CN1768881A - Method and apparatus for measuring and positioning golf club shafts - Google Patents

Abstract

By measuring the vibration (20, 21) of the golf club shaft (110) when the pulse is applied, a preferred orientation or planar vibration plane of the shaft (110) is determined. Preferably, out-of-plane vibration is measured at a large number of angular positions about the shaft (110) axis, and the principal planar vibration plane is identified by the pair of relative angular positions at which the out-of-plane vibration is minimal. The position of the preferred orientation may be marked on the shaft (110) and used to fit the golf club having the planar vibration face in a predetermined orientation. The straightness of the shaft (110) can also be determined by deriving its spring constant from its vibration frequency and then measuring the restoring force of the shaft when it is deflected by the same nominal amount at different angular positions; the difference in recovery forces can be considered to be the result of the difference in actual deflection distance caused by the difference in straightness.

Description

Method and apparatus for measuring and positioning golf club shafts

The present invention is a divisional application of the invention patent application No.01821553.X filed on November 9, 2001, entitled "Method and Device for Measuring and Positioning Golf Club Shaft".

technical field

This invention relates to the measurement and positioning of golf club shafts. In particular, the present invention relates to a method and apparatus for automatically and reliably identifying the position of the Planar oscillation plane of a golf club shaft, particularly the principal Planar oscillation plane, such that the Planar oscillation plane is positioned at Desired azimuth alignment, as well as determining golf club shaft performance parameters such as roundness, stiffness, and straightness that characterize golf clubs.

Background technique

When a golfer swings a golf club, the shaft of the golf club bends or twists, especially during the downswing. The direction in which the shaft bends or twists depends on how the golfer loads or accelerates the club, but the direction and magnitude of the bend or twist also depends on the stiffness of the shaft. If the shaft is soft, it is more likely to bend or twist during the known downswing than a stiffer shaft. In addition, if the shaft has different lateral stiffness in different planes, that is, if the stiffness, roundness and straightness of the shaft are not symmetrical, the shaft will bend or twist differently depending on the plane (direction) of its load.

Just before the head of the golf club hits the golf ball, the shaft of the golf club undergoes a series of tests in the top up/down direction (the plane perpendicular to the ball hitting direction) and the lead/lag direction (the plane parallel to the ball hitting direction). Noticeable vibratory movement. Studies have shown that the shaft of a golf club vibrates up and down in the top up/down direction just before the golf ball is hit. This up-and-down motion, known as "vertical deflection vibration," "vertical deflection vibration," or "tilt vibration," can be up to ±1.5 inches (±3.8 cm). Inconsistent flex or twist makes it more difficult for the golfer to reproduce the flex or twist of the downswing shaft from club to club, creating inconsistent shot repeatability in a set of clubs. Because it is essentially impossible for a golfer to correct any inconsistent bend or twist caused by asymmetrical shaft behavior just before impact with his or her swing, any aforementioned The reduction in vibration will help the golfer improve the repeatability of his or her shots, thereby improving performance. This works for golfers of all skill levels.

Also, just before hitting the ball, the golf club "bounces" forward in the direction of the impact. This is often referred to as the "bounce" of the shaft. If the shaft can be analyzed and positioned in such a way that the bouncing direction of the vibration is stable, the shaft position improves the golfer's ability to repeat the shot position. In other words, there is very little "wiggle" up and down the shaft just before impact, which improves shot repeatability.

Inconsistent flex or twist affects clubhead motion that would not exist if the shaft were perfectly symmetrical. Manufacturers of golf club shafts attempt to manufacture shafts with symmetric stiffness to minimize inconsistent flex or twist during the swing, but due to manufacturing limitations, it is difficult to manufacture golf club shafts that are completely symmetrical. In particular, golf club shafts are known to have a preferred angular orientation due to irregularities or variations in materials or manufacturing processes. For example, golf club shafts are sometimes referred to as having "spines," the orientation of which is apparent (see US Pat. Nos. 4,958,834 and 5,040,279, the entire contents of which are hereby incorporated by reference). Accordingly, substantially all golf club shafts have some degree of asymmetry that produces some degree of inconsistent flex or twist during the swing.

Asymmetry in golf club shafts can result from cross-sectional asymmetry (non-round shaft cross-section or uneven wall thickness), shafts that are not straight, or shaft material properties that vary around the circumference of the shaft cross-section. Because it is basically impossible to manufacture perfectly symmetrical golf club shafts, and the goal is to minimize club-to-club inconsistencies in a set of golf clubs and inconsistencies from cover to cover of a brand, such as Possibly, each golf club in a set can be analyzed to understand its asymmetric flex or twist behavior, and the golf clubs in a set can be made between clubs and clubs in a set As well as having the greatest consistency between sets of a grade.

For example, in above-incorporated U.S. Patent 5,040,279, it has been recognized that, while substantially all golf club shafts have some degree of asymmetry, substantially every golf club shaft has at least one orientation in which, When the shaft is clamped at its proximal or handle end and moved at the tip, the resulting vibration of the shaft will still be substantially in-plane. That is, the shaft still lies substantially in a single plane, and the tip of the shaft will vibrate back and forth substantially along a line.

It was also recognized in above-incorporated U.S. Patent 4,958,834 that, during a downswing, the configuration of all golf clubs in a set will exhibit Results: Shafts have less inconsistency in bending or twisting where their respective planar planes of oscillation ("POPs") are oriented in the same angular direction with respect to their corresponding clubfaces. In particular, a set of golf clubs will generally operate optimally if the corresponding preferred angular orientation of each golf club shaft is aligned in the "ball-strike direction", that is, substantially perpendicular to the corresponding golf club face .

However, to date there has not been any convenient automated way to consistently determine golf club shaft parameters that would allow manufacturers or others to predict golf club shaft performance. Co-pending, assigned U.S. Patent Application 09/494,525 shows a method and apparatus for determining the preferred angular orientation of a golf club shaft, in part manually, and relying on an iterative approach to identify Plane vibration planes are identified as plane vibration planes different from the main plane vibration planes, wherein the filing date of this application is February 1, 2000, the entire content of which is hereby incorporated by reference. It would be desirable to provide a method and apparatus for quickly and reliably determining the preferred angular orientation of a golf club shaft. It would also be desirable to be able to provide a method and apparatus for using the determination of preferred angular orientations to automatically fit golf clubs in which each golf club shaft is consistently aligned with respect to a corresponding club face. It would also be desirable to be able to determine parameters of golf club shafts to predict golf club performance.

Contents of the invention

It is an object of the present invention to provide a method and apparatus for quickly and reliably determining the preferred angular orientation of a golf club shaft.

Another object of the present invention is to provide a method and apparatus for assembling golf clubs (manually or automatically) using the determination of preferred angular orientations, such as planar vibration surfaces, especially principal planar vibration surfaces, wherein each golf club shaft is opposite consistent alignment with the corresponding clubface.

Yet another object of the present invention is to determine golf club shaft parameters to predict golf club performance.

In accordance with the present invention, there is provided a method of determining the preferred angular orientation of a golf club shaft about its longitudinal axis, wherein the golf club shaft has a proximal end held by a golfer and a shaft secured to the golf club. the distal end of the head. According to this method, the proximal end of the golf club shaft is held stationary and the distal end of the golf club shaft is initiated to vibrate in a direction that is not parallel to the longitudinal axis. The vibration is analyzed, and the preferred angular orientation is calculated from the analyzed vibration. The golf club shaft is then marked to indicate the preferred angular orientation. In another method of the invention, markings on the shaft indicating a preferred angular orientation can be used to manually or automatically fit golf clubs in which the golf club shaft is in a predetermined alignment with respect to the golf club head face.

Means for determining a preferred angular orientation and fitting a golf club are also provided.

In particularly preferred methods and apparatus, the vibration of the golf club shaft is analyzed at a plurality of angular positions about the longitudinal axis of the shaft. The more the number of positions, the more accurate the detection of the plane vibration surface, especially the main plane vibration surface. Additionally, at each location, the vibration frequency of the shaft, which is a measure of shaft stiffness, can be determined. Furthermore, if a shaft is deflected from its longitudinal axis, then by measuring the restoring force against the deflection and the amount of shaft deflection at each angular position, we can determine the straightness of the shaft, or rather the shaft The degree of uprightness. Roundness, straightness and stiffness are parameters that characterize golf club shaft performance, and shaft manufacturers have found ways to accurately determine these parameters.

Description of drawings

These and other objects and advantages of the present invention will be apparent from the following detailed description when read in conjunction with the accompanying drawings, in which like reference characters designate like parts, wherein:

Figure 1 is a view of simulating a flexible golf club shaft as a substance with a spring fixed thereto;

Figure 2 shows the horizontal and vertical displacement of the shaft of Figure 1 as a function of time, viewed from the endpoints, over two cycles of vibration after a pulse has been delivered to vibrate the shaft;

Figure 3 shows a phase diagram of the motion of Figure 2;

Figure 4 shows a phase diagram of shaft motion after 14 vibration cycles;

Figure 5 shows the motion in Figure 4, but as a function of time;

Figure 6 is a perspective view of a first preferred embodiment of the apparatus of the present invention for determining a preferred orientation of a golf club shaft;

Figure 7 is a perspective view of the shaft test assembly of the apparatus of Figure 6;

Figure 8 is a perspective view of the shaft fixing and rotating assembly of the apparatus of Figures 6 and 7;

Figure 9 is a perspective view of the measurement assembly of the apparatus of Figures 6-8;

Figure 10 is a perspective view of the tip mass and sensor assembly of the device of Figures 6-9;

Figure 11 is a view similar to Figure 7 with the golf club shaft installed in the device;

Figure 12 is an elevational view taken along line 12-12 of Figure 11 but with a deflected golf club shaft poised to vibrate in accordance with the present invention;

Figure 13 is a perspective view of the device of Figures 6-10 including a marker assembly;

14 is a flowchart of a preferred embodiment of a method of the present invention for determining a preferred orientation of a golf club shaft;

Figure 15 is a flow chart of a load test performed as part of the method of Figure 14 in accordance with the present invention;

Figure 16 is a flowchart of a "mark up" comparison test performed as part of the method of Figure 14 in accordance with the present invention;

Figure 17 is a flowchart of a planar vibration surface positioning test performed as part of the method of Figure 14 in accordance with the present invention;

Figure 18 is a perspective view of a second preferred embodiment of the apparatus of the present invention for determining a preferred orientation of a golf club shaft;

Figure 19 is a side view of the measuring assembly of the device of Figure 18;

Figure 20 is an end view of the measuring assembly of Figure 19;

21 is a graph of maximum out-of-plane acceleration or displacement of the shaft tip as a function of angle of rotation when measured using the apparatus of FIG. 18;

22 is a graph of the deviation of the center of the tip of a typical golf club shaft from the longitudinal axis running through the center of the butt end of a typical golf club shaft as a function of angle, as measured by the apparatus of FIG. 18;

Figure 23 is a view of the assembled golf club device of the present invention;

Figure 24 is a close-up view of the assembly station of the device of Figure 23;

Figure 25 is an example of a printout illustrating test results for individual shafts;

Figure 26 is a perspective view of an alternative preferred embodiment of the tip material assembly of the present invention;

Figure 27 is a schematic front view of the tip substance assembly of Figure 26 mounted on the tip of a golf club shaft in the rest position of the device of the present invention;

Fig. 28 is a schematic front view, similar to Fig. 27, of the tip substance assembly of Fig. 26 mounted on the tip of a golf club shaft in a shifted position of the apparatus of the present invention.

