, a control unit 14, and a communication unit 15. These units 11 to 15 are connected to each other via the bus line 16 and can communicate with each other. The display part 11 can be comprised with a liquid crystal display etc., and displays the analysis result etc. of a golf swing with respect to a user. In addition, a user here is a general term for the person who requires the analysis result of golf swings, such as golfer 7 itself, its instructor, the seller and developer of golf equipment. The input unit 12 can be configured with a mouse, a keyboard, a touch panel, or the like, and accepts an operation from the user for the analysis apparatus 1.

  The storage unit 13 can be configured with a hard disk or the like. In the storage unit 13, the analysis program 6 is stored, and measurement data sent from the measurement device 2 is stored. The control part 14 can be comprised from CPU, ROM, RAM, etc. The control unit 14 virtually operates as an acquisition unit 14a, an analysis unit 14b, a center calculation unit 14c, a determination unit 14d, and a display control unit 14e by reading and executing the analysis program 6 in the storage unit 13. Details of the operations of the respective units 14a to 14e will be described later. The communication unit 15 functions as a communication interface that transmits and receives data to and from an external device such as the measurement device 2.

<3. Analysis method>
Next, an analysis method for analyzing the behavior of the golf club 5 during the swing will be described. In the analysis model according to the present embodiment, the strength of the gripping force for gripping the golf club 5 when the golfer 7 swings the golf club 5 is considered. In the following, first, an analysis model that is the basis of the analysis process will be described, then an algorithm for determining the strength of the gripping force will be described, and finally the flow of the analysis process will be described.

<3-1. Analysis model>
The analysis model according to the present embodiment is a model according to the finite element method. The grip 51 and the shaft 52 are assumed to be multistage cylindrical beam elements, and the head 53 is assumed to be a rigid body. As shown in FIG. 6, the grip 51 and the shaft 52 are divided into a plurality of minute elements along the longitudinal direction. In the present embodiment, the grip 51 is divided into six elements, and the shaft 52 is divided into 16 elements. Further, the grip 51 and the element closest to the grip 51 in the shaft 52 are a physical region, and the remaining region is an elastic deformation region.

  Here, as shown in FIG. 7, the i-th element from the grip end 51a side is referred to as the i-th element (i = 1, 2,..., 22). In FIG. 7, the golf club 5 indicated by a solid line is a golf club as a rigid body without deformation, and the golf club 5 indicated by a dotted line is a golf club deformed by an inertial force. The inertial force here is an inertial force that acts on the golf club 5 that moves so as to rotate in the swing plane during the swing. Further, the node on the grip end 51a side of the i-th element is called the i-th node, and the node on the head 53 side is called the (i + 1) -th node.

  In addition, a shaft coordinate system having the origin at the i-th node of the golf club 5 without deformation is defined. The shaft coordinate system has x, y, and z axes. The x axis is parallel to the axial direction of the shaft 52 and is positive in the direction from the grip end 51a side to the head 53 side. The y-axis is substantially parallel to the toe-heel direction of the head 53, and the negative direction of the toe direction is positive. The z-axis is substantially parallel to the normal direction of the face surface 53a, and the direction from the face surface 53a toward the flying ball direction is a positive direction. For convenience of explanation, the three axes of the shaft coordinate system and the three axes of the xyz local coordinate system described above are represented by x, y, and z, respectively, but they are different axes as defined respectively. Also, a three-dimensional inertial coordinate system that is fixed with respect to the ground and has a golf ball installation position as an origin, and a three-dimensional object fixed coordinate system that has the grip end 51a as an origin are defined.

At this time, if each symbol is defined as in Equation 1, Equation 2 is established. In this specification, T on the right shoulder of a symbol means a transposed vector.

Further, the virtual displacement caused by the deformation of the golf club 5 is expressed as follows.
D _(i) is defined as follows. However, the following x, y, and z represent the displacements of the nodes in the x-axis, y-axis, and z-axis directions of the shaft coordinate system, respectively, and θ _x is the torsion angle around the x-axis, θ _y , θ _z Represents the deflection angles around the y-axis and the z-axis, respectively. The subscripts (i) and (i + 1) in the lower right represent node numbers.

Based on the above formula and the principle of d'Alembert, the following formula is established. In this specification, a dot on a symbol means differentiation, and two dots mean twice differentiation.

At this time, in order for the formula 5 to always hold, the following formula must hold.

Moreover, each term of the formula of Formula 6 is obtained as follows.

Substituting the equation (7) into the equation (6) yields the following equation.

Furthermore, considering the torsion, the mass matrix [M] is derived from the kinetic energy and the stiffness matrix [K] is derived from the potential energy (“Takuzo Iwabuchi et al.,“ Basics of Vibration Engineering ”, Morikita Publishing Co., Ltd., 2008, pp. 130-134 ”and“ Keiji Komatsu, “Fine Element Method and Response Analysis by Mechanical Structural Vibration MATLAB”, Morikita Publishing Co., Ltd., 2009, pp. 38-39 ”), the equation of motion of the i-th element is It is expressed as follows.

