JP6851038B2 - Analysis device for the behavior of hitting tools - Google Patents

Description

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

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

FIG. 1 shows an analysis model of Non-Patent Document 1. As shown in the figure, in this analytical model, it is assumed that the point of action of the inertial force acting on the golf club during the swing exists on the golf club as a rigid body without deformation.

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

However, in reality, since the shaft during the swing is bent, the point of action of the inertial force deviates from the position of the golf club as a rigid body without deformation (see FIG. 2). Therefore, the rotational torque, which is a twisting component, acts on the golf club due to the deviation due to the bending and the inertial force. However, in the analysis model of FIG. 1, such rotational torque is not taken into consideration, and an error occurs due to this, and as a result, the accuracy of analysis may decrease. This decrease in accuracy becomes remarkable especially when the amount of deflection is large. In FIGS. 1 and 2, the golf club shown by the solid line is a golf club as a rigid body without deformation, and the golf club shown by the dotted line is a golf club deformed by an inertial force.

An object of the present invention is to provide an analysis device, a method and a program capable of analyzing the behavior of a hitting tool with high accuracy by considering the rotational torque caused by the deformation of the hitting tool.

The analysis device according to the first aspect is an analysis device that analyzes the behavior of a hitting tool having a property of being deformed during a swing, and includes an acquisition unit and an analysis unit. The acquisition unit acquires measurement data that measures the behavior of the first portion included in the hitting tool during a swing. Based on the measurement data, the analysis unit analyzes the deformation of the hitting tool by using a model in consideration of the rotational torque acting on the hitting tool with the deformation of the hitting tool during the swing.

The analysis device according to the second viewpoint is the analysis device according to the first viewpoint, and the analysis unit uses the measurement data as a parameter to be input to the equation according to the model of the hitting tool during the swing. Calculate the posture.

The analysis device according to the third viewpoint is an analysis device according to the first viewpoint or the second viewpoint, and the analysis unit is performing a swing as a parameter input to an equation according to the model based on the measurement data. At least one of the acceleration, the angular velocity and the angular acceleration of the hitting tool is calculated.

The analysis device according to the fourth viewpoint is an analysis device according to any one of the first to third viewpoints, and the analysis unit includes the first one included in the hitting tool based on the deformation of the hitting tool. The behavior of the second part different from the part is derived.

The analysis device according to the fifth aspect is the analysis device according to the fourth aspect, and the behavior of the second part includes at least one of the angle, the speed, and the traveling direction of the second part.

The analysis device according to the sixth aspect is an analysis device according to the fourth or fifth aspect, the hitting tool is a golf club, the first part is a grip or a shaft, and the second part. Is the head.

The analysis device according to the seventh aspect is an analysis device according to any one of the first to sixth viewpoints, and the analysis unit includes an inertial force acting on the hitting tool, a rotational torque, and deformation of the hitting tool. The amount of deformation is calculated using an equation including a term representing the amount.

The analysis device according to the eighth viewpoint is an analysis device according to any one of the first to sixth viewpoints, and the analysis unit calculates the inertial force acting on the hitting tool based on the measurement data. By inputting the inertial force into the equation according to the model, the deformation amount of the hitting tool is calculated, the rotational torque is calculated based on the deformation amount, and the inertial force and the rotational torque are expressed in the equation. By re-entering, the amount of deformation is recalculated.

The analysis device according to the ninth viewpoint is an analysis device according to any one of the first to eighth viewpoints, and the model is a model in which the hitting tool is divided into minute elements according to the finite element method.

The analysis program according to the tenth aspect is an analysis program that analyzes the behavior of a striking tool having a property of deforming during a swing, and causes a computer to perform the following steps.
(1) A step of acquiring measurement data that measures the behavior of the first portion included in the hitting tool during a swing.
(2) A step of analyzing the deformation of the hitting tool by using a model considering the rotational torque acting on the hitting tool with the deformation of the hitting tool during the swing based on the measurement data.

The analysis method according to the eleventh aspect is an analysis method for analyzing the behavior of a striking tool having a property of deforming during a swing, and includes the following steps.
(1) A step of acquiring measurement data that measures the behavior of the first portion included in the hitting tool during a swing.
(2) A step of analyzing the deformation of the hitting tool by using a model considering the rotational torque acting on the hitting tool with the deformation of the hitting tool during the swing based on the measurement data.

According to the present invention, the behavior of a hitting tool having a property of deforming during a swing is analyzed based on the measurement data obtained by measuring the behavior of the first portion included in the hitting tool during the swing. At this time, the deformation of the hitting tool is analyzed by using a model considering the rotational torque acting on the hitting tool with the deformation of the hitting tool during the swing. Therefore, the behavior of the hitting tool can be analyzed with high accuracy in consideration of the rotational torque caused by the deformation of the hitting tool.

