Something else with teeth that the world has been waiting for: a face spline coupling aka Hirth coupling. I created it some time ago as part of a design, but it had a glitch that turned out to be because the circumference of a small sector of a circle is slightly longer than the straight line across it. This left tiny but visible gaps between the splines.

I thought it would be difficult to parametrise but it was not.

But it still has some sharp edges that need rounding. Any volunteers?

$fn=100;

$vpr=[ 60, 0, 315 ];

$vpt=[ 0, 0, 0 ];

$vpd=80;

/*

*/

a=60; // Base angle

r=12; // Radius

n=24; // Number of splines

module facespline()

{

difference()

{

intersection()

{

for(i = [1 : n])

rotate(i * 360/n)

polyhedron(

points = [

// Point 0

[0, 0, PI*r/2/n*tan(a)],

// Point 1

[r, r*tan(360/2/n), 0],

// Point 2

[r, -r*tan(360/2/n), 0],

// Point 3

[r, 0, PI*r/n*tan(a)],

// Point 4

[0, 0, 0]

],

faces = [

[1,2,3],

//[0,2,1],

[3,2,0],

[3,0,1],

[0,2,4], //

[0,4,1], //

[1,4,2] //

]);

cylinder(r=r, h=PI*r/16*tan(a)+1);

}

// Hole

translate([0,0,-1])

cylinder(r=6, h=5);

}}

// Face spline coupling

rotate([0, 0, $t*360])

{

translate([0, 0, -3])

facespline();

translate([0, 0, 3])

rotate([0, 180, 360/2/n])

facespline();

}

Works perfectly here.

Previews immediately with the cube-and-chevron icon, took a little longer with F6.

This is what you should see.

BTW I said sector above, but meant segment.

Still no joy?

Try deleting all //, /* and */.

Does this work for you?

$fn=100;

$vpr=[ 60, 0, 315 ];

$vpt=[ 0, 0, 0 ];

$vpd=80;

a=60; // Base angle

r=12; // Radius

n=16; // Number of splines

module facespline()

{

difference()

{

intersection()

{

for(i = [1 : n])

rotate(i * 360/n)

polyhedron(

points = [

[0, 0, PI*r/2/n*tan(a)],

[r, r*tan(360/2/n), 0],

[r, -r*tan(360/2/n), 0],

[r, 0, PI*r/n*tan(a)],

[0, 0, 0]

],

faces = [

[1,2,3],

[3,2,0],

[3,0,1],

[0,2,4],

[0,4,1],

[1,4,2]

]);

cylinder(r=r, h=PI*r/16*tan(a)+1);

}

// Hole

translate([0,0,-1])

cylinder(r=6, h=5);

}}

// Face spline coupling

{

translate([0, 0, -3])

facespline();

translate([0, 0, 3])

rotate([0, 180, 360/2/n])

facespline();

}

I think you guys not seeing it may have Lazy Union enable.

Problem is the intersection() of the for(), as each arm of the for() doesn't overlap, so intersection() returns empty.

With Lazy union disabled (or not in 2021.01) the for() does a union().

To fix, stick union() in front of the for().

From: Ken via Discuss [mailto:discuss@lists.openscad.org]
Sent: Fri, 20 Sep 2024 13:36
To: discuss@lists.openscad.org
Cc: Ken
Subject: [OpenSCAD] Re: Face spline

Sorry Mike, same result as before.

On 2024-09-20 11:07, Caddiy via Discuss wrote:

Does this work for you?

$fn=100;

$vpr=[ 60, 0, 315 ];

$vpt=[ 0, 0, 0 ];

$vpd=80;

a=60; // Base angle

r=12; // Radius

n=16; // Number of splines

module facespline()

{

difference()

{

intersection()

{

for(i = [1 : n])

rotate(i * 360/n)

polyhedron(

points = [

[0, 0, PIr/2/ntan(a)],

[r, r*tan(360/2/n), 0],

[r, -r*tan(360/2/n), 0],

[r, 0, PIr/ntan(a)],

[0, 0, 0]

],

faces = [

[1,2,3],

[3,2,0],

[3,0,1],

[0,2,4],

[0,4,1],

[1,4,2]

]);

cylinder(r=r, h=PIr/16tan(a)+1);

}

// Hole

translate([0,0,-1])

cylinder(r=6, h=5);

}}

// Face spline coupling

{

translate([0, 0, -3])

facespline();

translate([0, 0, 3])

rotate([0, 180, 360/2/n])

facespline();

}

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--
Cheers, Ken
bats059@gmail.com
https://vk7krj.com
https://vk7krj.com/running.html

A baby can be defined as an ego with a noise at one end and a smell at the other.
Your job as parents is to teach them to control all three.
My job as a grandad is to tell you how you are doing it all wrong!