From the equation (9), the equation of motion for the entire grip 51 and shaft 52 is expressed as follows. Note that the subscript t on the lower right indicates that each matrix and vector are added in all elements.

On the other hand, the equation of motion of the head 53 is expressed as follows.

The meanings of symbols in the formulas (11) and (12) are as follows. Note that the final node is the node closest to the head 53.

From the above equations (10) to (12), the equation of motion of the golf club 5 in the non-damped system is expressed as follows. Note that 0 _i × _j is i rows and j columns where all elements are zero.

Here, the mass matrix [M _c ] and the stiffness matrix [K _t ] are divided into a physical region and an elastic deformation region as follows. M _i × _j is a matrix of i × j columns in [M _c ], and K _i × _j is a matrix of i × j columns in [K _t ]. In particular, M ₉₀ × ₉₀ and K ₉₀ × ₉₀ are the mass matrix and the stiffness matrix of the elastic deformation region under the fixed end condition, respectively.

At this time, the attenuation matrix [C _t ] is expressed as follows (see “Akio Nagamatsu,“ Mode Analysis ”, Baifukan, 1985, pp. 176-216)).

However, the meaning of each symbol in the above formula is as follows.

From the above equations (14) and (18), the following equations are derived as equations of motion for the entire system of the golf club 5.

Further, when the reduction mode matrix [Q] is obtained from the constraint mode synthesis method, the equation of Equation 20 is reduced as follows.

  By the way, although the grip 51 is gripped by the golfer 7, it is gripped not to be gripped as hard as a fixed end but to move with a flexible hand movement. In this analysis model, in order to express such a flexible gripping condition, the grip 51 is modeled as a spring model as shown in FIG.

Specifically, attention is paid to the i-th element (i = 1, 2,..., 7) of the physical area. At this time, the potential energy stored by the deformation of the grip 51 is expressed as follows.

Where k _x , k _y , and k _z are spring constants for displacement in the x, y, and z axis directions of the shaft coordinate system, respectively, and kθ _x is a rotation spring constant for rotation about the x axis of the shaft coordinate system. U, v, and w are displacements in the x, y, and z-axis directions of the shaft coordinate system generated in the i-th element, respectively, L is the element length, and N _x1 and N _x2 are shape functions. From the above equation, the gripping force acting in each axial direction of the shaft coordinate system and the gripping torque around each axis are expressed as follows.

From the above, the gripping force F _G of the entire grip 51 becomes as follows.

Here, [K _G ] is the gripping rigidity and can be expressed using spring constants k _x , k _y , k _z , and kθ _x . Considering the gripping state by the golfer 7 based on the formula 24, the equation of motion of the above formula 21 is as follows.

  In addition, the derivation method of each above formula and the meaning of each symbol are known techniques as described in Non-Patent Document 1. Therefore, in the above, the meaning of each formula and each symbol has been briefly described, but Non-Patent Document 1 can be referred to for further understanding.

<3-2. Algorithm for judging the strength of gripping force>
The inventors conducted experiments described below, and based on time-series data representing the behavior of the hitting tool when the user uses the hitting tool, the strength of the gripping force with which the user holds the hitting tool The knowledge that it is possible to judge is obtained.

In this experiment, the golfer performed a golf swing. At this time, a golf club having an inertial sensor attached to the grip end, such as the above-described golf club 5, was used. FIG. 8A shows an example of time-series data of the angular velocity ω _z output from the angular velocity sensor during a golf swing by a golfer with a strong gripping force (hereinafter referred to as a strong golfer). FIG. 8B shows an example of time-series data of the angular velocity ω _z output from the angular velocity sensor during a golf swing by a golfer having a gripping force weaker than that of a strong golfer (hereinafter referred to as a weak golfer). The strength of the gripping force can be determined by holding a golf club with a pressure sensor attached to the grip and swinging it, and measuring the pressure value at this time, but it can also be determined visually. . The zeros on the horizontal axis in FIGS. 8A and 8B represent the timing of impact.

  The present inventors have accumulated a large amount of time-series data representing the movement of a golf club during a golf swing by a strong golfer and a weak golfer. In response, we discovered that a unique waveform appeared. More specifically, as shown in FIG. 8A, the waveform representing the movement of the golf club swung by the strong golfer is relatively smooth, whereas a small peak is observed in the same waveform by the weak golfer. It was done. That is, it has been found that the waveform of the weak golfer contains more high frequency components than the waveform of the strong golfer.

  In order to confirm the above findings more accurately, frequency analysis was performed. 9A and 9B are graphs of frequency spectra obtained by performing frequency analysis after passing the time series data of FIGS. 8A and 8B through a band-pass filter (extracting a band of 5 to 20 Hz), respectively. From the figure, a peak appears in the frequency spectrum of the weak golfer in the vicinity of 7 to 10 Hz, but such a peak does not appear in the frequency spectrum of the strong golfer.

  From the above experiment, it was found that the magnitude of the frequency component included in the time-series data representing the movement of the golf club during the swing changes according to the strength of the gripping force for gripping the golf club. Therefore, it has been found that the strength of the gripping force can be determined by acquiring time-series data representing the movement of the golf club during the swing and specifying the magnitude of the predetermined frequency component included therein. . This is presumably because the vibration characteristics of the hitting tool change according to the strength of the golfer's gripping force.

10A and 10B show the results when a golf swing is performed by intentionally changing the gripping force to the same golfer. FIG. 10B shows the case where FIG. Shows a case where the grip is intentionally weakly held. Also in this experiment, a large peak exists in the vicinity of 7 to 10 Hz in the frequency spectrum of the angular velocity ω _z when the gripping force is weak, but the frequency spectrum of the angular velocity ω _z when the gripping force is strong has a similar peak. There is no large peak. Therefore, the certainty of the above findings was further confirmed.

  8A and 8B, a high frequency component is confirmed mainly in a period from impact-2 seconds to impact-0.5 seconds. This period corresponds to a backswing period from the address to the top. In other words, when a golf club is swung up as during a backswing, the golf club moves relatively slowly compared to when the golf club after the top is swung down. This is thought to be due to the effect of. In addition, when the movement is fast, the gripping force is likely to increase, so that a slower behavior tends to produce a difference between golfers. Therefore, it is considered that more accurate analysis can be performed by paying attention to data in a period in which the movement of the hitting tool is relatively slow.

<3-3. Flow of analysis processing>
The analysis process proceeds according to the flowchart shown in FIG. First, in step S1, the golf club 5 with the inertial sensor unit 4 is swung by the golfer 7, and a motion including rotation is given to the golf club 5 held by the golfer 7. At this time, the behavior of the golf club 5 during the swing is measured by the measuring device 2. More specifically, the inertial sensor unit 4, the acceleration a _x in the three axial directions of the xyz local coordinate system of the grip end 51a, a _y, a _z, the angular velocity ω _x, ω _y, ω _z and geomagnetism m _x, m Sensor data (measurement data) regarding _y and m _z is acquired and transmitted to the analysis device 1 via the communication device 40. On the other hand, on the analysis device 1 side, the acquisition unit 14 a receives this via the communication unit 15 and stores it in the storage unit 13. In the present embodiment, time-series sensor data of at least the waggle operation period and the subsequent period from the address to the finish is collected.

  In step S1, simultaneously with the measurement by the inertial sensor unit 4, the distance image sensor 21 acquires image data (measurement data) that captures how the golf club 5 is swung from the front side of the golfer 7, and the communication unit It is transmitted to the analysis apparatus 1 via 21e. On the other hand, on the analysis device 1 side, the acquisition unit 14 a receives this via the communication unit 15 and stores it in the storage unit 13. In the present embodiment, time-series image data of at least the waggle operation period and the subsequent period from the address to the finish is collected. The image data referred to here includes two types of image data including an IR image and a depth image.

In the subsequent step S2, the analysis unit 14b derives the addresses t _a , t _t , and t _i of the address, the top, and the impact based on the measurement data stored in the storage unit 23. Various algorithms are known for calculating the addresses, top and impact times t _a , t _t , and t _i based on the measurement data (especially sensor data) as described above. The detailed explanation is omitted.

  In subsequent step S3, the center calculation unit 14c refers to the time of the address derived in step S2, and from the measurement data stored in the storage unit 23, during the waggle operation performed before the address. Sensor data (hereinafter referred to as waggle data) is extracted. The waggle data is data representing the movement given to the golf club 5 when the golfer 7 is performing the waggle operation.

  In step S4, the center calculation unit 14c calculates the true rotation center C of the golf club 5 during the golf swing based on the waggle data. Hereinafter, an algorithm for calculating the rotation center C will be described with reference to FIG.

  During the golf swing, the golfer 7 holds the grip 51 with the hand 71 and gives the golf club 5 a motion including rotation. As shown in FIG. 5, the motion of the golf club 5 during the waggle operation is mainly a rotational motion around the rotational center C, and almost no translational component is generated. The rotation center C is located in the vicinity of the gripping position on the grip 51 that the golfer 7 grips with the hand 71. During the waggle operation, the movement of the golf club 5 is minimized at the rotation center C. Therefore, in the present embodiment, the position where the movement is minimized in the golf club 5, more specifically, the position where the magnitude of acceleration is zero in the golf club 5 is calculated as the position of the rotation center C.

Here, the coordinate of an arbitrary point on the golf club 5 in the xyz local coordinate system is represented as h. Since the z axis of the xyz local coordinate system is defined along the longitudinal direction of the golf club 5, it can be expressed as h = (0, 0, h _z ). Further, h represents a relative position with respect to the grip end 51a that is the origin of the xyz local coordinate system, and the magnitude of h _z of the z component represents the distance from the grip end 51a to the rotation center C. At this time, the acceleration of the point of the coordinate h on the golf club 5 is expressed according to the following formula. However, a _s = (a _x , a _y , a _z ), ω _s = (ω _x , ω _y , ω _z ), and [G] is a coordinate transformation matrix from the xyz local coordinate system to the inertial coordinate system. It is. A tilde represents a tensor.

