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+/*
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+ * ISO-standard metric threads, following this specification:
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+ * http://en.wikipedia.org/wiki/ISO_metric_screw_thread
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+ *
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+ * Copyright 2020 Dan Kirshner - dan_kirshner@yahoo.com
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+ * This program is free software: you can redistribute it and/or modify
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+ * it under the terms of the GNU General Public License as published by
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+ * the Free Software Foundation, either version 3 of the License, or
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+ * (at your option) any later version.
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+ *
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+ * This program is distributed in the hope that it will be useful,
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+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
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+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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+ * GNU General Public License for more details.
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+ *
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+ * See <http://www.gnu.org/licenses/>.
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+ *
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+ * Version 2.5. 2020-04-11 Leadin option works for internal threads.
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+ * Version 2.4. 2019-07-14 Add test option - do not render threads.
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+ * Version 2.3. 2017-08-31 Default for leadin: 0 (best for internal threads).
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+ * Version 2.2. 2017-01-01 Correction for angle; leadfac option. (Thanks to
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+ * Andrew Allen <a2intl@gmail.com>.)
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+ * Version 2.1. 2016-12-04 Chamfer bottom end (low-z); leadin option.
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+ * Version 2.0. 2016-11-05 Backwards compatibility (earlier OpenSCAD) fixes.
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+ * Version 1.9. 2016-07-03 Option: tapered.
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+ * Version 1.8. 2016-01-08 Option: (non-standard) angle.
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+ * Version 1.7. 2015-11-28 Larger x-increment - for small-diameters.
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+ * Version 1.6. 2015-09-01 Options: square threads, rectangular threads.
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+ * Version 1.5. 2015-06-12 Options: thread_size, groove.
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+ * Version 1.4. 2014-10-17 Use "faces" instead of "triangles" for polyhedron
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+ * Version 1.3. 2013-12-01 Correct loop over turns -- don't have early cut-off
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+ * Version 1.2. 2012-09-09 Use discrete polyhedra rather than linear_extrude ()
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+ * Version 1.1. 2012-09-07 Corrected to right-hand threads!
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+ */
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+
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+// Examples.
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+//
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+// Standard M8 x 1.
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+// metric_thread (diameter=8, pitch=1, length=4);
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+
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+// Square thread.
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+// metric_thread (diameter=8, pitch=1, length=4, square=true);
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+
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+// Non-standard: long pitch, same thread size.
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+//metric_thread (diameter=8, pitch=4, length=4, thread_size=1, groove=true);
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+
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+// Non-standard: 20 mm diameter, long pitch, square "trough" width 3 mm,
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+// depth 1 mm.
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+//metric_thread (diameter=20, pitch=8, length=16, square=true, thread_size=6,
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+// groove=true, rectangle=0.333);
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+
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+// English: 1/4 x 20.
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+//english_thread (diameter=1/4, threads_per_inch=20, length=1);
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+
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+// Tapered. Example -- pipe size 3/4" -- per:
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+// http://www.engineeringtoolbox.com/npt-national-pipe-taper-threads-d_750.html
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+// english_thread (diameter=1.05, threads_per_inch=14, length=3/4, taper=1/16);
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+
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+// Thread for mounting on Rohloff hub.
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+//difference () {
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+// cylinder (r=20, h=10, $fn=100);
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+//
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+// metric_thread (diameter=34, pitch=1, length=10, internal=true, n_starts=6);
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+//}
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+
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+
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+// ----------------------------------------------------------------------------
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+function segments (diameter) = min (50, max (ceil (diameter*6), 25));
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+
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+
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+// ----------------------------------------------------------------------------
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+// diameter - outside diameter of threads in mm. Default: 8.
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+// pitch - thread axial "travel" per turn in mm. Default: 1.
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+// length - overall axial length of thread in mm. Default: 1.
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+// internal - true = clearances for internal thread (e.g., a nut).
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+// false = clearances for external thread (e.g., a bolt).
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+// (Internal threads should be "cut out" from a solid using
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+// difference ()). Default: false.
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+// n_starts - Number of thread starts (e.g., DNA, a "double helix," has
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+// n_starts=2). See wikipedia Screw_thread. Default: 1.
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+// thread_size - (non-standard) axial width of a single thread "V" - independent
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+// of pitch. Default: same as pitch.
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+// groove - (non-standard) true = subtract inverted "V" from cylinder
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+// (rather thanadd protruding "V" to cylinder). Default: false.
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+// square - true = square threads (per
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+// https://en.wikipedia.org/wiki/Square_thread_form). Default:
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+// false.
