KR20160099503A - Motion analysis method, motion analysis apparatus, and storage device - Google Patents

Abstract

A motion analysis method comprises: an impact analysis unit for specifying an angle of inclination with respect to a vertical plane of a hitting surface of a motion tool during an impact, by using the output of an inertia sensor; and a divided level analysis unit for specifying a divided level (3) of the angle of inclination with a reference angle of inclination obtained before the impact. According to the present invention, the angle of a batting surface of the motion tool in contact to a bat can be estimated during the impact.

Description

TECHNICAL FIELD [0001] The present invention relates to a motion analyzing method, a motion analyzing apparatus,

The present invention relates to a motion analysis method, an apparatus therefor, a motion analysis program, and the like.

Patent Document 1 proposes a device for mounting a three-axis acceleration sensor and a three-axis gyro sensor on a golf club and analyzing the swing using the output of these sensors. When this device is used, a camera is unnecessarily And convenience is improved.

However, when using a golf putter, especially a golf club, directionality and sense of distance are most important for making a cup in (hole in).

However, even if both the directionality and the sense of distance are accurate, duffing or swing of the upper-blow, which is caused by the rotation of the ball or the down-blow swing, Even in other phenomena such as topping, there are a lot of things not to be cupped.

In the case of golf clubs other than the putter, the dipping or topping is a cause that the ball does not hit as intended, while a suitable down blow is recommended for the iron, and a suitable upper blow is recommended for the driver.

There is also a scene where the ball is intentionally hit low or high.

Patent Document 1: JP-A-2008-73210

However, there has been a problem in that, in the motion analyzing apparatus using the inertial sensor, the inclination angle of the striking surface of the moving ball can not be estimated at the time of impact.

It is an object of the present invention to provide a motion analyzing method, an apparatus therefor, and a motion analyzing program for estimating an angle at which a striking surface of a running ball touches a hit ball at the time of impact.

(1) One embodiment of the present invention relates to a motion analysis method for specifying a difference between an inclination angle of a striking surface of a moving ball at the time of impact and a reference inclination angle acquired in advance, using the output of the inertia sensor will be.

According to one aspect of the present invention, the difference between the inclination angle of the striking surface of the moving ball and the reference inclination angle with respect to the virtual vertical plane at the time of impact is specified. Thereby, the angle at which the striking surface of the operating bulb touches the batted ball during impact can be obtained with high reproducibility, and the angle can be intentionally controlled to control the batting ball or to reduce the number of batting mistakes.

(2) In one embodiment of the present invention, the moving ball is a golf club, and the reference inclination angle may be a standard value which is a loft angle of the club club. The loft angle is the angle between the striking face (face) and the plane perpendicular to the ground when the sole (bottom) of the club head is grounded to a flat ground. If the difference is small, the impact is made in a state close to the standard value of the loft angle. If the difference is large, the impact is made in a state in which the loft angle is largely deviated from the standard value. In the case of a putter, the rotation of the batted ball is better when the ball hit the loft angle, which is a standard value, and it is easy to achieve the intended distance. On the other hand, for example, when the ball is lowered by the iron club, the face surface is closed so that the loft angle is small, or when the ball in the bunker is sandwiched by the sand wedge, the face angle is intentionally opened, . In this manner, the method of the present invention can be used in preparation for a scene in which the loft angle is changed as intended.

(3) In one aspect of the present invention, the reference inclination angle may be specified using the output of the inertial sensor when the moving ball is stationary. In this way, for example, in the case of a golf club, it is possible to verify whether or not the loft angle set at the time of addressing (at the time of stop) can be reproduced even at the time of impact by evaluating the above-described difference.

(4) In one aspect of the present invention, the inclination angle of the striking surface and the reference inclination angle can be displayed in the coordinate system. By doing so, the difference between them can be visually recognized by the reference inclination angle and the inclination angle indicated in the coordinate system.

(5) In an aspect of the present invention, an image of the moving ball may be superimposed and displayed on the coordinate system in a front view (a front view) facing the user who operates the moving ball. In this way, the angle of the striking surface can be visually recognized from the image superimposed on the coordinate system.

(6) In an embodiment of the present invention, the image of the moving ball is displayed on a constant position on the display screen, and the display position of the reference inclination angle can be rotated by the same angle as the difference. Thereby, an image of a relatively complicated shape is fixed on the screen, and then the coordinate system fixed as the background can be rotated by the same angle as the difference, so that there is an advantage that the display image control is not complicated.

(7) In an aspect of the present invention, the inclination angle of the striking face specified in the past may be displayed in the coordinate system by distinguishing it from the inclination angle of the striking face specified this time. By doing so, it is possible to visually recognize the effect of the exercise in the case of performing the repetitive motion.

(8) In an aspect of the present invention, the target area including the reference inclination angle can be distinguished from other areas and displayed. In this way, when aiming at a reference inclination angle at the time of impact, the target becomes a zone instead of a line, so that the goal achievement rate increases and becomes psychologically comfortable, so that the exercise practice effect can be improved .

(9) In one aspect of the present invention, the ratio of the number of times the inclination angle of the impact surface enters the target area with respect to the number of times of the specified inclination angle of the impact surface. By doing so, the target achievement rate can be recognized as a numerical value, and the exercise practice effect can be notified quantitatively.

(10) According to another aspect of the present invention, there is provided a tangential direction of a moving locus projected on a vertical surface by using an output of an inertial sensor, wherein a tangential direction at impact is specified, And a motion analysis method for specifying an intersection angle of the motion.

According to another aspect of the present invention, the intersection angle between the tangential direction at impact and the target direction projected on the vertical plane is specified for the movement trajectory of the moving ball projected on the vertical plane. Thereby, it is possible to reproduce an angle (an incidence angle such as an upper blow or a down blow) at which the impact surface of the operation mouth enters the hit ball at the time of impact, and the intentionally control the angle to control the hit or reduce the shot error can do. Also, in another embodiment of the present invention, the same forms as the above-mentioned (3) to (9) can be applied. In particular, when the form (5) is applied, an image of the moving ball can be displayed at a plurality of positions along the movement trajectory before the impact. This makes it easier to visually recognize the locus of the upper blow or down blow.

(11) According to another aspect of the present invention, there is provided an impact analysis apparatus comprising: an impact analyzing section for specifying an inclination angle of a striking surface of a moving orifice at the time of impact using an output of an inertia sensor; And a difference analyzing section for specifying a difference between the reference value and the reference value. According to still another aspect of the present invention, a motion analysis method (1) according to an aspect of the present invention can be preferably performed.

(12) According to another aspect of the present invention, there is provided an impact analyzing apparatus comprising: an impact analyzing unit that uses an output of an inertial sensor to specify a tangential direction at the time of impact with respect to a moving locus of a moving ball projected on a vertical plane; And a crossing angle analyzing unit for specifying an intersecting angle with the tangential direction. According to another aspect of the present invention, the motion analysis method (10) according to an aspect of the present invention can be preferably implemented.

(13) According to still another aspect of the present invention, there is provided a method of detecting an impact, comprising the steps of: specifying an inclination angle of a striking surface of a moving orifice at the time of impact using an output of an inertia sensor; And a memory for storing a motion analysis program for causing a computer to execute an order of specifying the motion analysis program.

(14) According to still another aspect of the present invention, there is provided an image processing method comprising the steps of: specifying the tangential direction at the time of impact with respect to the movement trajectory of a moving ball projected on a vertical surface using an output of an inertial sensor; And a memory for storing a motion analysis program for causing a computer to execute an order of specifying an intersecting angle with the tangential direction.

These programs can be installed in the memory of the motion analyzing apparatus in which the method of the present invention is implemented, or can be installed in the memory of the motion analyzing apparatus from the server or the storage medium.

According to the present invention, it is possible to estimate the angle at which the striking surface of the kicking hole touches the batted ball during impact.

1 is a conceptual diagram schematically showing a configuration of a golf swing analysis apparatus according to an embodiment of the present invention.
2 is a block diagram schematically showing a configuration of an arithmetic processing circuit according to an embodiment of the present invention.
Fig. 3A shows the first shift angle 1 (absolute face angle), Fig. 3B shows the second shift angle 2 (square degree) 3 (C) is a diagram showing the shift amount delta from the hit point, respectively.
4A shows the third shift angle 3 (delta-loft angle) and the impact speed V and FIG. 4B shows the fourth shift angle 4 (Attack angle)), and FIG. 4 (C) is a view showing the swing width L, respectively.
5 is a diagram showing an initial screen of an analysis screen.
Fig. 6 is a view showing an analysis screen after " Direction " is selected in Fig. 5. Fig.
FIG. 7 is a view showing an analysis screen after "FACE" is selected in FIG. 6
Fig. 8 is a view showing an analysis screen after " Histogram " is selected in Fig. 5 or Fig.
Fig. 9 is a diagram showing an analysis screen after " SQUARE " is selected in Figs. 6 to 8. Fig.
10 is a view showing an analysis screen after "Histogram" is selected in FIG.
Fig. 11 is a view of a display screen showing a shift amount of a hit position from a sweet spot. Fig.
FIG. 12 is a view showing an analysis screen after "Stroke" is selected in FIG. 5; FIG.
13 is a view showing an analysis screen after " SPAN-BACK " is selected in Fig.
Fig. 14 is a view showing an analysis screen after " Histogram " is selected in Fig. 12 or Fig.
Fig. 15 is a view showing an analysis screen after " SPEED " is selected in Figs. 12 to 14. Fig.
16 is a view showing an analysis screen after " Histogram " is selected in Fig.
17 is a view showing an analysis screen after " Rising " is selected in Fig.
18 is a view showing an analysis screen after " DELTA-LOFT " is selected in Fig.
Fig. 19 is a view showing an analysis screen after "Histogram" is selected in Fig. 17 or Fig.
20 is a view showing an analysis screen after " ATTACK " is selected in Figs. 17 to 19. Fig.
21 is a view showing an analysis screen after " Histogram " is selected in Fig.
22 is a flowchart for explaining the operation of detecting the posture on the swing locus.
23 is a view for explaining the first and second measurement points set apart in the horizontal direction on the face of the club head.
Fig. 24 is a diagram for explaining the first shift angle? 1 (absolute face angle) and the second shift angle? 2 (square degree).
25 is a diagram schematically showing a cup in (hole in) ratio in a cup unit.
26 is a diagram showing the correlation between the angular velocity (angular velocity) around the shaft longitudinal axis and the RB measurement value.
FIG. 27 is a diagram showing relational expressions obtained from the data shown in FIG. 26; FIG.
28 is a diagram showing a display example of projecting the swing width of the back swing on the projection plane
29 is a view for explaining the first and second measurement points set apart in the vertical direction on the face surface of the club head.
Fig. 30 is a view for explaining the third shift angle? 3 (delta-loft angle) and the fourth shift angle? 4 (attack angle).