Then, the magnitude of the acceleration of Equation 26 is minimized, that is, zero when the following equation is satisfied.

The center calculating unit 14c calculates h by substituting the values of the acceleration a _s and the angular velocity ω _s included in the waggle data into the equation (27). Note that h can be calculated if there is a data set of acceleration a _s and angular velocity ω _s at one timing. However, in the present embodiment, from the viewpoint of improving accuracy, h is calculated for a data set of acceleration a _s and angular velocity ω _s at a plurality of timings during the waggle operation, and these are averaged. Alternatively, the equation on the left side of Equation 27 may be integrated during the waggle operation period to calculate h such that it becomes zero.

  A golf swing is configured by a complex combination of translational motion and rotational motion. In this embodiment, the influence of the translational motion is small, and by focusing attention on the data at the time of the motion mainly including the rotational motion, the translational motion and the rotational motion can be separated and the rotational center C of the rotational motion can be accurately derived. .

In subsequent step S5, the analysis unit 14b corrects the measurement data stored in the storage unit 23 based on the rotation center C. The measurement data to be corrected in the present embodiment is sensor data of accelerations a _x , a _y , and a _z from the address to the finish. Acceleration a _x in the grip end 51a that is measured by the inertial sensor unit 4, the a _y, a _z, since the position of the inertial sensor unit 4 is offset by a distance h _z from the rotation center C, around the rotation center C Rotation component is included. This rotational component is acceleration due to the influence of the angular velocity and angular acceleration generated at the position of the inertial sensor unit 4 with the rotation around the rotation center C. The analysis unit 14b calculates the rotational component (the second term on the left side of Equation 27) based on the rotational center C, and removes it from a _s , thereby correcting the corrected acceleration a _s ′ = in the grip end 51a. Data of (a _x ′, a _y ′, a _z ′) is calculated. Hereinafter, the corrected measurement data and sensor data in the grip end 51a in step S5 may be simply referred to as measurement data and sensor data.

FIG. 12 is a graph of the grip end trajectory derived by a simulation actually performed by the present inventors. More specifically, after converting the time series data of acceleration in the xyz local coordinate system into a value in the inertial coordinate system, the time series data of the converted acceleration is integrated twice, whereby a grip during a golf swing is obtained. Time series data representing the position of the end was calculated. The graph “before correction” in FIG. 12 is a graph of the locus of the grip end derived from the time series data of the acceleration a _s and the angular velocity ω _s without performing the correction in step S5, and the graph “after correction”. These are graphs of the grip end locus derived from the time series data of the acceleration a _s ′ and the angular velocity ω _s after the correction in step S5. In calculating the corrected graph, the rotation center C was calculated to be h _z = 19.15 cm. As can be seen by comparing these graphs, the graph before correction is jagged, and noise that seems to be due to angular velocity and angular acceleration is confirmed in the graph, but such noise is confirmed from the graph after correction. It can be seen that is removed.

In subsequent step S6, the analysis unit 14b calculates the posture of the grip 51 at each time during the swing based on the measurement data corrected in step S5. The posture of the grip 51 can be represented by the orientation of the object fixed coordinate system described above in the inertial coordinate system fixed to the ground. Therefore, in the present embodiment, as the posture of the grip 51, the above-described matrix [S], which is a posture matrix for converting the inertial coordinate system to the object fixed coordinate system, is derived.

The meanings of the nine components of the posture matrix [S] are as follows.
Component c1: Cosine of the angle formed by the first axis of the inertial coordinate system and the first axis of the object fixed coordinate system Component c2: The angle formed by the second axis of the inertial coordinate system and the first axis of the object fixed coordinate system C3 Component c3: Cosine of angle formed between the third axis of the inertial coordinate system and the first axis of the object fixed coordinate system Component c4: The first axis of the inertial coordinate system and the second axis of the object fixed coordinate system Cosine of angle formed component c5: cosine of angle formed between second axis of inertial coordinate system and second axis of object fixed coordinate system component c6: third axis of inertial coordinate system and second axis of object fixed coordinate system The cosine of the angle formed by the component c7: The cosine of the angle formed by the first axis of the inertial coordinate system and the third axis of the object fixed coordinate system Component c8: The second axis of the inertial coordinate system and the first axis of the object fixed coordinate system Cosine of angle formed by three axes Component c9: cosine of angle formed by third axis of inertial coordinate system and third axis of fixed object coordinate system (C1, c2, c3) represents a unit vector in the first axis direction of the object fixed coordinate system, and vector (c4, c5, c6) represents a unit vector in the second axis direction of the object fixed coordinate system, The vectors (c7, c8, c9) represent unit vectors in the third axis direction of the object fixed coordinate system.

