US20260158331A1
2026-06-11
18/977,495
2024-12-11
Smart Summary: A new design for golf ball dimples is introduced. The dimples have unique shapes created using a mathematical curve called a roulette. Some of these shapes are specifically based on two types of curves known as epitrochoids and hypotrochoids. These special dimple patterns can improve the ball's performance. Overall, the design aims to enhance how golf balls behave when hit. 🚀 TL;DR
Various aspects of a dimple pattern for a golf ball are disclosed herein. In one aspect, the golf balls disclosed herein can include dimples having a plan shape that is defined by a roulette. In specific aspects, the golf balls disclosed herein can include dimples having a plan shape that is defined by an epitrochoid or a hypotrochoid.
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A63B37/0007 » CPC main
Solid balls; Marbles Rigid hollow balls;; Golf balls; Surface depressions or protrusions Non-circular dimples
A63B37/0012 » CPC further
Solid balls; Marbles Rigid hollow balls;; Golf balls; Surface depressions or protrusions Dimple profile, i.e. cross-sectional view
A63B37/00 IPC
Balls
A63B37/00 IPC
Solid balls; Marbles Rigid hollow balls;
This disclosure generally relates to a golf ball, and is more particularly related to a specific plan shape for a dimple on a golf ball.
Various dimple pattern designs and various golf ball dimple geometries are well known, which can include various cross-sectional profiles and/or plan shapes.
Aerodynamics continues to be a critical aspect of golf ball design, and there is an ever-present demand for improved pattern configurations and dimple geometries that provide for greater flexibility and control of parameters influencing aerodynamic performance.
Exemplary configurations directed to modifying plan shapes of dimples are disclosed in U.S. Pat. No. 11,724,159, which is commonly assigned to Acushnet Company and is incorporated by reference in its entirety as if fully set forth herein.
It would be desirable to provide greater flexibility with dimple design that allows for increased control, as well as additional boundary layer energy and optimal packing efficiency.
The present disclosure is generally directed to a golf ball that includes dimples having a plan shape defined by a roulette. By the term, “plan shape” it is meant the demarcation between the dimple and the outer surface of the golf ball or fret surface.
In one specific aspect, a golf ball having a generally spherical surface and comprising a plurality of dimples on the surface is disclosed herein. At least a portion of the plurality of dimples have a non-circular plan shape defined by a roulette where a trajectory of a fixed point relative to a moving curve traces a closed curve as the moving curve travels along a stationary curve.
The plan shape of the dimples can be an epitrochoid, where the moving curve is a moving circle and stationary curve is a stationary circle, and where the moving circle travels along the outside of the stationary circle. The plan shape can be defined according to the following parametric equations:
x = [ a + b ] * cos ( θ ) - d * cos [ a + b b θ ] y = [ a + b ] * sin ( θ ) - d * sin [ a + b b θ ]
where (a) is a radius of the stationary circle, (b) is a radius of the moving circle, (d) is a distance of a fixed point relative to the center of the moving circle, and (θ) is an angle from 0 to 2π.
In one aspect, the radius (b) is equal to the ratio of the radius (a) to any positive integer greater than 1. In one aspect, the distance (d) can be less than or equal to the radius (b). One of ordinary skill in the art would understand that the values for the radius (a), radius (b), and distance (d) can vary.
In another aspect, the plan shape of the dimples can be a hypotrochoid where the moving curve is a moving circle, and the stationary curve is a stationary circle, and where the moving circle travels along the inside of the stationary circle. The plan shape can be defined according to the following parametric equations:
x = [ a - b ] * cos ( θ ) + d * cos [ a - b b θ ] y = [ a - b ] * sin ( θ ) - d * sin [ a - b b θ ]
where (a) is a radius of the stationary circle, (b) is a radius of the moving circle, (d) is a distance of a fixed point relative to the center of the moving circle, and (θ) is an angle from 0 to 2π.
In one aspect, the radius (b) can be equal to the ratio of the radius (a) to any positive integer greater than 1. In one aspect, the distance (d) is less than or equal to the radius (b). One of ordinary skill in the art would understand that the values for the radius (a), radius (b), and distance (d) can vary.
Additional features and aspects of the present disclosure are described in further detail herein.
Further features and advantages of the present disclosure can be ascertained from the following detailed description that is provided in connection with the drawings described below:
FIG. 1 illustrates a dimple plan shape defined by an epitrochoid according to one aspect.
FIG. 2 illustrates a dimple plan shape defined by a hypotrochoid according to one aspect.
FIG. 3A illustrates a dimple plan shape defined by a first exemplary epitrochoid.
FIG. 3B illustrates a dimple plan shape defined by a second exemplary epitrochoid.
FIG. 3C illustrates a dimple plan shape defined by a third exemplary epitrochoid.
FIG. 3D illustrates a dimple plan shape defined by a fourth exemplary epitrochoid.
FIG. 4A illustrates a dimple plan shape defined by a fifth exemplary epitrochoid.
FIG. 4B illustrates a dimple plan shape defined by a sixth exemplary epitrochoid.
FIG. 4C illustrates a dimple plan shape defined by a seventh exemplary epitrochoid.
FIG. 4D illustrates a dimple plan shape defined by an eighth exemplary epitrochoid.
FIG. 5A illustrates a dimple plan shape defined by a first exemplary hypotrochoid.
FIG. 5B illustrates a dimple plan shape defined by a second exemplary hypotrochoid.
FIG. 5C illustrates a dimple plan shape defined by a third exemplary hypotrochoid.
FIG. 5D illustrates a dimple plan shape defined by a fourth exemplary hypotrochoid.
FIG. 6A illustrates a dimple plan shape defined by a fifth exemplary hypotrochoid.
FIG. 6B illustrates a dimple plan shape defined by a sixth exemplary hypotrochoid.
FIG. 6C illustrates a dimple plan shape defined by a seventh exemplary hypotrochoid.
FIG. 6D illustrates a dimple plan shape defined by an eighth exemplary hypotrochoid.
Details of a specific plan shape for use in designing a golf ball dimple are provided herein. A golf ball having at least some dimples with non-circular plan shapes produced from a roulette is disclosed herein.
In one aspect, the roulettes for the golf ball plan shapes are generated via closed curves tracing the path or trajectory of a fixed point relative to a moving curve which is allowed to roll, without slipping, along a stationary curve.
In one aspect, the specific roulettes can be comprised of epitrochoids or hypotrochoids, where the moving and stationary curves are circles.
In another aspect, the specific roulettes can include epitrochoids and/or hypotrochoids that produce low frequency low amplitude non-circular plan shapes.
In one aspect, the roulettes disclosed herein for defining a dimple plan shape can include cycloids, epicycloids, trochoids, involutes, hypotrochoids, epitrochoids, and/or hypocycloids. The roulette can generally be defined by a fixed curve and a rolling curve.
Particularly illustrative examples of roulettes for dimple plan shapes can include epitrochoids and hypotrochoids, which can be generated from a fixed point (p), a distance (d) from the center of rolling circle of radius (b) which moves along the outside or inside of a fixed circle of radius (a) through an angle θ, where θ=(θ, 2π).
In one aspect, the dimple plan shape is defined by an epitrochoid, which can be defined by the following parametric equations:
x = [ a + b ] * cos ( θ ) - d * cos [ a + b b θ ] y = [ a + b ] * sin ( θ ) - d * sin [ a + b b θ ]
In one aspect, the dimple plan shape is defined by an hypotrochoid, which can be defined by the following parametric equations:
x = [ a - b ] * cos ( θ ) + d * cos [ a - b b θ ] y = [ a - b ] * sin ( θ ) - d * sin [ a - b b θ ]
Referring now to FIGS. 1 and 2, as the rolling curve, circle of radius (b), travels along the path of the fixed curve, circle of radius (a), the locus of points traced by the point (p) lying a distance (d) from the center of the moving curve creates the dimple plan shape, which is shown as plan shape (P1) in FIG. 1 and plan shape (P2) in FIG. 2.
Referring specifically to FIG. 1, an epitrochoid is used to generate the dimple plan shape. More specifically, the epitrochoid dimple plan shape shown in FIG. 1 has the following values:
a = 1 ; b = 0.333 ; and = 0.15 .
Referring specifically to FIG. 2, a hypotrochoid is used to generate the dimple plan shape. More specifically, the hypotrochoid dimple plan shape shown in FIG. 2 has the following values:
a = 1 ; b = 0.2 ; and = 0.1 .
Manipulation of the relationship between the radii (a) and (b), as well as the position of the point (p) relative to the center of the moving curves, allows for a variety of dimple plan shapes.
In some aspects, dimple plan shapes are cyclically symmetric with concave and convex boundaries that can be particularly configured to interdigitate with neighboring dimples and/or to construct smooth, well-hidden mold cavity parting lines.
In one aspect, a golf ball having a generally spherical surface and comprising a plurality of dimples on the surface is disclosed herein. At least a portion of the plurality of dimples have a non-circular plan shape defined by a roulette or roulette curve. The roulette is defined such that a trajectory of a fixed point relative to a moving curve traces a closed curve as the moving curve travels along a stationary curve. The closed curve defined by the roulette defines the non-circular plan shape of a dimple.
In one aspect, the plan shape is an epitrochoid where the moving curve is a moving circle and stationary curve is a stationary circle, and wherein the moving circle travels along an outside of the stationary circle. For an epitrochoid, the plan shape can be defined according to the following parametric equations:
x = [ a + b ] * cos ( θ ) - d * cos [ a + b b θ ] y = [ a + b ] * sin ( θ ) - d * sin [ a + b b θ ]
where (a) is a radius of the stationary circle, (b) is a radius of the moving circle, (d) is a distance of a fixed point relative to a center of the moving circle, and (θ) is an angle from 0 to 2π. In one aspect, the radius (b) is equal to a ratio of the radius (a) to any positive integer greater than 1. In another aspect, the distance (d) is less than or equal to the radius (b). One of ordinary skill in the art would understand that the values for the radius (a), radius (b), and distance (d) can vary.
In another aspect, the plan shape is a hypotrochoid where the moving curve is a moving circle, and the stationary curve is a stationary circle, and wherein the moving circle travels along an inside of the stationary circle. For a hypotrochoid, the plan shape can be defined according to the following parametric equations:
x = [ a - b ] * cos ( θ ) + d * cos [ a - b b θ ] y = [ a - b ] * sin ( θ ) - d * sin [ a - b b θ ]
where (a) is a radius of the stationary circle, (b) is a radius of the moving circle, (d) is a distance of a fixed point relative to a center of the moving circle, and (θ) is an angle from 0 to 2π. The radius (b) can be equal to a ratio of the radius (a) to any positive integer greater than 1. The distance (d) can be less than or equal to the radius (b). One of ordinary skill in the art would understand that the values for the radius (a), radius (b), and distance (d) can vary.
In another aspect, a golf ball is disclosed that has a generally spherical surface and comprises a plurality of dimples on the surface. At least a portion of the plurality of dimples have a non-circular plan shape defined by either: (i) an epitrochoid, or (ii) a hypotrochoid, such that a trajectory of a fixed point relative to a moving curve traces a closed curve as the moving curve travels along a stationary curve, and the closed curve defines the non-circular plan shape. In one aspect, the non-circular plan shape is defined by an epitrochoid, such that the moving curve is a moving circle and stationary curve is a stationary circle, and the moving circle travels along an outside of the stationary circle. For an epitrochoid, the plan shape is defined according to the following parametric equations:
x = [ a + b ] * cos ( θ ) - d * cos [ a + b b θ ] y = [ a + b ] * sin ( θ ) - d * sin [ a + b b θ ]
where (a) is a radius of the stationary circle, (b) is a radius of the moving circle, (d) is a distance of a fixed point relative to a center of the moving circle, and (θ) is an angle from 0 to 2π.
In another aspect, the non-circular plan shape is defined by a hypotrochoid, such that the moving curve is a moving circle and the stationary curve is a stationary circle, and the moving circle travels along an inside of the stationary circle. For a hypotrochoid, the plan shape is defined according to the following parametric equations:
x = [ a - b ] * cos ( θ ) + d * cos [ a - b b θ ] y = [ a - b ] * sin ( θ ) - d * sin [ a - b b θ ]
where (a) is a radius of the stationary circle, (b) is a radius of the moving circle, (d) is a distance of a fixed point relative to a center of the moving circle, and (θ) is an angle from 0 to 2π.
The following non-limiting examples demonstrate plan shapes of golf ball dimples made in accordance with the present disclosure. The examples are merely illustrative of the preferred embodiments of the present disclosure, and are not to be construed as limiting the present disclosure and its various aspects.