Hereinafter, an embodiment of the present invention will be described with reference to the accompanying drawings. It should be noted that the present embodiment described below does not unduly limit the contents of the present invention described in claims, and it is not necessary that all of the configurations described in this embodiment are necessary as means for solving the present invention.

(1) Configuration of golf club interpretation device

1 schematically shows a configuration of a golf swing analysis apparatus (motion analysis apparatus) 11 according to an embodiment of the present invention. The golf swing analysis device 11 includes an inertial sensor 12, for example. The inertial sensor 12 is assembled with an acceleration sensor and a gyro sensor. The acceleration sensor can detect accelerations individually in three axial directions orthogonal to each other. The gyro sensor can detect an angular velocity (angular velocity) around each axis of three axes (x, y, z) orthogonal to each other. The inertial sensor 12 outputs a detection signal. The acceleration and angular velocity for each axis are specified by the detection signal. The acceleration sensor and the gyro sensor detect acceleration and angular velocity information with relatively high precision. The inertial sensor 12 is mounted on a golf club (moving ball) 13. A golf club, for example a golf putter 13, has a shaft 13a and a grip 13b. The grip 13b is gripped by hand. The grip 13b is formed coaxially with the shaft of the shaft 13a. The club head 13c is coupled to the tip of the shaft 13a. Preferably, the inertial sensor 12 is mounted on the shaft 13a or the grip 13b of the golf club 13. The inertia sensor 12 may be fixed relative to the golf club 13 so as to be relatively immovable.

Here, in mounting the inertial sensor 12, one (z-axis) of the detection axis of the inertial sensor 12 is aligned with the axis of the shaft 13a. The other one (x axis) of the detection axis of the inertia sensor 12 is a face face (striking face) 13c1 in a state in which the sole (ground face) of the club head 13c is horizontal, (Face normal direction) is projected on the horizontal plane. Since the face surface is not limited to the vertical surface but is inclined with respect to the vertical surface, the direction in which the face normal direction is projected on the horizontal plane is the x-axis. The y-axis is orthogonal to the x-axis and the z-axis. The sensor coordinate system Σxyz is defined on the x, y, and z axes.

The golf swing analysis device 11 is provided with an arithmetic processing circuit 14. The inertial sensor 12 is connected to the arithmetic processing circuit 14. In the connection box, a predetermined interface circuit 15 is connected to the arithmetic processing circuit 14. The interface circuit 15 may be connected to the inertial sensor 12 by wire or may be connected to the inertial sensor 12 wirelessly. A detection signal is supplied to the arithmetic processing circuit 14 from the inertial sensor 12.

A storage device 16 is connected to the arithmetic processing circuit 14. The storage device 16 can store, for example, a golf swing analysis software program (motion analysis program) 17 and related data. The arithmetic processing circuit 14 executes the golf swing analysis software program 17 to realize the golf swing analysis method. The storage device 16 may include a dynamic random access memory (DRAM), a mass storage device unit, a nonvolatile memory, and the like. For example, in implementing the golf swing analysis method, for example, in the DRAM, for example, a golf swing analysis software program 17 is downloaded temporarily from a server. Alternatively, the golf swing analysis software program 17 together with the data may be stored together with the data in a mass storage unit such as a hard disk drive (HDD). The nonvolatile memory stores relatively small-capacity programs and data such as a basic input / output system (BIOS).

The storage device 16 stores club specification information indicating the specifications of the golf club 13, sensor mounting position information, and the like. For example, the user inputs the product number of the golf club 13 to be used by operating the input device 21 (or selects it from the product number list), and stores it in the storage device 16 for each product number The specification information of the entered product number is used as the specification information among the specification information (e.g., the length of the shaft, the position of the center of gravity, the angle of the face, the angle of the loft, etc.). Alternatively, the sensor unit 12 may be mounted at a predetermined position (for example, a distance of 20 cm from the grip), and information about the predetermined position may be stored in advance as sensor mounting position information. As for the exercise conditions, for example, in the case of a golf putter, the distance from the address position to the cup (cup), the size of the cup, the speed of the grass, And is stored in the storage device 16.

An image processing circuit 18 is connected to the arithmetic processing circuit 14. The arithmetic processing circuit 14 sends predetermined image data to the image processing circuit 18. A display device 19 is connected to the image processing circuit 18. In connection with the image processing circuit 18, a predetermined interface circuit (not shown) is connected. The image processing circuit 18 sends an image signal to the display device 19 in accordance with the input image data. On the screen of the display device 19, an image specified by the image signal is displayed. The calculation processing circuit 14 or the image processing circuit 18 calculates the coordinate space of the sensor coordinate system? Xyz as an absolute reference coordinate system? XYZ (for example, the XZ plane is a horizontal plane , And the XY plane is a vertical plane). A liquid crystal display or other flat panel display or the like is used for the display device 19 and is displayed as a three-dimensional image or two-dimensional image in the absolute reference coordinate system? XYZ. Here, the arithmetic processing circuit 14, the storage device 16, and the image processing circuit 18 are provided as, for example, a computer apparatus.

An input device 21 is connected to the arithmetic processing circuit 14. The input device 21 has at least alphabetic keys and ten keys. Character information and numerical information are input from the input device 21 to the arithmetic processing circuit 14. The input device 21 may be constituted by, for example, a keyboard. The combination of the display device, the computer device, and the keyboard may be replaced with a portable terminal such as a smart phone or a tablet.

(2) Outline of operation processing circuit

Fig. 2 schematically shows the configuration of the arithmetic processing circuit 14 according to the embodiment. The operation processing circuit 14 includes a swing position coordinate detector 50, a velocity detector 60, an address (static) analyzer 70, an impact analyzer 80, a planar (planar) 90, a hit point analyzing unit 100, a front view direction analyzing unit 110, a stroke analyzing unit (swing width analyzing unit) 120, a score analyzing unit 130, And one or more analysis units 90 to 120 may be omitted depending on the grade of the motion analysis apparatus.

The swing position coordinate detection section 50 detects the swing position coordinate position from the swing start position (address position) to the swing turning position (top position), the impact position (impact virtual vertical position), and the swing end position And detects the coordinates of the club head 13c during the swing.

The velocity detecting section 60 detects the velocity V of the club head 13c at the time of impact, for example, using the output from the inertial sensor 12 (see Fig. 4 (B)). The address interpreting section 70 analyzes the posture or position of the face surface 13c1 of the club head 13c at the time of addressing (at the time of stopping). The impact analysis unit 80 analyzes the posture of the face surface 13c1 of the club head 13c at the time of impact and the trajectory of the face surface 13c1 in the vicinity of the impact.

The in-plane direction analysis unit 90 analyzes the direction of the club head 13c viewed from the plane. As shown in Fig. 3A, the planar directional analysis section 90 has a face surface 13c1 at the time of impact and a strike target direction (target line direction: for example, the face surface 13c1 at the time of addressing) (Absolute face angle)? 1 with the imaginary vertical plane 13c2 with respect to the imaginary vertical plane 13c2 with respect to the normal vertical plane 13c2 in the XZ plane) (Square degree) between the face surface 13c1 and the virtual vertical surface 13c3 with respect to the tangential direction (swing line direction or batted direction) in contact with the movement trajectory of the face surface 13c1, ) &thetas; 2.

The hit point analyzing unit 100 determines whether or not the hit point (hit position) of the ball 22 at the time of impact from the virtual reference position P0 set on the face surface 13c1 The shift amount delta is analyzed from the angular velocity around the shaft 13a.

The frontal direction analyzing unit 110 analyzes the direction of the club head 13c at the frontal face facing the golfer (the user who operates the exercise ball) in front. 4A, the frontal direction analyzing unit 110 calculates the inclination angle (actual loft angle) with respect to the vertical plane of the face surface 13c1 at the time of impact and the reference inclination angle (e.g., 3) (delta-loft angle) with respect to the face surface 13c1 projected on the vertical plane, and the third shift angle 3 (delta-loft angle) with the loft angle, At least one of the fourth shift angle? 4 (attack angle) formed by the tangential direction (swing line direction) at the time of impact tangential to the movement locus and the target direction (batting target direction) projected on the vertical plane is analyzed do.