  In step S6, the posture matrix [S] is calculated in time series at least in the period from the address to the impact. The attitude matrix [S] is calculated based on sensor data including time-series acceleration, angular velocity, and geomagnetism data. Note that various methods for deriving the posture matrix [S] representing the posture of the grip based on such sensor data are known, and thus detailed description is omitted here. It is possible to follow the methods described in Japanese Patent Application Laid-Open Nos. 2006-2429 and 2006-2430 by the applicants. In addition, it is possible to derive the attitude matrix [S] using only acceleration and angular velocity data out of the sensor data without using geomagnetic data. Detailed description is omitted. In the present embodiment, it is assumed that the xyz local coordinate system of the inertial sensor unit 4 is set to coincide with the object fixed coordinate system described above. However, the two coordinate systems do not have to coincide with each other. In that case, a transformation matrix for transforming the two coordinate systems may be determined in advance and held in the storage unit 13 and may be appropriately converted. Therefore, even if the xyz local coordinate system and the object fixed coordinate system are different, the two coordinate systems are substantially equivalent.

  As described above, the posture matrix [S] can be calculated only from the sensor data. However, in order to further improve the accuracy of the analysis, the posture matrix [S] is calculated with reference to the image data acquired in step S1. You can also Specifically, the acquisition unit 14a performs two-dimensional imaging in the inertial coordinate system of the attention point such as the grip end 51a or the shaft 52 to which the marker is attached by performing image processing on the time-series IR image acquired in step S1. Deriving coordinates. Subsequently, the depth coordinates of the point of interest are specified from the time-series depth image acquired in step S1. Thereby, the three-dimensional coordinates in the inertial coordinate system of the attention point are derived in time series. Then, the analysis unit 14b can derive an optimized posture matrix [S] by using various pieces of information included in the sensor data in addition to the position information of the attention point. For example, the posture matrix [S] is defined as an optimal solution that defines a predetermined objective function using the position information of the attention point of the golf club 5 and various information included in the sensor data, and minimizes or maximizes the objective function. Can be derived.

  In subsequent step S7, the analysis unit 14b, based on the measurement data corrected in step S5, the acceleration of the grip end 51a in the object fixed coordinate system at each time during the swing, the angular velocity of the grip 51 in the object fixed coordinate system, and Calculate angular acceleration. Specifically, the acceleration of the grip end 51a in the object fixed coordinate system is derived by canceling the gravity component from the output value of the acceleration sensor 41 corrected in step S5. The angular velocity of the grip 51 in the object fixed coordinate system matches the output value of the angular velocity sensor 42. The angular acceleration of the grip 51 in the object fixed coordinate system is calculated by differentiating the output value of the angular velocity sensor 42. The acceleration of the grip end 51a in the object fixed coordinate system and the values of the angular velocity and the angular acceleration in the object fixed coordinate system of the grip 51 are also calculated in time series at least in the period from the address to the impact.

  As described above, the acceleration in the object fixed coordinate system of the grip end 51a and the values of the angular velocity and the angular acceleration in the object fixed coordinate system of the grip 51 can be calculated from the sensor data alone, but the accuracy of the analysis is further improved. Accordingly, as in the case of the posture matrix [S], the optimum solution can be derived with reference to the image data acquired in step S1.

  In step S7, the analysis unit 14b derives three-dimensional coordinates in the inertial coordinate system of the grip end 51a at each time during the swing based on the measurement data corrected in step S5. Specifically, the analysis unit 14b converts the acceleration in the object fixed coordinate system of the grip end 51a into an inertial coordinate system value using the posture matrix [S], and integrates the converted acceleration twice. The three-dimensional coordinates in the inertial coordinate system of the grip end 51a are calculated in time series. That is, the trajectory of the grip end 51a is calculated. Further, as described above, the trajectory of the grip end 51a can be calculated based on the image data acquired in step S1.

In subsequent step S8, the analysis unit 14b inputs the posture matrix [S] calculated in steps S6 and S7, the acceleration of the grip end 51a, and the angular velocity and angular acceleration of the grip 51 into the equation 16 to thereby perform swing. The inertial force F _c at each time is calculated. The inertia force F _c is calculated in time series at least in the period from the address to the impact.

In step S9, the determination unit 14d (in this embodiment, the sensor data of omega _z) measurement data stored in the storage unit 23 to apply a band pass filter for passing only a predetermined frequency component. The predetermined frequency component here is a wave component in a predetermined frequency band in which a characteristic regarding the strength of the gripping force of the golfer 7 appears prominently. In this embodiment, the characteristic when the gripping force is weak is remarkable. Is a wave component in the 5-20 Hz band. For reference, in FIG. 8B, the waveform after application of the bandpass filter that passes the frequency component of 5 to 20 Hz is indicated by a broken line.

