Simple way of making Golf Ball with Solidworks!

yes, tedious, but fascinating. Modeling the ball is dull - just
patterning/mirroring a bunch of revolved cuts (yawn, and yes Cliff, I
tried it).
But trying to project an icosehedron on a sphere was quite educational.
One thing that caught me up in a big way was that, though you can
split a 2D triangle up into four identical 2D triangles, it doesn't
work that way on an equalaterial triangle on the face of the sphere
(which I didn't catch until wasting a fair amount of time)! The
phenomenon even shows up on the wikepedia (or whatever the reference
was that you posted) picture - if you look closely, the small triangles
(with the smaller dimples) aren't equalateral, and the spacing between
the dimples requires a little adjustment.
There were some otehr fun geoemtry tricks and gimmicks to pull this one
out, but its really about the icosehedron.

So, thanks for the reference info, Paul. Not a bad way to burn time on
a plane.
Ed

 

No need for projection, which would introduce trig errors.
Just get them the same "diameter" to begin with such that either
the vertexes or the face centerpoints lie on the sphere.
Then do the same with other icosehedrons rotated in 3D
about the center of the sphere.

Solid trig?
Not even in planar geometry IIRC.

Random guesses.

Tried other Platonic solids too?

 

No need for projection, which would introduce trig errors.

It would be interesting to see your version of the golf ball, Cliff (if you
modeled it...). At least in my version only a tiny piece of one icosahedron
was needed, and still the result (eg. dimple distribution) was pretty good.
Of course you can use multiple, whole icosahedrons but it sounds quite
tedious to me.

-h-

 

The "optimal" position of N dimples on a sphere can be found on
http://www.research.att.com/~njas/packings/.
Import the table in Excel, do some math to obtain the XYZ locations
of the points, export to .csv and use one of the many macros around
to read the points in a 3D Sketch. Then use the HoleWizard to create
the dimples.
Ensure you don't violate any patent on the dimples patterns, there
are MANY patents on the topic
Philippe Guglielmetti

 

I pointed out a way to decide the number of possible regular dimple
locations based on Platonic solids and checked a few suggested
examples.
Given that as a hint .... <G>.
Do they fudge gold balls?

 

[
4-dimensional arrangements, 5-dimensional arrangements, 6-dimensional
arrangements, 7-dimensional arrangements, 8-dimensional arrangements,
9-dimensional arrangements, 10-dimensional arrangements, 11-dimensional
arrangements, 12-dimensional arrangements, 13-dimensional arrangements,
14-dimensional arrangements, 15-dimensional arrangements, 16-dimensional
arrangements, 17-dimensional arrangements, 18-dimensional arrangements,
19-dimensional arrangements, 20-dimensional arrangements, 21-dimensional
arrangements, 22-dimensional arrangements, 23-dimensional arrangements,
24-dimensional arrangements, higher-dimensional arrangements,
]

 

" But I don't think you got good results <G>. "
Ummm... what makes you say that? My model is consistent with the
patent and the posted images on answers.com. It is also rigourously
precise - I don't just throw some crap down and call it 'close enough'
- there is no educational value to that. As I told Paul, if its worth
doing, its worth doing to ten decimal places.
the only thing I didn't do is insure that the dimple depth is 5.7% of
the diamnter (or whatever the hell it is - I do not have the patent
here). The locations are interesting - the depth to diameter ratio is
trivial (one equation away form setting that up).

I was writing quick on the road - you are correct that projection
doesn't cut it. I pointed that out to Paul a few posts back (maybe
Friday?)

The underlying icosehedron needs to be calculated to find the correct
intersection points on the sphere. then its an excercise in layout.
The icosehedron was fun - I like to use a single 2D sketch to derive
this stuff instead of using equations or looking up angles in some
reference. I can do an icosehdron in a few features now.

"> One thing that caught me up in a big way was that, though you can

To quote yourself, 'did you try it?". It will take maybe 30 seconds
for you to prove to yourself that a planar equalateral triangle can be
broken up into four equalateral triangles.