FIGS. 3A-3D and 4A-4D each generally disclose a dimple plan shape defined by an epitrochoid. The parametric equations for the shapes shown in FIGS. 3A-3D and 4A-4D are shown below:
x = [ a + b ] * cos ( θ ) - d * cos [ a + b b θ ] y = [ a + b ] * sin ( θ ) - d * sin [ a + b b θ ]
FIGS. 5A-5D and 6A-6D each generally disclose a dimple plan shape defined by a hypotrochoid. The parametric equations for the shapes shown in FIGS. 5A-5D and 6A-6D are shown below:
x = [ a - b ] * cos ( θ ) + d * cos [ a - b b θ ] y = [ a - b ] * sin ( θ ) - d * sin [ a - b b θ ]
Each of the specific plan shapes illustrated in FIGS. 3A-3D, 4A-4D, 5A-5D, and 6A-6D are described in further detail herein.
In a first example, a dimple plan shape 300a can have the shape shown in FIG. 3A, which is defined by an epitrochoid. In this specific example, the epitrochoid has the following values: a=1; b=a/2; and d=b/2.
In a second example, a dimple plan shape 300b can have the shape shown in FIG. 3B, which is defined by an epitrochoid. In this specific example, the epitrochoid has the following values: a=1; b=a/4; and d=b/2.
In a third example, a dimple plan shape 300c can have the shape shown in FIG. 3C, which is defined by an epitrochoid. In this specific example, the epitrochoid has the following values: a=1; b=a/6; and d=b/2.
In a fourth example, a dimple plan shape 300d can have the shape shown in FIG. 3D, which is defined by an epitrochoid. In this specific example, the epitrochoid has the following values: a=1; b=a/8; and d=b/2.
In a fifth example, a dimple plan shape 400a can have the shape shown in FIG. 4A, which is defined by an epitrochoid. In this specific example, the epitrochoid has the following values: a=1; b=a/5; and d=b.
In a sixth example, a dimple plan shape 400b can have the shape shown in FIG. 4B, which is defined by an epitrochoid. In this specific example, the epitrochoid has the following values: a=1; b=a/5; and d=b/2.
In a seventh example, a dimple plan shape 400c can have the shape shown in FIG. 4C, which is defined by an epitrochoid. In this specific example, the epitrochoid has the following values: a=1; b=a/5; and d=b/5.
In an eighth example, a dimple plan shape 400d can have the shape shown in FIG. 4D, which is defined by an epitrochoid. In this specific example, the epitrochoid has the following values: a=1; b=a/5; and d=b/10.
In a ninth example, a dimple plan shape 500a can have the shape shown in FIG. 5A, which is defined by a hypotrochoid. In this specific example, the hypotrochoid has the following values: a=1; b=a/3; and d=b/5.
In a tenth example, a dimple plan shape 500b can have the shape shown in FIG. 5B, which is defined by a hypotrochoid. In this specific example, the hypotrochoid has the following values: a=1; b=a/5; and d=b/5.
In an eleventh example, a dimple plan shape 500c can have the shape shown in FIG. 5C, which is defined by a hypotrochoid. In this specific example, the hypotrochoid has the following values: a=1; b=a/7; and d=b/5.
In a twelfth example, a dimple plan shape 500d can have the shape shown in FIG. 5D, which is defined by a hypotrochoid. In this specific example, the hypotrochoid has the following values: a=1; b=a/9; and d=b/5.
In a thirteenth example, a dimple plan shape 600a can have the shape shown in FIG. 6A, which is defined by a hypotrochoid. In this specific example, the hypotrochoid has the following values: a=1; b=a/11; and d=2b/3.
In a fourteenth example, a dimple plan shape 600b can have the shape shown in FIG. 6B, which is defined by a hypotrochoid. In this specific example, the hypotrochoid has the following values: a=1; b=a/11; and d=b/3.
In a fifteenth example, a dimple plan shape 600c can have the shape shown in FIG. 6C, which is defined by a hypotrochoid. In this specific example, the hypotrochoid has the following values: a=1; b=a/11; and d=b/5.
In a sixteenth example, a dimple plan shape 600d can have the shape shown in FIG. 6D, which is defined by a hypotrochoid. In this specific example, the hypotrochoid has the following values: a=1; b=a/11; and d=b/13.
