BOSL2 could generate the polyhedron "correctly".  I don't know how hard

what swapping the points does:  it causes BOSL2 to build the polyhedron

enough about "skin" to know how easy it would be to detect being

On 10/26/2024 5:44 PM, Bob Carlson wrote:

Thanks! I hear about these point ordering problems. It seems a shame one has to deal with them. Why can’t they be fixed automatically?

I don't know for sure.

There are two levels to the question here:  first BOSL2 builds a
polyhedron, and then second OpenSCAD processes the polyhedron.

BOSL2 could generate the polyhedron "correctly".  I don't know how hard
that would be, but that's essentially what swapping the points does:  it
causes BOSL2 to build the polyhedron the other way 'round.  I don't know
enough about "skin" to know how easy it would be to detect being backwards.

And then when OpenSCAD receives the "inside-out" polyhedron, it could
perhaps fix it.  I think that if it's completely inside out then
detecting that and fixing it isn't hard.  (But right now I'm not sure how
to tell which way is "inside".)  If it's partially inside-out (like one
face is backwards)  then I think I know how to detect that, and I guess
that if you can detect it then you can flip faces until they are all
consistent, and then you might be inside-out but you've reduced it to the
case above.  So my not-a-geometry-wizard sense is that it's doable.  (OCD
note:  you need to watch out for Klein bottles, lest you flip faces
infinitely.)

Is anybody interested in spending the effort?  Obviously not so far.  (And
I think we can all agree that we'd rather have the geometry wizards work on
Manifold and its huge performance improvement.)

When I'm building a polyhedron, mostly I just turn on Thrown Together and
fix backward faces as required.  That's less of an imposition on DIY
polyhedra than it is when your polyhedron is coming out of a library.

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I got really intrigued by the Hirth joint and have been working a library
entry that would generate them. I have it fully working, apparently,
because it renders perfectly as far as I can see. However when I load one
of the parts (a concave part) into PrusaSlicer, it reports thousands of
errors that it supposedly fixed. The visual rendering is fine, but when you
look at the slice it is completely screwed up.

First some explanation. When I looked up hirth joints I only saw flat ones
mentioned. The one I have actually encountered though is a conical one.
There is a concave part and a convex part. They fit together perfectly. I
had to invent some terminology since I did not find terms for some things I
found to be important. The outer center line is the plane that passes
through the midpoint of the teeth at the outer radius. In a flat hirth
joint all the teeth radiate from the center of this circle, call it the
origin. If the origin of the teeth is above the outer center line, then
joint has a conical shape and the two parts are concave and convex.

Each tooth at every point has the same profile, the top of the tooth
profile is either 60 or 90 degrees. The groove angle is the angle that the
groove forms from the origin to the outer radius. It will pass below (for a
convex part) the outer radius. It’s critical for making hirth joints
because it forms the tool path. The ridge angle is the angle formed by the
corresponding ridge.

If the joint is conical, then there is an inner center line that passes
through the center of the teeth at the inner radius. The tooth height is
the critical number to calculate. It is dependent on the number of teeth,
the profile angle and the inner and out radii. Something that really
complicates the mental gymnastics is that the tooth height is smaller at
the inner radius. My code adds a “base” of extra material at the bottom of
the convex part and the top of the concave part. What’s tricky is
positioning the base of the concave part relative to the inner center line.
The concave parts base is relatively easy to place because it depends on
the outer radius and center line.

I generate the raw teeth using the groove and ridge angles and spherical
coordinates to make two 2d tooth profiles. Then I complete a tooth using
skin(). A for loop generates the full set of N teeth. Then intersection or
difference is used the trim the teeth at the inner and outer radii. I
discovered something at that point, but solved it pretty simply. When
diffing a cylinder from the N teeth, each tooth took up a small portion of
the cylinder being diffed out. I had to raise the $fn on the cylinder or
tube being used so that I got enough points in each tooth that diff or
intersection was accurate. I kept raising it until the results stopped
improving. I ended up with the 16*360 you see in the code.