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+// rectangle - (non-standard) "Rectangular" thread - ratio depth/(axial) width
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+// Default: 0 (standard "v" thread).
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+// angle - (non-standard) angle (deg) of thread side from perpendicular to
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+// axis (default = standard = 30 degrees).
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+// taper - diameter change per length (National Pipe Thread/ANSI B1.20.1
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+// is 1" diameter per 16" length). Taper decreases from 'diameter'
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+// as z increases. Default: 0 (no taper).
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+// leadin - 0 (default): no chamfer; 1: chamfer (45 degree) at max-z end;
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+// 2: chamfer at both ends, 3: chamfer at z=0 end.
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+// leadfac - scale of leadin chamfer length (default: 1.0 = 1/2 thread).
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+// test - true = do not render threads (just draw "blank" cylinder).
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+// Default: false (draw threads).
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+module metric_thread (diameter=8, pitch=1, length=1, internal=false, n_starts=1,
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+ thread_size=-1, groove=false, square=false, rectangle=0,
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+ angle=30, taper=0, leadin=0, leadfac=1.0, test=false)
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+{
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+ // thread_size: size of thread "V" different than travel per turn (pitch).
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+ // Default: same as pitch.
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+ local_thread_size = thread_size == -1 ? pitch : thread_size;
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+ local_rectangle = rectangle ? rectangle : 1;
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+
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+ n_segments = segments (diameter);
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+ h = (test && ! internal) ? 0 : (square || rectangle) ? local_thread_size*local_rectangle/2 : local_thread_size / (2 * tan(angle));
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+
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+ h_fac1 = (square || rectangle) ? 0.90 : 0.625;
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+
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+ // External thread includes additional relief.
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+ h_fac2 = (square || rectangle) ? 0.95 : 5.3/8;
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+
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+ tapered_diameter = diameter - length*taper;
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+
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+ difference () {
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+ union () {
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+ if (! groove) {
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+ if (! test) {
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+ metric_thread_turns (diameter, pitch, length, internal, n_starts,
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+ local_thread_size, groove, square, rectangle, angle,
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+ taper);
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+ }
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+ }
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+
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+ difference () {
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+
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+ // Solid center, including Dmin truncation.
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+ if (groove) {
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+ cylinder (r1=diameter/2, r2=tapered_diameter/2,
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+ h=length, $fn=n_segments);
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+ } else if (internal) {
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+ cylinder (r1=diameter/2 - h*h_fac1, r2=tapered_diameter/2 - h*h_fac1,
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+ h=length, $fn=n_segments);
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+ } else {
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+
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+ // External thread.
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+ cylinder (r1=diameter/2 - h*h_fac2, r2=tapered_diameter/2 - h*h_fac2,
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+ h=length, $fn=n_segments);
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+ }
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+
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+ if (groove) {
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+ if (! test) {
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+ metric_thread_turns (diameter, pitch, length, internal, n_starts,
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+ local_thread_size, groove, square, rectangle,
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+ angle, taper);
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+ }
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+ }
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+ }
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+
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+ // Internal thread lead-in: take away from external solid.
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+ if (internal) {
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+
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+ // "Negative chamfer" z=0 end if leadin is 2 or 3.
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+ if (leadin == 2 || leadin == 3) {
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+ cylinder (r1=diameter/2, r2=diameter/2 - h*h_fac1*leadfac, h=h*h_fac1*leadfac,
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+ $fn=n_segments);
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+ }
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+
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+ // "Negative chamfer" z-max end if leadin is 1 or 2.
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+ if (leadin == 1 || leadin == 2) {
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+ translate ([0, 0, length + 0.05 - h*h_fac1*leadfac]) {
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+ cylinder (r1=tapered_diameter/2 - h*h_fac1*leadfac, h=h*h_fac1*leadfac,
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+ r2=tapered_diameter/2,
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+ $fn=n_segments);
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+ }
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+ }
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+ }
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+ }
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+
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+ if (! internal) {
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+
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+ // Chamfer z=0 end if leadin is 2 or 3.
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+ if (leadin == 2 || leadin == 3) {
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+ difference () {
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+ cylinder (r=diameter/2 + 1, h=h*h_fac1*leadfac, $fn=n_segments);
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+
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+ cylinder (r2=diameter/2, r1=diameter/2 - h*h_fac1*leadfac, h=h*h_fac1*leadfac,
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+ $fn=n_segments);
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+ }
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+ }
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+
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+ // Chamfer z-max end if leadin is 1 or 2.