The figure which shows the analysis model of the golf club in swing which concerns on the prior art. The figure which shows the analysis model of the golf club in swing which concerns on this invention. The figure which shows the whole structure of the swing analysis system including the analysis apparatus which concerns on one Embodiment of this invention. Functional block diagram of the swing analysis system. (A) The figure which shows the address state. (B) The figure which shows the top state. (C) The figure which shows the impact state. (D) The figure which shows the finish state. A perspective view of a golf club. The figure which modeled the golf club according to the finite element method. The figure which modeled the golf club at the time of deformation. The figure which modeled the golf club at the time of deformation in consideration of the rotational torque. A flowchart showing the flow of analysis processing. A perspective view of a golf club according to a modified example. The figure which shows the position of the marker attached to the head which concerns on a reference example. The figure which shows the simulation result of the trajectory of the golf club seen from the front side of the golfer which concerns on a reference example and a comparative example. The figure which shows the simulation result of the trajectory of the golf club seen from the right side of the golfer which concerns on a reference example and a comparative example. The figure which shows the simulation result of the trajectory of the 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 trajectory of the golf club seen from the right side of the golfer 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 a comparative example. The figure which shows the analysis result of the approach angle which concerns on a reference example and a comparative example. The figure which shows the analysis result of the face angle which concerns on a reference example and a comparative example. The figure which shows the analysis result of the blow angle which concerns on a reference example and a comparative 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 approach angle 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 blow angle which concerns on a reference example and an Example.

Hereinafter, an embodiment when the analyzer, method, and program according to the present invention are applied to the 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>
3 and 4 show an overall configuration diagram of the swing analysis system 100 including the analysis device 1 according to the embodiment of the present invention. The swing analysis system 100 is configured to be suitable for the golfer 7 to analyze the behavior of the golf club 5 during a swing. The portion of the golf club 5 to be analyzed, particularly the shaft 52, has a property of being deformed during a swing. The analysis device 1 analyzes the deformation of the golf club 5 based on the measurement data obtained by measuring the behavior of the grip 51 portion of the golf club 5 during the swing, and based on the deformation of the golf club 5, the head 53 The behavior is also analyzed. The above measurement is performed by the measuring device 2, and the measuring 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 a golf club 5 suitable for the golfer 7, improvement of the form of the golfer 7, development of golf equipment, and the like.

Hereinafter, the configuration of each part of the swing analysis system 100 will be described, and then the 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, they will be described in order.

<2-1-1. Inertia sensor unit>
As shown in FIG. 3, the inertial sensor unit 4 is attached to the grip end 51a of the golf club 5 and measures the behavior of the grip end 51a. The inertial sensor unit 4 according to the present embodiment is detachably configured and can be attached to any golf club 5. The golf club 5 is a general golf club, and is composed of 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 inertial sensor unit 4 is compact and lightweight so as not to interfere with the swing operation. As shown in FIG. 4, the inertial sensor unit 4 according to the present embodiment is equipped with an acceleration sensor 41, an angular velocity sensor 42, and a geomagnetic sensor 43. Further, 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 an analysis device 1 via a communication line 17. .. In the present embodiment, the communication device 40 is wireless so as not to interfere with the swing operation, but it may be connected to the analysis device 1 by wire via a cable.

The acceleration sensor 41, the angular velocity sensor 42, and the geomagnetic sensor 43 measure the acceleration, the angular velocity, and the geomagnetism in the local coordinate system, respectively. More specifically, the acceleration sensor 41 measures acceleration in three axial directions in a local coordinate system with reference to a predetermined grip end 51a. The angular velocity sensor 42 also measures the angular velocity in the triaxial direction in the same local coordinate system, and the geomagnetic sensor 43 also measures the geomagnetism in the triaxial direction in the same local coordinate system. The sensor data (measurement data) relating to these accelerations, angular velocities, and geomagnetism are acquired as time-series data having a predetermined short sampling period, at least in the period from the address to the impact.

The golf swing generally proceeds in the order of address, top, impact, and finish. The address means a stationary state in which the head 53 of the golf club 5 is arranged near the ball as shown in FIG. 5 (A), and the top means the golf club 5 from the address as shown in FIG. 5 (B). It means a state in which the head 53 is swung up most after taking back. The impact means the state at the moment when the golf club 5 is swung down from the top and the head 53 collides with the ball as shown in FIG. 5 (C), and the finish means the state at the moment when the head 53 collides with the ball, and the finish means as shown in FIG. 5 (D). It means a state in which the golf club 5 is swung forward after the impact.

In the present embodiment, the 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, the sensor data may be stored in the 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 completed and passed to the analysis device 1.