Detailed ways

If a golf club shaft is stationary at its handle end and moves in a direction perpendicular to its longitudinal axis, then if the direction of movement is in the plane of vibration of the shaft, the shaft will vibrate in that plane, from Looking at the tip forward, the far end of the shaft will vibrate back and forth along a line. For convenience, this line is referred to as the x-axis. However, if the direction of movement lies in a plane other than the plane of vibration, the distal end of the shaft vibrates with a motion having a component along the x-axis as well as a component along an axis perpendicular to the x-axis. For convenience, the This axis perpendicular to the x-axis is called the y-axis. This motion can be described as "orbital" motion, although its trajectory is different from that of a single ellipse or other closed curve, the tip will move in an enveloping surface, so that, if the motion does not weaken (and in fact does), it is expected that The tip ends up moving through every point in the envelope.

As described below, by observing the tip vibration of the shaft, we can mathematically calculate the orientation of one or more planar vibration planes. When one or more planar vibration surfaces have been positioned, we can assemble the golf club and position the shaft relative to the golf club head so that the planar vibration surfaces, especially the primary plane vibration surfaces, are aligned along the "ball-strike" direction, That is, substantially perpendicular to the ball striking face of the club head or 180° relative to that direction. When the planar vibrating surface of the golf club shaft has been positioned, it is also possible to align the planar vibrating surface relative to the golf club head not along the hitting direction, but along another predetermined direction.

For example, it may be desirable to align the shaft for a particular golfer to correct or direct hook or slice. Thus, for a right-handed golf club, to guide a slice or correct a slice, we turn the shaft counterclockwise (looking down at the clubhead toward the shaft), and to guide a slice or correct a slice, we turn will turn the shaft clockwise. For left-handed golf clubs, the direction of rotation is reversed. The amount of rotation is preferably less than about 90°.

It has been empirically observed that golf club shafts behave as if they are "harder" in one direction along any planar plane of vibration than in the opposite direction along that plane of vibration. The "hard" side of the shaft's planar vibrating surface may be referred to as the "hard" or "front" side of the planar vibrating surface, while the non-stiff side at 180° to the hard side may be referred to as the "hard" or "front" side of the planar vibrating surface. soft" or "rear" side. It has also been observed that locating the planar vibration plane perpendicular to the club head face produces different results compared to an accidental or random arrangement. It has further been observed that by aligning the planar vibrating surface perpendicular to the club head face with the hard side of the planar vibrating surface facing the club head face produces a different The result of the soft-side alignment. Also, if every golf club in a set were equally aligned, it would likely enable users of those clubs to achieve more even and consistent results across all clubs in the set, which could Expected to enhance performance.

Furthermore, it has been empirically observed that a golf club shaft will have several planar vibration surfaces. However, it has been found that there is only one principal planar vibration plane ("POPP"), which may also be referred to as the plane of uniform repeatability ("PURE"). A golf club aligned according to the principal plane of vibration may be expected to enhance optimum performance.

While the orientation of one or more planar vibration planes can be mathematically derived from data collected by moving the shaft tip and allowing the shaft to vibrate, it is computationally simpler to derive the orientation by the iterative method described below. Iterative calculations can be performed by employing a device that directs golf club shaft vibrations in multiple angular orientations, thereby measuring tip vibrations in each orientation. The device may be partly manual in that the shaft is manually rotated to a new orientation for the measurement, or the device may be used so that the shaft is automatically rotated to subsequent positions after measurements have been made at the previous position. If the rotation of the shaft is performed automatically, the device can operate more quickly, allowing golf club shafts to be measured at more angular orientations, which can be expected to more accurately determine the principal plane of vibration.

The preferred orientation of the plane of vibration, ie, the "hard" side of the golf club shaft in the case of the principal plane of vibration, cannot be determined mathematically by simply observing the shaft tip. Therefore, in a preferred embodiment of the present invention, the handle or butt end of the golf club shaft is stationary, the top end of the shaft moves perpendicular to the longitudinal axis, and the shaft rotates at least about 360° from the handle end. Measures the restoring force, the force required to return the tip to its resting position. The angle at which the restoring force is greatest indicates the hard side of the shaft. Although this angle will generally not align exactly with the orientation of the principal plane vibrating surface, it will indicate which of the two possible orientations of the principal plane vibrating surface corresponds to the hard side of the principal plane vibrating surface. Also, starting the analysis at the angle of maximum load will lead us to find the main plane of vibration rather than one of the other planes of vibration of the shaft. This is especially useful in an embodiment where shaft vibration is measured at only a relatively small number of angular positions, such as the partially manual embodiment described above. The initial position is less important in embodiments where measurements are made at a relatively large number of angular positions, such as the above-described embodiment in which the golf club shaft rotates automatically between positions. In both cases the starting orientation can be chosen arbitrarily.

Once the preferred angular orientation of the golf club shaft has been determined, one or more markings are preferably made on the shaft to indicate the preferred angular orientation. The one or more markings may be made at the position of the planar vibrating surface, or at a predetermined relative position with respect to the planar vibrating surface. Each marking may be made using ink or paint, or may be etched into the surface of the shaft using another technique such as mechanical, electrostatic or laser marking, or may be labeled with the marking (such as a sticker or decal) . Once one or more markings have been made, they can be used to align the shaft relative to the golf club head when assembling the golf club so that the plane of vibration of the golf club shaft markings is substantially perpendicular to the face of the club head or in other ideal positions.

Alignment of the shaft relative to the head can be done manually. Preferably, alignment is easily accomplished by also providing markings on the club head, which can be aligned with respect to positions on or near the iron socket or hole to create a suitable fit. A "spine-aligned" golf club. Alternatively, in another preferred embodiment, an assembly machine is used to mate the golf club head with the golf club shaft to match the alignment marks during operation. In this embodiment, the golf club head can be secured to the shaft just after the preferred angular orientation of the shaft has been determined, with the shaft still in the chuck of the planar vibrating surface positioning station (in this case, it is not necessary to use the shaft outside the shaft). Apply a visual marker, although it is useful for subsequent repair operations that remove the club). Alternatively, in yet another variation of this embodiment, the shaft may be removed from the planar vibration surface positioning station and moved to the club assembly station. This modification better accounts for any velocity differences between the planar vibration surface positioning process and the club assembly process. If the planar vibration surface positioning process is faster than the club assembly process, there may be more club assembly stations than planar vibration surface positioning stations. If the club assembly process is faster than the planar vibration surface positioning process, there may be more planar vibration surface positioning stations than club fitting stations. In both cases it is preferred to provide a hopper or other intermediate station to maintain the spine-aligned shafts between the planar vibration surface positioning station and the club fitting station. Normally, we would want to keep fewer shafts in the hopper, but if there is some reason for a break or other bottleneck at or downstream from one or more club fitting stations, the hopper can be used as a The vibratory surface positioning station accepts the container of shafts until it is full.

In addition to positioning the planar vibrating surface of the golf club shaft, whether realigning an existing golf club or fitting a new golf club, the present invention is particularly the above-described embodiment wherein the shaft is changed from a The angular position is automatically rotated to another angular position for measurement allowing measurements at more angular positions, providing the ability to measure certain characteristics of the shaft which can be used to monitor the shaft manufacturing process and the quality of the resulting shaft. These measurements provide quality criteria for the manufacture of golf shafts.

Specifically, at each angular position, the vibration frequency of the shaft is measured when the shaft is deflected and allowed to vibrate. This is simply done by counting the number of times the vibrating shaft passes a fixed point during a specified time interval. One way of performing this counting function is to provide a light source and a photodetector and count the number of times at specified time intervals when the light beam from the light source is broken by the vibrating shaft. In an alternative preferred method, the vibrations recorded by the accelerometer data (see below) can be counted in specific time intervals.

Once the characteristic frequency of vibration has been determined, the spring constant of the shaft can be estimated by considering the shaft as a prismatic beam of mass M and deriving the spring constant k from the frequency f using the relationship f≈(k/M) ^0.5 , It is a measure of shaft stiffness. The stiffness of the shaft can then be characterized by the value of k for each angle, all parameter values will be described in detail below.

At each angular position, the load test can also be carried out by deflecting the shaft perpendicular to its longitudinal axis by a fixed distance d and measuring the resulting restoring force F. From the force F and the spring constant k determined above, we can use the relationship F/k=d+δ to determine the deflection δ, which is a measure of the straightness of the shaft. The straightness of the shaft can then be characterized by the delta value for each angle, all parameter values will be described in detail below.

The present invention will now be described with reference to Figures 1-24.

The stiffness of a golf club shaft can be simulated by clamping the handle end of the golf club shaft in a clamp that holds the shaft horizontally and looking towards the tip of the distal end of the shaft, as shown in Figure 1. As can be seen from FIG. 1, the shaft 10 can be considered as a mass m to which two springs with different spring constants _k1 and _k2 are aligned in two directions normal to two different surfaces 11,12. Material connection. If the shaft 10 were symmetrically rigid, k ₁ and k ₂ would be equal. Usually, however, k ₁ and k ₂ are different. In fact, if we clamp the shaft in several different orientations and measure the horizontal and vertical restoring forces each time, we will get a different set of values for _k1 and _k2 . As shown, the force F is the force applied to move the tip of the clamped shaft 10, for example to vibrate it.