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+ if (leadin == 1 || leadin == 2) {
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+ translate ([0, 0, length + 0.05 - h*h_fac1*leadfac]) {
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+ difference () {
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+ cylinder (r=diameter/2 + 1, h=h*h_fac1*leadfac, $fn=n_segments);
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+
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+ cylinder (r1=tapered_diameter/2, r2=tapered_diameter/2 - h*h_fac1*leadfac, h=h*h_fac1*leadfac,
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+ $fn=n_segments);
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+ }
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+ }
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+ }
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+ }
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+ }
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+}
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+
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+
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+// ----------------------------------------------------------------------------
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+// Input units in inches.
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+// Note: units of measure in drawing are mm!
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+module english_thread (diameter=0.25, threads_per_inch=20, length=1,
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+ internal=false, n_starts=1, thread_size=-1, groove=false,
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+ square=false, rectangle=0, angle=30, taper=0, leadin=0,
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+ leadfac=1.0, test=false)
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+{
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+ // Convert to mm.
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+ mm_diameter = diameter*25.4;
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+ mm_pitch = (1.0/threads_per_inch)*25.4;
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+ mm_length = length*25.4;
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+
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+ echo (str ("mm_diameter: ", mm_diameter));
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+ echo (str ("mm_pitch: ", mm_pitch));
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+ echo (str ("mm_length: ", mm_length));
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+ metric_thread (mm_diameter, mm_pitch, mm_length, internal, n_starts,
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+ thread_size, groove, square, rectangle, angle, taper, leadin,
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+ leadfac, test);
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+}
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+
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+// ----------------------------------------------------------------------------
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+module metric_thread_turns (diameter, pitch, length, internal, n_starts,
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+ thread_size, groove, square, rectangle, angle,
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+ taper)
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+{
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+ // Number of turns needed.
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+ n_turns = floor (length/pitch);
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+
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+ intersection () {
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+
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+ // Start one below z = 0. Gives an extra turn at each end.
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+ for (i=[-1*n_starts : n_turns+1]) {
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+ translate ([0, 0, i*pitch]) {
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+ metric_thread_turn (diameter, pitch, internal, n_starts,
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+ thread_size, groove, square, rectangle, angle,
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+ taper, i*pitch);
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+ }
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+ }
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+
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+ // Cut to length.
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+ translate ([0, 0, length/2]) {
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+ cube ([diameter*3, diameter*3, length], center=true);
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+ }
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+ }
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+}
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+
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+
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+// ----------------------------------------------------------------------------
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+module metric_thread_turn (diameter, pitch, internal, n_starts, thread_size,
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+ groove, square, rectangle, angle, taper, z)
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+{
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+ n_segments = segments (diameter);
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+ fraction_circle = 1.0/n_segments;
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+ for (i=[0 : n_segments-1]) {
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+ rotate ([0, 0, i*360*fraction_circle]) {
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+ translate ([0, 0, i*n_starts*pitch*fraction_circle]) {
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+ //current_diameter = diameter - taper*(z + i*n_starts*pitch*fraction_circle);
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+ thread_polyhedron ((diameter - taper*(z + i*n_starts*pitch*fraction_circle))/2,
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+ pitch, internal, n_starts, thread_size, groove,
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+ square, rectangle, angle);
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+ }
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+ }
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+ }
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+}
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+
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+
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+// ----------------------------------------------------------------------------
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+module thread_polyhedron (radius, pitch, internal, n_starts, thread_size,
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+ groove, square, rectangle, angle)
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+{
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+ n_segments = segments (radius*2);
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+ fraction_circle = 1.0/n_segments;
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+
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+ local_rectangle = rectangle ? rectangle : 1;
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+
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+ h = (square || rectangle) ? thread_size*local_rectangle/2 : thread_size / (2 * tan(angle));
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+ outer_r = radius + (internal ? h/20 : 0); // Adds internal relief.
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+ //echo (str ("outer_r: ", outer_r));
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+
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+ // A little extra on square thread -- make sure overlaps cylinder.
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+ h_fac1 = (square || rectangle) ? 1.1 : 0.875;
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+ inner_r = radius - h*h_fac1; // Does NOT do Dmin_truncation - do later with
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+ // cylinder.
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+
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+ translate_y = groove ? outer_r + inner_r : 0;
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+ reflect_x = groove ? 1 : 0;
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+
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+ // Make these just slightly bigger (keep in proportion) so polyhedra will
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+ // overlap.
