/** 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 1.8. 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);// 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).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){// 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);}difference () {// Solid center, including Dmin truncation.if (groove) {cylinder (r=diameter/2, h=length, $fn=n_segments);} else if (internal) {cylinder (r=diameter/2 - h*h_fac1, h=length, $fn=n_segments);} else {// External thread.cylinder (r=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);}}}// ----------------------------------------------------------------------------// 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){// 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);}// ----------------------------------------------------------------------------module metric_thread_turns (diameter, pitch, length, internal, n_starts,thread_size, groove, square, rectangle, angle){// 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);}}// 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){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,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]);}}}}// Thread for mounting on Rohloff hub.difference () {cylinder (r=20, h=5, $fn=100);metric_thread (diameter=34, pitch=1, length=5, internal=true, n_starts=6);}metric_thread (diameter=33, pitch=1, length=10, internal=false, n_starts=6);