Figure 2 shows the nominal horizontal and vertical displacements of the vibrating tip of the shaft 10 as a function of time in two vibration cycles, where the horizontal displacement (x) is represented by the solid line 20 and the vertical displacement (y) by the dashed line 21 Representation, assume that the initial moving force is at an angle of θ = 40° to the horizontal. Figure 3 shows the same displacement of the tip of the shaft 10 in two cycles in the x and y directions as in the phase diagram 30, i.e., Figure 3 shows the displacement along the shaft 10 by the observer looking towards the Two cycles of the path taken by the tip as it is viewed on the vertical axis. Figure 4 shows a phase diagram 40 after 14 cycles. Analysis of these observed motions yields the position of the plane of vibration, i.e., the angular orientation of the shaft 10 along which the shaft 10 will substantially only vibrate if an initial movement force F is applied, The tip basically vibrates back and forth along a straight line.

As shown in FIG. 4 , the phase diagram 40 of tip movement after enough cycles is substantially a rectangle. The orientation of the planar vibrating surface is one of the two perpendicular axes of the rectangle, each axis of the rectangle is defined as a line located in the middle of a pair of corresponding sides of the rectangle and parallel to the corresponding pair of sides of the rectangle. In the case of a true rectangle, it is sufficient to determine the orientation of the sides, since by the definition just made the orientation of the sides and the axis is the same. However, if the phase diagram 40 of the tip motion of the golf club shaft cannot be a true rectangle unless we observe an infinite number of cycles, this is impractical, firstly, commercially unacceptable, and secondly, golf Vibration in the club shaft usually subsides before a true rectangle is observed. Therefore, by assuming that the lines drawn from the four vertices of the quasi-rectangle of the phase diagram are the diagonals of the rectangle, the orientation of each of the two axes can be calculated.

Now that the two axes of the rectangle have been found, it is desired to determine which one is the major axis corresponding to the main plane vibration plane and which one is the short axis, that is, to determine one of the one or more unstable plane vibration planes. This can be strictly determined by measuring the vibration frequency along the two axes, as will be described below. If the shaft is vibrated in a certain direction, the major axis is expected to correspond to the principal plane of vibration by measuring the angle-dependent load on the deflected shaft and selecting the angle of maximum load as the direction in which the shaft is to be vibrated And sure. It should be noted that this "load test" can be performed by clamping the top or distal end of the shaft, or the handle or proximal end, and measuring the load relative to the angle of deflection of the unclamped end. However, the subsequent step of positioning the planar vibrating surface is preferably performed with the handle or proximal end clamped, so the load test is also preferably performed in this manner. It should also be noted that, without load testing, we would find a plane of vibration, but this plane of vibration may not be the main plane of vibration.

Figure 5 shows a tip vibration profile 50 as a function of time, with individual traces of vibration 51 measured along the horizontal (x) axis and individual traces of vibration 52 measured along the vertical (y) axis. From these trajectories, the frequency can be determined, eg by calculating the positive zero crossings graphically. However, these horizontal and vertical axes x and y deviate from the planar vibration plane by an angle determined as described above. If this angle is denoted as θ, the frequencies determined from the curves in Figure 5 along these axes x and y can be converted to a coordinate system for the golf club shaft having axes x' and y' which correspond to a The stable plane of vibration corresponds to one of one or more unstable planes of vibration, as described below, _f1 is the frequency at an angle θ with the x-axis, i.e. along the x' axis, and _f2 is the frequency with the y-axis Frequency at angle θ (θ+90° from the x-axis), ie along the y' axis.

${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="f"\; filenames="A20051009991800461.png,A20051009991800601.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">y</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="cos"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">cos</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">y</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; cos</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="cos"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">cos</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; cos</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; 5</span>}}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">y</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="cos"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">cos</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="cos"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">cos</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="f\; x"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">f</figure-callout></span><figure-callout\; id="2"\; label="f\; x"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}^{\mathrm{<span\; class="notranslate">x</span>}}}<span\; class="notranslate">\; |</span>$

${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="f"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">y</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="cos"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">cos</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">y</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; cos</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="f\; x"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">f</figure-callout></span><figure-callout\; id="2"\; label="f\; x"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}^{\mathrm{<span\; class="notranslate">x</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="cos"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">cos</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; cos</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; 5</span>}}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">y</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="cos"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">cos</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="cos"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">cos</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="f\; x"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">f</figure-callout></span><figure-callout\; id="2"\; label="f\; x"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}^{\mathrm{<span\; class="notranslate">x</span>}}}<span\; class="notranslate">\; |</span>$

If f ₁ is greater than f ₂ , one of the golf club shaft's stable planar vibration planes is at an angle θ with respect to the x-axis. If f ₁ is less than f ₂ , one of the golf club shafts has a stable planar vibration plane at an angle θ with respect to the y-axis, ie at an angle θ+90° with respect to the x-axis. If a load test has been performed and used to determine the initial angle of vibration, the stable planar vibration plane thus positioned can become the principal plane of vibration.

While this mathematical method for determining which identified plane of vibration is the primary plane of vibration is rigorous and precise, it does not include all parameters that affect shaft vibration. Accordingly, in another preferred embodiment of the present invention, as described above and described in more detail below, the position of the principal plane of vibration is relative to the first Approximately positioned, i.e. at least positioned in the correct quadrant. This has the additional advantage of quickly identifying the "hard" side of the vibrating surface of the principal plane, as described above.

A first preferred embodiment of a device 60 for implementing the invention is shown in Figures 6-13. Although apparatus 60 can employ the rigorous mathematics described above, it has been determined in practice that a simpler iterative method described below achieves acceptable results at lower cost. Therefore, in a particularly preferred embodiment, device 60 employs this simpler approach.

In the preferred embodiment, the device 60 includes a shaft inspection device 70 and a processor 61 . Processor 61 may be any system capable of processing input data from sensors 74 and 77 of shaft inspection apparatus 70 and performing the rigorous mathematical calculations described above or the simple iterative calculations described below. As shown in FIG. 6, processor 61 is preferably a general-purpose computer such as a personal computer, such as a ^Pentium® central processing unit (CPU) 62 available from Intel Corporation, Santa Clara, California, running A version of the WINDOWS ^(R) operating system programmed with the software described below is available from Microsoft Corporation, Mond. However, processor 61 may also be hardwired circuitry or one or more programmable logic devices programmed to perform the necessary functions for positioning one or more planar vibration surfaces of the golf club shaft. In any event, the processor 61 preferably also includes a memory 63 and a mass storage 64 as well as interfaces to the sensors described below.

Shaft testing device 70 preferably includes an elongated base 71 that is at least as long as the golf club shaft. At one end of the base 71 is a measurement assembly 72 including a deflection assembly 73 and a deflection load sensor 74 . The other end of the base 71 is a shaft fixing and rotating assembly 75 including a rotatable chuck 76 for fixing the golf club shaft. Apparatus 60 also includes a tip mass and sensor assembly 77 mounted on the distal end of the golf club shaft and cooperating with deflection assembly 73 during testing of the golf club shaft.

As shown in FIG. 8, the shaft fixation and rotation assembly 75 preferably includes a rotatable chuck 76, preferably of a conventional type, preferably secured by applying a radially inward force substantially uniformly around the circumference of the shaft. Golf club shaft. The chuck 76 is preferably mounted on the end of a shaft 80 which is preferably journaled in a bearing 81 . Bearing 81 is preferably mounted on bracket 82 such that the axis of rotation of shaft 80, including chuck 76 and the extension of the detected golf club shaft, is at a predetermined height above base 71. The end of the shaft 80 remote from the chuck 76 is preferably connected via a universal joint 83 to a potentiometer 84, which is used as an angular position sensor described below. Universal joint 83 prevents any slight misalignment between the axis of shaft 80 and the shaft of potentiometer 84 from damaging potentiometer 84 . Likewise, a travel nut 85 is preferably provided on the shaft 80 to act as a rotational stop to limit the rotation of the shaft 80 to prevent damage that may result from over-rotation of the potentiometer 84 . A motor 86 is optionally provided to rotate the chuck 76, although manual rotation is also possible. In addition, a clamping plate 87 is preferably provided to minimize vibration when the chuck 76 is rotated. Cleat plate 87 preferably provides a friction fit with chuck 76 and is just light enough to allow chuck 76 to rotate. Screws 88 may be provided for adjusting the jaws of the clamping plate 87 .

As shown in FIG. 9 , the measurement assembly 72 includes a base plate 90 mounted on the base 71 . A load cell 91 is mounted on the base plate 90, such as a model LCAE-2KG available from Omega Engineering, Inc. of Stamford, Connecticut, and a shaft tip limit arm 92 is mounted on the load cell 91. on the side opposite the base plate 90 for purposes described below. The measurement assembly 72 also preferably includes a deflection arm 93 pivotally mounted on the base plate 90 . Preferably, the deflection arm 93 is mounted such that at least one side 930 thereof is substantially perpendicular to the base plate 90 so that it pivots about an axis 94 substantially parallel to the base plate 90 .

The deflection arm 93 preferably has a projection 931 which preferably extends from its side 930 . Protrusion 931 preferably has a surface 932 facing away from axis 94 that is at substantially the same angle to side 930 as side 100 to side 101 of tip mass and sensor assembly 77 for reasons described below.

As shown in FIG. 10, the tip mass and sensor assembly 77 preferably has a body 102 having a mass between about 190 grams and 220 grams, preferably about 200 grams, thereby simulating a golf club at the distal end of a golf club shaft. the quality of the head. In another embodiment, different tip materials may be provided to more closely simulate different types of club heads having different masses. However, this latter embodiment is more costly since each different mass requires its own set of transducers to collect displacement data and perform different calculations based on these data.

As described below, the body 102 on the end of the golf club shaft not only simulates the effect of the club head during the swing, but also provides a "reactive substance" when the shaft is deflected and allowed to vibrate during testing in accordance with the present invention, Prevent shaft vibration from dampening before sufficient data is collected. The transducers that collect displacement data are preferably two accelerometers 103, 104 aligned along two different axes, such as model 8303A available from Kistler Instrument, Inc., Amherst, NY. Preferably, the two axes are perpendicular to each other, but this is not required; as long as the angular relationship between the two axes is known, the motion recorded by the accelerometers 103, 104 can be decomposed computationally into two orthogonal component motions . Also preferably, the two axes are parallel and perpendicular to the base 71 respectively. However, again, this is not required.

The tip mass and sensor assembly 77 preferably has an attachment structure for attachment to the tip of the golf club shaft. Preferably, the connecting structure includes a hole 105 and a fixing screw 106, the hole 105 is located in the main body 102, the diameter is slightly larger than the shaft of a general golf club, the shaft can be inserted into the hole, and the fixing screw 106 is used for The body 102 is secured to the shaft. Alternatively, some sort of quick release clamp could be provided, especially for use in automated systems as described below.

