BEND-TWIST COUPLED GOLF CLUB SHAFT

CROSS-REFERENCE TO RELATED APPLICATION

The present application claims the benefit of U.S. Provisional Patent Application Serial No. 61/531,172, filed September 6, 2011, the disclosure of which is hereby incorporated by reference in its entirety, including any figures, tables, or drawings.

BACKGROUND OF INVENTION

In a normal golf swing, the shaft of the golf club bends a substantial amount. Generally, the shaft bends in the early part of the forward swing, because of the weight (mass) of the head tends to lag when the club is accelerated. In the later part of the forward swing, after the ball has been impacted, the club bends the opposite direction since the club head inertia continues through while the swing is decelerated.

Additionally, the shaft of a typical club twists during the forward swing because the club head is not centered with the axis of the shaft, or stated in another manner the center of mass of the club head is offset from the plane of swing of the golfer, and a torsion is developed in the shaft during the forward swing. This twist can have a negative effect on achieving a square club face at the moment of impact of the club head with the golf ball. If the head is twisted out at impact, for example twisted clockwise when viewed from the shaft handle to the club head for a right handed golfer's swing, the ball can tend to be hit to the right of straight ahead, or slice. Alternatively, if the club is twisted in at impact, such as twisted counter-clockwise when viewed from the handle to the club head for a right handed golfer's swing, the force applied to the golf ball again will not be straight ahead and can tend to hit the ball to the left of straight ahead, such that the ball can hook. Of course, there are other reasons that slices and hooks occur, but, in general, in order to hit the ball in the intended direction (straight ahead), the club face should preferably be square during the impact of the club face with the ball. By square at impact, it is meant that the face of the club head is in a plane perpendicular to the plane of the swing when the face of the club head contacts the golf ball.

Traditional shafts offer a narrow window, or portion of the golf swing, where the club face is square or substantially square, where substantially square can mean the club face is within a certain angle, such as one degree or two degrees, of being square. That window is sandwiched between portions of the swing where the club shaft is untwisting from the twist caused by the initial acceleration of the forward swing, and a portion of the swing where the club shaft then twists after impacting the ball, due to deceleration of the swing. Accordingly, there is a need for a golf club shaft that increases the portion of a golf swing where the club face is square or substantially square. Further, there is a need for a golf club that allows a golfer to alter the shape of the ball trajectory, such as adding to or reducing a fade or a draw.

BRIEF SUMMARY

Embodiments of the subject invention relate to a method and apparatus for providing an elongated club shaft that has coupling between one or more bending modes and one or more twisting modes of deformation, or bend/twist coupling. Specific embodiments can incorporate bend/twist coupling such that bending along the longitudinal axis of the shaft in a first plane incorporating the longitudinal axis results in twisting of the shaft about the longitudinal axis and bending in a second plane incorporating the longitudinal axis, wherein the second plane is perpendicular to the first plane, does not result in any twisting of the shaft about the longitudinal axis. In this way, bending the shaft about the longitudinal axis of the shaft in a third plane incorporating the longitudinal axis that is at an angle with respect to the first plane between 0 and 90 degrees results in twisting about the longitudinal axis, but less twisting than bending in the first plane.