<2-1-2. Distance image sensor>
The distance image sensor 21 is a camera having a distance measuring function of taking a two-dimensional image of the golfer 7 trying to hit the golf club 5 and measuring the distance to the subject. Therefore, the distance image sensor 21 can output a time-series depth image together with a time-series two-dimensional image. The two-dimensional image referred to here is an image obtained by projecting an image of the shooting space into a plane orthogonal to the optical axis of the camera. The depth image is an image in which the depth data of the subject in the optical axis direction of the camera is assigned to pixels within 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 in order 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). Further, the depth image can be 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. 4, the distance image sensor 21 has an IR light emitting unit 21a that emits infrared rays forward and an IR that receives infrared rays that are emitted from the IR light emitting unit 21a and reflected by the subject and returned. It has a light receiving unit 21b. The IR light receiving unit 21b is a camera having an optical system, an image sensor, and the like. In the dot pattern projection method, the infrared dot pattern emitted from the IR light emitting unit 21a is read by the IR light receiving unit 21b, the dot pattern is detected by image processing inside the distance image sensor 21, and the depth is calculated based on this. To. In the present embodiment, the IR light emitting unit 21a and the IR light receiving unit 21b are housed in the same housing 21f and arranged 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 has a built-in memory 21d that at least temporarily stores captured image data (measurement data). The control program that controls the operation of the distance image sensor 21 is stored in the memory 21d. Further, the distance image sensor 21 also has a built-in communication unit 21e, and the communication unit 21e transmits the captured image data to an external device such as an analysis device 1 via a wired or wireless communication line 17. Can be output to. 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 should be noted that the transfer of image data to the analysis device 1 does not necessarily have to be performed via the communication unit 21e. For example, if the memory 21d is removable, the image data can be 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 be done.

In the present embodiment, infrared imaging is performed by the distance image sensor 21, and the behavior of the grip 51 is analyzed based on the captured IR image. Therefore, a reflective sheet that efficiently reflects infrared rays is attached to the grip 51 (more accurately, the grip end 51a) as a marker so that the distance image sensor 21 can easily measure the grip 51. A similar infrared reflective sheet is also attached to the shaft 52 as a marker.

<2-2. Analyst>
The analysis device 1 is a general-purpose personal 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. 4, the analysis device 1 is manufactured by installing the analysis program 3 on 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. To. The analysis program 3 is software for analyzing the behavior of the golf club 5 during a swing based on the measurement data sent from the measuring device 2, and causes the analysis device 1 to execute the operation described later.

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 a bus line 16 and can communicate with each other. The display unit 11 can be configured by a liquid crystal display or the like, and displays the analysis result of the golf swing or the like to the user. The term "user" as used herein is a general term for golfers 7 themselves, their instructors, developers of golf equipment, and other persons who require analysis results of golf swings. The input unit 12 can be composed of a mouse, a keyboard, a touch panel, and the like, and receives an operation from the user on the analysis device 1.

The storage unit 13 can be configured by a hard disk or the like. In addition to storing the analysis program 3, the storage unit 13 stores the measurement data sent from the measuring device 2. The control unit 14 can be composed of a CPU, a ROM, a RAM, and the like. The control unit 14 virtually operates as the acquisition unit 14a, the analysis unit 14b, and the display control unit 14c by reading and executing the analysis program 3 in the storage unit 13. Details of the operation of each part 14a to 14c will be described later. The communication unit 15 functions as a communication interface for transmitting and receiving data to and from an external device such as the measuring device 2.

<3. Analysis method>
Next, the analysis method by the swing analysis system 100 will be described. In the following, first, the analysis model that is the basis of the analysis process will be described, and then 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, and the grip 51 and the shaft 52 are assumed to be multi-stage cylindrical beam elements, and the head 53 is assumed to be a rigid body. As shown in FIG. 7, the grip 51 and the shaft 52 are divided into a plurality of minute elements along the longitudinal direction. In this embodiment, the grip 51 is divided into 6 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 defined as a physical region, and the remaining region is defined as an elastic deformation region.

Here, as shown in FIG. 8, the i-th element from the grip end 51a side, which is the end opposite to the head 53 in the grip 51, is referred to as the i-th element (i = 1, 2, ... , 22). In FIG. 8 and FIG. 9 described later, the golf club 5 shown by a solid line is a golf club as a rigid body without deformation, and the golf club 5 shown by a dotted line is a golf club deformed by an inertial force. The inertial force referred to here is an inertial force acting 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-node, and the node on the head 53 side is called the (i + 1) node.

Further, a shaft coordinate system with the origin of the i-node of the golf club 5 at the time of no deformation is defined. The shaft coordinate system has x, y, and z axes, and the x axis is parallel to the axial direction of the shaft 52 and the direction from the grip end 51a side to the head 53 side is positive. The y-axis is substantially parallel to the toe-heel direction of the head 53, and the direction from the toe side to the heel side 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 to the flying ball direction is the positive direction. Further, a three-dimensional inertial coordinate system that is fixed to the ground and has the golf ball installation position as the origin and a three-dimensional object fixed coordinate system that has the grip end 51a as the origin are defined.