I got interested in the Hirth joint problem since I now know the name and understand what’s going on. Also, the part I needed to make had a conical Hirth joint. I was curious how that could be parameterized. It turned out to be fairly simple. Here is the current state of my test program. It uses BOSL2, but not my own library. It’s set up with the customizer so it’s easy to play around with. I’m running it on OpenSCAD.24.09.20 and BOSL2 from maybe a couple of months ago. It’s not entirely debugged, but works. Using hull and cheating a little, the math is minimal. It’s all in calculating toothBaseWidth and toothHeight. The “cheat” is that I hull the tooth profile with a tiny cube at the origin. For a conical joint, the origin just moves up. Most of the code is actually there to provide the base above or below the teeth. That’s where I think bugs still lurk.

include <BOSL2/std.scad>

showTooth = false;
showLower = false;
showUpper = false;
showFit = false;
showProfile = false;

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

// Inner Radius
innerR = 30;
// Outer Radius
outerR = 50;
// Is the coupling conical?
conical = 10;
// Tooth Profile Angle
profileAngle = 60; // [60, 90]
// Must be >= 0, Default used when left at 0
chamfer = 0; // .1

// Explosion distance in mm
ex = 0;

module Customizer_Limit () {}  // This actually works

$fn = 180;
tiny = 1 / 1024;

assembly();

module assembly() {
if (showTooth) {
tooth(conical);
}
if (showLower) {
teeth();
}
if (showUpper) {
up(ex == 0 ? .1 : ex)
upperTeeth();
}
if (showFit) {
teeth();

    up(ex == 0 ? .1 : ex)
    upperTeeth();
}
if (showProfile) {
    toothProfile();
}

}

a0 = assert(conical >= 0, "Conical must be >= 0");

outerR0 = outerR + 0;
rotationAngle = 360/N;
toothBaseWidth = 2 * (sin(rotationAngle/2) * outerR0);
toothHeight = (toothBaseWidth/2) / tan(profileAngle/2) ;
toothChamfer = chamfer == 0.0 ? min(3, toothHeight * .1) : chamfer;

e0 = echo(str("Tooth Width ", toothBaseWidth));
e1 = echo(str("Tooth Height ", toothHeight));
e2 = echo(str("Tooth Chamfer ", toothChamfer));
e3 = echo(str("Tooth Profile ", profileAngle));

module upperTeeth() {
zrot(rotationAngle/2)
xrot(180)
intersection() {
difference() {
union() {
teeth0(-conical);

            down(toothHeight/2 - toothChamfer/2) {
                if (conical > 0) {
                    difference() {
                        zcyl(l = conical - toothHeight/2, r = outerR, anchor = TOP);
                        zcyl(l = conical - toothHeight/2, r2 = outerR, r1 = 0, anchor = TOP);
                    }
                } else {
                    zcyl(l = toothHeight/2 + conical, r1 = outerR, r2 = 0, anchor = BOTTOM)
                    attach(BOTTOM, TOP)
                    zcyl(l = 1, r = outerR);
                }
                //attach(BOTTOM, TOP)
                //zcyl(l = 1, r = outerR);
                
            }
        }
        
        zcyl(h = 20, r = innerR, anchor = CENTER);
    }
    zcyl(h = 20, r = outerR, anchor = CENTER, $fn = 180);
}

}

module teeth() {
intersection() {
difference() {
union() {
teeth0(conical);

            down(toothHeight/2 - toothChamfer/2) {
                zcyl(l = toothHeight/2 + conical, r1 = outerR, r2 = 0, anchor = BOTTOM)
                attach(BOTTOM, TOP)
                zcyl(l = 1, r = outerR);
            }
        }
        
        zcyl(h = 20, r = innerR, anchor = CENTER);
    }
    zcyl(h = 20, r = outerR, anchor = CENTER, $fn = 180);
}

}

module teeth0(h) {
for (i = [0 : 360/N : 359]) {
zrot(i)
tooth(h);
}
}

module tooth(h) {
hull() {
up(h)
cube(tiny, anchor = CENTER);
right(outerR0)
toothProfile();
}
}

module toothProfile() {
path = [[0,  0],
[0, toothBaseWidth],
[toothHeight,  toothBaseWidth/2]];
//e0 = echo(path);

difference() {
    yrot(-90)
    left(toothHeight/2)
    fwd(toothBaseWidth/2)
    linear_extrude(tiny)
    polygon(path);

    up(toothHeight/2 - toothChamfer)
    cube(toothChamfer*2, anchor = BOTTOM);
}

}