Specific embodiments pertain to hollow elongated shafts with bend/twist coupling; elongated shafts with a circular outer circumference cross-sectional shape, having bend/twist coupling; elongated shafts with a taper along the length of the shaft, having bend/twist coupling; and a hollow elongated shaft with a circular outer circumference cross-sectional shape, with a taper along the length of the shaft, having bend/twist coupling, where one or more of these embodiments can be golf club shafts. In specific embodiments, the elongated shafts can have length to diameter ratios of at least 10:1, at least 20:1, at least 30:1, at least 40:1, at least 50:1, at least 100:1, at least 150:1, and/or at least 200:1. In embodiments having a tapered shaft, these ratios can be based on the diameter of the small diameter end of the shaft (such as end of a golf club shaft that connects to the golf club head), can be based on the diameter of the large diameter end of the shaft (such as the handle end of a golf club shaft), can be based on the diameter at the midpoint of the elongated shaft (midpoint of length), can be based on the average diameter along the length of the shaft, or can be based on some sort of effective diameter of the shaft. Normal golf club shafts do not have this bend/twist coupling, such that bending does not significantly affect twist and twist does not significantly affect bending. For elongated shafts having bend/twist coupling, bending the shaft along certain axes leads to a predictable twisting deformation. In a specific embodiment, bending the shaft along a central longitudinal axis of the shaft results in twisting of the shaft about the same central longitudinal axis of the shaft. Incorporating bend/twist coupling into a golf club shaft can lead to more accurate ball contact, and/or control, on a more frequent and repeatable basis. Embodiments of the subject invention pertain to golf clubs that can correct for undesirable tendencies such as slices and/or hooks. Further embodiments can orient the shaft (rotation) with respect to the club head (e.g., face of club head) such that the orientation can add to or reduce a fade or draw, or otherwise affect the ball trajectory of the golf shot in a desired manner. Embodiments of the subject invention relate to all types of golf clubs, including, but not limited to, putters, wedges, irons, fairway woods, drivers, and hybrids. BRIEF DESCRIPTION OF DRAWINGS

Figure 1 shows an overhead view of a golf swing, showing the bend of the shaft as well as the accumulated twist of the shaft shown by the twist angle.

Figure 2A shows how a golf club shaft in accordance with an embodiment of the subject invention keeps the club face more square through the impact zone than a traditional shaft.

Figure 2B shows a superposition of several club head locations near the point of contact with the golf ball for a club head on a traditional shaft and a club head on a shaft in accordance with the subject invention.

Figure 3 shows the impact offset of the ball impact location, which produces a torsional moment about the shaft axis when the ball is impacted.

Figure 4 shows the deflection vs. twist of a golf club shaft in accordance with an embodiment of the subject invention, loaded in cantilever loading.

Figure 5 shows a perspective view of an embodiment of a shaft in accordance with the subject invention.

Figure 6 shows a cross-section of the shaft shown in Figure 5.

Figure 7 shows a shaft before and after bending.

Figures 8A and 8B show the shaft of Figure 5 relative to a swing plane, at two different angles of rotation about the longitudinal axis. Figures 9A-9H show an embodiment of a club head showing various angles of rotation the shaft of Figure 5 can have with respect to the club head.

Figure 10 shows a c-channel being pushed down at one end at two differences places of applied force.

Figure 11 shows a plank shaped piece of material before and after having a distal end of the material pushed down.

Figures 12A-12D show cross-sections of various embodiments of shafts in accordance with the subject invention. DETAILED DISCLOSURE

Embodiments of the subject invention relate to a method and apparatus for providing a golf club shaft that has coupling between one or more bending modes and one or more twisting modes of deformation. Normal shafts do not have this bend/twist coupling, such that bending does not significantly affect twist and twist does not significantly affect bending. For bend/twist coupling, bending the shaft along certain axes leads to a predictable twisting deformation about the axes. In a specific embodiment, bending the shaft along a central longitudinal axis of the shaft in a plane of bending results in twisting of the shaft about the same central longitudinal axis of the shaft. Such bend/twist coupling effect can have at least two primary benefits, which are described below. Bending along an axis at a certain rotational angle with respect to the shaft can be used to describe the bending. Alternatively, the bending can be described as bending in a plane. These two descriptions are equivalent when the axis along which the bending occurs is in the plane, and the plane makes the same angle with respect to the shaft as the certain rotational angle makes with respect to the shaft. Referring to Figure 5, bending could be described as bending along longitudinal axis 24 at an angle made by line segment AB with respect to the longitudinal axis 24, or described as bending in the plane incorporating the longitudinal axis and line segment AB.

Embodiments of the present invention relate to a golf club having a shaft that bends the same in all directions along a central longitudinal axis of the shaft, twists the same about the central longitudinal axis in the clockwise direction as in the counter-clockwise direction, is circular in cross-sectional shape, and utilizes bend/twist coupling to provide improvements in performance and to help golfers deal with common swing flows. By bending the same in all directions it is meant that the shaft has the same bending stiffness for all planes of bending with respect to bending along the central longitudinal axis of the shaft. By twists the same about the central longitudinal axis it is meant that the torsional stiffness in a clockwise direction about the central longitudinal axis is the same as the torsional stiffness in a counterclockwise direction about the central longitudinal axis. The circular cross-sectional shape can vary in diameter (taper) along the central longitudinal axis.