Based on the coordinates of the two positions (the first position and the second position) from the swing position coordinate detecting section 50, the stroke analyzing section (swing width analyzing section) Specify the swing width to the position. For example, as shown in Fig. 4 (C), the stroke (swing width) from the address position (first position) to the swing turning position (second position) is analyzed.

The score analyzing unit 130 calculates a plurality of pieces of swing analysis data (shift angles? 1 to? 4, shift amounts?, Swing width L, (Performance score) for each of the plurality of swing analysis data (V), and a score (total performance score) calculated by weighting data selected from a plurality of swing analysis data. The statistical analysis unit 140 analyzes statistical values (total number, average value, standard deviation, and the like) from the accumulated data for each of the plurality of swing analysis data.

(3) Display example on the display device

(3-1) Initial Screen

5 is a diagram showing an example of an example of an initial screen of the swing analysis data displayed on the display device 19. In FIG. 5, at the upper part of the initial screen, information on the user name, date and time, type of putter (L-mullet), distance to the cup (10 ft) Is displayed. In the center of the initial screen, for example, a swing trajectory from the address position to the swing turning position is displayed together with the image (plural positions) indicating the putter 13. The swing locus is an image projected on the X-Y plane (vertical plane) of the absolute reference coordinate system. The black triangular mark on the lower left side of the swing locus image area is a playback button. When the play button is operated, the seek bar on the right side of the play button moves from the left to the right, and an image representing the putter 13 in the swing path image area is moved to a plurality of positions As shown in FIG. The white triangle on the upper side of the movement area of the time seek bar shows the address, top, impact, and finish positions in order from the left. The time seeking bar may be operated to support and stop the position of interest. At the center left of the initial screen, a performance score (for example, 100 points) interpreted by the score analyzing unit 130 is displayed. In the lower part of the initial screen, Direction (direction analysis data in the plane), Hitpoint (hit point analysis data), Stroke (stroke analysis data), and Rising do. Touching one of the four display areas in the lower part of the initial screen displays the details of the selected analysis data.

(3-2) Screen of individual analysis data

(3-2-1) Direction

Figs. 6 to 10 show an example of a screen displayed after " Direction " is selected in the initial screen. Fig. 7 shows an example of a display screen of analysis data in the plane direction of one swing. Fig. 6 is a screen displayed when " Direction " is selected on the initial screen. In FIG. 6, based on the analysis data in the in-plane direction analysis section 90 of FIG. 2, the first shift angle? 1 (the face surface 13c1 in the impact state as shown in FIG. ) And the imaginary vertical plane 13c2 with respect to the batting target direction (target line direction): absolute phase angle).

6, which is a screen when "FACE" in FIG. 6 is selected, the normal direction of the face 13c1 of the putter 13 at the time of impact is projected on the projection plane (horizontal plane) The striking direction and the velocity of the club head 13c of the putter 13 at the time of impact are displayed in the coordinate system in which the striking target direction is set. As this coordinate system, for example, a polar coordinate system is displayed. In each slaughter axis, which is one axis of the polar coordinate system, the 0 degree direction is the batting target direction. The specified batting direction is displayed as a line segment extending in a direction orthogonal to the face surface 13c1 of the image representing the club head 13c of the putter 13 in the polar coordinate system. In addition, in the sagittal axis which is one axis of the polar coordinate system, the direction of 0 degrees may be always displayed as the batting direction.

The angles on the respective sideways axes of the polar coordinate system are exaggerated to be larger than the actual angles, for example, the angular range of ± 5 degrees is exaggerated with an angular range of 90 degrees or more. So that it is easy to visually recognize the deviation of the batting direction with respect to the batting target direction. The other axis of the polar coordinate system is the velocity axis. The end position of the line segment indicating the batting direction extending from the face surface of the image representing the club head 13c of the putter 13 indicates the velocity of the club head 13c (face surface 13c1) at the time of impact.

In the present embodiment, considering the fact that the batting direction and velocity of the face surface 13c1 at the time of impact have a correlation with the directionality and distance feeling of the batted ball, the batting direction and velocity of the face surface 13c1 at the time of impact are set to the same coordinate system . It is possible to learn the accuracy to reproduce the directionality and the sense of distance of the batted ball by confirming the displacement and speed of the batting direction with respect to the batting target direction at the time of impact for every swing motion of the putter 13. [ Here, the batting direction at the time of impact can be a direction in which the normal direction to the face surface 13c1 at the time of impact is projected on the projection plane. Since the face surface 13c1 is not limited to being parallel to the vertical surface but may be inclined with respect to the vertical surface, the direction in which the normal direction to the face surface 13c1 is projected on the projection surface (horizontal surface) can be assumed as the hitting direction. As will be described later with respect to the specification of the batting direction, the batting direction at the time of impact (the tangential direction at impact on the movement path of the face surface) may be specified based on the motion vector of the face surface 13c1.

The striking target direction can be specified as a direction in which the normal direction of the face surface 13c1 at the time of addressing (stop) before the start of the swing motion is projected on the projection plane. The striking target direction may be a predetermined fixed direction, but it may be determined from the direction of the face surface 13c1 at the time of stop before the start of the swing motion for each swing motion, so that the discrepancy of consciousness and behavior can be easily grasped can do.

An image showing the putter 13 viewed in a plane in the polar coordinate system shown in Figs. 6 and 7 is displayed by setting the face surface 13c1 in the direction of the striking direction, so that the direction of the striking surface, The cause of the displacement of the hitting direction can be more easily recognized.

Furthermore, a target area of, for example, +/- 1 degrees including the batting target direction (0 degrees) in the polar coordinate system shown in Figs. 6 and 7 can be displayed separately from other areas. In this case, since the target becomes a zone rather than a line, the target achievement rate increases and becomes psychologically comfortable, and the exercise practice effect can be improved. In the case of the putter 13, the target area can be obtained as the angular range from the target line by the distance L from the address position to the cup center (center) and the radius R of the cup. For example, when R = 5.4 cm and L = 155.4 cm, ± arcsin (R / L) = ± 1.9 degrees.

Further, in the polar coordinate system shown in Figs. 6 and 7, the coordinate position (five coordinate positions in Figs. 6 and 7) determined by the hitting direction and velocity specified in the past is set to coordinates Can be displayed separately from the position. By doing so, it is possible to visually recognize the presence or absence of the exercise effect when the repetitive exercise is performed

When the "Histogram" in the lower left of the screen of Fig. 6 or Fig. 7 is selected, the screen of Fig. 6 or Fig. 7 to Fig. 8 is switched. In the lower part of the screen shown in Fig. 8, for example, a histogram showing the distribution of the batting direction is displayed based on the analysis data in the statistical analysis unit 140 in Fig. As shown in Fig. 8, the position of the batting direction measured this time can also be displayed in this histogram.

In Figs. 6 to 8, when the column of " SQUARE " in the upper right of the screen is selected, the screen is switched to Fig. 9, the second deviation angle? 2 (? 2) of the club head 13c at the time of impact is calculated in the column of "SQUARE" on the upper right of the screen based on the analysis data in the planar direction analysis section 90 of FIG. ) (Square diagram: see Fig. 3 (B)). Further, in the center of the screen in Fig. 8, the respective slaughter axes in the polar coordinate system are changed to the respective slaughter angles of the square degree? 2. The position of the square degree (? 2 = 0 degree) in each sagittal axis of the polar coordinate system becomes the target direction. 9, the normal to the face surface of the image representing the putter 13 is displayed at the position of the square degree (? 2 = -0.2 degrees). In this case as well, as shown in Fig. 9, the coordinate positions (five coordinate positions in Fig. 9) determined by the square degrees and velocities specified in the past are distinguished from the coordinate positions of the square degrees and velocities specified this time Can be displayed.

When the " Histogram " in the lower left of the screen in Fig. 9 is selected, the screens in Figs. 9 to 10 are switched. In the lower part of the screen shown in Fig. 10, a histogram showing the distribution of the velocity of the square degree is displayed based on the analysis data in the statistical analysis unit 140 in Fig. As shown in Fig. 10, the position of the square figure measured this time can also be displayed in this histogram.

(3-2-2) Hitpoint

Fig. 11 shows a part of the screen displayed when " Hitpoint " is selected in the initial screen. 11 shows the face surface 13c1 of the club head 13c, and the one-dot chain line SS, which is a vertical line in the figure, shows the sweet spot of the golf club 13.

The circle shown in Fig. 11 shows the hit position of the ball when the ball swings 10 times. The diameter of one circle in the horizontal direction represents the width of the position where the ball is hitting, and in the example of Fig. 11, the diameter is " 5 mm ". That is, the number of circles on the same vertical line indicates the frequency of the hit position of the ball. For example, in the example of FIG. 11, it can be seen that the frequency of the hit position "-5 ± 2.5 (mm)" is "twice".

A circle indicated by an oblique line indicates a hit position of the ball immediately before. In the example of Fig. 11, since the ball position of the immediately preceding ball is " + 1 mm ", the diagonally shaded circle is indicated by a rank of 0 +/- 2.5 (mm). Also, with respect to the hit point, the same histogram as in Fig. 8 or 10 may be displayed by selecting " Histogram ".

(3-2-3) Stroke

Figs. 12 to 16 show an example of a screen displayed after "Stroke" is selected in the initial screen. Fig. 12 shows an example of the display screen of the stroke analysis data of one swing when "Stroke" is selected in the initial screen. Fig. 13 shows a screen when "SPAN-BACK" is selected on the screen of Fig. 12 and 13, the stroke (SPAN-BACK) of the back swing of the putter 13 is enlarged by 37 cm on the basis of the analysis data in the stroke (swing width) analyzing section 120 shown in Fig. 2 . 12 or 13, the screen shown in Fig. 12 or 13 to 14 is switched. In the lower part of the screen shown in Fig. 14, a histogram showing the distribution of the stroke of the backswing is displayed based on the analysis data in the statistical analysis unit 140 in Fig. As shown in Fig. 14, the position of the stroke measured this time can also be displayed in this histogram.

In Figs. 12 to 14, when the column of " SPEED " in the upper right of the screen is selected, the screen is switched to the screen of Fig. In Fig. 15, 4.6 m / s as the velocity of the club head 13c at the time of impact is enlarged in the column of "SPEED" on the right side of the screen based on the analysis data in the velocity detecting section 60 in Fig. 2 Highlighted. In addition, a speed indicator is displayed on the right side of the screen center in Fig. When the "Histogram" in the lower left of the screen in FIG. 15 is selected, the screens in FIGS. 15 to 16 are switched. In the lower part of the screen shown in Fig. 16, a histogram showing the distribution of the velocity of the club head 13c at the time of impact is displayed based on the analysis data in the statistical analysis unit 140 shown in Fig. As shown in Fig. 16, the position of the velocity measured this time can also be displayed in this histogram.

(3-2-4) Rising

Figs. 17 to 21 show examples of screens displayed after " Rising " is selected on the initial screen. Fig. 17 shows an example of a display screen of one swing frontal direction analysis data when "Rising" is selected in the initial screen. 18 is a screen displayed when " DELTA-LOFT " of the screen shown in Fig. 17 is selected. 17 and 18, the third shift angle? 3 (the delta-loft angle: DELTA-LOFT) shown in FIG. 4A is calculated based on the analysis data in the frontal direction analysis unit 110 of FIG. -0.8 degrees is enlarged and highlighted.

In the center of the screen of Figs. 17 and 18, the specified inclination angle is displayed in the angular coordinate system indicating the shift angle from the reference inclination angle. In this angular coordinate system, 0 degree represents the reference inclination angle. An image representing the club head 13c of the putter 13 is displayed at the front face facing the golfer (the user using the kicking ball) facing the front face. In the angular coordinate system, the specified inclination angle is displayed as an extension of the face surface of the image. In Figs. 17 and 18, the specified inclination angle is displayed in coincidence with the center line of the angular coordinate system, and the position indicating the reference angle by the above-mentioned intersection angle (min) is displayed in the opposite direction to the sign of the crossing angle. The center line of the angular coordinate system may be coincident with the reference inclination angle (0 degree), and the line indicating the specified inclination angle may be rotated and displayed in the direction corresponding to the sign of the inclination angle by the inclination angle. Thus, by displaying the reference inclination angle and the inclination angle in the same coordinate system, the difference can be visually recognized.

The angle of the angular coordinate system is exaggerated to be larger than the actual angle, and the angular range of 1 degree is exaggerated by several times to ten times. This is to make it easier to recognize the deviation of the inclination angle with respect to the reference inclination angle.

In addition, in the angular coordinate system shown in Figs. 17 and 18, for example, the target area of ± 1 degree inclusive of the reference inclination angle (0 degrees) can be displayed separately from other areas. In this way, since the target is not a line but a zone, the target achievement rate is raised and becomes psychologically easy, and the exercise practice effect can be improved.

In addition, in the angular coordinate system shown in Figs. 17 and 18, the inclination angle specified in the past (five inclination angles in Figs. 17 and 18) can be displayed separately from the inclination angle specified at this time. By doing so, it is possible to visually recognize the effect of the exercise in the case of performing the repetitive motion.

17 or Fig. 18, the screen shown in Fig. 17 or 18 is switched to the screen of Fig. In the lower part of the screen shown in Fig. 19, a histogram showing the distribution of the tilt angle is displayed based on the analysis data in the statistical analysis unit 140 in Fig. As shown in Fig. 19, the position of the tilt angle measured this time can be displayed in this histogram.

In Figs. 17 to 19, when the column of " ATTACK " in the upper right of the screen is selected, the screen is switched to the screen of Fig. In FIG. 20, on the basis of the analysis data in the frontal view direction analysis unit 110 of FIG. 2, a column of "ATTACK" on the right side of the screen displays the club head 13c (The angle of attack) of -7.6 degrees is enlarged and highlighted. In addition, in the center of the screen in Fig. 20, the angles of the angular coordinate system are changed to angular axes of the attack angle. The position of the attack angle = 0 degrees in the angular coordinate system is set to the horizontal position on the screen, and this 0 degree becomes the reference inclination angle. In Fig. 20, a normal to the face surface of the image showing the putter 13 at the front face, which is the face facing the golfer (the user who uses the kick), at the position where the attack angle = -7.6 degrees is displayed. The specified inclination angle is indicated by this normal line. In this case as well, as shown in Fig. 20, the attack angle specified in the past (five attack angle in Fig. 20) can be displayed separately from the attack angle specified this time.

When the " Histogram " in the lower left of the screen in Fig. 20 is selected, the screens in Figs. 20 to 21 are switched. In the lower part of the screen shown in Fig. 21, a histogram showing the distribution of the attack angle is displayed based on the analysis data in the statistical analysis unit 140 in Fig. As shown in Fig. 21, the position of the attack angle measured this time can also be displayed in this histogram.

(4) Operation of Swing Position Coordinate Detection Unit

The calculation in the swing position coordinate detector 50 shown in Fig. 2 will be described. 22 is a flowchart showing an example of the sequence of processing for calculating the posture (posture from the initial position to the time N) of the sensor unit 12 in the swing position coordinate detecting section 50. [

22, first, the swing position coordinate detecting section 50 specifies the direction of the gravitational acceleration from the three-axis acceleration data at the time of stop at time t = 0 (S1) A quaternion (quaternion) p (0) indicating posture (attitude at time t = 0) is calculated (S2).

The three-dimensional coordinate position is represented by the following equation (1) as a quaternion q representing the rotation of the position vector.

[Equation 1]

In the formula (1), in each of the θ, the unit vector of the rotation axis rotation (r _x, r _y, r _z) If a, w, x, y, z, the following equation (2) of the rotation of the target Lt; / RTI >

[Equation 2]

The sensor unit 12 is stopped at the time t = 0 at the swing start (address), and thus the quaternion q (0) indicating the rotation angle at time t = 0 is set to 0 = 0 is substituted into the following equation (3).

[Equation 3]

Next, the swing position coordinate detection section 50 updates the time t to t + 1 (S3). Here, since the time t = 0, the time t = 1 is updated.

Next, the swing position coordinate detecting section 50 calculates the quaternion? Q (t) representing the rotation per unit time of the time t from the three-axis angular velocity data at time t (S4).

For example, supposing that the three-axis angular velocity data at time t is ω (t) = [ω _x (t), ω _y (t), ω _z (t)], the magnitude of angular velocity per sample |? (T) is calculated by the following equation (4).

[Equation 4]

Since the magnitude |? (T) | of the angular velocity is the rotation angle per unit time, the quaternion? Q (t + 1) representing the rotation per unit time of the time t is calculated by the following equation (5).

[Equation 5]

(1) = [omega _x (1), omega _y (1), omega _z (1)] at time t = 1 because t = (1) is calculated from the equation (5).

Next, the swing position coordinate detecting section 50 calculates the quaternion q (t) indicating the rotation from time 0 to t (S5). The quaternion q (t) is calculated by the following equation (6).

[Equation 6]

Here, since t = 1, the swing position coordinate detecting section 50 calculates q (1) by the equation (6) from the q (0) of the equation (3) and the q .

Next, the swing position coordinate detecting section 50 repeats the processes of steps S3 to S5 until t = N, and when t = N (S6 is YES), the swing position coordinate detecting section 50 determines that the quaternion the quaternion p (N) representing the posture at the time N is calculated (S7) from the quaternion q (N) representing the rotation from the time t = 0 to N calculated at the immediately preceding step S5 in p (0) Lt; / RTI >

The swing position coordinate detection section 50 detects the swing position coordinate information based on the attitude information acquired as described above and the distance information from the sensor unit 12 to the club head 13c (first and second measurement points 13d and 13e described later) The coordinates (X, Y, Z) in the absolute reference coordinate system of the club head 13c of the putter 13 from the time t = 0 to the time N can be obtained based on the above equation 2 can detect the velocity based on the output from the inertial sensor 12 with respect to the coordinate position obtained by the swing position coordinate detecting section 50. [

(5)

(5-1) Analysis and display of the first shift angle? 1, the second shift angle? 2, and the speed V

Next, an address analyzing unit 70, an impact analyzing unit 80, a planar direction analyzing unit 90, a statistical analyzing unit 140, and an image processing circuit 70, which are involved in generation of analysis screens shown in Figs. The configuration and operation of the control unit 18 will be described with reference to Figs. 23 to 25. Fig. First, referring to Fig. 23, a first measuring point 13d and a second measuring point 13e on the face surface 13c1 of the club head 13c will be described. As shown in Fig. 23, a first measurement point 13d and a second measurement point 13e are set on the face surface 13c1 in order to specify the posture and position of the face surface 13c1. The first measurement point 13d and the second measurement point 13e are disposed at positions apart from each other. Here, the first measurement point 13d is located on the heel side of the face surface 13c1, and the second measurement point 13e is located on the toe side of the face surface 13c1. The first measurement point 13d and the second measurement point 13e are preferably arranged on the face line h passing through the core (sweet spot) of the face surface 13c1 which is parallel to the paper surface. Therefore, the line segment 13f connecting the first measurement point 13d and the second measurement point 13e to each other can specify the direction of the face surface 13c1 when projected on the paper surface.