After I have the raw teeth, I generate a cone that is diffed away to
produce the chamfer at the top of the teeth. Then I add in the base. The
base also adds the “chamfer” at the bottom of the groove. It’s half the
size of the top chamfer to leave a little gap when the parts are joined.

When I comment out the everything but the raw teeth and import the STL
into PrusaSlicer, it reports errors fixed, but appears to slice correctly
when supports are added.

When I add the intersection to trim the raw teeth, the number of reported
errors goes way up.

When I add the diff to remove the chamfer, the number goes way up again.

When I add in the base, the number goes up again and it starts reporting
many open edges.

Throughout, OpenSCAD reports no errors. Using $fn at 16360, manifold
renders in 4+ seconds. At 32360, it’s 53+ seconds. I did check CSG and it
did not help.

Maybe the biggest hint is that the convex part uses almost identical code,
but produces no errors. Very weird.

So, is this an OpenSCAD problem? Or something in my code?

It’s also possible that my math is off somewhere. My formal trig training
was 60 years ago. However I doubt a math error is responsible for the
slicing problem and STL errors.

-Bob

include <BOSL2/std.scad>
include <BOSL2/structs.scad>

// Number of Teeth
_n = 36;          // Number Of Teeth

// Inner Radius
_ir = 30;
// Outer Radius
_or = 50;
// Is the coupling conical?
_conic = 10;
// Tooth Profile Angle
_profile = 60; // [60, 90]
// Percentage of tooth height
_chamfer = 5; // Default 5%
_base = 1;

$fn = 180;
tiny = 1 / 1024;

hirth_concave();

_irRatio = _ir / _or;
_toothAngle = 360/_n;
_toothHeight = (sin(_toothAngle/2) * _or) / tan(_profile/2);
_chamferHeight = _chamfer * _toothHeight / 100;
_grooveAngle =  atan(((_toothHeight/2) + _conic) / _or);
_ridgeAngle = -atan(((_toothHeight/2) - _conic) / _or);
_innerCenterLine = (1 - _irRatio) * _conic;
_stackHeight  = _innerCenterLine + _toothHeight + 2*_base;
_tubeHeight = 2*_conic + 2*_base + 2*_toothHeight;

module hirth_concave() {
zrot(_toothAngle/2)
union() {
difference() {
intersection() {
union() {
for (i = [0 : 360/_n : 359])
zrot(i)
_profileF();
}
tube(ir = _ir, or = _or, anchor = CENTER, l = _tubeHeight,
orient = UP, $fn = 16360);
}
_chamferF();
zcyl(r = _ir, h = _tubeHeight, $fn = 16360, anchor = CENTER);
}
_baseF();
}
} // hirth_concave

module _profileF() {
IR = _ir * .5;
OR = _or * 1.5;
tI = [spherical_to_xyz(IR,  0,            _grooveAngle + 90),
spherical_to_xyz(IR,  _toothAngle/2, _ridgeAngle + 90),
spherical_to_xyz(IR, -_toothAngle/2, _ridgeAngle + 90)];

 tO = [spherical_to_xyz(OR,   0,            _grooveAngle + 90),
       spherical_to_xyz(OR,  _toothAngle/2, _ridgeAngle + 90),
       spherical_to_xyz(OR, -_toothAngle/2, _ridgeAngle + 90)];
 up(_conic)
 skin([tI, tO], slices = 0);

}

module _chamferF() {
A = -_toothHeight/2 - .1;
B = -_toothHeight/2 + _chamferHeight;

 pts = [[0, _conic],
        [_or+tiny, A],
        [_or+tiny, B]];

 rotate_extrude(angle = 360, $fn = 16*360)
 polygon(pts);

}

module _baseF() {
A = _base + _irRatio*_toothHeight/2 + _innerCenterLine;
B = _irRatio * (_toothHeight/2 - _chamferHeight/2) + _innerCenterLine;
C = _toothHeight/2 - _chamferHeight/2;
pts = [
[_ir, A],
[_ir, B],
[_or, C],
[_or, A]
];

 rotate_extrude(angle = 360, $fn = 360*16)
 polygon(pts);

}

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The second is that I think your code measures tooth angle relative to the
vertical instead of relative to the tooth ridge.  This is not the normal
way that tooth angle would be measured, e.g. on a gear.  It means that
actual angle is never what you specify.