In step S10, the determination unit 14d (in this embodiment, the sensor data of omega _z) measurement data after passing through the band-pass filter in step S9 from the golf club 5 during the backswing (more precisely, a grip Time-series data representing the movement of the end 51a) is extracted. As can be seen from the results of the experiment described above, when the gripping force of the golfer 7 is weak, the waveform of the high frequency component appears remarkably in the time-series data during the backswing. Therefore, by cutting out the time-series data at the time of backswing in step S10, the strength of the gripping force can be determined more accurately in the subsequent analysis. Note that backswing refers to the movement from the address to the top, but as time series data at the time of back swing, time series data from a little before or after the address to a little before or slightly after the top is extracted. May be. It should be noted that the execution order of step S9 and step S10 can be reversed, that is, after sensor data during backswing is extracted, it can be passed through a bandpass filter.

  In subsequent step S11, the determination unit 14d performs frequency analysis on the time-series data extracted in step S10. More specifically, the time-series data extracted in step S10 is subjected to fast Fourier transform to derive a frequency spectrum. Then, by integrating this frequency spectrum, the magnitude D of the predetermined frequency component included in the time series data extracted in step S10 is specified. In addition, by passing through step S9, the integral value here becomes a value showing the magnitude | size of the component of the wave in the predetermined frequency band said at step S9.

  In subsequent step S12, the determination unit 14d determines the strength of the golfer's gripping force in accordance with the magnitude D of the predetermined frequency component specified in step S11. More specifically, since the predetermined frequency band in step S9 includes 7 to 10 Hz in which a difference in strength of gripping force tends to appear remarkably, the magnitude D (integrated value) indicates the strength of gripping force. It can be expressed accurately. Accordingly, the magnitude D of the predetermined frequency component is compared with a predetermined threshold, and if D is equal to or smaller than the predetermined threshold, it is determined that the gripping force is strong, and if it is larger than the predetermined threshold, it is determined that the gripping force is weak. To do. The threshold value used here is determined in advance through a number of experiments and is stored in the storage unit 23.

In step S13, the analysis unit 14b, by inputting an inertial force F _c which is calculated in step S8 to the number 25 expression, at each time during the swing, the deformation amount d _t due to the deflection of the grip 51 and the shaft 52 Is calculated. At this time, the analysis unit 14b determines spring constants k _x , k _y , k _z , and kθ _x representing the gripping conditions of the grip 51 by the golfer 7 according to the strength of the gripping force in step S12. Then, the analysis unit 14b substitutes the grip rigidity [K _G ] determined based on these spring constants into the formula 25. In this embodiment, the gripping force is strong, i.e., a more rigid holding state, the gripping force is weak, i.e., advance the spring constant k _x which corresponds to the more flexible gripping _{state, k y, k z, kθ} x respectively Appropriate spring constants k _x , k _y , k _z , and kθ _x are selected according to the result of step S12. The deformation amount _dt is calculated in time series at least in the period from the address to the impact.

In subsequent step S14, the analysis unit 14b derives the behavior of the head 53 based on the deformation amount d _t calculated in step S13. In this embodiment, the behavior of the head 53 includes the position of the center of gravity of the head 53 at each time during the swing, the speed of the head 53 immediately before the impact (hereinafter referred to as the head speed), the face angle, the approach angle, and the blow angle. Calculated. The position of the center of gravity of the head 53 is calculated in time series at least in the period from the address to the impact. That is, the trajectory of the center of gravity of the head 53 during the swing is calculated.

At the time of execution of step S14, the deformation amount _{dt and the} like at each node of the golf club 5 at each time during the swing are derived by the steps so far. Therefore, the analysis unit 14b derives the behavior of the final node on the shaft 52 at each time during the swing based on this information. Then, the positions of various attention points (including the center of gravity of the head 53) at each time during the swing are calculated from the behavior of the last node in the time series and the shape data of the head 53. The shape data of the head 53 is, for example, CAD data at the time of designing the head 53 and is stored in the storage unit 13 in advance. Then, the analysis unit 14 b derives the behavior of the head 53 as described above based on the positions of various attention points of the time-series head 53.

In subsequent step S15, the display control unit 14e displays the above analysis result on the display unit 11. The analysis result here is derived, for example, at the position of the grip end 51a in the inertial coordinate system at each time during the swing, the posture of the grip 51, the deformation amount d _t at each node of the shaft 52, and step S14. This is information on the behavior of the head 53. Further, as a result of analysis, as shown in FIGS. 13A and 13B, which will be described later, the path of the golf club 5 during a swing taking into account deformation can be displayed in a GUI.

<4. Modification>
As mentioned above, although one Embodiment of this invention was described, this invention is not limited to the said embodiment, A various change is possible unless it deviates from the meaning. For example, the following changes can be made. Moreover, the gist of the following modifications can be combined as appropriate.

<4-1>
In the above embodiment, the behavior of the golf club 5 during the swing is analyzed, but the above algorithm can also be applied to the analysis of other sports hitting tools such as a tennis racket and a baseball bat, It can also be applied to the analysis of non-sport use hitting tools.