As shown in Fig. 2, the arithmetic processing circuit 14 of Fig. 1 includes an address (stop) analyzing section 70 and an impact analyzing section 80. Fig. The address interpreting section 70 includes a posture specifying section 71 and a position specifying section 72. [ The posture specifying section 71 specifies the posture of the face surface 13c1 in the absolute reference coordinate system ΣXYZ at the time of stop (that is, at the time of the address). 24, the posture specifying unit 71 sets the coordinate = rh (0) of the first measurement point 13d and the coordinate = rt (0) of the second measurement point 13e at the time of stopping, (0) are connected to each other by the first line segment L1. The attitude of the face surface 13c1 in the first line segment L1 is specified. At this time, the first line segment L1 is projected on a horizontal plane (X-Z plane: plane spreading parallel to the ground plane) orthogonal to the Y axis within the absolute reference coordinate system? XYZ. The coordinates of the first measurement point 13d at the time of stopping and the coordinates of the second measurement point 13e at the time t = 0 are calculated by the swing position coordinate detecting section 50 The position of the first measurement point 13d and the second measurement point 13e can be specified.

The position specifying unit 72 specifies a second line segment L2 orthogonal to the face surface 13c1 within the absolute reference coordinate system XYZ at the time of stop. The second line segment L2 intersects the face surface 13c1 perpendicularly at the first measurement point 13d = rh (0). In specifying the second line segment L2, the position specifying unit 72 specifies the first line segment L1. The position specifying unit 72 sets the second line segment L2 in the vertical direction of the first line segment L1 at the first measurement point 13d. The second line segment L2 represents a so-called target line which is the batting target direction. At this time, the second line segment L2 is projected on a horizontal plane orthogonal to the Y axis within the absolute reference coordinate system? XYZ, like the first line segment L1.

2, the impact analysis unit 80 includes a posture specifying unit 81, a locus specifying unit 82, and a velocity specifying unit 63. [ The posture specifying section 81 specifies the posture of the face surface 13c1 in the absolute reference coordinate system XYZ at the time of impact. 24, the attitude determination unit 81 calculates the coordinates of the first measurement point 13d and the coordinates of the second measurement point 13e at the time of impact, (imp) to the third line segment (L3). The attitude of the face surface 13c1 at the time of impact at the third line segment L3 is specified. At this time, the third line segment L3 is projected on a horizontal plane orthogonal to the Y axis within the absolute reference coordinate system? XYZ. The coordinates = rh (imp) of the first measurement point 13d and the coordinates rt (imp) of the second measurement point 13e at the time of impact correspond to t = timp at the time of impact at the swing position coordinate detection section 50 The position of the first measurement point 13d and the second measurement point 13e can be specified. As an output of the inertial sensor 12 at the moment of impact, for example, a large acceleration in a specific direction is observed. Based on the threshold of this acceleration, t = timp is specified at impact.

The trajectory specifying unit 82 specifies the movement trajectory of the first measurement point 13d in the absolute reference coordinate system? XYZ at the time of impact. 24, the trajectory specifying section 82 specifies a trajectory of the first coordinate point 13d on the absolute reference coordinate system? XYZ that indicates the position rh (imp) of the first measuring point 13d at the time of impact And the second coordinate point P2 on the absolute reference coordinate system? XYZ that indicates the position rh (imp-1) of the first measurement point 13d at the sampling point preceding the impact. Here, the sampling point immediately before impact is assigned to the second coordinate point P2. The first coordinate point P1 and the second coordinate point P2 are connected to each other by a fourth line segment L4. The direction and length of the fourth line segment L4 indicate the direction and size of the motion vector. At this time, the fourth line segment L4 is projected on a horizontal plane orthogonal to the Y axis within the absolute reference coordinate system? XYZ, similarly to the above description. The direction L4 '(the tangential direction at the time of impact with respect to the movement trajectory) in which the fourth line segment L4 projected on the horizontal plane extends is defined as a correct hit direction at the time of impact.

The velocity specifying section 63 specifies the velocity of the face surface 13c1 at the time of impact, which is displayed together with the absolute face angle? 1 or the square degree? 2 in the polar coordinate system. The speed of the face surface 13c1 at the time of impact can be obtained from the information of the acceleration at the impact position and the like.

The in-plane direction analysis unit 90 includes a first deviation angle analysis unit 91 and a second deviation angle analysis unit 92 as shown in Fig. The first shift angle analyzing section 91 is connected to the position specifying section 72 of the address analyzing section 70 and the locus specifying section 82 of the impact analyzing section 80. At this time, the first deviation angle analyzing section 91 specifies the extended line L4 'of the fourth line segment L4 specified by the trajectory specifying section 82, for example, in the batted direction. The first deviation angle analyzing section 91 calculates the second line segment L2 (parallel to the target strike direction or the target line) orthogonal to the face surface 13c1 at the first measurement point 13d of the face surface 13c1 at the address Of the fourth line segment L4 orthogonal to the face surface 13c1 at the first measurement point 13d of the face surface 13c1 at the time of impact 1 misalignment angle: absolute face angle)? 1 is calculated. The first deviation angle analyzing section 91 may be connected to the position specifying section 72 of the address analyzing section 70 and the attitude specifying section 81 of the impact analyzing section 80. [ In this case, the first deviation angle analyzing section 91 specifies the batted direction L5 as a hypothetical direction in the vertical direction of the third line segment L3 specified by the posture specifying section 81. [ The first deviation angle analyzing section 91 calculates the second line segment L2 (parallel to the target strike direction or the target line) orthogonal to the face surface 13c1 at the first measurement point 13d of the face surface 13c1 at the address (First deviation angle: absolute face angle)? 1 between the face surface 13c1 and the hit direction L5 orthogonal to the face surface 13c1 at the time of impact.

The second deviation angle analyzing section 92 is connected to the posture specifying section 81 and the locus specifying section 82 of the impact analyzing section 80. The second deviation angle analyzing unit 92 specifies the batted ball direction L5 assuming the direction perpendicular to the third line segment L3 specified by the posture specifying unit 81. [ That is, as described above, the correct hit direction L4 'is set on the extension line of the motion vector (fourth line segment L4) (the tangential direction at the impact on the movement locus) The face surface 13c1 may not necessarily be orthogonal to the correct hit direction L4 '. This is because the face surface 13c1 is closed or opened at the time of impact and is non-orthogonal to the right hit direction L4 '. The second deviation angle analyzing unit 92 specifies the intersection angle? 2 between the correct hit direction L4 'and the virtual hit direction L5 as a square degree. The square degree [theta] 2 indicates a deviation angle between a virtual vertical surface with respect to the correct hit direction L4 'and the measured face surface 13c1 at the time of impact.

The statistical analysis unit 140 can calculate a statistical value indicating the deviation of the absolute face angle [theta] 1, the squareness [theta] 2, or the velocity V at the time of impact. The statistical analysis unit 140 has a histogram generation unit 141. The histogram generation section 141 classifies the measured absolute face angle? 1, square degree? 2 or velocity V into a plurality of zones as the histogram data shown in FIG. 8 or FIG. 10, And counts the number of samples included in the frame. The statistical analysis unit 140 has a deviation analysis unit 142. [ The deviation analyzing section 142 calculates an average value and a standard deviation of the total number of samples of the absolute face angle? 1, the square degree? 2, or the velocity V, In this manner, the reproducibility of the directionality of the batted ball and the reproducibility of the distance feeling can be evaluated by displaying statistical values indicating the deviation of the absolute face angle [theta] 1, the squareness [theta] 2 or the velocity V.

The image processing circuit 18 generates display information shown in Figs. 6 to 10 displayed on the display device 19 based on the information from the in-plane direction analyzing section 90 and the statistical analyzing section 140 . In addition, the image processing circuit 18 calculates the degree of deviation of the hitting direction from the target area based on the information from the in-plane direction analyzing section 90 as a multiple of the unit representing the area along the target area Can be displayed. For example, as shown in Fig. 25, for example, in the golf putter 13, the unit indicating the region along the target area is the size of the cup. For example, by indicating that the golf putter 13 is shifted by 2 cups, .

The image processing circuit 18 calculates the ratio of the number of times the batting direction enters the target area (for example, 46%) with respect to the number of motions in which the batting direction is specified, based on the information from the statistical analyzing section 140 Can be displayed. By doing so, the target achievement rate can be recognized as a numerical value, and the exercise practice effect can be notified quantitatively.

(5-2) Analysis and display of shift amount (delta) from the sweet spot

The hit point analyzing unit 100 shown in Fig. 2 has an impact time velocity acquiring unit 101 and a displacement amount analyzing unit 102. Fig. The impact time velocity obtaining section 101 obtains the angular velocity around the long axis (z axis of the sensor coordinate system) of the club shaft 13a at the time of impact from the output of the inertia sensor 12. [ The shift amount analyzing unit 102 analyzes the shift amount? From the hit point shown in FIG. 3 (C) from the obtained angular speed.

Here, the relationship between the angular speed GyroZ around the long axis (z-axis of the sensor coordinate system) of the club shaft 13a and the displacement amount delta of the hitting position from the sweet spot in the horizontal direction of the face surface 13c1 Is shown in Fig. According to Fig. 26, when the GyroZ shown is -114.6 (rad / s), it can be seen that the displacement amount of the hit position from the sweet spot was " 8 (mm) ". 27 is a graph showing the relationship of Fig. 26. Fig. The horizontal axis of the graph shown in Fig. 27 represents the angular velocity, and the vertical axis represents the shift amount of the hit position. The correlation in Fig. 27 can be expressed by a linear equation. The coefficients and intercepts of the linear equation can be obtained by a regression analysis. In the example of FIG. 27, the linear equation is expressed by the following equation (7).

y = -0.0604x + 2.4944 ... (7)

The odd rate is " R2 = 0.8954 ".

This formula (7) is calculated in advance and stored in the storage device 16. Thereby, the shift amount analyzing unit 102 can calculate the shift amount delta of the hitting position from the sweet spot based on the information from the inertial sensor 12 and the storage device 16.

The statistical analysis unit 140 can calculate a statistical value indicating the deviation of the shift amount [delta]. The histogram generation unit 141 classifies the measured shift amount delta into a plurality of zones and counts the number of samples of the shift amount delta contained in each zone in the same manner as in Fig. 8 or Fig. The deviation analyzing section 142 calculates an average value, a standard deviation, and the like with respect to the total number of samples of the shift amount delta. In this manner, a statistical value indicating the deviation of the shift amount delta can be displayed.

The image processing circuit 18 can generate the display information shown in Fig. 11 displayed on the display device 19 based on the information from the hit point analyzing unit 100 and the statistical analyzing unit 140. [

The image processing circuit 18 determines whether or not the shift amount delta is smaller than the shift amount delta in the target area (for example, from the sweet spot) to the number of times the shift amount delta is specified based on the information from the statistical analysis unit 140. [ 5mm) can be displayed. By doing so, the target achievement rate can be recognized as a numerical value, and the exercise practice effect can be notified quantitatively.

(5-3) Analysis and display of swing width

Next, the analysis and display of the stroke (swing width) L shown in Figs. 12 to 16 will be described. The stroke (swing width) analyzing unit 120 may have a position determining unit 121 and a stroke (swing width) determining unit 122 as shown in FIG. The position determining section 121 determines a first position that is a starting point of the swing width and a second position that is an end point of the swing width based on an output from the inertial sensor 12 or the like. In the present embodiment, since the first position is the address position, a position corresponding to t = 0 can be designated. The second position is the swing turning position, and this position can designate, for example, the position where the sign of the acceleration in the X-axis direction (back swing direction) of the absolute reference coordinate system is completely switched. The position determination section 121 can also determine the impact position (impact position). As an output of the inertial sensor 12 at the moment of impact, for example, a large acceleration in a specific direction is observed. The moment of impact is specified based on the threshold of this acceleration. The velocity detecting section 60 can obtain the velocity of the club head 13c at each position from the information of the position from the first position to the second position and the acceleration at the impact position.

The stroke (swing width) determining section 122 can calculate the length of a path tracing the swing locus from the first position (address position) to the second position (swing turning position) as the swing width L. [ Since a plurality of sampled coordinate positions are obtained from the first position to the second position, the distance of the three-dimensional space between neighboring coordinate positions sampled at a minute pitch can be integrated It can be calculated almost accurately.

Instead, the stroke (swing width) judging section 122 determines the distance between the coordinates of the horizontal axis X between the first position and the second position projected on the projection plane (for example, the vertical XY plane of the absolute reference coordinate system) , The swing width L can be obtained from the first position to the second position. This is because, depending on the golfer, it is sufficient to obtain the swing width L of the back swing rather than the swing width of the more accurate distance, that is, the length subtracted in the backswing direction (that is, the distance between the projected coordinates). In Fig. 28, the distance between the coordinates of the horizontal axis X between the first position and the second position is shown on the horizontal axis. 28, the distance between the coordinates of the vertical axis Y between the first position projected on the vertical (X-Y) plane of the absolute reference coordinate system and the second position is shown on the vertical axis. However, the distance between the coordinates of the vertical axis Y may be omitted.

The statistical analysis unit 140 can calculate a statistical value indicating a deviation of the swing width L. [ The histogram generation unit 141 classifies the measured swing width or velocity into histogram data for histogram shown in Fig. 14 or Fig. 16, and counts the number of samples included in each zone. The deviation analyzer 142 of the statistical analyzer 140 calculates an average value, a standard deviation, and the like with respect to the total number of samples of the swing width L or the speed V. [ In this manner, the reproducibility of the swing width L or the speed V of the ball in accordance with the reaching distance of the ball can be evaluated by displaying statistical values indicating the deviation of the swing width L and the speed V.

The image processing circuit 18 generates the display information shown in Figs. 17 to 21 displayed on the display device 19 based on the information from the front view direction analyzing section 110 and the statistical analyzing section 140 . In addition to this, the image processing circuit 18 calculates, based on the information from the statistical analysis unit 140, the third shift amount? 3 or the fourth shift amount? 4, The ratio (for example, 48%) of the number of times the angle? 3 or the fourth shift angle? 4 enters the target area (for example,? 3 =? 4 = ± 1 °) can be displayed. By doing so, the target achievement rate can be recognized as a numerical value, and the exercise practice effect can be notified quantitatively.

4 to 7 displayed on the display device 19 on the basis of the information from the stroke (swing width) analyzing unit 120 and the statistical analyzing unit 140 Can be generated. In particular, the display pitch of the image showing the putter 13 displayed at a plurality of positions in Fig. 13 can be made short in a period in which the swing speed is high and in a period in which the swing speed is low. In addition, one image representing the putter 13 can be displayed at predetermined time intervals (for each of a plurality of sampling data). Thereby, both of the swing width and the swing speed of the putter 13 can be visually recognized.

The image processing circuit 18 can sequentially display an image representing the putter 13 displayed at a plurality of positions in Fig. 13 synchronously with the swing motion of the putter 13 in synchronism with the swing motion. Thereby, the swing width of the putter 13 can be dynamically confirmed.

The first position and the second position, which are the starting points of the swing width L, are not limited to the above-described setting of the address position and the swing turning position. As a combination of the first position / second position, the swing turning position / impact position that defines the swing width L of the down swing, the impact position / swing end position that defines the swing width of the follow through, Swing start position / swing end position that defines the swing width L of the entire swing. These swing widths L are also related to the swing width of the back swing. For example, in the golf putter or the half swing of the iron club, it is possible to contribute to the improvement of the sense of distance with good reproducibility.

(5-4) Analysis and display of the third shift angle? 3 and the fourth shift angle?

Next, a front view directional analysis unit 110 (see FIG. 17) which is involved in generation of an analysis screen of the third shift angle 3 (delta-loft angle) or the fourth shift angle 4 ), The statistical analysis unit 140, and the image processing circuit 18 will be described with reference to FIGS. 29 and 30. FIG. First, referring to Fig. 29, the first measurement point 13d and the second measurement point 13e on the face surface 13c1 of the club head 13c will be described. 29, a first measurement point 13d and a second measurement point 13e are set on the face surface 13c1 in order to specify the posture and position of the face surface 13c1. The first measurement point 13d and the second measurement point 13e are disposed at positions apart from each other. Here, the first measurement point 13d is located on the upper side of the face surface 13c1, and the second measurement point 13e is located on the lower side of the face surface 13c1. The first measuring point 13d and the second measuring point 13e are preferably arranged on a face vertical line passing through the padding (sweet spot) of the face face 13c1, which is preferably perpendicular to the paper face. Therefore, the line segment 13f connecting the first measurement point 13d and the second measurement point 13e to each other can specify the inclination angle of the face surface 13c1 with respect to the vertical plane when projected on the ground.

The arithmetic processing circuit 14 includes an address (stop) analyzing section 70 and an impact analyzing section 80 as shown in Fig. The posture specifying unit 71 of the address interpreting unit 70 specifies the posture of the face surface 13c1 in the absolute reference coordinate system? XYZ at the time of stop (i.e., at the time of addressing). According as the specific posture, for example as shown in FIG. 30 example, the position specifying unit 71, the coordinate of the coordinate = r _h (0) and the second measuring point (13e) of the first measurement point (13d) at the time of stopping = rt (0) are connected to each other by the first line segment L1. The attitude of the face surface 13c1 is specified by the first line segment L1. At this time, the first line segment L1 is projected on the vertical plane (XY plane: plane perpendicular to the paper plane) orthogonal to the Z axis within the absolute reference coordinate system? XYZ. The coordinates of the first measurement point 13d at the time of stopping and the coordinates of the second measurement point 13e at the time t = 0 are calculated by the swing position coordinate detecting section 50 The position of the first measurement point 13d and the second measurement point 13e can be specified.

The position specifying unit 72 specifies a second line segment L2 orthogonal to the face surface 13c1 within the absolute reference coordinate system XYZ at the time of stop. The second line segment L2 intersects the face surface 13c1 vertically at the first measurement point 13d = rh (0). In specifying the second line segment L2, the position specifying unit 72 specifies the first line segment L1. The position specifying unit 72 sets the second line segment L2 in the vertical direction of the first line segment L1 at the first measurement point 13d. The second line segment L2 represents a so-called target line which is the batting target direction. At this time, the second line segment L2 is projected on the vertical plane orthogonal to the Z axis within the absolute reference coordinate system? XYZ, like the first line segment L1.

The posture specifying section 81 of the impact analyzing section 80 specifies the posture of the face surface 13c1 in the absolute reference coordinate system? XYZ at the time of impact. 30, the posture specifying unit 81 sets the coordinate = rh (imp) of the first measurement point 13d and the coordinate = rt (imp) of the second measurement point 13e at the time of impact, for example, (imp) to the third line segment (L3). The attitude of the face surface 13c1 at the time of impact is specified by the third line segment L3. At this time, the third line segment L3 is projected onto the vertical plane orthogonal to the Z axis within the absolute reference coordinate system? XYZ. The coordinates = rh (imp) of the first measurement point 13d and the coordinates rt (imp) of the second measurement point 13e at the time of impact correspond to t = timp at the time of impact at the swing position coordinate detection section 50 The position of the first measurement point 13d and the second measurement point 13e can be specified. As an output of the inertial sensor 12 at the moment of impact, for example, a large acceleration in a specific direction is observed. Based on the threshold of this acceleration, t = timp is specified at impact.

The trajectory specifying unit 82 specifies the movement trajectory of the first measurement point 13d in the absolute reference coordinate system? XYZ at the time of impact. 30, the trajectory specifying unit 82 specifies a trajectory of the first coordinate point 13d on the absolute coordinate system 裡 XYZ that represents the position rh (imp) of the first measuring point 13d at the time of impact And the second coordinate point P2 on the absolute reference coordinate system? XYZ that indicates the position rh (imp-1) of the first measurement point 13d at the sampling point preceding the impact. Here, the sampling point immediately before impact is assigned to the second coordinate point P2. The first coordinate point P1 and the second coordinate point P2 are connected to each other by a fourth line segment L4. The direction and length of the fourth line segment L4 indicate the direction and size of the motion vector. At this time, the fourth line segment L4 is projected on the vertical plane orthogonal to the Z axis within the absolute reference coordinate system? XYZ, similarly to the above description. The direction L4 '(the tangential direction at impact with respect to the movement trajectory projected on the vertical plane) in which the fourth line segment L4 projected on the vertical plane extends is defined as a hit direction at the time of impact.

As shown in Fig. 9, the frontal direction analyzing unit 110 includes a third shift angle analyzing unit 111 and a fourth shift angle analyzing unit 112. As shown in Fig. The third shift angle analyzing unit 111 is connected to the position specifying unit 72 of the address analyzing unit 70 and the attitude specifying unit 81 of the impact analyzing unit 80. At this time, the third deviation angle analyzing unit 111 calculates the difference between the first line segment L1 (line segment representing the reference inclination angle) specified by the position specifying unit 72 and the third line segment (The line segment indicating the inclination angle) is specified as the third shift angle (delta-loft angle) 3.

The fourth shift angle analyzing unit 112 is connected to the posture specifying unit 71 of the address analyzing unit 70 and the locus specifying unit 82 of the impact analyzing unit 80. The fourth shift angle analyzing unit 112 specifies the extended line L4 'of the fourth line segment L4 specified by the trajectory specifying unit 82, for example, in the batted direction. The fourth shift angle analyzing unit 112 calculates the second line segment L2 (parallel to the target strike direction or the target line) orthogonal to the face surface 13c1 at the first measurement point 13d of the face surface 13c1 at the time of addressing Of the fourth line segment L4 orthogonal to the face surface 13c1 at the first measurement point 13d of the face surface 13c1 at the time of the impact and the extension line L4 ' And calculates the fourth shift angle (attack angle)? 4.

The statistical analysis unit 140 can calculate a statistical value indicating the deviation of the third shift angle? 3 or the fourth shift angle? 4. As the histogram data shown in Fig. 19 or 21, the measured third shift angle? 3 or the fourth shift angle? 4 is classified into a plurality of zones, and the number of samples included in each zone is counted. In addition, the statistical analysis unit 140 may calculate an average value, a standard deviation, and the like for the total number of samples of the third shift angle? 3 or the fourth shift angle? 4. Thus, the reproducibility of the directionality and the sense of distance can be evaluated by displaying the statistical value indicating the deviation of the third shift angle 3 or the fourth shift angle 4.

The image processing circuit 18 generates the display information shown in Figs. 17 to 21 displayed on the display device 19 based on the information from the front view direction analyzing section 110 and the statistical analyzing section 140 . In addition to this, the image processing circuit 18 calculates, based on the information from the statistical analysis unit 140, the third shift amount? 3 or the fourth shift amount? 4, The ratio (for example, 48%) of the number of times the angle? 3 or the fourth shift angle? 4 enters the target area (for example,? 3 =? 4 = ± 1 °) can be displayed. By doing so, the target achievement rate can be recognized as a numerical value, and the exercise practice effect can be notified quantitatively.

(6) Scoring

Next, the score analysis unit 130 for scoring the swing based on the above-described plurality of analysis data will be described. The scoring is largely divided into scoring of the analysis items (the first to fourth shift angles? 1 to? 4, the swing width L, the shift amount? From the sweet spot, and the velocity V at the time of impact) And a scoring of a summing point to which a plurality of analysis items are weighted.

(6-1) Scoring for each analysis item

The performance score (PS) is shown in the following equation.

PS = P- (1-Ta) xS ... (8)

Here, P is a perfect score (100 points), Ta is a target zone evaluation,

Ta = (Tz- (| T-R |)) / Tz ... (9)

Lt; / RTI > Here, Tz is the target zone, T is the target value, and R is the analysis data. (1-Ta) is 0 to 1, it indicates that it is in the target zone. (1-Ta) is closer to zero, it means that it is close to the target value. (1-Ta) is 1 or more, it means that it is outside the target zone. S is a scale number, which is used for scaling the score and the data value. S = P / A, and A represents an interpretable range.

(6-1-1) The performance score PsF of the first shift angle?

The first shift angle? 1 is? 1 = 0 when a square impact is applied toward the target line, and in this case, PsF = 100 points is given. The score of the first shift angle? 1 is calculated by substituting, for example, P = 100, T = 0, Tz = 1, A = 30, R =? 1 in the expressions (8) and (9). In this case, the target zone Tz is a variable value that can be set to ± arcsin (R / L) by using the radius R of the cup and the distance L from the address position to the center of the cup as described above.

(6-1-2) The performance score PsS of the second shift angle?

The second deviation angle? 2 becomes? 2 = 0 when a square impact is applied to the club path, and PsS = 100 points is given in this case. The score of the second shift angle? 2 is calculated by substituting, for example, P = 100, T = 0, Tz = 1, A = 30, R =? 2 in the expressions (8) and (9).

(6-1-3) Performance score PsH of the shift amount delta from the sweet spot

The shift amount? Becomes? = 0 when hit in a sweet spot, and PsH = 100 points in this case. Scoring of the shift amount? Is calculated by substituting P = 100, T = 0, Tz = 5, A = 100, and R =? In the expressions (8) and (9).

(6-1-4) Performance score of swing width (L) PsB

The swing width L is aimed at entering a standard deviation of 1 sigma. The scoring of the swing width L is calculated by substituting, for example, P = 100, T = 0, Tz = 1σ, A = 100 and R = L in equations (8) and (9).

(6-1-5) Performance score of impact speed (V) PsI

The impact speed (V) is also aimed at entering a standard deviation of 1σ. The scoring of the impact speed V is calculated by substituting P = 100, T = 0, Tz = 1σ, A = 10, R = V, for example in equations (8) and (9).

(6-1-6) The performance score PsL of the third shift angle?

The third shift angle? 3 becomes? 3 = 0 when applying the standard loft angle or the actual loft angle at the time of addressing, and PsL = 100 points is given. The scoring of the third shift angle? 3 is calculated by substituting P = 100, T = 0, Tz = 1, A = 15, R =? 3 in the equations (8) .

(6-1-7) The performance score of the fourth shift angle? 4 Psa

The fourth shift angle? 4 becomes? 4 = 0 and PsA = 100 points when the impact is made parallel to the target line. Scoring of the fourth shift angle? 4 is calculated by substituting P = 100, T = 0, Tz = 1, A = 15, R =? 4 in the equations (8) .

The performance score PS for each analysis item is displayed as a numerical value in the PS column of the analysis screen for each analysis item described above.

(6-2) Scoring of total points

The above analytic items are largely divided, and the analysis items (the first shift angle? 1, the second shift angle? 2 and the shift distance from the sweet spot) related to the directionality and the analysis items (V), swing width (L), third shift angle? 3, and fourth shift angle? 4). Therefore, the sum of the weighted points of the analytical items is as follows: 1) a total point about directionality, 2) a total point about distance feeling, and 3) a total point about directionality and distance feeling.

(6-2-1) Scoring of total point of analysis item about directionality of batting

The weighting coefficient when three analytical items relating to the directionality (the first shift angle? 1, the second shift angle? 2, and the shift amount? From the sweet spot) is used is defined as follows. WS is the weighting coefficient of the performance score PsS with respect to the first deviation angle (absolute face angle)? 1, WF is the weighting factor of the performance score PsF with respect to the second deviation angle (square degree)? 2, WH is the weight coefficient of the performance score PsH with respect to the displacement amount delta from the spot.

The weighting coefficient WS for the first shift angle? 1 is larger than the weighting coefficient WH for the shift amount? (WS> WH), taking into consideration the degree of influence on the directionality of the ball. Further, the weighting coefficient WH for the shift amount? Is larger than the weighting coefficient WF for the second shift angle? 2 (WH> WF). Therefore, the relationship of the three weighting coefficients is as follows.

WS> WH> WF ... (10)

The total point of the analysis items regarding the directionality of the batted ball is as follows when three data? 1,? 2 and? Are used.