At this time, if each symbol is defined as in Equation 1, the equation in Equation 2 holds. In the present specification, T attached to the right shoulder of the symbol means a transposed vector.

また、ｄ_(i)は、以下のとおり定義される。ただし、ｘ，ｙ，ｚは、それぞれｘ軸、ｙ軸、ｚ軸方向の節点の変位を表し、θ_xは、ｘ軸回りの捩じり角、θ_y，θ_zは、それぞれｙ軸、Ｚ軸回りの撓み角を表す。右下の添え字（ｉ）及び（ｉ＋１）は、節点の番号を表す。

The virtual displacement caused by the deformation of the golf club 5 is expressed as follows.

Further, d _(i) is defined as follows. However, x, y, and z represent the displacement of the nodes in the x-axis, y-axis, and z-axis directions, respectively, θ _x is the twist angle around the x-axis, and θ _y and θ _z are the y-axis, respectively. Represents the deflection angle around the Z axis. The subscripts (i) and (i + 1) at the lower right represent the node numbers.

Based on the above equation and D'Alembert's principle, the following equation holds. In the present specification, the dot attached above the symbol means the derivative, and the two dots mean the derivative twice.

At this time, in order for the equation of Equation 5 to always hold, the following equation must hold.

Further, each term of the equation of Equation 6 is obtained as follows.

Substituting the equation of equation 7 into the equation of equation 6 gives the following equation.

Furthermore, considering the twist, the mass matrix [M] is derived from the kinetic energy and the rigidity matrix [K] is derived from the potential energy ("Takuzo Iwatsubo et al.," Basics of Vibration Engineering ", Morikita Publishing Co., Ltd., 2008, pp. 130-134 ”and“ Keiji Komatsu, “Limited 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.

Further, from the equation of Equation 9, the equation of motion of the grip 51 and the shaft 52 as a whole is expressed as follows. The subscript t at the lower right indicates that each matrix and vector are added by all elements.

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

The meanings of the symbols in the equations of numbers 11 and 12 are as follows. 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-damping system is expressed as follows. Note that 0 _i × _j is an i-row and j-column in which all elements are zero. F _c includes the inertial force, or more accurately, the nodal force, which is a translational component of the inertial force acting on each node, as well as the torque that contributes to the bending and twisting of the shaft 52.

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 columns i × j in [M _{c ], and K i} × _j is a matrix of columns i × j in [K _t ]. In particular, M ₉₀ × ₉₀ and K ₉₀ × ₉₀ are the mass matrix and the rigidity 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 of Equation 14 and Equation 18, the following equation is derived as the equation of motion of the entire system of the golf club 5.

The method for deriving each of the above equations and the meaning of each symbol are known techniques as described in Non-Patent Document 1. Therefore, although the meanings of each formula and each symbol have been briefly described above, Non-Patent Document 1 can be referred to in order to deepen the understanding.

In the present embodiment, in the equation of motion of Eq. 20, the rotational torque generated by the inertial force (nodal force) is further considered. The rotational torque is a twisting component that acts on the golf club 5 as the golf club 5 is deformed during the swing due to the inertial force.

Specifically, in the present embodiment, as shown in FIG. 9, the point of action of the inertial force (node force which is a translational component calculated from the inertial force) F _(i) acting on the i-node is deformed. Placed on golf club 5. In this case, a rotational torque T _(i) is generated at the i-node before deformation due to the deflection of the i-node (deflection amount d _{(i)). At this time, the virtual work performed by the inertial force F (i),} which is a translational component, is expressed as follows, _{where δθ (i)} is the virtual displacement of the i-node due to rotation.

At this time, the following equation is derived based on D'Alembert's principle. Comparing with the equation of Equation 5, it can be seen that the rotational torque is taken into consideration in the following equation.

ただし、Ｔ_cとは、回転トルクを表し、以下の式のとおり表される。

From the above, the equation of motion of the i-th element when the rotational torque is taken into consideration is as shown in the following equation.

However, T _c represents the rotational torque and is represented by the following equation.

The equation of equation 20 is the _{equation of motion of the golf club 5 that does not consider the rotational torque T c,} while the equation of equation 23 is the equation of motion of the golf club 5 that does not consider the rotational torque T _c . Therefore, the equation of Equation 23 includes a term representing the _{rotational torque T c} in addition to a term _{representing the inertial force F c} and a term representing the deformation amount _dt.

By the way, although the grip 51 is gripped by the golfer 7, it is not gripped as hard as the fixed end, but is gripped so as to move with a flexible hand movement. In the present embodiment, in order to express such a flexible gripping condition, as shown in FIG. 7, the grip 51 is modeled as a spring model and analysis is performed. Since the modeling method is a known technique as described in Non-Patent Document 1, detailed description thereof will be omitted here.

