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threads.scad
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/*
* ISO-standard metric threads, following this specification:
* http://en.wikipedia.org/wiki/ISO_metric_screw_thread
*
* 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 1.9. 2016-07-03 Option: tapered.
* Version 1.8. 2016-01-08 Option: (non-standard) angle.
* Version 1.7. 2015-11-28 Larger x-increment - for small-diameters.
* Version 1.6. 2015-09-01 Options: square threads, rectangular threads.
* Version 1.5. 2015-06-12 Options: thread_size, groove.
* 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.
//
// Standard M8 x 1.
// metric_thread (diameter=8, pitch=1, length=4);
// Square thread.
// metric_thread (diameter=8, pitch=1, length=4, square=true);
// Non-standard: long pitch, same thread size.
//metric_thread (diameter=8, pitch=4, length=4, thread_size=1, groove=true);
// Non-standard: 20 mm diameter, long pitch, square "trough" width 3 mm,
// depth 1 mm.
//metric_thread (diameter=20, pitch=8, length=16, square=true, thread_size=6,
// groove=true, rectangle=0.333);
// English: 1/4 x 20.
//english_thread (diameter=1/4, threads_per_inch=20, length=1);
// Tapered. Example -- pipe size 3/4" -- per:
// http://www.engineeringtoolbox.com/npt-national-pipe-taper-threads-d_750.html
// english_thread (diameter=1.05, threads_per_inch=14, length=3/4, taper=1/16);
// Thread for mounting on Rohloff hub.
//difference () {
// cylinder (r=20, h=10, $fn=100);
//
// metric_thread (diameter=34, pitch=1, length=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.
// thread_size - (non-standard) size of a single thread "V" - independent of
// pitch. Default: same as pitch.
// groove - (non-standard) subtract inverted "V" from cylinder (rather than
// add protruding "V" to cylinder).
// square - Square threads (per
// https://en.wikipedia.org/wiki/Square_thread_form).
// rectangle - (non-standard) "Rectangular" thread - ratio depth/width
// Default: 1 (square).
// angle - (non-standard) angle (deg) of thread side from perpendicular to
// axis (default = standard = 30 degrees).
// taper - diameter change per length (National Pipe Thread/ANSI B1.20.1
// is 1" diameter per 16" length).
module metric_thread (diameter=8, pitch=1, length=1, internal=false, n_starts=1,
thread_size=-1, groove=false, square=false, rectangle=0,
angle=30, taper=0)
{
// thread_size: size of thread "V" different than travel per turn (pitch).
// Default: same as pitch.
local_thread_size = thread_size == -1 ? pitch : thread_size;
local_rectangle = rectangle ? rectangle : 1;
n_segments = segments (diameter);
h = (square || rectangle) ? local_thread_size*local_rectangle/2 : local_thread_size * cos (angle);
h_fac1 = (square || rectangle) ? 0.90 : 0.625;
// External thread includes additional relief.
h_fac2 = (square || rectangle) ? 0.95 : 5.3/8;
if (! groove) {
metric_thread_turns (diameter, pitch, length, internal, n_starts,
local_thread_size, groove, square, rectangle, angle,
taper);
}
difference () {
// Solid center, including Dmin truncation.
tapered_diameter = diameter - length*taper;
if (groove) {
cylinder (r1=diameter/2, r2=tapered_diameter/2,
h=length, $fn=n_segments);
} else if (internal) {
cylinder (r1=diameter/2 - h*h_fac1, r2=tapered_diameter/2 - h*h_fac1,
h=length, $fn=n_segments);
} else {
// External thread.