Twist of the golf club shaft is generally considered to be deleterious. Twist can occur due to, for example, the offset of the center of mass of the club-head with respect to the longitudinal axis of the shaft, where the offset of the center of mass is a distance from the longitudinal axis of the shaft to the center of mass of the club head in a direction normal to a plane, such as the plane of the swing of a golfer swinging the club. During down-swing acceleration of the club, the center of mass of the head being offset from the shaft causes twisting of the shaft. This phenomenon is depicted in Figure 1. Figure 1 shows an overhead view of a golf swing for a right handed golfer, showing the bend of the shaft, as well as the accumulated twist of the shaft, shown as the twist angle. For illustration, the relative rotational position of the shaft and club head has been simplified, and exaggerated, in order to illustrate the effect described. Actual swings of golfers can vary as to the rotational position the golfer holds the shaft in at various points in the swing, the curved path the shaft takes during the golfer's swing, and the position on the shaft (e.g., handle) that the golfer applied forces and/or torque to the shaft at various points of the swing, as well as other aspects of the golfer's swing that may affect the bending and/or twisting of the shaft. As shown in Figure 1, the shaft twists clockwise, when viewed from the handle to the club head, during the initial portion of the forward swing. During a specific swing, the shaft untwists to a square position at the moment of impact with the ball. In other swings, the ball may be struck before, or after, the square position and, thus, lead to applying a force to the ball that is not straight ahead, potentially resulting in an errant shot. Although Figure 1 shows contact with the ball occurring when the arc of the swing is nearest the ground, other swings can result in contact with the ball occurring earlier or later, depending on the preference of the golfer for a particular shot.

Traditional shafts offer a very narrow window where the club face is square. That window is sandwiched between where the club untwists from the initial acceleration during the initial portion of the forward swing that causes the shaft to twist, and where the shaft then twists after the impact zone due to deceleration during the latter portion of the forward swing. This phenomenon is depicted in Figures 1 and 2B, where Figure 1 shows an overview of a golf swing with a traditional shaft, and Figure 2B shows a superposition of the location and twist of the club head through the window just before contact between the club face and the ball and just after contact between the club face and the ball. Although Figure 1 shows the ball being contacted at the point of the swing where the club head is closest to the ground, the ball can be contacted earlier or later in the swing, as desired by the golfer. By incorporating bend/twist coupling, a shaft can be designed to tend to twist in the opposite direction from the twist that would tend to be caused by the inertia of the club head when bent along certain axes. In a specific embodiment, a golf club shaft can incorporate bend/twist coupling such that the shaft tends to twist inward in the early part of the forward swing and then tends to twist outward in the latter part of the forward swing. Incorporating such bend/twist coupling can effectively cancel the twist due to the mass of the club head being offset from the longitudinal axis of the shaft in a direction normal to a plane, such as the plane of the swing. Hence a window, or portion of the forward swing, where the club face of the club head is square, or within plus or minus an angle φ of being square, can be substantially extended. In this way, this window can cover a longer portion, or all of, the impact zone, where the impact zone is the portion of the forward swing during which the club head contacts the golf ball. Extending this window makes the club much more forgiving and, thus, can improve shot consistency. In specific embodiments, φ is Γ, 2°, 3°, 4°, 5°, 6°, 7°, 8°, 9°, or 10°. Therefore, by incorporating such bend/twist coupling, the criticalness of swing timing can be reduced and the likelihood of a good shot can be enhanced.

In addition to making the club more forgiving to imperfect swing timing, shafts can be fabricated to compensate for poor swings, such as consistent slicing or hooking. By adjusting the amount of bend/twist coupling, a specific deficiency, such as a slice can be partially, or completely, compensated for. The head of the club can also be positioned relative to the shaft to compensate for poor swings.

Another benefit that can result from incorporating bend/twist coupling comes at the instant when the ball is impacted by the club head. When the club head impacts the ball, the impact force on the club head is typically offset from the longitudinal axis of the shaft in a direction normal to the plane of the swing when the club is square by a distance which can be referred to as the impact offset, as shown in Figure 3. The force times the impact offset distance equals the torsional moment applied to the shaft by the impact force. This torsional moment causes the shaft to tend to twist upon impact. By incorporating bend/twist coupling in the shaft, the torsional moment applied to the shaft by the impact force can be partially, or completely, compensated for.