Bullshit, its not random guesses. Try to model the fucking thing.
There is nothing random about my exploration of this problem


">There were some other fun geoemtry tricks and gimmicks to pull
this one

Nope. The guy asked about a golf ball, so I went off a reference for a
golf ball. I have no interest in modeling every possible golf ball
becasue, as I have said several times at this point, modeling a
golf-ball-looking-object is boring - just an excercise in a few revolve
cuts and some patterning. This one was worth the time because (a), I
had time to kill on the plane and (b) it was a defined pattern and (c)
I figured it had some educational posiblilities regarding layout of
subdivsions of an icoshedron as they translate onto a sphere. I am
quite fond of the precision I acheived. The three large dimples at the
center of the icosehdron are dead on, and I learned that (due to the
FACT that you can't subdivide that arced face into four equalateral
segments that can project back to the center of the sphere) some design
judgment needs to be applied - in this case, coming up with 3-D
sketches that insure that the axes of the smaller dimples, when
considered as pairs, are equally distant to the major intersecting
circles.

I can't speak for Heikki, but I have no problem sharing hte model I
made. Anyone got a website to host? (we use DimonteGroup for
presentations, not little stuff like this - BTW, I still have to get
the final versions of this years SWx World stuff up there.. I haven't
forgotten)

-Ed

 

you seem to be up late Ed...
I am pleased you haven't forgotten about posting your SWW presentations.
Looking to download more valuable insights sometime soon )

 

I can't speak for Heikki, but I have no problem sharing hte model I

Of course I am ready to share my model, too - especially if Cliff is going
to share his model as well <G>. My model is not a precise copy of golf ball,
since I was just interested about the idea of how a such thing is modeled.
If the model works it is just a matter of patience and measuring to get the
dimensions right; I did not have a real golf ball and proper measuring
device to use.

-h-

 

The golf ball thing came up in this group last year. Here is part of a
discription I posted at that time: I thought it might be of interest to
post again.

http://appft1.uspto.gov/netacgi/nph...39".PGNR.&OS=DN/20050009639&RS=DN/20050009639

This is from the above site:

The Dimple Pattern of the Cover

[0088] Turning now to the dimple technology employed in the instant
invention, as was discussed previously, the manipulation of the dimple
configuration also yield a golf ball with improved characteristics of
play. As stated previously, the preferred geometry is a
rhombicosadodecahedron. Accordingly, the scope of this invention
provides a golf ball mold whose molding surface contains a uniform
pattern to give the golf ball a dimple configuration superior to those
of the art. The invention is preferably described in terms of the golf
ball that results from the mold, but could be described within the scope
of this invention in terms of the mold structure that produces a golf ball.

[0089] To assist in locating the dimples on the golf ball, the golf ball
of this invention has its outer spherical surface partitioned by the
projection of a plurality of polygonal configurations onto the outer
surface. That is, the formation or division that results from a
particular arrangement of different polygons on the outer surface of a
golf ball is referred to herein as a "plurality of polygonal
configurations." A view of one side of a golf ball 5 showing a preferred
division of the golf ball's outer surface 7 is illustrated in FIG. 2.

[0090] In the preferred embodiment, a polygonal configuration known as a
rhombicosadodecahedron is projected onto the surface of a sphere. A
rhombicosadodecahedron is a type of polyhedron which contains thirty
(30) squares, twenty (20) polyhedra of one type, and twelve (12)
polyhedra of another type. The term "rhombicosadodecahedron" is derived
from "dodecahedron," meaning a twelve (12) sided polyhedron;
"icosahedron," meaning a twenty (20) sided polyhedron, and "rhombus"
meaning a four sided polyhedron.

[0091] The rhombicosadodecahedron of the preferred embodiment is
comprised of thirty (30) squares 12, twelve (12) pentagons 10, and
twenty (20) triangles 14, as shown in FIG. 2. It has a uniform pattern
of pentagons with each pentagon bounded by triangles and squares. The
uniform pattern is achieved when each regular pentagon 10 has only
regular squares 12 adjacent to its five boundary lines, and when a
regular triangle 14 extends from each of the five vertices of the
pentagon. Five (5) squares 12 and five (5) triangles 14 form a set of
polygons around each pentagon. Two boundary lines of each square are
common with two pentagon boundary lines, and each triangle has its
vertices common with three pentagon vertices.