In addition, the body 102 may be separated by a flat or other surface through the hole 105 so that it fits around the shaft rather than sliding over the top of the shaft. This is especially useful when analyzing pre-existing golf club shafts without removing the clubhead from the shaft. The two parts (not shown) of the body 102 may be fastened together by any suitable clamps or other fasteners after fitting around the shaft. For example, the two parts may be hinged on one edge of the separating surface using one or more fasteners provided on the opposite edge.

As discussed above, preferably the azimuthal relationship between the tip material and the sides 100 , 101 of the sensor assembly 77 is the same as the azimuthal relationship between the surfaces 930 , 932 of the deflection arm 93 . In this way, the tip mass and sensor assembly 77 can be repeatedly aligned in the same manner in each test by having the sides 100, 101 resting on the surfaces 930, 932.

To test a golf club shaft, the shaft 110 is installed in the chuck 76 shown in FIG. 11 . The top or distal end of the shaft 110 is then deflected and constrained under the lip 120 of the shaft top restraining arm 92, as shown in phantom in FIG. force. The chuck 76 is then turned either manually, or by a motor 86 preferably under the control of the processor 61, while the restoring force is recorded by the computer 61 as a function of angle, determined by a potentiometer 84 to which a known voltage is applied. By the well-known voltage divider technique, the varying resistance is converted into a varying voltage, which can be converted into an angle.

It might be expected that the point of greatest asymmetry of the shaft representing the hard side of the principal plane of vibration faces upward when the upward restoring force is maximum. However, it has been empirically observed that this is not the case and that the hard side lies in the quadrant facing up where the maximum force is measured. Therefore, the angle of maximum force is recorded within this static part of the test, and the remaining dynamic part of the test is carried out.

During the dynamic portion of the test, the tip or distal end of the golf club shaft 110 was vibrated with the tip mass and sensor assembly 77 in place. The tip is preferably deflected vertically during the static portion of the test and horizontally during the dynamic portion of the test, although any orientation may be used during either portion of the test. The reason why horizontal deflection is preferred in the dynamic part of the test is, firstly, to minimize the effect of gravity on the tip mass from the results, and secondly, to make it easier to vibrate the shaft without hitting the base 71 . Therefore, before starting the dynamic portion of the test, the chuck 76 is preferably rotated approximately 90° so that the orientation of the estimated principal plane of vibration changes from vertical to horizontal.

In the presently described arrangement, a tip mass and sensor assembly 77 is applied to the golf club shaft 110 with a horizontal pulse. With the proximal end or handle end 111 of the golf club shaft 110 secured in the chuck 76 and the deflection arm 93 held upright, the hole 105 in the body 102 of the tip material and sensor assembly 77 is located in the golf club shaft 110. on the distal or tip 112. The tip mass and sensor assembly 77 is then operated until the surfaces 100, 101 of the body 102 abut the surfaces 930, 932 of the deflection arm 93, thereby positioning the accelerometers 103, 104 in their predetermined assigned orientations. The portion of surface 100 not occupied by accelerometer 103 is used for this purpose so that accelerometer 103 does not interfere with the seating of body 102 . Although the accelerometers 103, 104 are shown connected to the processor 61 by wires 62, wireless connections (not shown) are also possible.

By deflecting the tip 112 of the golf club shaft 110 to the side 120 of the deflection arm 93 opposite the side 930, a preferably substantially horizontal pulse is applied to the tip mass and sensor assembly 77, as shown in FIG. Next, preferably in a momentary motion, the deflection arm 93 is pivoted away from its upright position, thereby allowing the restoring force in the deflection golf club shaft 110 to provide a horizontal pulse to activate the top end 112 of the golf club shaft 110 in a manner consistent with The manner described above in relation to FIGS. 2-5 begins to vibrate with the apex mass and sensor assembly 77 .

Although the initial deflection of the golf club shaft 110 behind the deflection arm 93 and the pivoting of the deflection arm 93 to vibrate the tip 112 can be done manually, they can also be done automatically. Thus, the arm 121 supporting the finger 122 can be used to move the tip 112 of the golf club shaft 110 from its inactive position 1200 to a position behind the deflection arm 93, with the finger 122 passing through a suitable gear or linkage 124. Driven by motor 123, it provides the necessary horizontal and vertical components of motion. This can cause both vertical and horizontal movement of the tip 110 through the fingers 122, or the fingers 122 can only move horizontally when the motor 125 temporarily pivots the deflection arm 93 sideways and then returns the deflection arm 93 to an upright position. Likewise, the pivoting of the deflection arm 93 to initiate vibration can be done by the motor 125 rather than by hand.

As a further option, a horizontal plunger or punch (not shown) can be used to quickly and briefly strike the tip material and sensor assembly 77 instead of applying the force by deflecting the shaft 110 behind the deflecting arm 93 and then releasing the arm 93. pulse.

Each of the accelerometers 103, 104 respectively records acceleration in one of two corresponding directions, which are preferably mutually orthogonal and preferably horizontal and vertical. However, any two directions can be used as long as they are known and the horizontal and vertical components can be calculated. Acceleration can be integrated twice over time to determine horizontal and vertical displacement, but acceleration generally represents displacement and can be used directly, saving the computational resources and time needed to do the integration. Alternatively, the displacement can be measured directly, for example by placing a light source instead of the accelerometers 103, 104 on the end of the tip mass and sensor assembly 77, such as a laser or light emitting diode (not shown), along the golf club shaft 110. emit light in the direction of the longitudinal axis. An array of photosensitive detectors (also not shown) can be positioned substantially perpendicular to the emitted beam, which tracks the displacement of the tip 112 across the detector array, so that displacement is recorded directly. Regardless of how the data are collected, they can be plotted as a function of time and used to obtain displacement and then frequency data used, as described above, to mathematically determine the preferred angular orientation in which the principal plane vibration surfaces are located. The direction of the principal plane of vibration close to the estimated orientation determined by the load sensor 91 will be considered the "hard" side of the principal plane of vibration of the golf club shaft 110, which should preferably face or be relative to the shaft perpendicular to the face of the club head. The head face is positioned in any other predetermined orientation. However, the load cell test can be waived, as long as the golf club shaft 110 is aligned with a planar vibration plane at a specified orientation relative to the club head face, whether the hard side of the planar vibration plane faces or faces away from the club head face, is better than It is better to make the planar vibration surface at any orientation with respect to the head surface, and as long as it is aligned with any planar vibration surface with respect to the club head surface, even if it is not the main plane vibration surface, it is better to be at any orientation. However, it should be kept in mind that if an arbitrary plane of vibration other than the principal plane of vibration is found for each golf club shaft in a set, even if the plane of vibration found for each shaft is relative to its corresponding clubhead Similarly positioned, the group cannot be conceived to be uniformly positioned.

Once the location of the ideal plane of vibration (preferably the primary plane of vibration) has been determined, the shaft 110 is preferably marked to indicate the orientation of the plane of vibration. Marking may be accomplished by applying a color such as paint or ink to the surface of the shaft 110 . For example, an ink marker 130 having a marking head 131 may be mounted on the frame 132 shown in FIG. After the preferred orientation has been determined, the shaft 110 can be rotated to align the preferred orientation with the marking head 131 , which applies markings to the shaft 110 . Alternatively, 130 may represent a paint container, while 131 represents a paint brush or a jet of paint. As a further option, the marking of the shaft 110 may be accomplished using a directed energy beam or particle beam to etch the markings onto the surface of the shaft 110 . In such an option, 130 denotes a high-energy laser and 131 denotes a laser beam, or 130 denotes an electron gun and 131 denotes an electron beam. Alternatively, the shaft 110 or marking assembly may move during marking parallel to the longitudinal axis of the shaft so that the marking on the shaft is a line rather than a point, thereby enhancing visibility. Alternatively, as discussed above, a label, such as a sticker or decal, is applied to the shaft 110 to support the alignment marks.

Figures 14-17 illustrate a preferred method 140 of the present invention employing apparatus 60 to determine a preferred orientation (ie, any planar vibration plane or principal plane vibration plane). The method 140 preferably begins with a load test 141, as described above, which employs the load cell 91 to estimate the orientation of the principal plane of vibration, and by measuring the restoring force associated with the angle of the deflected shaft rotated at least 360°, at least Identify which of the two sides of the principal planar vibration surface is the "hard" side of the planar vibration surface. The load test 141 can be omitted, but only if any plane of vibration is to be found, not a specific principal plane of vibration (unless another technique is used to identify the principal plane of vibration). Where the load test 141 is performed, the results are used as the starting point for the following planar vibration surface positioning step 143 . Alternatively, load test 141 may be performed on an independent basis to measure shaft symmetry.

After performing the load test 141, for control purposes, an optional "logo up" test 142 is performed to collect data on the vibration of the golf club shaft in its factory installed orientation. Conventional golf clubs are typically assembled with the manufacturer's logo, which is printed on the shaft, facing the face of the clubhead in a configuration known as "logo up." Some manufacturers make the logo offset 180° from the face of the clubhead in a "logo down" configuration or other configurations. In the "logo up" test 142, the shaft is in its original factory installed position, but test 142 is referred to as the "logo up" test because, normally, the factory location has the logo facing up. In any case, since the logo is printed at an arbitrary location on the shaft circumference, that is, without the benefit of knowing the location of any planar vibrating surface, the factory orientation is completely arbitrary, regardless of the actual logo location.

As mentioned above, the positioning step 143 of the planar vibrating surface is performed next. After performing step 143, an optional report printing step 144 is performed in which some or all of the various parameters relating to the golf club shaft whose preferred orientation has been found are printed. Finally, in an optional save data step 145, the various data obtained in steps 141-144 are saved (eg in mass storage 64).

Load test 141 is shown in more detail in FIG. 15 . In step 150 , golf club shaft 110 , which may have been removed from the golf club, is positioned in chuck 76 at an arbitrary starting angle. The tip 112 of the golf club shaft 110 is deflected and restrained below the shaft tip restraint arm 92 so that the load cell 91 can measure the restoring force in the deflected shaft 110 . The shaft can be deflected and secured manually, or it can be done automatically. In this way, the arm 126 supporting the finger 127 can be used to move the tip 112 of the golf club shaft 110 from its inactive/neutral position 1200 to a position 1201 below the shaft tip retention arm 92, the finger 127 Driven by motor 128 through suitable gears or linkages 129, the necessary horizontal and vertical components of motion are provided.