The shear center of a shaft incorporating bend/twist coupling is related to the mechanics of the materials of the shaft. The shear center can be defined as distance from the longitudinal axis of the shaft, in a direction normal to a plane, such as the plane of the swing, that application of an impact force parallel to the plane of the swing, or the moment caused by the club head offset, results in little or no twisting of the club shaft about the longitudinal axis. The shear center is defined assuming the proximal end of the shaft (handle end) is held fixed and the impact force, or other force, is applied at the distal end (club head end) at a certain distance from the point of the proximal end held fixed. The shear center may change if the force is applied at a different distance from the point of the proximal end held fixed. For specific embodiments, any force applied through the shear center results in no twisting, independent of the direction of the force, such that bending is achieved without twisting. The shear center can be positioned inside or outside of the shaft, and in the case of the shear center being positioned outside of the shaft, the force through the shear center is applied via a structure (such as a club head) rigidly affixed to the distal end of the shaft such that the shear center lies on the structure.

Referring to a shaft with a shear center, and the impact force direction through the shear center, the impact force of the ball on the club head at a distance from the longitudinal axis in a direction normal to the plane of the swing tends to twist (first type twist) the shaft about the longitudinal axis, but also tends to bend the shaft along the longitudinal axis, which tends to twist (second type twist) the shaft about the longitudinal axis in an opposite direction to the first twist. When the impact is at the shear center, or in a direction passing through the shear center, no first type twist occurs due to the impact, because the first type twist cancels the second type twist. If the shear center of the shaft coincides with the center of mass offset of the club head, then the twist (third type twist) that tends to be caused by the mass of the club head during acceleration of the golf club during the initial portion of the forward swing and deceleration of the golf club during the later portion of the forward swing will be offset by the second-type twist. In this case, the third type of twist tending to be caused can cause bending of the shaft. Accordingly, if the shear center coincides with the center of mass offset of the club head, and the golf ball is contacted by the club face at a distance from the longitudinal axis in a direction normal to the plane of the swing that equals the shear center, little, or no, twist will occur. Further, when the shear center of the shaft is at the same distance from the longitudinal axis as the impact location, the shaft will appear torsionally rigid, yet retain bending compliance.

The shear center of the shaft at the distal end can be oriented with respect to the shaft such that it is in the opposite direction of the center of mass offset of the club head. Twist of the second type (twist caused by bend twist coupling) would be in the opposite direction as that if the shear center was oriented in the same direction as the club head offset. This second type of twist would add to instead of cancel the twist of the first type (that caused by the offset mass). Additional embodiments through all orientations of the shaft with respect to the club head would lead to various degrees from acting to cancel through increasing the degree of first type twist.

The shaft and club head can be designed such that, with a certain orientation of the shaft (i.e., shear center) with respect to the club head, a fade can be enhanced, or reduced, with respect to hitting the ball the same way with a golf club without bend-twist coupling, or a draw can be enhanced, or reduced, with respect to hitting the ball the same way with a golf club without bend-twist coupling.

Embodiments of the subject invention relate to shafts that have a shear center that changes position with respect to the distance along the shaft from the proximal end of the shaft. The shear center can vary in a variety of measures. Specific embodiments involve a shear center that remains at a certain rotational angle with respect to the longitudinal axis of the shaft, where the shear center can then continuously move away from the longitudinal axis (e.g., monotonically increasing, linearly increasing, exponentially increasing, or other function with respect to distance along the shaft from the proximal end of the shaft) as the distance along the shaft away from the proximal end increases. In specific embodiments, the shear center can move towards or away from, or remain steady, with respect to the longitudinal axis as the distance along the shaft away from the proximal end increases, and can go back to the longitudinal axis at one or more locations along the longitudinal axis, such as when the shaft reaches the distal end (e.g., where head is attached). Preferably, the shear center is away from the longitudinal axis at the distal end such that the shaft as a whole has bend/twist coupling. In other embodiments, bend/twist coupling can be implemented at different rotational angles for different portions of the length of the shaft, be implemented at different amounts for different portions of the length, can be implemented for only certain portions of the length, or can be implemented in a variety of other manners. By implementing bend/twist coupling at different rotational angles for different portions of the length of the shaft it is meant that the plane of bending that provides the maximum bend/twist coupling, where such plane of bend can be said to be at a certain rotational direction with respect to the longitudinal axis, can be different for different portions of the shaft. In a specific embodiment, the rotational direction of the plane of bending with the maximum bend/twist coupling can vary continuously along the length of the shaft. Accordingly, the shear center can rotate as a function of the distance along the shaft from the proximal end of the shaft, again in a variety of manners, as desired, such as rotating in a constant direction (clockwise or counter-clockwise) about the longitudinal axis, rotating back and forth about the longitudinal axis, remaining at a constant rotational angle for portions of the length, and rotating about the longitudinal axis for other portions of the length of the shaft, as a function of distance along the shaft from the proximal end of the shaft.

In specific embodiments, the center of mass offset is within 90% to 110% of the shear center, greater than the shear center, and/or less than the shear center.

In further specific embodiments, the desired point of contact on the face of the club head is within 90%> to 110% of the shear center, greater than the shear center, and/or less than the shear center. In specific embodiments, the shear center is on the same side of the longitudinal axis from the shaft as the center of mass of the club head, and in other specific embodiments, the shear center is on the opposite side of the longitudinal axis of the shaft as the center of mass of the club head (such that the longitudinal axis lies between the shear center and the center of mass of the club head). By orienting the shaft with the shear center on the same side of the shaft as the center of mass offset, the twist due to the center of mass being off the longitudinal axis can be partially, or fully, compensated for (negated), or a twist in an opposite direction can be created.

In further specific embodiments, the shear center is 10%> to 300% of the center of mass offset, 10%> to 100% of the center of mass offset, 100%) to 300%, of the center of mass offset, and/or 90% to 110%> of the center of mass offset. Embodiments of the subject golf club shafts can have a shear center that is a distance from the longitudinal axis that is in the range of 0 inches to 12 inches, 0 inches to 5 inches, 1 radius (of the distal end of the shaft) to 30 radii, less than 1 radius, 1 radius to 5 radii, and greater than 1 radius.

In a specific embodiment, both an extension of the window, or portion of the forward swing, where the club face of the club head is square, or within plus or minus a desired angle Θ of being square can be accomplished, and the torsional moment caused by the impact force occurring at an impact offset from the axis of the shaft, can be at least partially compensated for, with the same shaft design. In other words, by orienting the bend/twist coupled shaft appropriately with the head of the club, the benefit of having a more square club face and resistance to twisting during impact can both be achieved.

The amount of bend/twist coupling in the shaft can be controlled by controlling the materials used to manufacture the shaft and/or the structure of the shaft. In a specific embodiment, materials having anisotropic behavior can be used for the manufacture of the shaft in order to achieve bend/twist coupling. In a further specific embodiment, materials having anisotropic stiffness can be used for the manufacture of the shaft in order to achieve bend/twist coupling. In an embodiment, proper alignment of composite reinforcement, such as carbon fiber or other reinforced materials, can result in bend/twist coupling of the shaft. In an embodiment, a proper fiber layup can be used for manufacture of the club shaft. For example, carbon fibers having an orientation at an angle to the longitudinal axis between 0° degrees and 90° can contribute to bend/twist coupling and, if not offset by other materials contributing bend/twist coupling, can contribute to a new bend/twist coupling of the shaft. The bend/twist coupling can be mathematically analyzed and/or modeled in order to optimize the shaft design for a particular application. Shafts in accordance with embodiments of the subject invention can have length to diameter (proximal or distal end) ratios in the range of at least 10:1, at least 20: 1 , at least 30:1, at least 40: 1 , at least 50: 1 , at least 100: 1 , at least 150:1, at least 200: 1, less than 10: 1, less than 20:1, less than 30: 1, less than 40:1, less than 50: 1, less than 100: 1 , less than 150: 1, and/or less than 200: 1.