[0092] The outer surface of the ball is further defined by a pair of
poles and an uninterrupted equatorial great circle path around the
surface. A great circle path is defined by the intersection between the
spherical surface and a plane that passes through the center of the
sphere. (An infinite number of great circle paths may be drawn on any
sphere.) The uninterrupted equatorial great circle path in the preferred
embodiment corresponds to a mold parting line, which separates the golf
ball into two hemispheres. The uninterrupted great circle path is
described as uninterrupted because it has no dimples on it. The mold
parting line is located from the poles in substantially the same manner
as the equator of the earth is located from the north and south poles.

[0093] Referring to FIG. 3, the poles 70 are located at the center of a
pentagon 10 on the top and bottom sides of the ball, as illustrated in
this view of one such side. The mold parting line 30 is at the outer
edge of the circle in this planar view of the golf ball. In the
embodiment shown in FIG. 4, the poles 72 are both located at the center
of the square on the top and bottom of the golf ball, as illustrated in
this view of one such side. (The top and bottom views are identical.)
The mold parting line 40 is at the outer edge of the circle in this
planar view of the golf ball.

[0094] Dimples are placed on the outer surface of the golf ball based on
segments of the plurality of polygonal configurations described above.
In the preferred embodiment, three (3) dimples are associated with each
triangle, five (5) dimples are associated with each square, and sixteen
(16) dimples are associated with each pentagon. The term "associated" as
used herein in relation to the dimples and the polyhedra means that the
polyhedra are used as a guide for placing the dimples.

[0095] In the preferred embodiment, there are a total of 402 dimples.
Advantageously, this decrease in the number of dimples when compared to
prior art golf balls results in a geometrical configuration that
contributes to the aerodynamic stability of the instant golf ball.
Aerodynamic stability is reflected in greater control over the movement
of the instant golf ball.

[0096] The dimple configuration of the preferred embodiment is shown in
FIGS. 5-8. It is based on the projection of the rhombicosadodecahedron
shown in FIG. 3. The ball has a total of 402 dimples. The plurality of
dimples on the surface of the ball are selected from three sets of
dimples, with each set having different sized dimples. Dimples 200 are
in the first set, dimples 202 are in the second set, and dimples 204 are
in the third set. Dimples are selected from all three sets to form a
first pattern associated with the pentagon 10. All sides 206 of each
pentagon are intersected by two dimples 200 from the first set of
dimples and one dimple 202 from the second set of dimples. All pentagons
10 have the same general first pattern arrangement of dimples.

[0097] Dimples 200, 202 and 204 (from all three sets of dimples) are
also used to form a second pattern associated with the squares 12. All
sides 208 of each square 12 are intersected by dimples 202 from the
second set of dimples, and all squares have the same general second
pattern arrangement of dimples.

[0098] Dimples 202 from the second set of dimples form a third pattern
associated with the triangles 14. All sides 210 of each triangle are
intersected by a dimple 202 from this second set of dimples. All
triangles have this same general third pattern arrangement of dimples.
The mold parting line 30 is the only dimple free great circle path on
this ball.

[0099] Advantageously, the use of a single uninterrupted mold parting
line leads to superior aerodynamic properties in the instant golf ball.
The single mold parting line results in less severe separation between
the dimples, i.e. less "bald spots" on the surface of the ball. This in
turn increases the effectiveness of the dimples on the golf ball.
Advantageously, increasing the effectiveness of the dimples by reducing
the land area on the surface of the golf ball improves the aerodynamic
properties of the instant golf ball with regard to distance and control.

