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threads.scad
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threads.scad
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/*
* Dan Kirshner - dan_kirshner@yahoo.com
*
* You are welcome to make free use of this software. Retention of my
* authorship credit would be appreciated.
*
* Version 1.4. 2014-10-17 Use "faces" instead of "triangles" for polyhedron
* Version 1.3. 2013-12-01 Correct loop over turns -- don't have early cut-off
* Version 1.2. 2012-09-09 Use discrete polyhedra rather than linear_extrude()
* Version 1.1. 2012-09-07 Corrected to right-hand threads!
*/
// Examples:
//metric_thread(8, 1, 4);
//english_thread(1/4, 20, 1);
// Rohloff hub thread:
//metric_thread(34, 1, 10, internal=true, n_starts=6);
// ----------------------------------------------------------------------------
function segments(diameter) = min(50, ceil(diameter*6));
// ----------------------------------------------------------------------------
// internal - true = clearances for internal thread (e.g., a nut).
// false = clearances for external thread (e.g., a bolt).
// (Internal threads should be "cut out" from a solid using
// difference()).
// n_starts - Number of thread starts (e.g., DNA, a "double helix," has
// n_starts=2). See wikipedia Screw_thread.
module metric_thread(diameter=8, pitch=1, length=1, internal=false, n_starts=1)
{
// Number of turns needed.
n_turns = floor(length/pitch);
n_segments = segments(diameter);
h = pitch * cos(30);
union() {
intersection() {
// Start one below z = 0. Gives an extra turn at each end.
for (i=[-1*n_starts : n_turns+1]) {
translate([0, 0, i*pitch]) {
metric_thread_turn(diameter, pitch, internal, n_starts);
}
}
// Cut to length.
translate([0, 0, length/2]) {
cube([diameter*1.1, diameter*1.1, length], center=true);
}
}
// Solid center, including Dmin truncation.
if (internal) {
cylinder(r=diameter/2 - h*5/8, h=length, $fn=n_segments);
} else {
// External thread includes additional relief.
cylinder(r=diameter/2 - h*5.3/8, h=length, $fn=n_segments);
}
}
}
// ----------------------------------------------------------------------------
// Input units in inches.
// Note: units of measure in drawing are mm!
module english_thread(diameter=0.25, threads_per_inch=20, length=1,
internal=false, n_starts=1)
{
// Convert to mm.
mm_diameter = diameter*25.4;
mm_pitch = (1.0/threads_per_inch)*25.4;
mm_length = length*25.4;
echo(str("mm_diameter: ", mm_diameter));
echo(str("mm_pitch: ", mm_pitch));
echo(str("mm_length: ", mm_length));
metric_thread(mm_diameter, mm_pitch, mm_length, internal, n_starts);
}
// ----------------------------------------------------------------------------
module metric_thread_turn(diameter, pitch, internal, n_starts)
{
n_segments = segments(diameter);
fraction_circle = 1.0/n_segments;
for (i=[0 : n_segments-1]) {
rotate([0, 0, i*360*fraction_circle]) {
translate([0, 0, i*n_starts*pitch*fraction_circle]) {
thread_polyhedron(diameter/2, pitch, internal, n_starts);
}
}
}
}
// ----------------------------------------------------------------------------
// z (see diagram) as function of current radius.
// (Only good for first half-pitch.)
function z_fct(current_radius, radius, pitch)
= 0.5*(current_radius - (radius - 0.875*pitch*cos(30)))
/cos(30);
// ----------------------------------------------------------------------------
module thread_polyhedron(radius, pitch, internal, n_starts)
{
n_segments = segments(radius*2);
fraction_circle = 1.0/n_segments;
h = pitch * cos(30);
outer_r = radius + (internal ? h/20 : 0); // Adds internal relief.
//echo(str("outer_r: ", outer_r));
inner_r = radius - 0.875*h; // Does NOT do Dmin_truncation - do later with
// cylinder.
// Make these just slightly bigger (keep in proportion) so polyhedra will
// overlap.
x_incr_outer = outer_r * fraction_circle * 2 * PI * 1.005;
x_incr_inner = inner_r * fraction_circle * 2 * PI * 1.005;
z_incr = n_starts * pitch * fraction_circle * 1.005;
/*
(angles x0 and x3 inner are actually 60 deg)
/\ (x2_inner, z2_inner) [2]
/ \
(x3_inner, z3_inner) / \
[3] \ \
|\ \ (x2_outer, z2_outer) [6]
| \ /
| \ /|
z |[7]\/ / (x1_outer, z1_outer) [5]
| | | /
| x | |/
| / | / (x0_outer, z0_outer) [4]
| / | / (behind: (x1_inner, z1_inner) [1]
|/ | /
y________| |/
(r) / (x0_inner, z0_inner) [0]
*/
x1_outer = outer_r * fraction_circle * 2 * PI;
z0_outer = z_fct(outer_r, radius, pitch);
//echo(str("z0_outer: ", z0_outer));
//polygon([[inner_r, 0], [outer_r, z0_outer],
// [outer_r, 0.5*pitch], [inner_r, 0.5*pitch]]);
z1_outer = z0_outer + z_incr;
// Rule for face ordering: look at polyhedron from outside: points must
// be in clockwise order.
polyhedron(
points = [
[-x_incr_inner/2, -inner_r, 0], // [0]
[x_incr_inner/2, -inner_r, z_incr], // [1]
[x_incr_inner/2, -inner_r, pitch + z_incr], // [2]
[-x_incr_inner/2, -inner_r, pitch], // [3]
[-x_incr_outer/2, -outer_r, z0_outer], // [4]
[x_incr_outer/2, -outer_r, z0_outer + z_incr], // [5]
[x_incr_outer/2, -outer_r, pitch - z0_outer + z_incr], // [6]
[-x_incr_outer/2, -outer_r, pitch - z0_outer] // [7]
],
faces = [
[0, 3, 7, 4], // This-side trapezoid
[1, 5, 6, 2], // Back-side trapezoid
[0, 1, 2, 3], // Inner rectangle
[4, 7, 6, 5], // Outer rectangle
// These are not planar, so do with separate triangles.
[7, 2, 6], // Upper rectangle, bottom
[7, 3, 2], // Upper rectangle, top
[0, 5, 1], // Lower rectangle, bottom
[0, 4, 5] // Lower rectangle, top
]
);
}