SUM (each PS × each weighting factor) / SUM (each weighting factor)

= (PsFWF + PsSWS + PsHWW) / (WF + WS + WH) (11)

The total point of the analysis items relating to the directionality of the batted ball is as follows when two data? 1 and? Are used.

SUM (each PS × each weighting factor) / SUM (each weighting factor)

= (PsF x WF + PsH x WH) / (WF + WH) (12)

The total point of the analysis items relating to the directionality of the batted ball is as follows when two data? 2 and? Are used.

SUM (each PS × each weighting factor) / SUM (each weighting factor)

= (PsS 占 WS + PsH 占 WH) / (WS + WH) ... (13)

The total point of the analysis items regarding the directionality of the batted ball is as follows when two data? 1 and? 2 are used.

SUM (each PS × each weighting factor) / SUM (each weighting factor)

= (PsF x WF + PsS xWs) / (WF + WS) ... (14)

(6-2-2) Scoring of total point of analysis item about distance feeling of batting

The weighting coefficient when four analytical items (impact speed (V), swing width (L), third shift angle (? 3), and fourth shift angle (? 4)) regarding the sense of distance are used is defined as follows. The weight coefficient of the performance score PsI with respect to the impact speed V is WI, the weight coefficient with respect to the performance score PsB of the swing width L is WB, and the third shift angle (delta-loft angle) The weighting coefficient of the performance score PsL relating to the fourth shift angle (attack angle) 4 is WA, and the weighting coefficient of the performance score PsA related to the fourth shift angle (attack angle) 4 is WA.

The weighting factor WI for the impact speed V is greater than the weighting factor WB for the swing width L (WI > WB), taking into account the degree of influence on the distance sensibility of the batted ball. The weighting coefficient WB for the swing width L is larger than the weighting coefficient WA for the weighting coefficient WL and the fourth shift angle? 4 with respect to the third shift angle? 3 (WI> WB> WL, WI> WB> WA). Since the third shift angle? 3 and the fourth shift angle? 4 are correlated with each other, the weighting coefficient WA for the weighting coefficient WL and the fourth shift angle? 4 with respect to the third shift angle? (WL = WA). Therefore, the relationship of the four weighting coefficients is as follows.

WI> WB> WL = WA ... (15)

The total point of the analysis items concerning the sense of distance of the batted ball is as follows when four data V, L,? 3 and? 4 are used.

SUM (each PS × each weighting factor) / SUM (each weighting factor)

= (PsIWI + PsBWB + PsLWL + PsAWA) / (WI + WB + WL + WA) (16)

The total point of the analysis items regarding the sense of distance of the batted ball is as follows when three data V, L and? 3 are used.

SUM (each PS × each weighting factor) / SUM (each weighting factor)

= (PsIWI + PsBWB + PsLWL) / (WI + WB + WL) (17)

The total point of the analysis items related to the sense of distance of the batted ball is as follows when three data V, L and? 4 are used.

SUM (each PS × each weighting factor) / SUM (each weighting factor)

= (PsI x WI + PsB x WB + PsA x WA) / (WI + WB + WA) ... (18)

The total point of the analysis items regarding the sense of distance of the batted ball is as follows when two data V and L are used.

SUM (each PS × each weighting factor) / SUM (each weighting factor)

= (PsI x WI + PsB x WB) / (WI + WB) (19)

(6-2-3) Scoring of the total points of analysis items about directionality and distance feeling

Considering the directionality and distance feeling of the ball, considering the degree of swing improvement and influence on the athletic game, the directionality of the ball is important. Also, among the analysis items related to the directionality of the batted ball, the analysis items (for example, V and L) having a high degree of influence among the analysis items related to the distance feeling of the ball are more important than the analysis items having low influence have. Based on the equations (10) and (15), the relationship of the weighting factors to the seven analytical items (θ1, θ2, δ, V, L, θ3 and θ4) Together.

WS> WH> WI> WB> WF> WL = WB ... (20)

The sum of the performance score Ps (directionality) relating to the directionality represented by any one of the expressions (11) to (14) and the performance score Ps (distance feeling) relating to the directionality represented by any one of the expressions (16) Of the performance score Ps (stability and distance) is as follows.

Performance Score Ps (Stiffness + Distance)

= a × performance score Ps (directional)

 + B × performance score Ps (distance sense) ... (21)

Here, the weighting coefficients a and b may be a = b = 1, and in addition to them, a> b may be regarded as the directionality.

A performance score Ps, a performance score Ps (directionality) or a b performance score Ps (distance feeling) are displayed in a score, and analysis data of a plurality of analysis items used for the displayed performance score are displayed, for example, A radar-chart or the like.

As described above, the present embodiment has been described in detail, but it will be readily understood by those skilled in the art that many modifications are possible without departing from the novel features and effects of the present invention. Accordingly, all such modifications are included in the scope of the present invention. For example, in the specification or drawings, terms described with other terms that are at least once more broadly or synonymously may be substituted with other terms in the specification or drawings at any point. The configuration and operation of the inertial sensor 12, the golf club 13, the arithmetic processing circuit 14, and the like are not limited to those described in the present embodiment, and various modifications are possible. For example, the present invention is not limited to golf but can be applied to sports balls such as baseball and tennis.

11: Motion analysis device (golf swing analysis device) 12: Inertial sensor
13: Running track (golf club, putter) 13c: Club head
13c1: face surface 13d: first measurement point
13e: second measuring point 14: computer (arithmetic processing circuit)
17: Motion Analysis Program (Golf Swing Analysis Software Program)
18: Image processing circuit 19: Display device
50: swing coordinate position detecting unit 60: speed detecting unit
70: Address interpreting section 71:
72: Position specifying section 80: Impact analyzing section
81: Attitude specifying section 82: Trajectory specifying section
90: Planar direction analysis unit 100: Hit point analysis unit
110: frontal direction analysis section
111: Third misalignment angle analysis section (difference analysis section)
112: fourth misalignment angle analysis section (difference analysis section)
140: Statistical analysis section
L1: face face posture at the address
L2: target direction (target line)
L3: Face surface attitude at impact
L4: motion vector component
L4 ': the virtual batting direction set on the extension line of L4
L5: Striking direction set as the normal of L3
? 3: Third shift angle (delta-loft angle)
? 4: fourth shift angle (attack angle)

Claims (20)

(Difference) between an inclination angle of a striking surface of a moving ball at the time of impact and a reference inclination angle acquired in advance by using the output of the inertia sensor. The method according to claim 1,
The exercise area is a golf club,
Wherein the reference inclination angle is a standard value which is a loft angle of a golf club. The method according to claim 1,
Wherein the reference inclination angle is specified using the output of the inertial sensor when the moving ball is stationary. The method according to claim 1,
Wherein the inclination angle of the impact surface and the reference inclination angle are displayed in a coordinate system. The method of claim 4,
In a front view (a front view) facing the user operating the exercise ball in front,
And an image of the moving ball is displayed in a superimposed manner on the coordinate system. The method of claim 5,
The image of the moving ball on the display screen is displayed at a predetermined position,
And the display position of the reference inclination angle is rotated by the same angle as the difference and displayed. The method of claim 4,
Wherein the tilt angle of the striking surface specified in the past is displayed on the coordinate system separately from the tilt angle of the striking surface specified this time. The method of claim 4,
Wherein the target area including the reference inclination angle is distinguished from other areas and displayed. The method of claim 8,
Wherein the ratio of the number of times the inclination angle of the impact surface enters the target area is displayed for the number of times the inclination angle of the impact surface is specified. An output of the inertial sensor is used to specify the tangential direction at the time of impact with respect to the movement trajectory of the moving ball projected on the vertical surface,
Wherein a crossing angle between the target direction projected on the vertical surface and the tangential direction is specified. An impact analyzing unit for specifying an inclination angle of a striking surface of the moving ball at the time of impact using the output of the inertial sensor,
And a difference analysis unit for specifying a difference between the inclination angle of the striking surface and a reference inclination angle acquired in advance. The method of claim 11,
The exercise area is a golf club,
Wherein the reference inclination angle is a standard value which is a loft angle of a golf club. The method of claim 12,
Wherein the reference inclination angle is specified by using the output of the inertia sensor when the moving ball is stopped. The method of claim 12,
Wherein the inclination angle of the impact surface and the reference inclination angle are displayed in a coordinate system. 15. The method of claim 14,
In a frontal view facing the user operating the exercise ball in front,
And displays the image of the moving ball overlaid on the coordinate system. 16. The method of claim 15,
The image of the moving ball on the display screen is displayed at a predetermined position,
And the display position of the reference inclination angle is rotated by the same angle as the difference and displayed. 16. The method of claim 15,
Wherein the inclination angle of the impact surface specified in the past is displayed in the coordinate system separately from the inclination angle of the impact surface specified in the present time. An impact analyzing unit for specifying the tangential direction at the time of impact with respect to the movement locus of the moving ball projected on the vertical surface by using the output of the inertial sensor,
And a crossing angle analyzing unit for specifying an intersection angle between the target direction projected on the vertical surface and the tangential direction. The order of specifying the inclination angle of the striking surface of the moving ball at the time of impact using the output of the inertia sensor,
And a movement analyzing program for causing the computer to execute a procedure for specifying a difference between the inclination angle of the impact surface and a reference inclination angle acquired in advance. The order of specifying the tangential direction at the time of impact with respect to the movement trajectory of the moving ball projected on the vertical plane using the output of the inertial sensor,
And a movement analyzing program that causes the computer to execute a procedure of specifying an intersection angle between the target direction projected on the vertical surface and the tangential direction.

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