<4-2>
The object whose behavior is measured by the measuring device 2 is not limited to the grip end 51a, and may be another part of the grip 51 or the shaft 52, for example. In the case of the shaft 52, it is preferable to measure the behavior of a portion of the shaft 52 near the grip 51. For example, the inertial sensor unit 4 can be attached to the shaft 52. According to the principle of the present invention, the behavior of various parts of the golf club 5 is measured by the measuring device 2, the deformation of the golf club 5 is analyzed based on the measurement data by the analyzing device 1, and based on the analysis result. The behavior of various other parts of the golf club 5 can be analyzed.

<4-3>
In the above embodiment, the inertial sensor unit 4 acquires measurement data for calculating the rotation center C (hereinafter referred to as first analysis data). However, the present invention is not limited to this example. For example, the measuring device 2 is constituted by one or a plurality of cameras (the distance image sensor 3 or another camera may be used), and such a camera. The movement of the hitting tool may be photographed by the above. In this case, the acquisition unit 14a performs image processing on the time-series data (that is, moving image data) of the image output from the measurement device 2, thereby obtaining, for example, the grip end position, velocity, acceleration, and angular velocity as the first analysis data. Data such as angular acceleration can be acquired. The first analysis data can also be acquired by combining the inertial sensor unit 4 and the camera.

<4-4>
In the above embodiment, the first analysis data is waggle data, but is not limited thereto. For example, the golf club 5 is caused to grip the golf club 5, and the golf club is swung while being aware that only the rotational motion is given without giving the translational motion. The sensor data at this time can be preferably used as the first analysis data.

<4-5>
In the above embodiment, the time series data representing the movement of the hitting tool, which is measurement data for analyzing the gripping state of the golfer 7 (hereinafter referred to as second analysis data), is acquired by the inertial sensor unit 4. However, the present invention is not limited to this example. For example, the measuring device 2 is constituted by one or a plurality of cameras (the distance image sensor 3 or another camera may be used), and such a camera. The movement of the hitting tool may be photographed by the above. In this case, the acquisition unit 14a performs image processing on the time-series data (that is, moving image data) of the image output from the measurement device 2, thereby obtaining, for example, the grip end position, acceleration, angular velocity, and the like as the second analysis data. Data can be acquired. Moreover, analysis data can also be acquired by combining the inertial sensor unit 4 and a camera.

Further, in the case of obtaining a second analysis data from the inertial sensor unit 4 also, instead of or in addition to the angular velocity omega _z, the angular velocity omega _x, omega _y and accelerations _{a x, a y, a z} , geomagnetic m _x, m Data such as _y and m _z can be used as the second analysis data.

<4-6>
In the embodiment described above, the magnitude D of the predetermined frequency component is specified by integrating the frequency spectrum in the predetermined frequency band. However, the magnitude D of the predetermined frequency component may be the maximum value of the spectral power in the predetermined frequency band, or may be the value of the spectral power of a specific frequency.

  Further, instead of or in addition to this, in the above-described embodiment, the size D of the predetermined frequency component is specified by passing the second analysis data through the band-pass filter. However, after analyzing the frequency of the second analysis data without passing through the bandpass filter, the magnitude D of the predetermined frequency component may be specified from the result.

<4-7>
In the above embodiment, the magnitude D of the predetermined frequency component is specified by performing frequency analysis. However, after passing the second analysis data through a band-pass filter that passes a predetermined frequency component of interest or a component other than the predetermined frequency component, this is compared with the wave of the original second analysis data, The degree of change of the wave and the wave after passing through the band-pass filter can be set to a predetermined frequency component magnitude D.

<4-8>
In step S5 of the above embodiment, the data of accelerations a _x , a _y , and a _z are corrected. Of course, instead of or in addition to this, the data of angular velocities ω _x , ω _y , and ω _z are corrected. You can also.

<4-9>
In the above-described embodiment, the strength of the gripping force is expressed in two levels of strong or weak. However, it can be determined in three or more levels, or can be determined numerically.

<Reference example>
A plurality of markers were attached to appropriate locations on the golf club, and the trajectory of the marker during the swing was measured by a motion capture system. In addition, a plurality of markers were attached to appropriate positions on the head, and the trajectories of these markers during the swing were measured by a motion capture system. The motion capture system here is a system consisting of a large number of cameras that enable highly accurate three-dimensional measurement. Then, from the above-described marker trajectories, the grip and shaft trajectories during the swing, the head speed immediately before the impact, the face angle, the approach angle, and the blow angle were calculated. Further, the trajectory of the head during the swing was calculated from the above marker trajectory and CAD data.

<Example>
The strength of the gripping force of the rotation center C and the golfer during the swing was calculated by a method similar to the method described in the above embodiment, and the trajectory of each node of the grip and the shaft was calculated based on these. Further, the position of the center of gravity of the head at each time during the swing, the head speed immediately before the impact, the face angle, the approach angle, and the blow angle were calculated by a method similar to the method described in the above embodiment.