Once the tip 112 is under the shaft tip retention arm 92, the chuck 76 is preferably rotated in step 151 approximately 200° in one direction (which may be designated as the negative rotational direction). Next, in step 152, chuck 76 is rotated at least 360° in the opposite direction (which may be designated as a positive rotational direction) while data is acquired from load cell 91 and recorded as a function of angle. Preferably, in step 152, chuck 76 is rotated approximately 400°, with 40° being rounded (preferably 20° first and last). However, the reverse rotation of step 151 may also be omitted, as long as the data is recorded by rotating at least 360°, and if the data is recorded by rotating more than 360°, any amount of rotation greater than 360° can be used, and any starting and ending points can be discarded. Part or any combination of start and end points, thus providing 360° equivalent data.

In step 153 the data collected in step 152 is checked and the angle A corresponding to the maximum load measured by the load sensor 91 is determined. If desired, a graph can be used to represent the load as a function of angle. Next, in step 154, the start angle S used in the planar vibration surface positioning test 143 is set to A-90°. This takes into account the change in orientation from vertical to horizontal between the load test 141 and the planar vibration surface positioning test 143, as described above.

After the conclusion of the load test 141, a "logo up" test 142 can be performed as shown in detail in FIG. 16 . The purpose of the "mark up" test is mainly to make a "before" comparison of the "before" results obtained after performing the planar vibration surface positioning test 143. Thus, as described above, the "mark up" test 142 is optional. In particular, although the "logo up" test 142 according to the present invention is primarily used as a promotional tool in subsequent market situations, i.e., through golf club refreshes to show the improvement achieved by realigning golf club shafts, it will likely not be used Used by golf club manufacturers who produce "ridged alignment" golf clubs because it is not necessary to show comparative data.

The "logo up" test 142 begins in step 160 with the golf club shaft 110 , which may again be removed from the golf club, located in the chuck 76 . If it were previously part of a complete golf club, the shaft 110 is located in the chuck 76 in the same orientation as it would be in a golf club, because the club is positioned before the golfer begins his swing. near the ball. In most cases this will make the manufacturer's logo face up, but sometimes the logo will be face down or in an arbitrary orientation. If Test 142 is performed on a golf club shaft that has never been a part of the golf club, it is preferably tested with the logo up, or regardless of whether it is up or not, with the logo in any position recommended by the shaft manufacturer for use. Align markings when fitting golf clubs. The tip mass and sensor assembly 77 is then mounted on the tip 112 of the shaft 110 .

Next, in step 161, a pulse is applied to the tip mass and sensor assembly 77 in one of the ways described above, and orthogonal, preferably horizontal and vertical acceleration data is collected, preferably for about 4 seconds. These data are preferably integrated in step 162 to produce orthogonal, preferably horizontal and vertical displacement data as a function of time, which are preferably saved in step 163 for subsequent comparison with the results after positioning the shaft 110, and these The data is preferably graphed in step 163 for display to the owner of the golf club of which shaft 110 is a part. The largest out-of-plane displacement, preferably the largest vertical displacement, is also preferably stored in step 163 and displayed to the owner. Trial 142 has been completed so far.

The system next proceeds to the planar vibration surface positioning test 143 . As shown in FIG. 17, trial 143 begins in step 170 of initializing counter J to zero. Next, in step 170 , the chuck 76 , still holding the shaft 110 , is rotated to the pre-calculated start angle S . If no starting angle S is calculated, trial 143 starts with an arbitrary angle.

In step 172, if the tip material and sensor assembly 77 is not pre-fixed on the tip 112, and in any case in one of the ways described above, a pulse is applied to the tip material and sensor assembly 77, and the quadrature Horizontal and vertical acceleration data are preferred, preferably around 4 seconds. These data are preferably integrated in step 173 to produce quadrature preferred horizontal and vertical displacement data as a function of time. In step 174, counter J is incremented by one. In step 175, the system checks if J=1. If it is checked that J=1 when the program executes the first pass, the system just jumps to step 177 directly.

In step 177 , the system sets a variable YMAX(J) equal to the value of the maximum out-of-plane deviation in step 173 . The system then proceeds to step 178 where it is determined if J = 1, thus signifying a first pass through a cycle. It is generally preferred to pass at least three cycles. If J=1 in step 178, 10° is added to angle S in step 179. In step 1700, to keep S between +180° and -180°, if S>180°, set S to S-360°. Next, in step 1701, the horizontal and vertical vibration frequencies are determined, which can be derived from the displacement versus time data in step 173. Frequency data is commonly used to measure the stiffness of golf club shafts, and these data are used for comparison. It should be noted, however, that the frequency at which the shaft vibrates depends on the length of the shaft protruding from any fixture used and the characteristics of the fixture (eg, length and tightness). So, if any comparisons are to be made, care should be taken to use the same fixture and leave the same length of shaft free to vibrate.

After step 1701, the system returns to step 172 and executes steps 172-174 again. At this time, J≠1 in step 175 , the data in step 173 is saved together with the angle S in step 176 , and the system proceeds to step 177 . The variable YMAX(J) is again set in step 177 equal to the maximum out-of-plane deviation value in step 173 . At this point, J≠1 in step 178, the system proceeds to step 1702 to determine if J=2. In this second pass of program execution, J=2, the system proceeds to step 1703 to determine if YMAX(J)>YMAX(J-1). If not, it means that the out-of-plane deviation is small in the iterative method, thereby meaning that the angle S is close to the preferred orientation, that is, close to the plane vibration plane. In step 1704, the variable SIGN is set to +1, and the variable Y is set to Set to the value of YMAX(J), the variable AMP is set to 1.0, and the system proceeds to step 1706 . If in step 1703, YMAX(J)>YMAX(J-1), it means that the out-of-plane deviation is larger in the iterative method, which means that the angle S is far away from the plane vibration plane. In step 1705, the variable SIGN is Set to -1, the variable S(J) is set to the value of S(J-1), the variable YMAX(J) is set to the value of YMAX(J-1), and the variable Y is set to YMAX( J), the variable AMP is set to 1.0 again, and the system proceeds to step 1706. No matter in step 1704 or step 1705, it should be noted that setting AMP to a small value can converge the result quickly but with poor accuracy, while setting AMP higher improves accuracy but increases the number of iterations before convergence. This is the comparative assessment between speed and accuracy.

In step 1706, the system calculates the variable POP=SIGN(45-(90/π)cos ^-1 (Y/AMP)), and in step 1707, the value of S is set to S+POP. In step 1708, in order to keep S between +180° and -180°, if S>180°, set S to S-360°. Likewise, in step 1709, in order to keep S between +180° and -180°, if S<-180°, set S to S+360°. The system then returns to step 1701 to calculate the frequency, and returns to step 172 again. At this time, when the program is executed for the third time, in step 178, J≠1, in step 1702, J≠2, the system proceeds to step 1710 to determine whether YMAX(J)>YMAX(J−1). If so, the values are converged and the system proceeds to step 1711 to determine if the out-of-plane deviation (YMAX(J-1)) of the last iteration is less than the maximum out-of-plane deviation during the "mark up" trial 142. If so, the current bearing is the preferred bearing, and in step 1712, the variable POP representing the preferred bearing is set to the value of variable S, thereby representing the current bearing. In step 1713 , the frequency of the shaft is calculated again as in step 1701 , and in step 1714 trial 143 ends.

If in step 1711 the out-of-plane deviation (YMAX(J-1)) of the last iteration is not less than the maximum out-of-plane deviation during the "mark up" trial 142, then in step 1715 the variable POP representing the preferred orientation is replaced by Set to "Logo Up" angle. In step 1713 , the frequency of the shaft is calculated again as in step 1701 , and in step 1714 trial 143 ends.

If in step 1710, YMAX(J)≯YMAX(J−1), it means that the value has not converged, then in step 1716, Y is set to the value of YMAX(J). The system then recalculates the POP in step 1706, and loops at least once more from here.

If the optional "mark up" test 142 is not performed, and step 1710 indicates convergence, then step 1711 is not executed and the system proceeds to step 1712 directly from step 1710.

After completing the Plane Vibration Surface Orientation Test 143, the system proceeds to the Report Printing Step 144, where the values of the following data are preferably printed (and determined if necessary): Load as a function of angle (determined in Load Test 141); Load Symmetry Index (LSI), which is a measure of the variability in shaft stiffness (LSI = 100(1-((Pmax-Pmin)/Pmax)), where Pmax and Pmin are the maximum and minimum loads measured in step 152, respectively) ;displacement curve for "mark up" angle; displacement curve for POP angle; displacement as a function of time for "mark up" angle and "hard" and "soft" POP angles (the latter two angles should be exactly 180° apart);" Horizontal and vertical frequencies of logo up" and POP angles and maximum out-of-plane deviation; a frequency index equal to the ratio of the horizontal frequency of POP angles to the horizontal frequencies of "logo up" angles, which is the raw A measure of the stiffness in the ball hitting direction between the "logo up" structure and the alignment structure, expressed as a percentage increase.

Next in step 145 the data is saved. On a full save, all data is saved. Also preferred is a "quick save" where all data printed in step 144 is saved except for the full load versus angle data and the full displacement data for "mark up" and POP angle. After saving step 145 , program 140 ends in step 146 .

An alternate embodiment of an apparatus 1870 for determining a principal planar plane of vibration of a golf club shaft and related methods will now be described with reference to FIGS. 18-22.

Device 1870 is essentially fully automatic. In fact, the only steps that are performed manually when employing device 1870 are adjusting the position of instrumentation table 1872 to coincide with the measured length of golf club shaft 110, installing shaft 110 in chuck 1876, and Mounted on the shaft 110 is a tip mass and sensor assembly 1877.

Shaft testing assembly 1870 preferably includes an elongated base 1871 that is at least as long as the longest golf club shaft to be tested. At one end of the base 1871 is a gauge platform 1872 that can translate along the base 1871 to accommodate golf club shafts of different lengths. Preferably, the dashboard 1872 has a base 1890 with downward projections (not shown) that snap into slots 1891 of the base 1871 and rollers 1892 that sit on the support surface 1800 of the housing 1801 . Screws 1874 are preferably provided to lock instrument panel 1872 in a selected position.

The instrument panel 1872 includes a deflector/deflection load sensor assembly 1878 for determining straightness. The instrument panel 1872 also includes a vibration actuator assembly 1873 for initiating vibration of the shaft 110 to determine stiffness and position the planar vibration surface of the shaft 110, and a vibration damper assembly 1897, the function of which will be described below.

The other end of the base 1871 is a shaft fixing and rotating assembly 1875 including a rotatable chuck 1876 for fixing the golf club shaft 110 .