[0100] A single radius (Radius 1) describes the entire shape of the
dimple. Dimple size is measured by a diameter and depth generally
according to the teachings of U.S. Pat. No. 4,936,587 (the '587 patent),
which is included herein by reference thereto. An exception to the
teaching of the '587 patent is the measurement of the depth, which is
discussed below. A cross-sectional view through a typical dimple 6 is
illustrated in FIG. 9. The diameter Dd used herein is defined as the
distance from edge E to edge F of the dimple. Edges are constructed in
this cross-sectional view of the dimple by having a periphery 50 and a
continuation thereof 51 of the dimple 6. The periphery and its
continuation are substantially a smooth surface of a sphere. An arc 52
is inset about 0.003 inches below curve 50-51-50 and intersects the
dimple at point E' and F'. Tangents 53 and 53' are tangent to the dimple
6 at points E' and F" respectively and intersect periphery continuation
51 at edges E and F respectively. The exception to the teaching of '587
noted above is that the depth d is defined herein to be the distance
from the chord 55 between edges E an F of the dimple 6 to the deepest
part of the dimple cross sectional surface 6(a), rather than a
continuation of the periphery 51 of an outer surface 50 of the golf
ball. In the preferred embodiment, dimples 200 from the first set have a
diameter of 0.156 inches; dimples 202 from the second set have a
diameter of 0.145 inches, and dimples 204 from the third set have a
diameter of 0.142 inches. Dimples 200 have a depth of 0.0080 inches.
Dimples 202 have a depth of 0.0078 inches. Dimples 204 have a depth of
0.0076 inches. All dimples 200, 202, and 204 are single radius in cross
section.

[0101] Advantageously, the use of dimples that are single radius in
cross section improves the performance of the instant golf ball with
respect to both distance and control of the movement of the golf ball
given the high spin rate of the instant high performance three-piece
ball. The presence of single radius dimples allows for a soft trajectory
in the golf ball's flight on iron shots. In turn, this soft trajectory
leads to a soft entry of the golf ball onto the golf course green, which
in turn results in greater control over the movement of the instant golf
ball. Remarkably, the single radius provides a boring trajectory during
driver shots.

[0102] The radius (radius 1) for dimples 200 in the preferred embodiment
is about 0.7874 inches, the radius for dimples 202 is about 0.3325
inches, and the radius for dimples 204 is 0.3191 inches. However, it is
understood that the following dimple size ranges are within the scope of
this invention. Dimples 200 from the first set may have a diameter in
the range of 0.154 inches to 0.158 inches; dimples 202 from the second
set may have a diameter in the range of 0.142 to 0.147 inches; dimples
204 from the third set may have a diameter in the range of 0.140 to
0.144 inches and the radius may be in the range of 0.3150 to 0.3850 inches.

 

IOW Kludge & fudge the model based on guesses.
LOL ...

 

Well, call it what you want, I call it "parametric modeling".

-h-

 

Cliff, it's a really stupid idea to argue with these two guys (Heikki and
Ed) about modeling. They are very good at what they do. Laughing at them is
even stupider.

Jerry Steiger
Tripod Data Systems
"take the garbage out, dear"

 

Jerry, they may be good at fudging & making pictures and/or
using SolidWorks but I'm sorry --- I'm not otherwise impressed
at this point on this topic..... (actual design of golf balls via
measuring & fudging & etc. vs. .... or grasp of 3D geometry in
general ....)
My comments were on modeling issues and it would seem
that uniform spacings of dimples on the surface of same are only
possible for those with certain numbers of dimples and other
types of spacings limited to certain other numbers.
OTOH You can have fun teaching pigs to sing while flying, right <G>?

 

What part of measure & fudge was parametric from
root geometric/mathematical/logical needs?
I must have missed that bit .. <g>.

Where's jb when you need him?

 

My comments were on modeling issues and it would seem

Yeah... And while you were discussing modelling issues, the others were
actually modeling the golf ball and solving those issues...

If I remember it correctly, the very original question in this thread was
how the modelling is actually done, in real life.

-h-

 

Some probably like to get it right. The first time. And know why
it's right.
Kludge, fudge, measure & copy is hardly good design OR engineering,
though it may make sort-of pretty pictures.
HTH

 

Did you get it right, then? Did you even try it? Do you even use SW?

The point was not to design a new, ultimate solution for golf ball dimple
pattern, but just how to model one in practise.

I must be a some kind of masochist to continue this stoopid head banging
with some besserwisser...

-h-

 

Umm .. is it requred to use SW in order to begin to grasp the fairly
simple problems involved?

Just a guess but .. did you grasp my comments about primes &
Platonic solids? Probably not.

So "in practice" you measure things & kludge & fudge models til the
pretty picture is, well, pretty (in your eyes)?

Where's jb when you need him??

You might learn a thing or two too <g>.

 

Heikki,

Maybe we should have a modelilng challenge every month or so like Rob
is doing with PhotoWorks? I might be willing to provide web space if
you and Ed would be willing to help get us started.