One of ordinary skill in the art would understand that the quantity of dimples having a plan shape defined by a roulette can vary. In one aspect, the subset of the plurality of the dimples having a plan shape defined by a roulette can include at least 50% of a total quantity of the plurality of dimples. In one aspect, the subset of the plurality of the dimples having a plan shape defined by a roulette can include at least 75% of a total quantity of the plurality of dimples. In one aspect, the subset of the plurality of the dimples having a plan shape defined by a roulette can include 25%-80% of a total quantity of the plurality of dimples. In one aspect, the subset of the plurality of the dimples having a plan shape defined by a roulette can include 100% of a total quantity of the plurality of dimples, such that every dimple on the golf ball has a roulette plan shape. In one aspect, the subset of the plurality of the dimples having a plan shape defined by a roulette can include 80%-90% of a total quantity of the plurality of dimples. In one aspect, the subset of the plurality of the dimples having a plan shape defined by a roulette can include less than 50% of a total quantity of the plurality of dimples.
The total number of dimples having a plan shape defined by a roulette can be at least 100, or at least 200, or at least 300, or at least 400, or at least 500, or at least 600, or at least 700. In one aspect, total number of dimples having a plan shape defined by a roulette can be 150-350 dimples, or 200-450 dimples, or 300-400 dimples, or 350-650 dimples. In one aspect, total number of dimples having a plan shape defined by a roulette can be less than 400 dimples, or less than 350 dimples, or less than 300 dimples, or less than 250 dimples, or less than 200 dimples, or less than 150 dimples.
In one aspect, the dimples having a plan shape defined by a roulette can cover at least 50% of a total surface area of the golf ball. In another aspect, the dimples having a plan shape defined by a roulette can cover less than 65% of a total surface area of the golf ball. In another aspect, the dimples having a plan shape defined by a roulette can cover at least 70% of a total surface area of the golf ball. In another aspect, the dimples having a plan shape defined by a roulette can cover less than 70% of a total surface area of the golf ball. In another aspect, the dimples having a plan shape defined by a roulette can cover at least 75% of a total surface area of the golf ball. In another aspect, the dimples having a plan shape defined by a roulette can cover at least 80% of a total surface area of the golf ball. In another aspect, the dimples having a plan shape defined by a roulette can cover at least 85% of a total surface area of the golf ball.
The dimples having a plan shape defined by a roulette can have various dimple diameters, as one of ordinary skill in the art would appreciate. Since the plan shape perimeters of the present disclosure are noncircular, the plan shapes can be defined by an effective dimple diameter which is twice the average radial dimension of the set of points defining the plan shape from the plan shape centroid. For example, in one embodiment, dimples according to the present invention have an effective dimple diameter within a range of about 0.005 inches to about 0.300 inches. In another embodiment, the dimples have an effective dimple diameter of about 0.020 inches to about 0.250 inches. In still another embodiment, the dimples have an effective dimple diameter of about 0.100 inches to about 0.225 inches. In yet another embodiment, the dimples have an effective dimple diameter of about 0.125 inches to about 0.200 inches. Regardless of how the diameters are measured, one of ordinary skill in the art would understand that differently sized dimple diameters can be provided among the dimples having a plan shape defined by a roulette.
Edge angle and chord depth relate generally to spherical dimples, but the same or similar parameters can also be determined for other shapes. For example, non-circular shapes may include an edge angle or an effective edge angle (collectively referred to herein as “edge angle”) and a chord depth or effective chord depth (collectively referred to herein as “chord depth”). These and other variables together define other dimple parameters, such as dimple volume (i.e., the amount of a material removed from a spherical ball to produce the dimple). A methodology for measuring various aspects of a dimple, such as edge angle, dimple depth, volume, etc., is disclosed in more detail in U.S. Pat. No. 11,724,159, which is incorporated in its entirety as if fully set forth herein.
The dimples having a plan shape defined by a roulette can have various chord depths. In one aspect, the chord depth can be at least 0.0040 inches. In one aspect, the chord depth can be at least 0.0052 inches. In one aspect, the chord depth can be less than 0.0050 inches. In one aspect, the chord depth can be less than 0.0042 inches. In other aspects, the chord depth can be 0.0030 inches-0.0070 inches, or 0.0045 inches-0.0055 inches, or 0.0045 inches-0.0055 inches. The dimples having a plan shape defined by a roulette can have various edge angles. In one aspect, the edge angle can be 10.0 degrees-18.0 degrees. In another aspect, the edge angle can be 12.0 degrees-14.0 degrees. In another aspect, the edge angle can be at least 14.0 degrees. In another aspect, the edge angle can be at least 15.0 degrees. In another aspect, the edge angle can be less than 13.0 degrees. In another aspect, the edge angle can be less than 12.0 degrees.