As shown in Figure 18, the shaft fixation and rotation assembly 1875 preferably includes a rotatable chuck 1876, which preferably may be of a conventional type, preferably by applying a radially inward force substantially uniformly around the circumference of the shaft. Fix the golf club shaft. Chuck 1876 is preferably mounted on the end of shaft 1880 which is preferably journalled in bearing 1881 . Bearing 1881 is preferably mounted on bracket 1882 such that the axis of rotation of shaft 1880, including chuck 1876 and the extension of the golf club shaft being tested, is at a predetermined height on base 1871. A toothed pulley 1883 is preferably mounted on the end of the shaft 1880 away from the chuck 1876, the pulley 1883 is connected to a toothed pulley 1884 similar to the servo motor 1885 through a toothed belt 180, the corner of the servo motor 1885 The position can be precisely controlled by a processor 61, such as a smart motor model SM2315 available from Animatics, Inc., Santa Clara, CA. Motor 1885 is preferably mounted below bracket 1882 . Preferably, the space below bracket 1882 is also used for a junction box for various sensors and other electrical and electronic components described below. It is also preferred that the space below the bracket 1882 be enclosed by an acrylic plate (not shown) to keep dust out and prevent the user from contacting any exposed electrical contacts.

Instrument panel 1872 is shown in greater detail in FIGS. 19 and 20 . The deflector/deflection load cell assembly 1878 includes a vertically extending rod 190 mounted so that the golf club shaft 110 passes through but is spaced from its upper end. Rod 190 is vertically movable, and an actuator such as a pneumatic cylinder 191 is preferably provided to move rod 190 upward until its upper end engages shaft 110 and deflects shaft 110 upward by a predetermined amount. Any other suitable actuator may be used, including linear actuators such as solenoids or hydraulic cylinders, or rotary actuators such as motors. Preferably, the upper end of the rod 190 has a seat such as a V-shaped seat 193 to engage with the shaft 110 . A compression load cell 192, such as a model 9222 from Kistler Instruments, Inc., Amherst, NY, is positioned below the pneumatic cylinder 191 to measure the restoring force exerted when the shaft 110 is deflected upward by the rod 190. As discussed above in connection with the previous examples, since the load test is measured vertically and the position of the planar vibrating surface is measured horizontally, the load test data are recorded at angles offset by 90° from the angle at which they were measured.

The vibration actuator assembly 1873 of the instrument panel 1872 preferably includes an electromagnet 1894 preferably mounted for horizontal movement perpendicular to the longitudinal axis of the shaft 110 , preferably under the action of a pneumatic cylinder 1895 mounted on a bracket 1896 . Any other suitable actuator may be used, including linear actuators such as solenoids or hydraulic cylinders, or rotary actuators such as motors.

Apparatus 1870 also preferably includes proximal shaft marking mechanism 1887 and distal shaft marking mechanism 1886 for marking on golf club shaft 110 the location of the principal plane of vibration once determined. The distal shaft marking mechanism 1886 preferably includes one or more (e.g., two, as shown) recording heads 1888 for making one or more (e.g., two) marks on the distal end of the shaft 110, which can be used The proximal shaft marking mechanism 1886 preferably includes one or more recording heads 1888 for aligning the shaft 110 with the golf club head at a given orientation, thereby making one or more markings on the proximal end of the shaft 110 . In both shaft marking mechanisms, a corresponding pneumatic cylinder is preferably used to lift the recording head 1888 into contact with the shaft 110 . Preferably, in order to stabilize the shaft 110 during marking, the shaft deflection rod 190 is raised by a pressure cylinder or other actuator 191 so that the shaft 110 is vertically deflected and, more importantly, fixed during the marking process. The shaft keeps it from moving horizontally. Another cylinder or other actuator 194 then activates the recording head 1888 of the distal shaft marking mechanism 1886 . The cylinder or other actuator 1889 of the proximal shaft marking mechanism 1887 also activates the proximal recording head 1888 to mark the shaft 110, preferably as the rod 190 continues to deflect and secure the shaft 110. Alternatively, as discussed above, one or more stickers or decals bearing the alignment marks may be applied to the shaft 110 . The markings on the shaft 110 are primarily used to align the shaft 110 with the golf club head, so can be independently secured to the shaft based on the needs of the equipment used to secure the club head to the shaft 110, or by hand. 110 to select the number and location of the markers.

Tip substance and sensor assembly 1877 is similar to assembly 77 described above. To initiate the process, after inserting golf club shaft 110 into chuck 1876, the user installs tip mass and sensor assembly 1877, using the surface of electromagnet 1894 as the alignment surface. The pressure cylinder or other actuator 1895 is arranged such that, in its rest position, it places the electromagnet 1894 in the correct position to be used as an alignment surface for mounting the tip material and sensor assembly on the shaft 110, Shaft 110 is in its inactive position. After the tip mass and sensor assembly 1877 has been installed and aligned, the electromagnet 1894 is energized. The pressure cylinder or other actuator 1895 is then activated to move the electromagnet 1894 in a direction away from the longitudinal axis of the shaft 110, thereby deflecting the shaft 110 horizontally. At the end or before the movement of the electromagnet 1894 in the removal direction, the electromagnet 1894 is de-energized, thereby releasing its hold on the assembly 1877, thereby vibrating the shaft 110 substantially horizontally.

As the shaft 110 vibrates, the movement of the shaft tip detected by the tip mass and sensor assembly 1877 is recorded by the processor 61, noting in particular the maximum out-of-plane vertical acceleration or displacement and the frequency of vibration.

Preferably, after sufficient data has been collected, a bumper 1898 , such as a foam pad, is moved into engagement with the shaft 110 , preferably via a pressure cylinder 1899 mounted on the bracket 1900 , to stop vibration of the shaft.

Whether or not the bumper assembly 1897 is provided, the electromagnet 1894 then re-engages the assembly 1877 . As servo motor 1885 rotates shaft 110 to the next angular position, which is preferably 10° from the current position, assembly 1877 is aligned by engaging the surface of electromagnet 1894 during rotation of the shaft. Set screw 106 preferably has a nylon tip so that if assembly 1877 is stopped by electromagnet 1894, shaft 110 can still rotate relative to assembly 1877. The electromagnet 1894 is energized or remains energized and is removed again to deflect the shaft 110, again preferably by de-energizing the electromagnet 1894 to vibrate the shaft 110. At this new angular position, displacement data including maximum out-of-plane deflection of the shaft tip and frequency data are again recorded. This is preferably repeated at uniform angular intervals, preferably every 10°, so that out-of-plane deviation and frequency data are obtained for 36 angular positions. While it is preferred that the angular spacing be uniform, the time spent at each angular position is not uniform. For example, in a preferred embodiment, more data can be obtained at the "logo up" position and at the position of the main plane vibrating surface for a more detailed graphical display (see below).

As an alternative to tip mass and sensor assembly 1877, a tip mass assembly 261, as shown in FIG. 26, may be used. Tip mass assembly 261 is similar in size and mass to tip mass and sensor assembly 1877, except that it does not include an accelerometer or any other sensor, thereby requiring no wired or wireless connection to processor 61. Tip matter assembly 261 includes a flat plate 262 that engages electromagnet 1894 . For reasons discussed below, it is preferred to mount the plate 262 at a 45° angle to the surface of the tip mass assembly 261 .

For use with the tip material assembly 261, the device 1870 is preferably equipped with a pair of laser distance sensors 263, 264, each of which may be an OADM type laser distance sensor available from Baumer Electric AG, Frauenfeld, Switzerland. As shown in Figures 27 and 28, the sensors 263, 264 are preferably mounted such that when the tip mass assembly 261 is mounted on the shaft 110, the sensors 263, 264 are located on the opposite side of the tip mass assembly 261 away from the electromagnet 1894. superior. More preferably, when the top material assembly 261 is mounted substantially vertically with the plate 262, the upper sensor 263 is mounted at a height such that its beam hits substantially the center of the side 270, while the lower sensor 264 is mounted so that Its beam strikes substantially at the height of the center of side 271 . It should be noted that the set screw 106 is shown in dashed lines in FIGS. 27 and 28 because although the set screw is located on the side 270 , it is located along the longitudinal axis of the shaft 110 than the beam 272 of the sensor 263 intersects the side 270 . The point is even lower on the side 270 position. Therefore, the set screw 106 does not interfere with the operation of the sensor 263 .

Each sensor 263, 264 includes a laser source and a photodetector and operates by measuring the time for a laser pulse to reach the tip matter assembly 261 and return to the photodetector. As can be clearly seen from FIG. 27, if the top matter assembly is only vibrating horizontally, then the distance _dU from the upper sensor 263 to the side 270 is always approximately equal to the distance _dL from the lower sensor 264 to the side 271 . However, it can be seen from FIG. 28 that if there is any vertical component in the vibration of the tip material assembly 261, then the two distances d _U and d _L will be different even if there is no horizontal vibration component.

assumed:

(1) The horizontal and vertical displacements of the tip of the shaft 110 are denoted as x and y, respectively;

(2) The difference between the dU measured while the apical matter assembly 261 is at rest and _{the dU} measured during the performance of a particular measurement is denoted as _xU ;

(3) The difference between the _dL measured while the apex matter assembly 261 is at rest and the _dL measured during a particular measurement is denoted as _xL ;

x and y can then be derived from x _U and x _L as follows:

x＝(x _L +x _U )/2

y＝(x _L -x _U )/2

It is apparent from the geometry that the tip material assembly 261 can be mounted such that the sides 270 and 271 are not at a 45 degree angle to the vertical (or horizontal vibration plane), but rather to the vertical (or the plane) Tilt angles into some other angles, but the math to derive x and y from x _L and x _U is significantly more complicated. Obviously, it is also not necessary to mount the sensors 263, 264 opposite the corresponding midpoints of the sides 270, 271, as long as the beam of the sensor 263 intersects the side 270 and the beam of the sensor 264 intersects the side 271 when the top mass assembly 261 vibrates. However, if other mounting locations are used for the sensors 263, 264, care should be taken not to select a location such that the above conditions are violated by vibration levels within the expected vibration range of the tip material assembly 261.