cylinder (r1=diameter/2 - h*h_fac2, r2=tapered_diameter/2 - h*h_fac2,
h=length, $fn=n_segments);
}
if (groove) {
metric_thread_turns (diameter, pitch, length, internal, n_starts,
local_thread_size, groove, square, rectangle,
angle, taper);
}
}
}
// ----------------------------------------------------------------------------
// 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, thread_size=-1, groove=false,
square=false, rectangle=0, angle=30, taper=0)
{
// 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,
thread_size, groove, square, rectangle, angle, taper);
}
// ----------------------------------------------------------------------------
module metric_thread_turns (diameter, pitch, length, internal, n_starts,
thread_size, groove, square, rectangle, angle,
taper)
{
// Number of turns needed.
n_turns = floor (length/pitch);
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,
thread_size, groove, square, rectangle, angle,
taper, i*pitch);
}
}
// Cut to length.
translate ([0, 0, length/2]) {
cube ([diameter*3, diameter*3, length], center=true);
}
}
}
// ----------------------------------------------------------------------------
module metric_thread_turn (diameter, pitch, internal, n_starts, thread_size,
groove, square, rectangle, angle, taper, z)
{
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]) {
current_diameter = diameter - taper*(z + i*n_starts*pitch*fraction_circle);
thread_polyhedron (current_diameter/2, pitch, internal, n_starts,
thread_size, groove, square, rectangle, angle);
}
}
}
}
// ----------------------------------------------------------------------------
// z (see diagram) as function of current radius.
// (Only good for first half-pitch.)
function z_fct (current_radius, radius, pitch, angle)
= 0.5* (current_radius - (radius - 0.875*pitch*cos (angle)))
/cos (angle);
// ----------------------------------------------------------------------------
module thread_polyhedron (radius, pitch, internal, n_starts, thread_size,
groove, square, rectangle, angle)
{
n_segments = segments (radius*2);
fraction_circle = 1.0/n_segments;
local_rectangle = rectangle ? rectangle : 1;
h = (square || rectangle) ? thread_size*local_rectangle/2 : thread_size * cos (angle);
outer_r = radius + (internal ? h/20 : 0); // Adds internal relief.
//echo (str ("outer_r: ", outer_r));
// A little extra on square thread -- make sure overlaps cylinder.
h_fac1 = (square || rectangle) ? 1.1 : 0.875;
inner_r = radius - h*h_fac1; // Does NOT do Dmin_truncation - do later with
// cylinder.
translate_y = groove ? outer_r + inner_r : 0;
reflect_x = groove ? 1 : 0;
// Make these just slightly bigger (keep in proportion) so polyhedra will
// overlap.
x_incr_outer = (! groove ? outer_r : inner_r) * fraction_circle * 2 * PI * 1.02;
x_incr_inner = (! groove ? inner_r : outer_r) * fraction_circle * 2 * PI * 1.02;
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, thread_size, angle);
//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;
// Give internal square threads some clearance in the z direction, too.
bottom = internal ? 0.235 : 0.25;
top = internal ? 0.765 : 0.75;
translate ([0, translate_y, 0]) {
mirror ([reflect_x, 0, 0]) {
if (square || rectangle) {
// Rule for face ordering: look at polyhedron from outside: points must
// be in clockwise order.
polyhedron (
points = [
[-x_incr_inner/2, -inner_r, bottom*thread_size], // [0]
[x_incr_inner/2, -inner_r, bottom*thread_size + z_incr], // [1]
[x_incr_inner/2, -inner_r, top*thread_size + z_incr], // [2]
[-x_incr_inner/2, -inner_r, top*thread_size], // [3]
[-x_incr_outer/2, -outer_r, bottom*thread_size], // [4]
[x_incr_outer/2, -outer_r, bottom*thread_size + z_incr], // [5]
[x_incr_outer/2, -outer_r, top*thread_size + z_incr], // [6]
[-x_incr_outer/2, -outer_r, top*thread_size] // [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
]
);
} else {
// 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, thread_size + z_incr], // [2]
[-x_incr_inner/2, -inner_r, thread_size], // [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, thread_size - z0_outer + z_incr], // [6]
[-x_incr_outer/2, -outer_r, thread_size - 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
]
);
}
}
}
}