Good luck with following the calculations---I think my calculations are
pretty obscure when divorced from the approach and a diagram.  Basically
you need to figure out at what radius the side length of an n-gon is
exactly double the side length of a 2-n gon at radius R.  Then that gives
you the position you need to rotate to, and you have to do some trig to
figure out the angle of rotation.  The "extra" business is about oversizing
the shape for later intersection with a cylinder.  Part of the reason I
favor Bob's projection approach is that ultimately it is just much simpler
conceptually and hence the computations are much more straight forward.

On Sun, Nov 17, 2024 at 9:26 PM Caddiy via Discuss <
discuss@lists.openscad.org> wrote:

Adrian Mariano wrote:

That’s interesting. It’s similar to what I was trying to do. I did have the feeling the problem was caused by a discrepancy somewhere in the circumference of the thing.

Yes, I had to do that too. It’s inevitable if the splines are tilted.

You have to measure the radius of the two polygons by their internal
length, so there is a cos(180/n) or cos(180/2n) factor there.  A nice
thing about Bob's approach is that when you project onto a cylinder, you
naturally construct the model at the correct size and shape with the points
on the cylinder, so then if you don't mind a polygonal result (or at larger
tooth counts it really doesn't matter) there's no reason to bother
intersecting with a cylinder.  It's already round enough.

On Sun, Nov 17, 2024 at 10:17 PM Caddiy via Discuss <
discuss@lists.openscad.org> wrote:

Adrian Mariano wrote:

The distance from the centre to the middle of a side rather than to an angle?

It shouldn’t be too difficult to correct for an exact spline angle.

Intersecting with a cylinder is perhaps not the purist’s approach, but it is on a level of proficiency that I can cope with.

Yes, the distances are to the center of the sides, not to corners.  Think
about arranging 2n triangles (alternating point up/point down) on a regular
2n-gon.  You need the side length of the 2n-gon, which you will want to
compute based on the distance to the center of the side.  The rotation is
around the line halfway up the triangle, which is why you want to work
based on distance to center of side and not distance to corner.  You then
compute the distance to the regular n-gon as distance to side and that
rotation can then be calculated.

I could not figure out how to make this construction work for nonzero cone
angles.  It was one of the reasons I switched to Bob's method.  I'm not
sure I agree that this approach is any less "pure."

By correction for spline angle do you mean to create teeth that actually
have the nominal angle?  I'm not sure such correction is as easy as you
think, because suppose you say, the triangle is tilted at angle theta, and
therefore I need to apply this certain correction to find the right
adjusted tooth angle.  You make this adjustment...and oops, the tilt angle
of the triangle is now different with the new tooth angle.  So you still
don't have the desired result.

On Sun, Nov 17, 2024 at 10:43 PM Caddiy via Discuss <
discuss@lists.openscad.org> wrote:

On 17/11/2024 21:44, Adrian Mariano via Discuss wrote:

Yes, it is is 60 degree perpendicular to the path of the bottom of the
groove. It does not matter in many cases, since two identical units will
still mesh with each other and self centre. Back in the day, if
precision fitting was required, then most likely Prussian blue and hand
scraping would be the requirement. It would be possible to fine adjust
the angle, (increase it) by having the wheel at at a slight angle to the
traversing path (but then you get slightly curved flanks.) Since the
angle of the groove to the centre is shallow, the difference from 60
degree, say, will be small, but could be significant in high load
situations. A simple way to overcome that, with minimum effort, if it is
not essential that both parts have identically shaped mating surfaces,
would be to generate one, and difference from the other, so to speak,
but I don't think that would be a design for a Hirth joint.

Of course, similar 'errors' occur all over the place, thread cutting for
example, where the 60degree thread angle, in many cases, pays no
attention to the thread pitch.

On 11/18/24 06:33, Raymond West via Discuss wrote:

This is something I've contemplated in actual machining, where there are
different tools depending on the tpi, but there is quite a broad range
of threads that can be cut with the same carbide chip, in my case from
1/2-13 to something in the 3/8-50 range using G76, including a couple
cases of taper for squeezing a rosette socket onto a ball screw. Been
working that way for a decade+ in my 11x54 Sheldon of WW-II vintage. I
would assume any pitch ramping needed would be incorporated in the
larger tooling I've never acquired. I did early on buy a 60 degree
cutter for bigger holes, but have never used it, lots of math involved
as but it is .750" in diameter. I'd assume a 1" hole would be the
smallest it could cut threads in. Big limited by the Y table of ones
mill. At least 5.5" on my grizzly go704. I have a bigger mill but it
hasn't the torque to turn that thing.

Cheers, Gene Heskett, CET.

"There are four boxes to be used in defense of liberty:
soap, ballot, jury, and ammo. Please use in that order."
-Ed Howdershelt (Author, 1940)
If we desire respect for the law, we must first make the law respectable.

• Louis D. Brandeis

Also, as someone had mentioned before, it would be good to be able to
modify the tooth profile so it is rounded at the bottom, and truncated at
the top - this relieves potential stress points on the bottom of the teeth,
and allows a little clearance for dust, etc., on the top, and its mating
surface.

Gene, best of success machining a few.  Should be a challenge to set up the
first time, but crankable once the details are worked out.  Please share
pictures if you go ahead with machining them.

Cheers!

EBo --

On Mon, Nov 18, 2024 at 8:54 AM gene heskett via Discuss <
discuss@lists.openscad.org> wrote:

I've done a few extra calculations, and for a slope of 4.2885 degrees
then 60 degrees becomes 59.861 perpendicular to the horizontal. Since
the angles on both pieces will be the same, then afaik, they will still
mesh with the flanks of the teeth contacting each other. The teeth on
the sample that I printed were 90 degrees, and the slope was 2.4881
degrees, which would give a much less change in angle. In practice, for
sharper teeth, then simply flatten the peaks a bit more, if they tend to
bottom out. Fwiw, it is unlikely that I will be building aircraft
engines/whatever, not even for Boeing.

On 18/11/2024 11:33, Raymond West via Discuss wrote:

Rounded teeth?  You mean like this?

[image: image.png]
As I've said, my code does rounding.

On Mon, Nov 18, 2024 at 10:22 AM John David via Discuss <
discuss@lists.openscad.org> wrote: