CGAL error found in bevel_gear about mcad

[MichaelAtOz]

In case anyone with gear maths is looking, apex_to_apex appears to be wrong. Affecting the last cylinder in the difference (and probably more).

[MichaelAtOz]

Nope, more complex than that...

[MichaelAtOz]

<edit duplicate>

[MichaelAtOz]

Getting warmer, but my head hurts...

Use this modified module

module involute_bevel_gear_tooth (
	back_cone_radius,
	root_radius,
	base_radius,
	outer_radius,
	pitch_apex,
	cone_distance,
	half_thick_angle,
	involute_facets)
{
//	echo ("involute_bevel_gear_tooth",
//		back_cone_radius,
//		root_radius,
//		base_radius,
//		outer_radius,
//		pitch_apex,
//		cone_distance,
//		half_thick_angle);

	min_radius = max (base_radius*2,root_radius*2);

	pitch_point =
		involute (
			base_radius*2,
			involute_intersect_angle (base_radius*2, back_cone_radius*2));
	pitch_angle = atan2 (pitch_point[1], pitch_point[0]);
	centre_angle = pitch_angle + half_thick_angle;

	start_angle = involute_intersect_angle (base_radius*2, min_radius);
	stop_angle = involute_intersect_angle (base_radius*2, outer_radius*2);

	res=(involute_facets!=0)?involute_facets:($fn==0)?5:$fn/4;
c=["red","green","blue","black","orange","purple"];
	translate ([0,0,pitch_apex])
	rotate ([0,-atan(back_cone_radius/cone_distance),0])
	translate ([-back_cone_radius*2,0,-cone_distance*2])
	!union ()
	{ translate([-5260,0,0])
		for (i=[1:res])
		{ 
			assign (
				point1=
					involute (base_radius*2,start_angle+(stop_angle - start_angle)*(i-1)/res),
				point2=
					involute (base_radius*2,start_angle+(stop_angle - start_angle)*(i)/res))
			{
				assign (
					side1_point1 = rotate_point (centre_angle, point1),
					side1_point2 = rotate_point (centre_angle, point2),
					side2_point1 = mirror_point (rotate_point (centre_angle, point1)),
					side2_point2 = mirror_point (rotate_point (centre_angle, point2)))
				{
						points=[
							[back_cone_radius*2+0.1,0,cone_distance*2],
							[side1_point1[0],side1_point1[1],0],
							[side1_point2[0],side1_point2[1],0],
							[side2_point2[0],side2_point2[1],0],
							[side2_point1[0],side2_point1[1],0],
							[0.1,0,0]];
						faces=[[0,2,1],[0,3,2],[0,4,3],[0,1,5],[1,2,5],[2,3,5],[3,4,5],[0,5,4]];
					polyhedron (points=points,faces=faces);
          for (point=[0:len(points)-1])
            let( p=points[point]) {
              translate([p.x,p.y,p.z])
                color(c[i]) {
                  cube([0.01,0.01,1],true);
                  translate([0,0,-0.2*point]) 
                    linear_extrude(0.1)
                      text(str(point),size=0.5);
                }
              echo(i=i,c[i],point,p=p);
            }
				}
			}
		}
	}
}

The echo output

Parsing design (AST generation)...
Saved backup file: /home/mebd/.local/share/OpenSCAD/backups/unsaved-backup-knnS8520.scad
Compiling design (CSG Tree generation)...
ECHO: "bevel_gear", "teeth", 36, "cone distance", 24.001, 20, 240, 40, 0.2, 9, 0, 1
ECHO: "Num Teeth:", 36, " Pitch Angle:", 89.477, "Pitch Apex:", 0.219091, " Apex to Apex:", 2629.26
ECHO: back_cone_descent = 3.53327
DEPRECATED: The assign() module will be removed in future releases. Use a regular assignment instead. in file , line 282
DEPRECATED: The assign() module will be removed in future releases. Use a regular assignment instead. in file , line 288
ECHO: i = 1, "green", 0, p = [5258.4, 0, 48.002]
ECHO: i = 1, "green", 1, p = [5255.23, -4.66318, 0]
ECHO: i = 1, "green", 2, p = [5256.38, -3.70363, 0]
ECHO: i = 1, "green", 3, p = [5256.38, 3.70363, 0]
ECHO: i = 1, "green", 4, p = [5255.23, 4.66318, 0]
ECHO: i = 1, "green", 5, p = [0.1, 0, 0]
ECHO: i = 2, "blue", 0, p = [5258.4, 0, 48.002]
ECHO: i = 2, "blue", 1, p = [5256.38, -3.70363, 0]
ECHO: i = 2, "blue", 2, p = [5257.53, -2.74306, 0]
ECHO: i = 2, "blue", 3, p = [5257.53, 2.74306, 0]
ECHO: i = 2, "blue", 4, p = [5256.38, 3.70363, 0]
ECHO: i = 2, "blue", 5, p = [0.1, 0, 0]
ECHO: i = 3, "black", 0, p = [5258.4, 0, 48.002]
ECHO: i = 3, "black", 1, p = [5257.53, -2.74306, 0]
ECHO: i = 3, "black", 2, p = [5258.67, -1.78147, 0]
ECHO: i = 3, "black", 3, p = [5258.67, 1.78147, 0]
ECHO: i = 3, "black", 4, p = [5257.53, 2.74306, 0]
ECHO: i = 3, "black", 5, p = [0.1, 0, 0]
ECHO: i = 4, "orange", 0, p = [5258.4, 0, 48.002]
ECHO: i = 4, "orange", 1, p = [5258.67, -1.78147, 0]
ECHO: i = 4, "orange", 2, p = [5259.82, -0.81887, 0]
ECHO: i = 4, "orange", 3, p = [5259.82, 0.81887, 0]
ECHO: i = 4, "orange", 4, p = [5258.67, 1.78147, 0]
ECHO: i = 4, "orange", 5, p = [0.1, 0, 0]
ECHO: i = 5, "purple", 0, p = [5258.4, 0, 48.002]
ECHO: i = 5, "purple", 1, p = [5259.82, -0.81887, 0]
ECHO: i = 5, "purple", 2, p = [5260.97, 0.144747, 0]
ECHO: i = 5, "purple", 3, p = [5260.97, -0.144747, 0]
ECHO: i = 5, "purple", 4, p = [5259.82, 0.81887, 0]
ECHO: i = 5, "purple", 5, p = [0.1, 0, 0]
ECHO: "bgbc1"
Compiling design (CSG Products generation)...
Geometries in cache: 34
Geometry cache size in bytes: 87504
CGAL Polyhedrons in cache: 0
CGAL cache size in bytes: 0
Compiling design (CSG Products normalization)...
Normalized CSG tree has 65 elements
Compile and preview finished.
Total rendering time: 0 hours, 0 minutes, 0 seconds

These two points are the problem
ECHO: i = 5, "purple", 2, p = [5260.97, 0.144747, 0]
ECHO: i = 5, "purple", 3, p = [5260.97, -0.144747, 0]

They are on the opposite side of the axis to the preceeding points, making this tip crossed over.

But as I said, my head hurts trying to understand why.
And i don't want to learn gear geometry...
TAG someone else

p.s. also swap the commented lines in bevel_gear() line ~193 to get one tooth

//				for (i = [1:number_of_teeth])
				for (i = [1:1])

[MichaelAtOz]

Make that line ~180

[MichaelAtOz]

..and it involves pressure_angle, 36 is OK, 38 crosses the tip.

[MichaelAtOz]

@hamiltont if you want a hack that gets past the CGAL error, in
module involute_bevel_gear_tooth () at line 282 replace points= with this

points=[
  [back_cone_radius*2+0.1,0,cone_distance*2],
  [side1_point1[0],side1_point1[1],0],
  [side1_point2[0],min(side1_point2[1],side2_point2[1]),0],
  [side2_point2[0],max(side1_point2[1],side2_point2[1]),0],
  [side2_point1[0],side2_point1[1],0],
  [0.1,0,0]];

It just forces the points to be on the correct side of the axis.
The end of the tooth is slightly wonky, but that end gets trimmed off.

There is also a bug with the sprocket like protrusions inside the hole, but you can fix that with a difference.

[hamiltont]

@MichaelAtOz Wow! Thanks for the effort here. I'm crunched with my day job, but as soon as I resume this side project I'll try to follow along with your work. Maybe I can contribute something

[MichaelAtOz]

@hamiltont Actually the above hack does affect the involute profile:

This (also a hack) is closer, but also loses the flat top:

points=[
  [back_cone_radius*2+0.1,0,cone_distance*2],
  [side1_point1[0],side1_point1[1],0],
  [side1_point2[0],min(side1_point2[1],0),0],
  [side2_point2[0],max(0,side2_point2[1]),0],
  [side2_point1[0],side2_point1[1],0],
  [0.1,0,0]];

I don't know the basis for the shape of the tooth that loop is trying to calculate.