Important properties of the shaft include bending stiffness, torsional stiffness, and location of the shear center. In addition, with respect to golf clubs, these same three properties are important, as well as the orientation of the shaft, rotationally, with respect to the club head. The bending stiffness of the shaft is determined by the sectional property of EI, where E is the effective modulus of elasticity of the material (in units of Newtons per square meter, N/m ² , or Pascals, Pa) and I is the moment of inertia of the cross-sectional shape (in units of meters to the fourth power, m ⁴ ), thus yielding units of Newtons times meters squared or Nm ² . Shafts in accordance with specific embodiments of the subject invention can have a bending stiffness in the range from 0.2 Nm to 500 Nm . The torsional stiffness is determined by the sectional property of GJ, where G is the effective shear modulus of the material (in units of Newtons per square meter, N/m ² , or Pascals, Pa) and J is the polar moment of inertia of the cross-sectional shape (in units of meters to the fourth power, m ⁴ ), thus yielding units of Newtons times meters squared or Nm ² . Shafts in accordance with specific embodiments of

• 2 2 the subject invention can have a torsional stiffness m the range from 0.1 Nm' to 300 Nm".

Referring to Figures 5 and 6, an embodiment is shown that was fabricated using unidirectional carbon fiber prepreg. The carbon fibers are orientated such that a first axis of stiffness is at an angle, Θ, to the longitudinal axis of the shaft, where Θ is between 0° and 90°. When Θ is between 90° and 180°, the twist tends to go in the opposite direction for the same bend. In specific embodiments, Θ can remain constant, such as the embodiment shown in Figure 5 where Θ is constant for each half 22, 23 of the shaft. Alternatively, Θ can vary with radius and/or position along the length of the shaft, such as the alignment of the carbon fibers such that the first axis of stiffness follows ellipses that travel around the contour of the curve of the shaft continuously from half 22 to half 23. This first axis of stiffness is shown in Figure 5 as reference number 11 and follows the curve of the tapered cylindrical shaft. The second axis of stiffness, which is not shown, is perpendicular to the first axis and also follows the curve of the tapered cylindrical shaft.

The first axis of stiffness can follow various patterns, such as helices, ellipses, or others that provide bend/twist coupling. The embodiment shown in Figure 5 and 6 has two halves of the shaft 22 and 23, separated by a dividing plane outlined by reference 12 and 15 such that the two halves 22 and 23 are mirror images of each other with respect to the plane 12, 15. In this way, when the shaft is bent, or loaded in cantilever loading, along the longitudinal axis 24 about line AB (in the swing plane), as shown in Figure 7, where the plane defined by 12 and 15 is perpendicular to the page of Figure 7, a torsional moment about the longitudinal axis 24 causes the shaft to twist about the longitudinal axis 24. Reference 21 shows the deflection referred to in Figure 4, which is the deflection of the end of the shaft during cantilever loading while the handle is held in place. In contrast, if the shaft were bent along the longitudinal axis 24, as shown in Figure 7, where the plane defined by 12 and 15 is in the page of Figure 7, no net torsional moment, and, therefore, no twisting would occur.

A variety of materials and shaft structures can be utilized to achieve the bend/twist coupling in accordance with embodiments of the subject invention. Fiber reinforced materials such as carbon fiber reinforced materials can be used. Shafts can be hollow, and/or have hollow portions, and the entire shaft and/or portions of the shaft can contribute to the bend/twist coupling.

Figure 6 shows a cross-sectional view of the shaft which has a hollow center, one or more layers of carbon fiber prepreg 18 with the first axis of stiffness parallel to the longitudinal axis 24, and one or more layers of carbon fiber prepreg 16 and 17 (corresponding to halves 23 and 22, respectively) with the first axis of stiffness of the carbon fiber prepreg at an angle Θ with respect to the longitudinal axis and in the curve of the layers 16 and 17. In a specific embodiment, Θ is less than 45°, greater than 0° and less than 90°, and/or greater than or equal to 45° and less than 90°. Preferably, the shaft has the same bending stiffness along the longitudinal axis at each orientation of the plane 12, 15 with the page of Figure 7. Preferably, the torsional stiffness of the shaft is the same clockwise as it is counterclockwise. Preferably, the stiffness along a first axis of stiffness for the material having an anisotropic stiffness used to manufacture the shaft is at least one and a half orders of magnitude higher, or more preferably at least two orders of magnitude higher, than the stiffness along the second axis of stiffness, where the second axis of stiffness is perpendicular to the first axis of stiffness. Specific embodiments have stiffness along a first axis that is at least 2 times, at least 5 times, at least 10 times, at least 50 times, at least 100 times, at least 200 times, at least 500 times, at least 1,000 times, and/or greater than 1000 times the stiffness along the second (perpendicular) axis.

