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diff --git a/threads.scad b/threads.scad new file mode 100644 index 0000000..8dd0b7b --- a/dev/null +++ b/threads.scad @@ -0,0 +1,332 @@ +/*
+ * 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
+ ]
+ );
+ }
+ }
+ }
+}
+
+
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