In one aspect, the present disclosure provides for dimples having shapes that allow for greater control and flexibility in defining the dimple geometry and provide an increased ability to introduce additional boundary layer energy, which can provide beneficial aerodynamic performance.
In another aspect, the present plan shapes provide optimal packing efficiency by allowing greater dimple interdigitation with adjacent dimples thus creating greater ability to control overall surface coverage of the dimple pattern. In another aspect, the present plan shapes provide an improved ability for concealment of a mold cavity parting line.
All of the dimple plan shapes disclosed herein can be paired or matched with varying cross-sectional profiles. One of ordinary skill in the art would recognize that the presently disclosed dimple plan shapes are not tied to any particular dimple cross-sectional profile, and instead the presently disclosed dimple plan shapes are adaptable to any dimple cross-sectional profile. Exemplary dimple profiles are disclosed in: U.S. Pat. Nos. 6,796,912, 6,729,976, and 11,207,571, and U.S. Patent Pub. Nos. 2012/0165130 and 2013/0172123, all of which are each incorporated in their entirety as if fully set forth herein. Exemplary dimple cross-sectional profiles can include: curves, catenary curves, polynomial curves, ellipses, spherical curves, saucer-shapes, truncated cones, trigonometric curves, exponential curves, logarithmic curves, and/or flattened trapezoids. Additionally, the dimple cross-sectional profile can be defined by a combination of two or more different curves. In one aspect, a dimple can be provided having a dimple cross-sectional profile with a periodicity that matches a periodicity of any one or more of the plan shapes disclosed herein.
The present disclosure may be used with any type of golf ball construction. For instance, the golf ball may have a two-piece construction, a double cover or veneer cover construction or other multi-layer constructions depending on the type of performance desired of the ball. Examples of these and other types of ball constructions that may be used with the present disclosure include those described in U.S. Pat. Nos. 5,713,801, 5,885,172, 5,919,100, 5,965,669, 5,981,654, 5,981,658, and 6,149,535, which are each incorporated in their entirety as if fully set forth herein. In one aspect, the golf ball can be a two-piece, three-piece, four-piece, five-piece, six-piece, or more than six-piece golf ball. In one aspect, the core of the golf ball can be a single core, dual core, or triple core. In one aspect, the cover can include more than one layer, and/or the casing can include more than one layer.
Further exemplary golf ball constructions, including further details on the various layers, materials, dimensions, and other characteristics of golf balls are disclosed in U.S. Pat. Nos. 7,361,102, 7,927,233, 8,834,300, 8,845,456, 9,205,308, and 9,795,836, which are each incorporated in their entirety as if fully set forth herein.
Exemplary golf ball constructions are also disclosed in commercially available golf balls, such as the following golf balls which are produced by Titleist®.
Different materials also may be used in the construction of the golf balls made with the present disclosure. For example, the cover of the golf ball may be made of a polyurea material, a polyurethane-urea hybrid material, a polyurea-urethane hybrid material, ionomer material, or any other suitable cover material known to those skilled in the art. Different materials also may be used for forming core and intermediate layers of the golf ball.
The golf ball plan shape of the present disclosure can be part of an overall dimple pattern selected to achieve various desired aerodynamic characteristics. Dimple patterns that provide a high percentage of surface coverage are well known in the art. For example, U.S. Pat. Nos. 5,562,552, 5,575,477, 5,249,804, and 4,925,193, which are each hereby incorporated by reference in their entirety as if fully set forth herein, disclose geometric patterns for positioning dimples on a golf ball.
While it is apparent that the illustrative embodiments disclosed herein fulfill the objectives stated above, it is appreciated that numerous modifications and other embodiments may be devised by those skilled in the art. Therefore, it will be understood that the appended claims are intended to cover all such modifications and embodiments, which would come within the spirit and scope of the present disclosure.
The terms “first,” “second,” and the like are used to describe various features or elements, but these features or elements should not be limited by these terms. These terms are only used to distinguish one feature or element from another feature or element. Thus, a first feature or element discussed below could be termed a second feature or element, and similarly, a second feature or element discussed below could be termed a first feature or element without departing from the teachings of the disclosure.
The golf balls described and claimed herein are not to be limited in scope by the specific embodiments herein disclosed, since these embodiments are intended as illustrations of several aspects of the disclosure. Any equivalent embodiments are intended to be within the scope of this disclosure. Indeed, various modifications of the device in addition to those shown and described herein will become apparent to those skilled in the art from the foregoing description. Such modifications are also intended to fall within the scope of the appended claims. All patents and patent applications cited in the foregoing text are expressly incorporated herein by reference in their entirety.
1. A golf ball having a generally spherical surface and comprising a plurality of dimples on the surface, wherein at least a portion of the plurality of dimples have a non-circular plan shape defined by a roulette where a trajectory of a fixed point relative to a moving curve traces a closed curve as the moving curve travels along a stationary curve, and the closed curve defines the non-circular plan shape.
2. The golf ball of claim 1, wherein the plan shape is an epitrochoid, where the moving curve is a moving circle and stationary curve is a stationary circle, and wherein the moving circle travels along the outside of the stationary circle.
3. The golf ball of claim 2, wherein the plan shape is defined according to the following parametric equations:
x = [ a + b ] * cos ( θ ) - d * cos [ a + b b θ ] y = [ a + b ] * sin ( θ ) - d * sin [ a + b b θ ]
where (a) is a radius of the stationary circle, (b) is a radius of the moving circle, (d) is a distance of a fixed point relative to a center of the moving circle, and (θ) is an angle from 0 to 2π.
4. The golf ball of claim 3, wherein the radius (b) is equal to a ratio of the radius (a) to any positive integer greater than 1.
5. The golf ball of claim 3, wherein the distance (d) is less than or equal to the radius (b).
6. The golf ball of claim 1, wherein the plan shape is a hypotrochoid where the moving curve is a moving circle, and the stationary curve is a stationary circle, and wherein the moving circle travels along the inside of the stationary circle.
7. The golf ball of claim 6, wherein the plan shape is defined according to the following parametric equations:
x = [ a - b ] * cos ( θ ) + d * cos [ a - b b θ ] y = [ a - b ] * sin ( θ ) - d * sin [ a - b b θ ]
where (a) is a radius of the stationary circle, (b) is a radius of the moving circle, (d) is a distance of a fixed point relative to a center of the moving circle, and (θ) is an angle from 0 to 2π.
8. The golf ball of claim 7, wherein the radius (b) is equal to a ratio of the radius (a) to any positive integer greater than 1.
9. The golf ball of claim 7, wherein the distance (d) is less than or equal to the radius (b).
10. A golf ball having a generally spherical surface and comprising a plurality of dimples on the surface, wherein at least a portion of the plurality of dimples have a non-circular plan shape defined by either: (i) an epitrochoid, or (ii) a hypotrochoid, such that a trajectory of a fixed point relative to a moving curve traces a closed curve as the moving curve travels along a stationary curve, and the closed curve defines the non-circular plan shape.
11. The golf ball of claim 10, wherein the non-circular plan shape is defined by an epitrochoid, wherein the moving curve is a moving circle and stationary curve is a stationary circle, and wherein the moving circle travels along the outside of the stationary circle, and the plan shape is defined according to the following parametric equations:
x = [ a + b ] * cos ( θ ) - d * cos [ a + b b θ ] y = [ a + b ] * sin ( θ ) - d * sin [ a + b b θ ]
where (a) is a radius of the stationary circle, (b) is a radius of the moving circle, (d) is a distance of a fixed point relative to a center of the moving circle, and (θ) is an angle from 0 to 2π.
12. The golf ball of claim 10, wherein the radius (b) is equal to a ratio of the radius (a) to any positive integer greater than 1.
13. The golf ball of claim 10, wherein the distance (d) is less than or equal to the radius (b).
14. The golf ball of claim 10, wherein the non-circular plan shape is defined by a hypotrochoid, wherein the moving curve is a moving circle and the stationary curve is a stationary circle, and wherein the moving circle travels along an inside of the stationary circle, and the plan shape is defined according to the following parametric equations:
x = [ a - b ] * cos ( θ ) + d * cos [ a - b b θ ] y = [ a - b ] * sin ( θ ) - d * sin [ a - b b θ ]
where (a) is a radius of the stationary circle, (b) is a radius of the moving circle, (d) is a distance of a fixed point relative to a center of the moving circle, and (θ) is an angle from 0 to 2π.
15. The golf ball of claim 14, wherein the radius (b) is equal to a ratio of the radius (a) to any positive integer greater than 1.
16. The golf ball of claim 14, wherein the distance (d) is less than or equal to the radius (b).