<3-2. Analysis process flow>
The analysis process proceeds according to the flowchart shown in FIG. First, in step S1, the golf club 5 is swung 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 included in the measuring device 2 acquires sensor data (measurement data) relating to acceleration, angular velocity, and geomagnetism in the three axial directions in the local coordinate system of the grip end 51a, and causes the communication device 40 to operate. It is transmitted to the analyzer 1 via. On the other hand, on the analysis device 1 side, the acquisition unit 14a receives this via the communication unit 15 and stores it in the storage unit 13. In this embodiment, at least time-series sensor data from the address to the impact is collected.

Further, in step S1, at the same time as the measurement by the inertial sensor unit 4, the distance image sensor 21 acquires image data (measurement data) capturing the swing of the golf club 5 from the front side of the golfer 7, and the communication unit. It is transmitted to the analyzer 1 via 21e. On the other hand, on the analysis device 1 side, the acquisition unit 14a receives this via the communication unit 15 and stores it in the storage unit 13. In this embodiment, at least time-series image data from the address to the impact is collected. That is, the image data acquired in step S1 is moving image data. The image data referred to here includes two time-series image data including an IR image and a depth image.

In the following step S2, the analysis unit 14b calculates the posture of the grip 51 at each time during the swing based on the measurement data acquired in step S1. The posture of the grip 51 can be represented by the orientation of the above-mentioned object fixed coordinate system in the above-mentioned inertial coordinate system fixed to the ground. Therefore, in the present embodiment, the above-mentioned matrix [S], which is a posture matrix for converting the inertial coordinate system into the object fixed coordinate system, is derived as the posture of the grip 51.

The meanings of the nine components of the posture matrix [S] are as follows.
Component c1: Cosine of the angle between the first axis of the inertial coordinate system and the first axis of the object fixed coordinate system Component c2: Angle formed by the second axis of the inertial coordinate system and the first axis of the object fixed coordinate system Cosine component c3: Cosine of the angle formed by the third axis of the inertial coordinate system and the first axis of the object fixed coordinate system C4: The first axis of the inertial coordinate system and the second axis of the object fixed coordinate system Cosine component of the angle formed c5: The cosine component of the angle formed by the second axis of the inertial coordinate system and the second axis of the object fixed coordinate system c6: The third axis of the inertial coordinate system and the second axis of the object fixed coordinate system Cosine component of the angle formed by c7: The cosine component of the angle formed by the first axis of the inertial coordinate system and the third axis of the object fixed coordinate system c8: The second axis of the inertial coordinate system and the third axis of the object fixed coordinate system Cosine of the angle formed by the three axes Component c9: Cosine of the angle formed by the third axis of the inertial coordinate system and the third axis of the object fixed coordinate system Here, the vectors (c1, c2, c3) are the object fixed coordinates. The unit vector in the first axis direction of the system is represented, the vector (c4, c5, c6) represents the unit vector in the second axis direction of the object fixed coordinate system, and the vector (c7, c8, c9) is the object fixed coordinate. It represents the unit vector in the third axis direction of the system.

In step S2, the attitude 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 the sensor data acquired in step S1, that is, sensor data including time-series acceleration, angular velocity, and geomagnetic data. Since various methods for deriving the posture matrix [S] representing the posture of the grip based on the sensor data output from the inertial sensor unit mounted on the grip 51 are known, detailed explanations will be given here. Although omitted, if necessary, the methods described in JP-A-2016-2429, JP-A-2016-2430, and the like by the same applicants can be followed. It is also possible to derive the attitude matrix [S] using only the acceleration and angular velocity data among the sensor data without using the geomagnetic data, but since various such methods are known, here, A detailed description will be omitted. In the present embodiment, it is assumed that the local coordinate system of the inertial sensor unit 4 is set to match the above-mentioned fixed object coordinate system. However, both coordinate systems do not have to match, but in that case, a conversion matrix for converting both coordinate systems may be determined in advance, stored in the storage unit 13, and appropriately converted. Therefore, even if the local coordinate system and the fixed object coordinate system are different, both coordinate systems are substantially equivalent.

As described above, the attitude matrix [S] can be calculated only from the sensor data, but in order to further improve the accuracy of the analysis, the attitude matrix [S] is calculated with reference to the image data acquired in step S1. You can also do it. Specifically, the analysis unit 14b performs image processing on the time-series IR image acquired in step S1 to perform two-dimensional image processing in the inertial coordinate system of the point of interest such as the grip end 51a with the marker and the shaft 52. Derived the coordinates. Subsequently, the coordinates of the depth of the point of interest are specified from the time-series depth image acquired in step S1. As a result, the three-dimensional coordinates in the inertial coordinate system of the point of interest are derived in time series. Then, the analysis unit 14b can derive an optimized posture matrix [S] by using various information included in the sensor data in addition to such position information of the point of interest. For example, a posture matrix [S] is used as an optimum solution for defining a predetermined objective function using the position information of the point of interest of the golf club 5 and various information included in the sensor data and minimizing or maximizing the predetermined objective function. Can be derived.