It is also understood that the sides 270, 271 of the tip matter assembly 261 should not be completely reflective. If the sides 270, 271 were fully reflective, all of the laser energy emitted by the laser sources in the sensors 263, 264 would be reflected off the detectors in those sensors. There must be sufficient specular reflection to allow some laser light to return to its laser source. Preferably, the surfaces of the sides 270, 271 are made to approximate a "white paper surface", ie one that when excited by laser energy re-emits as omnidirectionally as possible at the same wavelength as the incident beam. The two sensors 263, 264 should be separated far enough so that reflected or re-emitted energy from side 270 does not reach the detector of sensor 264 and reflected or re-emitted energy from side 271 does not reach the detection of sensor 263 device. Alternatively, the two sensors can operate at different wavelengths so that the signal from one sensor is not read by the other sensor.

Using sensors 263, 264 instead of accelerometers 103, 104 provides displacement data directly without integrating the acceleration data. However, as noted above, for the purposes of the present invention, acceleration measurements and displacement measurements yield the same results.

When all measurements have been made at all angular positions, the assembly 1877 or 261 is then manually removed from the shaft 110 .

The drive of the servo motor 1885 and the various cylinders/actuators is preferably automated under the control of the processor 61 so that multiple measurements can be made quickly. If measurements are taken at 10° intervals, the entire series of measurements is preferably completed in about 2 minutes or less, preferably in about 30 seconds. If pneumatic cylinders are used as actuators, various pneumatic cylinders are preferably driven by a compressor 2000 , and the compressor is preferably located in the housing 1801 and connected to various pressure cylinders through hoses 2001 . Housing 1801 may be used to house other components of device 1870 (not shown).

With respect to each angular position, the measurement results are a list of tip positions (especially out-of-plane displacements) and vibration frequencies. To locate the principal plane of vibration, the out-of-plane displacement can be plotted in polar coordinates as a function of angle. An example of such a graph is shown in FIG. 21 . At each angular position, the distance of the curve from the origin represents the out-of-plane displacement for that angle. A typical golf club shaft will have a multi-lobed graph such as that shown in Figure 21, although the number of lobes may vary among different shafts. The point of tangency 210 at which the coordinate curves between the lobes are closer to the origin is the local minimum of the out-of-plane displacement. Except for very irregular shafts, the number of points of tangency 210 is envisioned to be even, and each point of tangency 210 at a particular angle should have a mate point 180° apart from it. Each such pair (shown by dashed line 211) represents one of the planes of vibration of the shaft, the principal plane of vibration being generally represented by the pair of points of tangency closest to the origin. It should be noted that by graphically plotting the observed data, the principal plane of vibration can be accurately located even though its position is not one of the angular positions where the measurement was actually made. Processor 61 is preferably programmed with software to automatically plot the data and select the principal plane of vibration.

In a preferred embodiment, the software fits curve 212 to data points 213 by using a Fourier series asymptotic method. If for each point 213 taken at a particular angle θ denote the distance from the origin as r(θ), the points 213 can be fitted with the following series:

r(θ)＝A ₀ +A ₁ cosθ+B ₁ sinθ+A ₂ cos(2θ)+B ₂ sin(2θ)+…+A _m cos(mθ)+B _m sin(mθ)

Among them, the precision of fitting increases with the increase of the number of items m. However, when N is the number of data points, the number of items is limited:

m＜(N-1)/2

Thus, in the preferred embodiment, with 36 points, the maximum number of entries is 17.

In the above series, the coefficients are bounded as follows:

${\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; )</span>\underset{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; r</span>}$

(ie, the average distance of point 221 from the origin);

${\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; )</span>\underset{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j\&theta;</span>}<span\; class="notranslate">\; )</span>$

and

${\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; )</span>\underset{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j\&theta;</span>}<span\; class="notranslate">\; )</span>$

It has been empirically observed that a minimum of 4 terms (m=4) is required for a satisfactory curve fit. As m increases, the fit is also better.

Once the curve 212 is fitted to the point 213, the first derivative is calculated and set to zero to find the maximum (cusp of the multilobes) and minimum (point of tangency 210). Calculate the second derivative at each extreme value to identify which is the minimum or tangent point (positive second derivative) and which is the maximum (negative second derivative). It has been found that for curve fitting purposes 36 data points should be taken (0°-350°) if the endpoints (0° and 360°) will have the same frequency and displacement, but 37 points should be used for the derivative (0°-360°).

The formulas for the first and second derivatives are as follows:

${\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j\&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j\&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="j"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">j</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j\&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="j"\; filenames="A20051009991800641.png"\; state="\{\{state\}\}">j</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j\&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

A commercial root-finding subroutine known as ZREAL, available from Visual Numerics, Inc. of Houston, Texas as part of the International Mathematical Subroutine Library, is preferably used to find the roots of first derivatives, i.e., those where the first derivative equals zero. point. This subroutine needs to make an initial guess about the number and location of the roots. Although it is known that there are generally 8 roots (four maxima and four minima), it was found that guessing at the 8 roots (which were arbitrarily guessed to be equiangularly spaced) did not find all of them. However, it was found that guessing at 20 equiangularly spaced roots yielded correct results. However, it was also found that for higher order fits (m > 10), the curve fits better, yielding biases in the data that fluctuate in the fitted curves that read as local extrema, resulting in additional roots. Thus, m is preferably less than 10; most preferably m=7.

Once the roots are found and the extrema are identified, the second derivative of each root is found and those points where the second derivative is positive are identified as minima. The lines connecting relatively spaced pairs of minima are planar vibration planes, and the loading data is preferably used to identify the principal plane vibration planes, as described above.

As stated above, the vibration frequency at each angular position was also recorded. Also as explained above, the stiffness of the shaft can be derived from the frequency of vibration using the following relationship:

f≈(K/M) ^0.5

Among them, the spring constant k of the shaft in its transverse bending mode is a measure for measuring the stiffness of the shaft. Mass M is the total mass of the vibration system, in this case golf club shaft 110 plus tip mass and sensor assembly 1877 . Approximate the golf club shaft 110 as a prismatic beam of mass _mshaft (i.e., a beam of constant cross-section, which is not the case for most golf club shafts in practice), and designate the mass of the tip mass as _mtip , In this way, the total mass M in the above relational formula can be approximated as M=0.23m _shaft +m _tip . Therefore, the frequency can be approximated as:

f＝(k/(0.23m _shaft +m _tip )) ^0.5

The solution yields k=(0.23m _shaft +m _tip )f ² .

By determining k, a measure of stiffness is provided whereby the shaft can be compared to other shafts (assuming shafts of the same length vibrate as described above). Determining k also allows us to determine the toe-to-butt deflection of the shaft from the restoring force measurements collected in load tests at different angles. This deviation can also be determined using a mobile meter, or preferably using optical techniques.

As stated above, for each angle:

F/k＝d+δ

where F is the measured restoring force and d is the displacement applied during the load test. If k is also known, δ, the deviation of the center of the shaft tip from the longitudinal axis passing through the center of the butt end of the shaft, can be determined.

In an alternative and particularly preferred embodiment, the deflection δ can be determined in a modified load test without first determining the stiffness (which is measured by the spring constant k). In this embodiment, the pressure cylinder 191 raises the shaft 110 by a first displacement d1 and collects data on the restoring force, and then the pressure cylinder 191 raises the shaft 110 to a second displacement d2 and collects data on the restoring force again. Two restoring force data points for each angular position may be collected by moving the cylinder 191 up and down at each angular position for which vibration data is collected. More preferably, the restoring force data points are collected as part of a load test modification as described above, wherein the pressure cylinder 191 is moved to position d1 while the data is being collected, the shaft 110 is rotated at least 360°, and the pressure cylinder 191 is pressed while the data is being collected again. 191 moves to position d2, and shaft 110 rotates at least 360° again. In a particularly preferred embodiment, data is collected at a displacement d1 when the shaft 110 is rotated at least 360° in a first direction, for example approximately 400°, and the same total amount when the shaft 110 is rotated in an opposite second direction. Data were collected again at displacement d2 during the angular displacement. This sets up two equations with two unknowns k and δ, which can be solved with respect to δ:

F ₁ =k(d ₁ +δ)

F ₂ =k(d ₂ +δ)

k=k, ∴

F ₁ /(d ₁ +δ)=F ₂ /(d ₂ +δ)

F ₁ d ₂ +F ₁ δ＝F ₂ d ₁ +F ₂ δ

δ=(F ₂ d ₁ -F ₁ d ₂ )/(F ₁ -F ₂ )

Since the load test is performed with the tip material attached, it is preferred to subtract the weight of the tip material from the measured restoring force. Load test data measured at a specific location were recorded relative to a different location 90° from the specific location where the measurement was made, thus taking into account the fact that the load test was performed vertically while the plane vibrating at the same angular location Surface position measurements are made horizontally.

In general, when delta is plotted as a function of angle, as shown in FIG. 22 , the result shows that the large circle 214 is centered on the origin 215 and the small circle 216 is offset from the origin 215 . The relationship between the diameters of the large and small circles is proportional to the relationship between the butt and tip diameters of the shaft 110, and in a preferred embodiment, the diameters of the corresponding circles are equal to the diameters of the corresponding ends. Thus, the graph shows the position of the tip relative to the longitudinal axis of the shaft 110, or in other words, the degree to which the shaft 110 is not straight. Line 217 indicates the direction of bending. The resilience data of the load test provided that the results were expected. If the golf club shaft is bent in a particular direction, applying a force in the load test along the direction of the bend will produce less restoring force than applying a force against the direction of the bend. Thus, with respect to each angle, if the restoring force is relatively small, the restoring force is relatively large for an angle turned 180°, and vice versa.

The method and apparatus of the present invention may be used as part of a larger scale method or apparatus for fitting golf clubs, thereby producing a "ridge-aligned" golf club. Like this, each golf club shaft 110 can be delivered to the golf club fitting station, and they have been marked with reference marks (whether or not marked as indicating " "hard" side) at the golf club fitting station where markings on the shaft are identified and used to fit a golf club with a planar vibration face that is preferably substantially perpendicular to the golf club head face. Depending on the relative speed of the planar vibrating surface positioning apparatus 60 or 1870 compared to the golf club fitting stations, more or less planar vibrating surface positioning stations or assembly stations may be provided as appropriate. Thus, several planar vibrating surface positioning stations 60, 1870 may be used to feed a single golf club assembly station. A hopper may be provided at the golf club fitting station to act as a buffer if the fitting station slows down or stops, or is not ready to accept new golf club shafts 110 when they arrive.

The golf club fitting station is preferably equipped with a scanner for identifying indicia on the golf club shaft 110 indicating the location of the plane of vibration. Once the mark has been identified, the shaft 110 is rotated so that the mark is in a predetermined orientation for a certain golf club head to be secured to the shaft 110, and when the shaft 110 is assembled to the golf club head, the The golf club head is fixed in a predetermined orientation.