A third observation is that you should be chamfering the valleys just like
the peaks.  Internal corners are stress concentration points on an object
and will weaken it.  So my version can apply varying chamfers in both
places.

On Oct 26, 2024, at 16:21, Jordan Brown openscad@jordan.maileater.net wrote:

Also, a tidbit:  _chamferF() generates a conical figure that might as well be a cone.
up(_conic + _chamferHeight) scale(1.5) zcyl(h = _toothHeight/2 + _conic, r1 = _or, r2 = 0, anchor=TOP);
Since it's anchored at the top, I didn't have to fiddle with making sure that it was slightly larger than the thing it's cutting from and could just scale it up a bit.

On Oct 28, 2024, at 21:35, Adrian Mariano avm4@cornell.edu wrote:

So Bob, you have said you don't care about speed, which is your choice, obviously.  But for me this code is intolerably slow.  Preview is useless even after I remove the chamfering and intersection to make it have cylindrical edges.  And render takes 20s with manifold.  Because the original code was unpreviewable I couldn't easily assess how well my rewrite matched, but it previews instantly and renders in 0.1s.  (Note: a reason I care about preview is that I can color things that I overlay to see for example if two things match.)

Another few things.  In BOSL2, global variables that start with underscore are reserved for BOSL2 internal use, so you shouldn't be using those.  You could clobber an internal definition.  (Not sure why anyone would use variables that start with underscore as a choice---I find them very annoying.)

The second is that I think your code measures tooth angle relative to the vertical instead of relative to the tooth ridge.  This is not the normal way that tooth angle would be measured, e.g. on a gear.  It means that actual angle is never what you specify.

A third observation is that you should be chamfering the valleys just like the peaks.  Internal corners are stress concentration points on an object and will weaken it.  So my version can apply varying chamfers in both places.

I personally find the rewritten code simpler than the original, as well as much faster, and there's probably room to clean it up more.  (Could probably compute inner shape from outer with a scale() computation for example.)  It does produce a polygonal result and could be intersected with a tube like the original to fix that if you think it's necessary.  I imagine that one intersection wouldn't be a major drag on the speed.  I agree that trying to compute the profile on a circular arc would be a pain.

include <BOSL2/std.scad>

// Number of Teeth
_n = 36;          // Number Of Teeth

// Inner Radius
_ir = 30;
// Outer Radius
_or = 50;
// Is the coupling conical?
_conic = 15;
// Tooth Profile Angle
_profile = 90; // [60, 90]
// Percentage of tooth height
_chamfer = 5; // Default 5%
_base = 1;

function basic_profile(angle,chamfer_top, chamfer_bot) =
let(
width = tan(angle/2),
pts = [
[0,(-1+chamfer_bot)width,chamfer_bot],
[0,-chamfer_topwidth,1-chamfer_top]
],
)
concat(pts, reverse(yflip(pts)));

profwidth = tan(_profile/2);
outside = _ortan(180/_n);
inside = _irtan(180/_n);

prof_out = right(_or,scale(outside/profwidth,basic_profile(_profile, _chamfer/100, _chamfer/200)));
prof_in = right(_ir,scale(inside/profwidth,basic_profile(_profile, _chamfer/100, _chamfer/200)));

offset = (_or-_ir) * tan(_conic);

outfull = up(offset,[for(i=lerpn(0,360,_n,endpoint=false))
each zrot(i,prof_out)]);
infull = [for(i=lerpn(0,360,_n,endpoint=false))
each zrot(i,prof_in)];

inbot = [for(val=infull) [val.x,val.y,-_base]];
outbot = [for(val=outfull) [val.x,val.y,-_base]];

vnf_polyhedron(vnf_vertex_array([outfull, infull, inbot, outbot], reverse=true, col_wrap=true, row_wrap=true));

<image.png>

An anticone needs rotate_extrude?