In the following step S3, the analysis unit 14b determines the acceleration in the object fixed coordinate system of the grip end 51a at each time during the swing, and the angular velocity and the angular velocity of the grip 51 in the object fixed coordinate system based on the measurement data acquired in step S1. Calculate the angular acceleration. Specifically, the acceleration of the grip end 51a in the fixed object coordinate system is derived by canceling the gravity component from the output value of the acceleration sensor 41 acquired in step S1. The angular velocity of the grip 51 in the fixed object coordinate system matches the output value of the angular velocity sensor 42. The angular acceleration of the grip 51 in the fixed object coordinate system is calculated by differentiating the output value of the angular velocity sensor 42. The acceleration of the grip end 51a in the fixed object coordinate system, and the angular velocity and angular acceleration values of the grip 51 in the fixed object coordinate system are also calculated in time series at least in the period from the address to the impact.

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

Further, in step S3, 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 acquired in step S1. Specifically, the analysis unit 14b converts the acceleration of the grip end 51a in the fixed object coordinate system into a value in the inertial coordinate system using the attitude 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, the trajectory of the grip end 51a can also be calculated based on the image data acquired in step S1 as described above.

In the following step S4, the analysis unit 14b inputs the posture matrix [S] calculated in steps S2 and S3, the acceleration of the grip end 51a, and the angular velocity and the angular acceleration of the grip 51 into the equation of equation 16, thereby swinging. Calculate the _{inertial force F c} at each time in the middle. The inertial force F _c is calculated in chronological order at least in the period from address to impact.

In the following step S5, the analysis unit 14b _{inputs the inertial force F c calculated in step S4 into the equation of Eq. 20, so that the amount of deformation dt} due to the bending of the grip 51 and the shaft 52 at each time during the swing. The first deformation amount is calculated. The first deformation amount _dt is calculated in chronological order at least in the period from the address to the impact.

In the following step S6, the analysis unit 14b adds the posture matrix [S] calculated in steps S2 and S3, the acceleration of the grip end 51a, and the angular velocity and the angular acceleration of the grip 51, and the first deformation calculated in step S5. By inputting the quantity d _t into the equation of equation 24, the rotational torque T _c at each time during the swing is calculated. The rotational torque T _c is calculated in chronological order at least in the period from the address to the impact.

In the following step S7, the analysis unit 14b _{inputs the inertial force F c} and the rotational torque T _c calculated in steps S4 and S6 into the equation of equation 23, so that the amount of deformation due to the bending of the grip 51 and the shaft 52 _dt Is recalculated as the second deformation amount. The second deformation amount _dt is calculated at each time during the swing, and is calculated in chronological order at least in the period from the address to the impact.

Here, the equation of equation 23 is obtained by adding the _{rotational torque T c} to the right side of the equation of equation 20. That is, it can be said that step S7 is a step in which the value is re-entered as _{F c} = F _c + T _{c in} the equation of Eq. 20.

In the following step S8, the analysis unit 14b derives the behavior of the head 53 based on _{the second deformation amount dt calculated in step S7.} In the present 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 chronological order 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 executing step S8, the second 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, from the behavior of the final node in this time series and the data of the shape of the head 53, the positions of various points of interest (including the center of gravity of the head 53) of the head 53 at each time during the swing are calculated. The shape data of the head 53 is, for example, CAD data at the time of designing the head 53, and is assumed to be stored in advance in the storage unit 13. Then, the analysis unit 14b derives the behavior of the head 53 as described above based on the positions of various points of interest of the head 53 in these time series.

In the following step S9, the display control unit 14c displays the above analysis result on the display unit 11. The analysis results referred to here are, for example, 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 second deformation amount _dt at each node of the shaft 52, and step S8. It is the information of the behavior of the derived head 53. Further, as an analysis result, it is possible to display the trajectory of the golf club 5 during the swing in consideration of the deformation by GUI as shown in FIGS. 14A and 14B described later.

<4. Modification example>
Although one embodiment of the present invention has been described above, the present invention is not limited to the above embodiment, and various modifications can be made without departing from the spirit of the present invention. For example, the following changes can be made. In addition, the gist of the following modified examples can be combined as appropriate.

<4-1>
The target whose behavior is measured by the measuring device 2 is not limited to the grip 51, and may be, for example, the shaft 52. However, in this case, it is preferable to measure the behavior of the portion of the shaft 52 near the grip 51. For example, the inertial sensor unit 4 can be attached to the shaft 52. Further, 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 by the analysis device 1 based on the measurement data, and the analysis result is obtained. Based on this, the behavior of various other parts of the golf club 5 can be further analyzed.

<4-2>
The configuration of the measuring device 2 is not limited to the above-mentioned example, and for example, a motion capture system including a plurality of cameras can be used as the measuring device 2. In this case, the above steps S2 to S7 can be executed based on the image data (measurement data) acquired from the motion capture system. Further, in this case, it is preferable to attach the jig 50 as shown in FIG. 11 to the golf club 5.

In FIG. 11, the jig 50 is attached to the grip 51 near the end on the head 53 side. The jig 50 includes two rod-shaped or beam-shaped protrusions 54, 55 that protrude from the grip 51 and extend orthogonally to the extending direction of the shaft 52. Further, the protrusion 54 and the protrusion 55 are substantially orthogonal to each other. Sphere-shaped markers 54a and 55a are attached to the tips of the protrusions 54 and 55, respectively, and spherical markers 54b are also attached to the position at the base of the protrusion 54 and the position opposite to the shaft 52. It is attached. Further, a spherical marker 54c is attached to the tip end of the shaft 52. These markers 54a to 54c, 55a are markers that facilitate tracking by the measuring device 2 and are configured to efficiently reflect light. Then, the analysis unit 14b extracts the images of these markers 54a to 54c and 55a appearing in the plurality of captured images, and based on the principle of triangulation and the like, the third order of the markers 54a to 54c and 55a in the inertial coordinate system. Derived the original coordinates. Subsequently, the posture of the grip 51 is derived based on the three-dimensional coordinates in the inertial coordinate system of the markers 54a, 54b, 55a. Then, from the posture of the grip 51, the angular velocity of the grip 51 in the fixed object coordinate system and the angular acceleration obtained by differentiating the angular velocity are derived. Further, since the positional relationship between the jig 50 and the grip end 51a is known, the inertial coordinate system of the grip end 51a is based on the positional relationship and the three-dimensional coordinates in the inertial coordinate system of the markers 54a, 54b, 55a. Derived the three-dimensional coordinates in. Then, based on the posture of the grip 51, the three-dimensional coordinates in the inertial coordinate system of the grip end 51a are converted into the values of the object fixed coordinate system, and then the object fixed coordinates of the grip end 51a are converted based on the converted three-dimensional coordinates. Derivation of acceleration in the system. Subsequent processing proceeds in the same manner as in the above embodiment.

<Reference example>
A jig similar to that shown in FIG. 11 was attached to the golf club, and the trajectory of the marker of the jig was measured by a motion capture system. Further, as shown in FIG. 12, markers are affixed to the positions near the face surface on the crown portion of the head, near the end on the toe side and near the end on the heel side, and these are affixed by a motion capture system. The orbit of the marker was measured. The motion capture system referred to here is a system composed of a plurality of cameras that enable the three-dimensional measurement described in the modified example 4-2. Then, from the trajectories of the above markers, the trajectories of the grip and shaft during the swing, and the head speed, face angle, approach angle, and blow angle immediately before the impact were calculated. Further, the trajectory of the head during the swing was calculated from the trajectory of the above markers and the CAD data.

<Comparison example>
_{The first deformation amount dt} during the swing is calculated by the same method as the method described in the above embodiment, and the first deformation amount _{dt is used instead of the second deformation amount dt} , and the grip and the grip considering the deformation are used. The trajectory of each node of the shaft was calculated. Further, based on the position of the final node derived in this way, 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, and the approach are performed by the same method as that described in the above embodiment. The angle and blow angle were calculated. Here, the position corresponding to the position of the marker on the crown portion of the head described in the reference example is specified from the position of the center of gravity of the head and the CAD data of the head, and based on these positions, the head speed immediately before the impact , Face angle, approach angle and blow angle were calculated. In this comparative example, the posture of the grip during the swing, the acceleration in the fixed object coordinate system of the grip end, and the angular velocity and the angular acceleration in the fixed object coordinate system of the grip are not the distance image sensor and the inertial sensor unit, but the reference example and the deformation. It was calculated based on the measurement data measured by the same motion capture system as in Example 4-2.
<Example>

_{The second deformation amount dt} during the swing is calculated by the same method as the method described in the above embodiment, and the trajectory of each node of the grip and the shaft considering the deformation is calculated based on the second deformation amount _dt. did. Further, the position of the center of gravity of the head at each time during the swing, and the head speed, face angle, approach angle and blow angle immediately before the impact were calculated by the same method as that described in the above embodiment. Here, the position corresponding to the position of the marker on the crown portion of the head described in the reference example is specified from the position of the center of gravity of the head and the CAD data of the head, and based on these positions, the head speed immediately before the impact , Face angle, approach angle and blow angle were calculated. In this embodiment, the posture of the grip during the swing, the acceleration in the fixed object coordinate system of the grip end, and the angular velocity and the angular acceleration in the fixed object coordinate system of the grip are not the distance image sensor and the inertial sensor unit, but the reference example and the deformation. It was calculated based on the measurement data measured by the same motion capture system as in Example 4-2.

<Verification>
FIG. 13A shows a state in which the track of the golf club according to the reference example and the comparative example is viewed from the front side of the golfer, and FIG. 13B shows a state in which the track is viewed from the right side. Further, FIG. 14A shows a state in which the trajectory of the golf club (and the golfer's arm) according to the reference example and the embodiment is viewed from the front side of the golfer, and FIG. 14B shows a state in which the trajectory is viewed from the right side. Shown. From these figures, it can be seen that the orbit of the example is closer to the orbit of the reference example than the orbit of the comparative example. Therefore, the high accuracy of the method according to the embodiment was confirmed. Further, paying particular attention to the trajectory of the tip of the shaft near the impact circled in FIGS. 13B and 14B, it can be seen that the accuracy of the analysis is significantly improved in the examples as compared with the comparative example.

15A to 15D are graphs showing the correlation between the head speed, face angle, approach angle and blow angle immediately before impact according to the reference example and the comparative example, respectively, and FIGS. 16A to 16D are reference examples, respectively. It is a graph which shows the correlation of the head speed, the face angle, the approach angle and the blow angle just before the impact which concerns on an Example and an Example. From this result, it can be seen that the results of the examples and the reference examples are similar, especially with respect to the face angle, and the accuracy of the analysis is greatly improved.

1 Analytical device 14a Acquisition unit 14b Analytical unit 2 Measuring device 5 Golf club (striking tool)
51 Grip (1st part)
52 Shaft 53 Head (2nd part)
F _c , F _(i) Inertial force T _c , T _(i) Rotational torque d _t , d _(i) Deformation amount

Claims (11)

It is an analysis device that has the property of deforming during a swing and analyzes the behavior of a striking tool equipped with a grip and a shaft.
An acquisition unit that acquires measurement data that measures the behavior of the first portion, which is at least one of the grip and the shaft, during a swing, and an acquisition unit.
Based on the measurement data, it is provided with an analysis unit that analyzes the deformation of the shaft by using a model that considers the rotational torque acting on the shaft with the deformation of the shaft during the swing.
The analysis unit calculates the inertial force acting on the shaft based on the measurement data, calculates the rotational torque based on the inertial force, and calculates the rotational torque based on the inertial force and the rotational torque. Calculate the amount of deformation of
Analyst. Based on the measurement data, the analysis unit calculates the posture of the hitting tool during the swing as a parameter input to the equation according to the model.
The analyzer according to claim 1. Based on the measurement data, the analysis unit calculates at least one of the acceleration, the angular velocity, and the angular acceleration of the hitting tool during the swing as parameters input to the equation according to the model.
The analyzer according to claim 1 or 2. Based on the deformation of the shaft, the analysis unit derives the behavior of the second portion contained in the hitting tool, which is different from the first portion.
The analyzer according to any one of claims 1 to 3. The behavior of the second part includes at least one of the angle, speed and direction of travel of the second part.
The analyzer according to claim 4. The hitting tool is a golf club, and the second portion is a head.
The analyzer according to claim 4 or 5. The analysis unit calculates the deformation amount by using an equation including a term representing the inertial force, the rotational torque, and the deformation amount.
The analyzer according to any one of claims 1 to 6. The analysis unit calculates the deformation amount by inputting the inertial force into an equation according to the model, calculates the rotational torque based on the deformation amount, and calculates the inertial force and the rotational torque into the equation. By re-entering in, the amount of deformation is recalculated.
The analyzer according to any one of claims 1 to 6. The model is a model in which the hitting tool is divided into minute elements according to the finite element method.
The analyzer according to any one of claims 1 to 8. It is an analysis program that analyzes the behavior of a striking tool equipped with a grip and a shaft while having the property of deforming during a swing.
A step of acquiring measurement data for measuring the behavior of the first portion, which is at least one of the grip and the shaft, during a swing, and
Based on the measurement data, a computer is made to perform a step of analyzing the deformation of the shaft by using a model considering the rotational torque acting on the shaft with the deformation of the shaft during the swing.
In the step to analyze, the inertial force acting on the shaft is calculated based on the measurement data, the rotational torque is calculated based on the inertial force, and the rotational torque is calculated based on the inertial force and the rotational torque. Including the step of calculating the amount of deformation of the shaft,
Analysis program. It is an analysis method that has the property of deforming during a swing and analyzes the behavior of a striking tool equipped with a grip and a shaft.
A step of acquiring measurement data for measuring the behavior of the first portion, which is at least one of the grip and the shaft, during a swing, and
Including a step of analyzing the deformation of the shaft by using a model considering the rotational torque acting on the shaft with the deformation of the shaft during the swing based on the measurement data.
In the step to analyze, the inertial force acting on the shaft is calculated based on the measurement data, the rotational torque is calculated based on the inertial force, and the rotational torque is calculated based on the inertial force and the rotational torque. Including the step of calculating the amount of deformation of the shaft,
analysis method.

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