Tests show, referring to Figure 4, that this non-optimized embodiment can achieve approximately 2 degrees of twist for every 1 inch of deflection, such as the deflection 21 shown in Figure 7, under cantilever bending conditions, for a shaft having a length of approximately 42 inches long and having a taper from the handle end (larger diameter) to the club head end (smaller diameter). For the testing, a portion of the proximal end (handle end) was used to hold the proximal end rigidly fixed in position so the bending of the shaft could be accomplished and the twisting measured, such that approximately 39 inches of the 42-inch shaft was bent. This amount of bend/twist coupling is quite pronounced and well within the practical range necessary to achieve one or both primary benefits discussed above. In specific embodiments, the amount of twist is at least 0.Γ, at least , at least 2°, at least 3°, and/or at least 4° for every deflection of 2% of the length of the shaft for a tapered shaft. In other specific embodiments, the amount of twist is at least Γ, at least 2°, at least 3°, and/or at least 4 ^° for every deflection of 2% of the length of the shaft for a non-tapered shaft. Additionally, the shear center of the shaft was measured to be approximately 3 inches from the axis of the shaft, which allows for the shaft to partially, or completely, compensate for the torque caused by the impact being at the offset impact distance away from the longitudinal axis during the ball strike. A club incorporating a shaft having such benefits can also allow the shaft to be more flexible, resulting in a higher club-head speed, while retaining control.

In a preferred embodiment, the club head is attached to the shaft such that the plane defined by 12 and 15 is perpendicular to the plane of the swing such that the bending of the shaft during the forward swing due to the inertia of the club head is such that, referring to the bending shown in Figure 7, the plane defined by 12 and 15 is perpendicular to the page of Figure 7. Figures 8A and 8B show how the shaft is oriented in this preferred embodiment, such that the plane defined by 12 and 15 is perpendicular to the swing plane. In additional embodiments, the shaft can be rotated with respect to the club head such that the plane defined by 12 and 15 is at an angle with the plane of the swing between -180 ^° and 180 ^° , in order to alter the performance of the golf club. As an example, the shaft can be rotated with respect to the club head in order to correct a slice or hook, or for the preference of the golfer.

Figures 9A-9H show a top view of a golf club head, similar to the golf club head shown in Figure 3, with an indication of the orientation of the plane defined by 12 and 15 within the shaft shown in Figures 5 and 6 indicated by line AB. Figure 9 A shows what can be referred to as the standard rotational orientation of the shaft with respect to the club head, where A and B are shown in Figures 5, 8A, and 8B. In this standard rotational orientation, when the shaft bends such that the bottom of the shaft bends to the right looking down on top of the club head, the shaft rotates such that the club head tends to rotate counterclockwise looking down on top of the club head. If the shaft shown in Figure 9A was in a left-handed club head, then the shaft can be maintained in the same orientation, with a left hand club head switched in for the right hand club head shown, such that A and B are in the same orientation. In this way, the shaft shown in Figures 5, 8 A, and 8B can be used in either a right-handed golf club or a left-handed golf club, in the standard rotational orientation with respect to the club head. In this way, for a left hand golfer, when the shaft bends to the left looking down on top of the club head, the shaft rotates such that the club head tends to rotate clockwise looking down on top of the club head.

There are situations where it can be desirable to rotate the shaft with respect to the club head away from the standard position, where Figure 9A shows the standard position. Figures 9B-9H show various embodiments where the shaft is rotated with respect to the standard position where Figure 9B shows an embodiment where the shaft is rotated counterclockwise between 0 ^° and 90°; Figure 9C shows an embodiment where the shaft is rotated counterclockwise 90°; Figure 9D shows an embodiment where the shaft is rotated counterclockwise between 90° and 180 ^° ; Figure 9E shows an embodiment where the shaft has been rotated either counterclockwise, or clockwise, 180°; Figure 9F shows an embodiment where the shaft has been rotated clockwise between 90° and 180 ^° ; Figure 9G shows an embodiment where the shaft has been rotated clockwise 90°; and Figure 9H shows an embodiment where the shaft has been rotated clockwise between 0° and 90°.

Figure 10 shows a piece of c-channel made using an isotropic material, which is used to show the concept of a shear center, e. The c-channel is held securely at one end by a bracket 42 or other apparatus. A force, F _cm , is applied directly over the center of mass (or centroid) of the c-channel' s cross section and as the end of the c-channel is pushed down to a new position 42, the c-channel rotates. However, if a bracket 44 is affixed to the c-channel that allows a force, Fsc, to be applied a distance away from the position directly over the center of mass (or centroid) of the cross-section equal to the shear center distance, e, then, as the c-channel is pushed down, the c-channel does not rotate. The reason the c-channel does not rotate when the force, Fsc, is applied at the shear center is that the torsional moment caused by the force, Fsc, offsets the twisting of the c-channel. Figure 11 shows a piece of material having a rectangular cross-section in all directions extending out from a cantilever support. The piece of material has anisotropic stiffness in at least the plane of the top of the piece of material, such that the stiffness along a first axis of stiffness (principal axis shown in Figure 11) is higher than the stiffness along a second axis of stiffness, which is perpendicular to the first axis of stiffness. In Figure 11, the first axis of stiffness (principal axis) makes an angle relative to the longitudinal axis of the piece of material such that when a force, F _T , is applied to the top of the distal end of the material, the distal end of the piece of material tends to rotate about the longitudinal axis. Due to the anisotropic stiffness of the material, as the force, F _T , is applied, the distal end rotates around the longitudinal axis, clockwise or counterclockwise, depending on the angle of the first axis of stiffness (principal axis) with respect to the longitudinal axis of the piece of material.

There are many shaft structure and material combinations that can provide bend/twist coupling in accordance with embodiments of the subject invention. In addition to the embodiment shown in Figures 5 and 6, Figure 12 A - 12D shows cross sections of a variety of shaft structures and material combinations that can be utilized in accordance with the subject invention. Figure 12A shows an embodiment that can incorporate a piece of material, such a material as shown in Figure 11, with filler material on either side. Figure 12A shows a cross- section of the shaft where the middle section is a cross-section of the piece of material from Figure 1 1 cut through the longitudinal axis. Figure 12B shows a cross-section of a shaft having lines representing pieces of material having the properties of the material shown in Figure 1 1 within a background material, such that each line represents a cross-sectional view of the piece of material shown in Figure 11 cut through the longitudinal axis. Figure 12C shows a cross section through the longitudinal axis of an embodiment, where the center portions are pieces of material shown in Figure 1 1, much like Figure 12A. There are hollow portions in Figure 12C, but these portions can be filled with a filler material. The outer portions of the embodiment of Figure 12C can also provide bend/twist coupling, similar to the embodiment of Figure 5, or can use materials without bend/twist coupling. Figure 12D shows an embodiment that shows a cross section of a shaft having lines representing pieces of material having the properties of the material shown in Figure 11 within a background material, such that each line represents a cross-sectional view of the piece of material shown in Figure 11 through the longitudinal axis. The embodiment of Figure 12D can have an optional one of more hollow portions within the shaft. In a specific embodiment, the materials having anisotropic properties, such as anisotropic stress/strain properties can be located along the entire shaft and located uniformly. In further embodiments, such materials having anisotropic properties, such as anisotropic stress/strain properties can be located in certain segments or sections, only on half 23 or half 22, only on portions of halves 23 and 22, or other combinations of locations to achieve a desired performance of the golf club.

All patents, patent applications, provisional applications, and publications referred to or cited herein are incorporated by reference in their entirety, including all figures and tables, to the extent they are not inconsistent with the explicit teachings of this specification.

It should be understood that the examples and embodiments described herein are for illustrative purposes only and that various modifications or changes in light thereof will be suggested to persons skilled in the art and are to be included within the spirit and purview of this application.