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+ x_incr_outer = (! groove ? outer_r : inner_r) * fraction_circle * 2 * PI * 1.02;
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+ x_incr_inner = (! groove ? inner_r : outer_r) * fraction_circle * 2 * PI * 1.02;
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+ z_incr = n_starts * pitch * fraction_circle * 1.005;
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+
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+ /*
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+ (angles x0 and x3 inner are actually 60 deg)
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+
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+ /\ (x2_inner, z2_inner) [2]
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+ / \
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+ (x3_inner, z3_inner) / \
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+ [3] \ \
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+ |\ \ (x2_outer, z2_outer) [6]
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+ | \ /
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+ | \ /|
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+ z |[7]\/ / (x1_outer, z1_outer) [5]
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+ | | | /
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+ | x | |/
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+ | / | / (x0_outer, z0_outer) [4]
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+ | / | / (behind: (x1_inner, z1_inner) [1]
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+ |/ | /
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+ y________| |/
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+ (r) / (x0_inner, z0_inner) [0]
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+
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+ */
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+
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+ x1_outer = outer_r * fraction_circle * 2 * PI;
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+
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+ z0_outer = (outer_r - inner_r) * tan(angle);
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+ //echo (str ("z0_outer: ", z0_outer));
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+
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+ //polygon ([[inner_r, 0], [outer_r, z0_outer],
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+ // [outer_r, 0.5*pitch], [inner_r, 0.5*pitch]]);
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+ z1_outer = z0_outer + z_incr;
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+
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+ // Give internal square threads some clearance in the z direction, too.
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+ bottom = internal ? 0.235 : 0.25;
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+ top = internal ? 0.765 : 0.75;
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+
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+ translate ([0, translate_y, 0]) {
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+ mirror ([reflect_x, 0, 0]) {
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+
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+ if (square || rectangle) {
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+
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+ // Rule for face ordering: look at polyhedron from outside: points must
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+ // be in clockwise order.
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+ polyhedron (
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+ points = [
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+ [-x_incr_inner/2, -inner_r, bottom*thread_size], // [0]
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+ [x_incr_inner/2, -inner_r, bottom*thread_size + z_incr], // [1]
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+ [x_incr_inner/2, -inner_r, top*thread_size + z_incr], // [2]
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+ [-x_incr_inner/2, -inner_r, top*thread_size], // [3]
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+
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+ [-x_incr_outer/2, -outer_r, bottom*thread_size], // [4]
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+ [x_incr_outer/2, -outer_r, bottom*thread_size + z_incr], // [5]
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+ [x_incr_outer/2, -outer_r, top*thread_size + z_incr], // [6]
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+ [-x_incr_outer/2, -outer_r, top*thread_size] // [7]
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+ ],
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+
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+ faces = [
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+ [0, 3, 7, 4], // This-side trapezoid
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+
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+ [1, 5, 6, 2], // Back-side trapezoid
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+
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+ [0, 1, 2, 3], // Inner rectangle
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+
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+ [4, 7, 6, 5], // Outer rectangle
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+
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+ // These are not planar, so do with separate triangles.
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+ [7, 2, 6], // Upper rectangle, bottom
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+ [7, 3, 2], // Upper rectangle, top
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+
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+ [0, 5, 1], // Lower rectangle, bottom
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+ [0, 4, 5] // Lower rectangle, top
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+ ]
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+ );
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+ } else {
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+
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+ // Rule for face ordering: look at polyhedron from outside: points must
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+ // be in clockwise order.
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+ polyhedron (
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+ points = [
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+ [-x_incr_inner/2, -inner_r, 0], // [0]
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+ [x_incr_inner/2, -inner_r, z_incr], // [1]
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+ [x_incr_inner/2, -inner_r, thread_size + z_incr], // [2]
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+ [-x_incr_inner/2, -inner_r, thread_size], // [3]
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+
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+ [-x_incr_outer/2, -outer_r, z0_outer], // [4]
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+ [x_incr_outer/2, -outer_r, z0_outer + z_incr], // [5]
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+ [x_incr_outer/2, -outer_r, thread_size - z0_outer + z_incr], // [6]
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+ [-x_incr_outer/2, -outer_r, thread_size - z0_outer] // [7]
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+ ],
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+
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+ faces = [
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+ [0, 3, 7, 4], // This-side trapezoid
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+
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+ [1, 5, 6, 2], // Back-side trapezoid
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+
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+ [0, 1, 2, 3], // Inner rectangle
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+
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+ [4, 7, 6, 5], // Outer rectangle
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+
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+ // These are not planar, so do with separate triangles.
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+ [7, 2, 6], // Upper rectangle, bottom
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+ [7, 3, 2], // Upper rectangle, top
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+
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+ [0, 5, 1], // Lower rectangle, bottom
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+ [0, 4, 5] // Lower rectangle, top
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+ ]
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+ );
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+ }
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+ }
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+ }
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+}
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+
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+
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+
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Johannes Kreutz