Alternatively, each golf club head may have an alignment mark that must match the mark on the golf club shaft 110 . The scanner scans the alignment marks on the shaft 110 and the head, and rotates the shaft 110 until the two marks are aligned. This eliminates the need for the golf club head securing mechanism to "know" the particular orientation of securing various types of golf club heads for alignment with marked shafts. Conversely, each golf club head can be fixed in the same orientation, and when the shaft 110 is about to be assembled, the shaft 110 can be rotated until the shaft 110 and the club head are connected before the shaft 110 is attached to the golf club head. until the markings are perfectly aligned.

23 and 24 illustrate an apparatus 220 of the present invention for fitting golf clubs. The device 220 includes at least one device 60 or 1870 (one device 60 is shown), a conveyor 221, a feeding mechanism 223 and the assembly station 224 itself, wherein the conveyor 221 is used to remove from the device 60, 1870 to complete the inspection shafts 110 and put them into the hopper 222 , the feeding mechanism 223 is used to transfer each shaft 110 from the hopper 222 to the assembly station 224 .

At assembly station 224, a supply device comprising an arm 225 connected to a motor (not shown) delivers shaft 110 to chuck 230, which is similar to chuck 76, 1876 and extends from the proximal end of shaft 110. It is fixed rotatably. Clamping member 231 fixes golf club head 232, and the latter can carry or not carry alignment mark 233; If do not have alignment mark 233, golf club head 232 is just fixed on the known position by clamping member 231, and it follows golf club. Varies by header type. As the chuck 230 rotates, the scanner 234 scans the indicia 235 on the shaft 110 . When scanner 234 recognizes marker 235 , processor 61 commands chuck 230 to align marker 235 with alignment marker 233 located by scanner 236 , or with a predetermined orientation of golf club head 232 . Chuck 230 and clip 231 are then moved together by moving one or both of them, and shaft 110 is attached to golf club head 232 in other conventional ways if necessary, such as using any kind of adhesive , hoops, etc.

Figure 25 is an example of a printout provided to the user in the case of a modified golf club, showing the characteristics of the shaft and comparing the original configuration of the club with its new configuration. This printout provides the user with information about the characteristics of the golf club and also provides the improver with a database of information about each type of club that has been improved.

Although the data is listed in the particular layout of Figure 25, other layouts are possible and within the scope of the present invention. User and shaft identification data is preferably provided in area 250 . Preferably included in the identification data is a barcode or other machine-readable indicium (not shown), which may be located in box 258 of area 250 and may be used to retrieve data from a database for a particular shaft. A matching barcode or other marking may be affixed to the shaft itself. In particular, if a label is used to mark the alignment on the shaft as described above, the label can support the marking as well.

The printout preferably includes a graph 251 showing the results of the load test discussed above. In particular, the load symmetry index (LSI) discussed above is reported and the normalized load during the load test is related to the stiffness in foot pounds per inch. 252 shows the result of a "spin" or planar vibration plane position measurement. In particular, the two phase diagrams 253, 254 respectively show the vibration characteristics of the shaft in the "logo up" position and on the principal plane vibration plane where it is positioned. Similar to Fig. 21, a coordinate diagram 255 is also provided, except that lines 259, 260 representing all planar vibration planes are preferably shown, preferably the line 259 representing the main plane vibration plane is darkened or otherwise differentiated from any other line 260 different. Also, a graph 256 identical to the graph in Figure 22 is provided to show the straightness of the shaft, while a graph 257 is also provided which shows the frequency of vibration in relation to angular position (a measure of stiffness) . In the graph 257, the circular data points represent an "ideal" shaft where the shaft stiffness and thus the frequency are the same at all angles, while the square data points show the frequency data for the measured shaft.

Although the invention has so far been described using a golf club shaft, it can be used to determine the symmetry/asymmetry, roundness, straightness and/or stiffness of any elongated element, including but not limited to baseball bats , billiard sticks, arrows, fishing rods or any components.

Thus, it can be seen that a method is provided for quickly and reliably determining the preferred angular orientation of a golf club shaft or other elongated member and using the determination of the preferred angular orientation to automatically fit the golf club, Wherein each golf club shaft is aligned in unison with respect to a corresponding club face. Those skilled in the art will appreciate that the invention may be practiced in forms other than the described embodiments, which are illustrative and not restrictive, the invention being limited only by the following claims.

Claims (18)

CLAIMS 1. A method of determining the straightness of a golf club shaft having a handle end and a head mating tip, the method comprising: immobilizing said handle end of said golf club shaft and defining a longitudinal axis extending through said handle end and perpendicularly relative to a plane perpendicular to said handle end; determining a spring constant of the golf club shaft in a lateral flex mode; and For each of a plurality of angles about the longitudinal axis: moving the top end of the shaft laterally relative to the longitudinal axis a predetermined distance, Measuring the restoring force during the movement, determining a difference between said measured restoring force and an expected restoring force during said movement based on said predetermined distance and said spring constant, The angular deviation of the tip from the longitudinal axis is derived from the difference and the spring constant. 2. The method of claim 1, further comprising plotting said deviation over said plurality of angles to visually represent said straightness of said shaft. 3. The method according to claim 2, wherein the determination of the spring constant comprises: activating vibration of the shaft in the lateral flex mode; measuring the frequency of said vibration; The spring constant is derived from the frequency. 4. The method of claim 1, wherein the determination of the spring constant comprises: activating vibration of the shaft in the lateral flex mode; measuring the frequency of said vibration; The spring constant is derived from the frequency. 5. A method of determining the straightness of a golf club shaft having a handle end and a head mating tip, the method comprising: immobilizing said handle end of said golf club shaft and defining a longitudinal axis extending through said handle end and perpendicularly relative to a plane perpendicular to said handle end; For each of the plurality of angles about the longitudinal axis: initiating movement of the top end of the shaft laterally relative to the longitudinal axis by a first predetermined distance, measuring a first restoring force during said initiation of movement, subsequently moving the top end of the shaft laterally relative to the longitudinal axis a second predetermined distance, measuring a second restoring force during said subsequent movement, The angular deviation of the tip from the longitudinal axis is derived from the first and second restoring forces and the first and second predetermined distances. 6. The method of claim 5, further comprising plotting the deviation over the plurality of angles to visually represent the straightness of the shaft. 7. An apparatus for determining the straightness of a golf club shaft having a handle end and a tip cooperating with a head, said apparatus comprising: means for immobilizing said handle end of said golf club shaft and defining a longitudinal axis extending through said handle end and perpendicularly relative to a plane perpendicular to said handle end; means for determining the spring constant of the golf club shaft in a lateral flex mode; means relative to each of a plurality of angles about said longitudinal axis for: moving the top end of the shaft laterally relative to the longitudinal axis a predetermined distance, Measuring the restoring force during the movement, determining a difference between said measured restoring force and an expected restoring force during said movement based on said predetermined distance and said spring constant, The angular deviation of the tip from the longitudinal axis is derived from the difference and the spring constant. 8. The apparatus of claim 7, further comprising means for plotting said deviation over said plurality of angles to visually represent said straightness of said shaft. 9. The apparatus of claim 8, wherein the means for determining the spring constant comprises: means for activating vibration of said shaft in said lateral flex mode; means for measuring said vibration frequency; means for deriving said spring constant from said frequency. 10. The apparatus of claim 7, wherein the means for determining the spring constant comprises: means for activating vibration of said shaft in said lateral flex mode; means for measuring said vibration frequency; means for deriving said spring constant from said frequency. 11. An apparatus for determining the straightness of a golf club shaft having a handle end and a tip cooperating with a head, the apparatus comprising: means for immobilizing said handle end of said golf club shaft and defining a longitudinal axis extending through said handle end and perpendicularly relative to a plane perpendicular to said handle end; means relative to each of a plurality of angles about said longitudinal axis for: initiating movement of the top end of the shaft laterally relative to the longitudinal axis by a first predetermined distance, measuring a first restoring force during said initiation of movement, subsequently moving the top end of the shaft laterally relative to the longitudinal axis a second predetermined distance, measuring a second restoring force during said subsequent movement, The angular deviation of the tip from the longitudinal axis is derived from the first and second restoring forces and the first and second predetermined distances. 12. The apparatus of claim 11, further comprising means for plotting said deviation over said plurality of angles to visually represent straightness of said shaft. 13. An apparatus for determining the straightness of a golf club shaft having a handle end and a tip cooperating with a head, the apparatus comprising: a clamp for immobilizing said handle end of said golf club shaft and defining a longitudinal axis extending through said handle end and perpendicularly relative to a plane perpendicular to said handle end; an analyzer for determining a spring constant of the golf club shaft in a lateral flex mode; a deviation calculator relative to each of a plurality of angles about said longitudinal axis for: moving the top end of the shaft laterally relative to the longitudinal axis a predetermined distance, Measuring the restoring force during the movement, determining a difference between a measured restoring force and an expected restoring force during said movement based on said predetermined distance and said spring constant, The angular deviation of the tip from the longitudinal axis is derived from the difference and the spring constant. 14. The apparatus of claim 13, further comprising a plotter for plotting said deviation at said plurality of angles to visually represent said straightness of said shaft. 15. The apparatus of claim 14, wherein the spring constant analyzer comprises: a vibration generator for initiating vibration of the shaft in the lateral bending mode; a frequency counter for measuring said vibration frequency; a processor for deriving said spring constant from said frequency. 16. The apparatus of claim 13, wherein the spring constant analyzer comprises: a vibration generator for initiating vibration of said shaft in said lateral flex mode; a frequency counter for measuring said vibration frequency; a processor for deriving said spring constant from said frequency. 17. An apparatus for determining the straightness of a golf club shaft having a handle end and a tip cooperating with a head, the apparatus comprising: a clamp for immobilizing said handle end of said golf club shaft and defining a longitudinal axis extending through said handle end and perpendicularly relative to a plane perpendicular to said handle end; With respect to each of a plurality of angles about said longitudinal axis, a deviation calculator is used to: initiating movement of the top end of the shaft laterally relative to the longitudinal axis by a first predetermined distance, measuring a first restoring force during said initiation of movement, subsequently moving the top end of the shaft laterally relative to the longitudinal axis a second predetermined distance, measuring a second restoring force during said subsequent movement, The angular deviation of the tip from the longitudinal axis is derived from the first and second restoring forces and the first and second predetermined distances. 18. The apparatus of claim 17, further comprising a plotter for plotting said deviation at said plurality of angles to visually represent the straightness of said shaft.

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