<Verification>
FIG. 13A shows a golf club (and a golfer's arm) according to the reference example and the embodiment viewed from the front side of the golfer, and FIG. 13B shows the same track viewed from the right side. Yes. From these graphs, it can be seen that the trajectory of the example approximates the trajectory of the reference example in which the position of the point of interest is directly measured using a marker. Therefore, the high accuracy of the method according to the example was confirmed. By the way, normally, when the trajectory of the tip of the shaft is derived based on the grip measurement data, an error is likely to occur particularly in the vicinity of the impact. However, according to the present embodiment, as shown in a circle in FIG. 13B, there is almost no error even at the tip of the shaft near the impact. The golfer at this time was a golfer with strong gripping force, and the rotation center C was calculated to be about 19 cm from the grip end.

  14A to 14D are graphs showing the correlation among the head speed, the face angle, the approach angle, and the blow angle immediately before the impact according to the reference example and the example, respectively. As can be seen from the figure, the error of the embodiment with respect to the reference example is about ± 1.5 m / s for the head speed, about ± 1.5 deg for the face angle and the approach angle, and about ± 1.5 deg for the blow angle, It was very small. Also from this result, the results according to the example and the reference example are approximate, and the high accuracy of the method according to the example was confirmed.

DESCRIPTION OF SYMBOLS 1 Analysis apparatus 14a Acquisition part 14b Analysis part 14c Center calculation part 14d Determination part 2 Measuring apparatus 4 Inertial sensor unit 5 Golf club (hitting tool)
51 Grip 51a Grip end (first part)
52 Shaft 53 Head (second part)
6 Analysis program C Center of rotation F _c , F _(i) Inertial force d _t , d _(i) Deformation

Claims (14)

An analysis device for analyzing the behavior of a hitting tool having a property of deforming during a swing,
An acquisition unit for acquiring measurement data obtained by measuring the behavior of the first part included in the hitting tool during the swing;
Based on the measurement data, a center calculation unit that calculates the rotation center of the hitting tool during a swing,
An analysis apparatus comprising: an analysis unit that analyzes deformation of the hitting tool during a swing based on the measurement data and the rotation center. The analysis unit corrects the measurement data based on the rotation center, and analyzes the deformation of the hitting tool during a swing based on the corrected measurement data.
The analysis device according to claim 1. The acquisition unit acquires first measurement data that is the measurement data at a first timing, and acquires second measurement data that is the measurement data at a second timing;
The center calculation unit calculates the rotation center based on the first measurement data,
The analysis unit analyzes deformation of the hitting tool during a swing based on the second measurement data and the rotation center.
The analysis device according to claim 1 or 2. The center calculation unit is data included in the measurement data, the data measuring the behavior of the first part when the user of the hitting tool performs a waggle operation, and the user of the hitting tool Is based on at least one of the data obtained by measuring the behavior of the first part when the hitting tool is operated with the intention of giving only the rotary motion without giving a translational motion to the hitting tool. Calculate the center,
The analysis device according to claim 1. The center calculation unit calculates, based on the measurement data, a position where movement is minimized in the hitting tool as the rotation center,
The analysis device according to claim 1. A determination unit that determines a strength of a gripping force with which the user of the hitting tool holds the hitting tool based on the measurement data;
The analysis unit analyzes the deformation of the hitting tool during a swing based on the strength of the gripping force;
The analysis device according to claim 1. The determination unit specifies the magnitude of a predetermined frequency component included in the measurement data, and determines the strength of the gripping force according to the magnitude of the predetermined frequency component.
The analysis device according to claim 6. The acquisition unit acquires, as the measurement data, data measured by an inertial sensor attached to the first part.
The analysis device according to claim 1. The analysis unit derives a behavior of a second part different from the first part included in the hitting tool based on the deformation of the hitting tool.
The analysis device according to claim 1. The hitting tool is a golf club, the first part is a grip or a shaft, and the second part is a head.
The analysis device according to claim 9. The hitting tool is a golf club.
The analysis device according to claim 1. The analysis unit calculates an inertial force acting on the hitting tool based on the measurement data, and calculates a deformation amount of the hitting tool by a finite element method model based on the inertial force.
The analysis device according to claim 1. An analysis program for analyzing the behavior of a hitting tool having a property of deforming during a swing,
Obtaining measurement data obtained by measuring the behavior of the first part included in the hitting tool during the swing;
Calculating a center of rotation of the hitting tool during a swing based on the measurement data;
Analyzing the deformation of the hitting tool during a swing based on the measurement data and the rotation center;
Analysis program. An analysis method for analyzing the behavior of a hitting tool having a property of deforming during a swing,
Obtaining measurement data obtained by measuring the behavior of the first part included in the hitting tool during the swing;
Calculating a center of rotation of the hitting tool during a swing based on the measurement data;
Analyzing the deformation of the hitting tool during a swing based on the measurement data and the center of rotation.