I think it's tough to tell what the angles are in the fixed view like that
due to the distortion from perspective.  In my code the triangles that form
the teeth are constructed with the specified angle, but then they end up
getting projected at a different angle depending on the cone angle you
pick.  Furthermore, there's the question of where the angle is measured.  I
think the wikipedia page suggested it is measured relative to the cylinder
axis, but I'd normally expect tooth angle to be measured on the tooth,
which means the slope of the tooth will also lead to a change in the
effective angle.  (Maybe this factor is what you're talking about?)  I
decided for my implementation to treat the requested angle as "nominal" and
not worry about these various deviations.  As long as you pick the same
angle (and other parameters) for both sides of the joint, the parts will
mate.  And if you don't like the angle you get---change it.

On Sun, Nov 17, 2024 at 12:15 AM Caddiy via Discuss <
discuss@lists.openscad.org> wrote:

I did ponder the idea of trying to compute a correction factor to the
tooth angle, but given the uncertainty about what the right angle actually
is, and also uncertainty on my part about how to actually compute that
correction factor, I didn't pursue this idea.  Wouldn't angle between
adjacent flanks be equivalent to angle on the tooth, which is basically the
other angle between flanks?  In the case of no cone angle these angles
must be the same because the part mates with itself.

Another thing is that my code supports skewing the teeth so you can make
teeth with one face vertical, for example.  This distorts the angle.  I
didn't see a compelling reason the angle needs to be "correct".  Here an
example of what you get if you ask for 60 degrees with maximal skew:

[image: image.png]
If I change the tooth angle to try to achieve actual 60 deg at the tops I
get something like this

[image: image.png]
Note that the tooth height has radically changed.  From a design
perspective, I think it's maybe nicer for a user to be able to skew the
teeth while keeping the tooth height fixed, rather than having these
parameters coupled.

In the case of very high cone angle (here 75 deg), weird stuff happens and
I get shapes like this:

[image: image.png]
where the adjacent teeth flanks become coplanar, and then if I push cone
angle higher (85 deg here) the "valley" between the teeth becomes a second
ridge

[image: image.png]
It's not clear if forms like this are useful for anything.  The
construction still works, producing a mating shape that looks like this:

[image: image.png]
But clearly the tooth angle measured at the tooth ridge or the complement
of the angle between the flanks is wildly different from the requested 60
deg.  I'll note also that the very high cone angles look less weird when
the tooth count is high, though the tooth angle is still wildly different
from what was requested.  This is 75 deg angle with lots of teeth:

[image: image.png]
I'm not going to show another image, but if I line it up along a ridge by
eye the tooth ridge angle looks like around 120 deg.  But note how the
triangles running around the baes actually look like 60 deg triangles.

On Sun, Nov 17, 2024 at 2:38 AM Caddiy via Discuss <
discuss@lists.openscad.org> wrote:

OpenSCAD mailing list
To unsubscribe send an email to discuss-leave@lists.openscad.org

søn. 17. nov. 2024 14.17 skrev Adrian Mariano via Discuss <
discuss@lists.openscad.org>:

I did ponder the idea of trying to compute a correction factor to the
tooth angle, but given the uncertainty about what the right angle actually
is, and also uncertainty on my part about how to actually compute that
correction factor, I didn't pursue this idea.  Wouldn't angle between
adjacent flanks be equivalent to angle on the tooth, which is basically the
other angle between flanks?  In the case of no cone angle these angles
must be the same because the part mates with itself.

Another thing is that my code supports skewing the teeth so you can make
teeth with one face vertical, for example.  This distorts the angle.  I
didn't see a compelling reason the angle needs to be "correct".  Here an
example of what you get if you ask for 60 degrees with maximal skew:

[image: image.png]
If I change the tooth angle to try to achieve actual 60 deg at the tops I
get something like this

[image: image.png]
Note that the tooth height has radically changed.  From a design
perspective, I think it's maybe nicer for a user to be able to skew the
teeth while keeping the tooth height fixed, rather than having these
parameters coupled.

In the case of very high cone angle (here 75 deg), weird stuff happens and
I get shapes like this:

[image: image.png]
where the adjacent teeth flanks become coplanar, and then if I push cone
angle higher (85 deg here) the "valley" between the teeth becomes a second
ridge

[image: image.png]
It's not clear if forms like this are useful for anything.  The
construction still works, producing a mating shape that looks like this:

[image: image.png]
But clearly the tooth angle measured at the tooth ridge or the complement
of the angle between the flanks is wildly different from the requested 60
deg.  I'll note also that the very high cone angles look less weird when
the tooth count is high, though the tooth angle is still wildly different
from what was requested.  This is 75 deg angle with lots of teeth:

[image: image.png]
I'm not going to show another image, but if I line it up along a ridge by
eye the tooth ridge angle looks like around 120 deg.  But note how the
triangles running around the baes actually look like 60 deg triangles.

On Sun, Nov 17, 2024 at 2:38 AM Caddiy via Discuss <
discuss@lists.openscad.org> wrote:

OpenSCAD mailing list
To unsubscribe send an email to discuss-leave@lists.openscad.org

Sanjeev, your definition of cone angle is not the same as mine, it would
appear.  I measure cone angle by the line through the center of the
triangle so a zero cone angle is when the mating parts are identical, which
I consider to be the standard joint configuration.  Two parts will mate if
their cone angles are the opposite sign with my approach.

So 60 deg tooth angle, 0 deg cone angle:

[image: image.png]

And the case of 50 teeth, 40 deg cone angle, 75 deg tooth angle for me is
this:

[image: image.png]
Are you constructing your model so that the 75 deg angle is achieved as
measured on the tooth ridge?

On Sun, Nov 17, 2024 at 9:06 AM Sanjeev Prabhakar <
sprabhakar2006@gmail.com> wrote: