BOSL2/threading.scad

//////////////////////////////////////////////////////////////////////
// LibFile: threading.scad
//   Triangular and Trapezoidal-Threaded Screw Rods and Nuts.
//   To use, add the following lines to the beginning of your file:
//   ```
//   include <BOSL2/constants.scad>
//   use <BOSL2/threading.scad>
//   ```
//////////////////////////////////////////////////////////////////////

/*
BSD 2-Clause License

Copyright (c) 2017, Revar Desmera
All rights reserved.

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modification, are permitted provided that the following conditions are met:

* Redistributions of source code must retain the above copyright notice, this
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  and/or other materials provided with the distribution.

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*/

include <constants.scad>
use <transforms.scad>
use <masks.scad>
use <math.scad>


function _trpzd_thread_pt(thread, threads, start, starts, astep, asteps, part, parts) =
	astep + asteps * (thread + threads * (part + parts * start));


// Section: Generic Trapezoidal Threading

// Module: trapezoidal_threaded_rod()
// Description:
//   Constructs a generic trapezoidal threaded screw rod.  This method makes
//   much smoother threads than the naive linear_extrude method.
//   For metric trapezoidal threads, use thread_angle=15 and thread_depth=pitch/2.
//   For ACME threads, use thread_angle=14.5 and thread_depth=pitch/2.
//   For square threads, use thread_angle=0 and thread_depth=pitch/2.
//   For normal screw threads, use thread_angle=30 and thread_depth=pitch*3*sqrt(3)/8.
// Arguments:
//   d = Outer diameter of threaded rod.
//   l = Length of threaded rod.
//   pitch = Length between threads.
//   thread_depth = Depth of the threads.  Default=pitch/2
//   thread_angle = The pressure angle profile angle of the threads.  Default = 14.5 degree ACME profile.
//   left_handed = If true, create left-handed threads.  Default = false
//   bevel = if true, bevel the thread ends.  Default: true
//   starts = The number of lead starts.  Default = 1
//   orient = Orientation of the rod.  Use the `ORIENT_` constants from `constants.scad`.  Default: `ORIENT_Z`.
//   align = Alignment of the rod.  Use the constants from `constants.scad`.  Default: `CENTER`.
//   center = If given, overrides `align`.  A true value sets `align=CENTER`, false sets `align=UP`.
// Examples:
//   trapezoidal_threaded_rod(d=10, l=100, pitch=2, thread_angle=15, $fn=32);
//   trapezoidal_threaded_rod(d=3/8*25.4, l=20, pitch=1/8*25.4, thread_angle=29, $fn=32);
//   trapezoidal_threaded_rod(d=60, l=16, pitch=8, thread_depth=3, thread_angle=45, left_handed=true, $fa=2, $fs=2);
//   trapezoidal_threaded_rod(d=60, l=16, pitch=8, thread_depth=3, thread_angle=45, left_handed=true, starts=4, $fa=2, $fs=2);
//   trapezoidal_threaded_rod(d=16, l=40, pitch=2, thread_angle=30);
//   trapezoidal_threaded_rod(d=10, l=40, pitch=3, thread_angle=15, left_handed=true, starts=3, $fn=36);
//   trapezoidal_threaded_rod(d=25, l=100, pitch=10, thread_depth=8/3, thread_angle=50, starts=4, center=false, $fa=2, $fs=2);
//   trapezoidal_threaded_rod(d=50, l=75, pitch=8, thread_angle=30, starts=3, bevel=true);
//   trapezoidal_threaded_rod(l=25, d=10, pitch=2, thread_angle=15, starts=3, $fa=1, $fs=1, orient=ORIENT_X, align=UP);
module trapezoidal_threaded_rod(
	d=10,
	l=100,
	pitch=2,
	thread_angle=15,
	thread_depth=undef,
	left_handed=false,
	bevel=false,
	starts=1,
	orient=ORIENT_Z,
	align=CENTER,
	center=undef
) {
	astep = 360 / quantup(segs(d/2), starts);
	asteps = ceil(360/astep);
	threads = ceil(l/pitch/starts)+(starts<4?4-starts:1);
	depth = min((thread_depth==undef? pitch/2 : thread_depth), pitch/2/tan(thread_angle));
	pa_delta = min(pitch/4-0.01,depth*tan(thread_angle)/2);
	dir = left_handed? -1 : 1;
	r1 = max(0, d/2-depth);
	r2 = d/2;
	rads = [r1, r2, r2, r1];
	delta_zs = [
		-pitch/4-pa_delta,
		-pitch/4+pa_delta,
		pitch/4-pa_delta,
		pitch/4+pa_delta
	];
	parts = len(delta_zs);
	poly_points = concat(
		[
			for (
				start = [0 : starts-1],
				part = [0 : parts-1],
				thread = [0 : threads-1],
				astep = [0 : asteps-1]
			) let (
				r = rads[part],
				dz = delta_zs[part],
				a = astep / asteps,
				c = cos(360 * (a * dir + start/starts)),
				s = sin(360 * (a * dir + start/starts)),
				z = (thread + a - threads/2) * starts * pitch
			) [r*c, r*s, z+dz]
		],
		[[0, 0, -threads*pitch*starts/2-pitch/4], [0, 0, threads*pitch*starts/2+pitch/4]]
	);
	point_count = len(poly_points);
	poly_faces = concat(
		// Thread surfaces
		[
			for (
				start = [0 : starts-1],
				part = [0 : parts-2],
				thread = [0 : threads-1],
				astep = [0 : asteps-1],
				trinum = [0 : 1]
			) let (
				n = ((thread * asteps + astep) * starts + start) * parts,
				p0 = _trpzd_thread_pt(thread, threads, start, starts, astep, asteps, part, parts),
				p1 = _trpzd_thread_pt(thread, threads, start, starts, astep, asteps, part+1, parts),
				p2 = _trpzd_thread_pt(thread, threads, start, starts, astep+1, asteps, part, parts),
				p3 = _trpzd_thread_pt(thread, threads, start, starts, astep+1, asteps, part+1, parts),
				tri = trinum==0? [p0, p1, p3] : [p0, p3, p2],
				otri = left_handed? [tri[0], tri[2], tri[1]] : tri
			)
			if (!(thread == threads-1 && astep == asteps-1)) otri
		],
		// Thread trough bottom
		[
			for (
				start = [0 : starts-1],
				thread = [0 : threads-1],
				astep = [0 : asteps-1],
				trinum = [0 : 1]
			) let (
				p0 = _trpzd_thread_pt(thread, threads, start, starts, astep, asteps, parts-1, parts),
				p1 = _trpzd_thread_pt(thread, threads, (start+(left_handed?1:starts-1))%starts, starts, astep+asteps/starts, asteps, 0, parts),
				p2 = p0 + 1,
				p3 = p1 + 1,
				tri = trinum==0? [p0, p1, p3] : [p0, p3, p2],
				otri = left_handed? [tri[0], tri[2], tri[1]] : tri
			)
			if (
				!(thread >= threads-1 && astep > asteps-asteps/starts-2) &&
				!(thread >= threads-2 && starts == 1 && astep >= asteps-1)
			) otri
		],
		// top and bottom thread endcap
		[
			for (
				start=[0:starts-1],
				part=[1:parts-2],
				is_top=[0:1]
			) let (
				astep = is_top? asteps-1 : 0,
				thread = is_top? threads-1 : 0,
				p0 = _trpzd_thread_pt(thread, threads, start, starts, astep, asteps, 0, parts),
				p1 = _trpzd_thread_pt(thread, threads, start, starts, astep, asteps, part, parts),
				p2 = _trpzd_thread_pt(thread, threads, start, starts, astep, asteps, part+1, parts),
				tri = is_top? [p0, p1, p2] : [p0, p2, p1],
				otri = left_handed? [tri[0], tri[2], tri[1]] : tri
			) otri
		],
		// body side triangles
		[
			for (
				start=[0:starts-1],
				is_top=[false,true],
				trinum=[0,1]
			) let (
				astep = is_top? asteps-1 : 0,
				thread = is_top? threads-1 : 0,
				ostart = (is_top != left_handed? (start+1) : (start+starts-1))%starts,
				ostep = is_top? astep-asteps/starts : astep+asteps/starts,
				oparts = is_top? parts-1 : 0,
				p0 = is_top? point_count-1 : point_count-2,
				p1 = _trpzd_thread_pt(thread, threads, start, starts, astep, asteps, 0, parts),
				p2 = _trpzd_thread_pt(thread, threads, start, starts, astep, asteps, parts-1, parts),
				p3 = _trpzd_thread_pt(thread, threads, ostart, starts, ostep, asteps, oparts, parts),
				tri = trinum==0?
					(is_top? [p0, p1, p2] : [p0, p2, p1]) :
					(is_top? [p0, p3, p1] : [p0, p3, p2]),
				otri = left_handed? [tri[0], tri[2], tri[1]] : tri
			) otri
		],
		// Caps
		[
			for (
				start = [0 : starts-1],
				astep = [0 : asteps/starts-1],
				is_top = [0:1]
			) let (
				thread = is_top? threads-1 : 0,
				part = is_top? parts-1 : 0,
				ostep = is_top? asteps-astep-2 : astep,
				p0 = is_top? point_count-1 : point_count-2,
				p1 = _trpzd_thread_pt(thread, threads, start, starts, ostep, asteps, part, parts),
				p2 = _trpzd_thread_pt(thread, threads, start, starts, ostep+1, asteps, part, parts),
				tri = is_top? [p0, p2, p1] : [p0, p1, p2],
				otri = left_handed? [tri[0], tri[2], tri[1]] : tri
			) otri
		]
	);
	orient_and_align([d,d,l], orient, align, center) {
		difference() {
			polyhedron(points=poly_points, faces=poly_faces, convexity=threads*starts*2);
			zspread(l+4*pitch*starts) cube([d+1, d+1, 4*pitch*starts], center=true);
			if (bevel) cylinder_mask(d=d, l=l+0.01, chamfer=depth);
		}
	}
}


// Module: trapezoidal_threaded_nut()
// Description:
//   Constructs a hex nut for a threaded screw rod.  This method makes
//   much smoother threads than the naive linear_extrude method.
//   For metric screw threads, use thread_angle=30 and leave out thread_depth argument.
//   For SAE screw threads, use thread_angle=30 and leave out thread_depth argument.
//   For metric trapezoidal threads, use thread_angle=15 and thread_depth=pitch/2.
//   For ACME threads, use thread_angle=14.5 and thread_depth=pitch/2.
//   For square threads, use thread_angle=0 and thread_depth=pitch/2.
// Arguments:
//   od = diameter of the nut.
//   id = diameter of threaded rod to screw onto.
//   h = height/thickness of nut.
//   pitch = Length between threads.
//   thread_depth = Depth of the threads.  Default=pitch/2.
//   thread_angle = The pressure angle profile angle of the threads.  Default = 14.5 degree ACME profile.
//   left_handed = if true, create left-handed threads.  Default = false
//   starts = The number of lead starts.  Default = 1
//   slop = printer slop calibration to allow for tight fitting of parts.  default=0.2
//   bevel = if true, bevel the thread ends.  Default: true
//   orient = Orientation of the nut.  Use the `ORIENT_` constants from `constants.scad`.  Default: `ORIENT_Z`.
//   align = Alignment of the nut.  Use the constants from `constants.scad`.  Default: `CENTER`.
// Examples:
//   trapezoidal_threaded_nut(od=16, id=8, h=8, pitch=2, slop=0.2, align=UP);
//   trapezoidal_threaded_nut(od=17.4, id=10, h=10, pitch=2, slop=0.2, left_handed=true);
//   trapezoidal_threaded_nut(od=17.4, id=10, h=10, pitch=2, thread_angle=15, starts=3, $fa=1, $fs=1);
module trapezoidal_threaded_nut(
	od=17.4,
	id=10,
	h=10,
	pitch=2,
	thread_depth=undef,
	thread_angle=15,
	left_handed=false,
	starts=1,
	bevel=true,
	slop=PRINTER_SLOP,
	orient=ORIENT_Z,
	align=CENTER
) {
	depth = min((thread_depth==undef? pitch/2 : thread_depth), pitch/2/tan(thread_angle));
	orient_and_align([od/cos(30),od,h], orient, align) {
		difference() {
			cylinder(d=od/cos(30), h=h, center=true, $fn=6);
			zspread(slop, n=slop>0?2:1) {
				trapezoidal_threaded_rod(
					d=id+2*slop,
					l=h+1,
					pitch=pitch,
					thread_depth=depth,
					thread_angle=thread_angle,
					left_handed=left_handed,
					starts=starts
				);
			}
			if (bevel) {
				zflip_copy() {
					down(h/2+0.01) {
						cylinder(r1=id/2+slop, r2=id/2+slop-depth, h=depth, center=false);
					}
				}
			}
		}
	}
}


// Section: Triangular Threading

// Module: threaded_rod()
// Description:
//   Constructs a standard metric or UTS threaded screw rod.  This method
//   makes much smoother threads than the naive linear_extrude method.
// Arguments:
//   d = Outer diameter of threaded rod.
//   l = length of threaded rod.
//   pitch = Length between threads.
//   left_handed = if true, create left-handed threads.  Default = false
//   bevel = if true, bevel the thread ends.  Default: false
//   orient = Orientation of the rod.  Use the `ORIENT_` constants from `constants.scad`.  Default: `ORIENT_Z`.
//   align = Alignment of the rod.  Use the constants from `constants.scad`.  Default: `CENTER`.
// Examples:
//   threaded_rod(d=10, l=30, pitch=1.25, left_handed=true, $fa=1, $fs=1);
module threaded_rod(d=10, l=100, pitch=2, left_handed=false, bevel=false, orient=ORIENT_Z, align=CENTER) {
	trapezoidal_threaded_rod(
		d=d, l=l, pitch=pitch,
		thread_depth=pitch*3*sqrt(3)/8,
		thread_angle=30,
		left_handed=left_handed,
		bevel=bevel,
		orient=orient,
		align=align
	);
}



// Module: threaded_nut()
// Description:
//   Constructs a hex nut for a metric or UTS threaded screw rod.  This method
//   makes much smoother threads than the naive linear_extrude method.
// Arguments:
//   od = diameter of the nut.
//   id = diameter of threaded rod to screw onto.
//   h = height/thickness of nut.
//   pitch = Length between threads.
//   left_handed = if true, create left-handed threads.  Default = false
//   bevel = if true, bevel the thread ends.  Default: false
//   slop = printer slop calibration to allow for tight fitting of parts.  default=0.2
//   orient = Orientation of the nut.  Use the `ORIENT_` constants from `constants.scad`.  Default: `ORIENT_Z`.
//   align = Alignment of the nut.  Use the constants from `constants.scad`.  Default: `CENTER`.
// Examples:
//   threaded_nut(od=16, id=8, h=8, pitch=1.25, left_handed=true, slop=0.2, $fa=1, $fs=1);
module threaded_nut(
	od=16, id=10, h=10,
	pitch=2, left_handed=false,
	bevel=false, slop=0.2,
	orient=ORIENT_Z, align=CENTER
) {
	trapezoidal_threaded_nut(
		od=od, id=id, h=h,
		pitch=pitch, thread_angle=30,
		thread_depth=pitch*3*sqrt(3)/8,
		left_handed=left_handed,
		bevel=bevel, slop=slop,
		orient=orient, align=align
	);
}


// Section: Metric Trapezoidal Threading

// Module: metric_trapezoidal_threaded_rod()
// Description:
//   Constructs a metric trapezoidal threaded screw rod.  This method makes much
//   smoother threads than the naive linear_extrude method.
// Arguments:
//   d = Outer diameter of threaded rod.
//   l = length of threaded rod.
//   pitch = Length between threads.
//   left_handed = if true, create left-handed threads.  Default = false
//   bevel = if true, bevel the thread ends.  Default: false
//   starts = The number of lead starts.  Default = 1
//   orient = Orientation of the rod.  Use the `ORIENT_` constants from `constants.scad`.  Default: `ORIENT_Z`.
//   align = Alignment of the rod.  Use the constants from `constants.scad`.  Default: `CENTER`.
// Examples:
//   metric_trapezoidal_threaded_rod(d=10, l=30, pitch=2, left_handed=true, $fa=1, $fs=1);
module metric_trapezoidal_threaded_rod(
	d=10, l=100, pitch=2,
	left_handed=false,
	starts=1,
	bevel=false,
	orient=ORIENT_Z,
	align=CENTER
) {
	trapezoidal_threaded_rod(
		d=d, l=l,
		pitch=pitch,
		thread_angle=15,
		left_handed=left_handed,
		starts=starts,
		bevel=bevel,
		orient=orient,
		align=align
	);
}



// Module: metric_trapezoidal_threaded_nut()
// Description:
//   Constructs a hex nut for a metric trapezoidal threaded screw rod.  This method
//   makes much smoother threads than the naive linear_extrude method.
// Arguments:
//   od = diameter of the nut.
//   id = diameter of threaded rod to screw onto.
//   h = height/thickness of nut.
//   pitch = Length between threads.
//   left_handed = if true, create left-handed threads.  Default = false
//   bevel = if true, bevel the thread ends.  Default: false
//   starts = The number of lead starts.  Default = 1
//   slop = printer slop calibration to allow for tight fitting of parts.  default=0.2
//   orient = Orientation of the nut.  Use the `ORIENT_` constants from `constants.scad`.  Default: `ORIENT_Z`.
//   align = Alignment of the nut.  Use the constants from `constants.scad`.  Default: `CENTER`.
// Examples:
//   metric_trapezoidal_threaded_nut(od=16, id=10, h=10, pitch=2, left_handed=true, bevel=true, $fa=1, $fs=1);
module metric_trapezoidal_threaded_nut(
	od=17.4, id=10.5, h=10,
	pitch=3.175,
	starts=1,
	left_handed=false,
	bevel=false,
	slop=PRINTER_SLOP,
	orient=ORIENT_Z,
	align=CENTER
) {
	trapezoidal_threaded_nut(
		od=od, id=id, h=h,
		pitch=pitch, thread_angle=15,
		left_handed=left_handed,
		starts=starts,
		bevel=bevel,
		slop=slop,
		orient=orient,
		align=align
	);
}


// Section: ACME Trapezoidal Threading

// Module: acme_threaded_rod()
// Description:
//   Constructs an ACME trapezoidal threaded screw rod.  This method makes
//   much smoother threads than the naive linear_extrude method.
// Arguments:
//   d = Outer diameter of threaded rod.
//   l = length of threaded rod.
//   pitch = Length between threads.
//   thread_depth = Depth of the threads.  Default = pitch/2
//   thread_angle = The pressure angle profile angle of the threads.  Default = 14.5 degrees
//   starts = The number of lead starts.  Default = 1
//   left_handed = if true, create left-handed threads.  Default = false
//   bevel = if true, bevel the thread ends.  Default: false
//   orient = Orientation of the rod.  Use the `ORIENT_` constants from `constants.scad`.  Default: `ORIENT_Z`.
//   align = Alignment of the rod.  Use the constants from `constants.scad`.  Default: `CENTER`.
// Examples:
//   acme_threaded_rod(d=3/8*25.4, l=20, pitch=1/8*25.4, $fn=32);
//   acme_threaded_rod(d=10, l=40, pitch=2, starts=3, $fa=1, $fs=1);
module acme_threaded_rod(
	d=10, l=100, pitch=2,
	thread_angle=14.5,
	thread_depth=undef,
	starts=1,
	left_handed=false,
	bevel=false,
	orient=ORIENT_Z,
	align=CENTER
) {
	trapezoidal_threaded_rod(
		d=d, l=l, pitch=pitch,
		thread_angle=thread_angle,
		thread_depth=thread_depth,
		starts=starts,
		left_handed=left_handed,
		bevel=bevel,
		orient=orient,
		align=align
	);
}



// Module: acme_threaded_nut()
// Description:
//   Constructs a hex nut for an ACME threaded screw rod.  This method makes
//   much smoother threads than the naive linear_extrude method.
// Arguments:
//   od = diameter of the nut.
//   id = diameter of threaded rod to screw onto.
//   h = height/thickness of nut.
//   pitch = Length between threads.
//   thread_depth = Depth of the threads.  Default=pitch/2
//   thread_angle = The pressure angle profile angle of the threads.  Default = 14.5 degree ACME profile.
//   left_handed = if true, create left-handed threads.  Default = false
//   bevel = if true, bevel the thread ends.  Default: false
//   slop = printer slop calibration to allow for tight fitting of parts.  default=0.2
//   orient = Orientation of the nut.  Use the `ORIENT_` constants from `constants.scad`.  Default: `ORIENT_Z`.
//   align = Alignment of the nut.  Use the constants from `constants.scad`.  Default: `CENTER`.
// Examples:
//   acme_threaded_nut(od=16, id=3/8*25.4, h=8, pitch=1/8*25.4, slop=0.2);
//   acme_threaded_nut(od=16, id=10, h=10, pitch=2, starts=3, slop=0.2, $fa=1, $fs=1);
module acme_threaded_nut(
	od, id, h, pitch,
	thread_angle=14.5,
	thread_depth=undef,
	starts=1,
	left_handed=false,
	bevel=false,
	slop=PRINTER_SLOP,
	orient=ORIENT_Z,
	align=CENTER
) {
	trapezoidal_threaded_nut(
		od=od, id=id, h=h, pitch=pitch,
		thread_depth=thread_depth,
		thread_angle=thread_angle,
		left_handed=left_handed,
		bevel=bevel,
		starts=starts,
		slop=slop,
		orient=orient,
		align=align
	);
}


// Section: Square Threading

// Module: square_threaded_rod()
// Description:
//   Constructs a square profile threaded screw rod.  This method makes
//   much smoother threads than the naive linear_extrude method.
// Arguments:
//   d = Outer diameter of threaded rod.
//   l = length of threaded rod.
//   pitch = Length between threads.
//   left_handed = if true, create left-handed threads.  Default = false
//   bevel = if true, bevel the thread ends.  Default: false
//   starts = The number of lead starts.  Default = 1
//   orient = Orientation of the rod.  Use the `ORIENT_` constants from `constants.scad`.  Default: `ORIENT_Z`.
//   align = Alignment of the rod.  Use the constants from `constants.scad`.  Default: `CENTER`.
// Examples:
//   square_threaded_rod(d=10, l=30, pitch=2, starts=2, $fn=32);
module square_threaded_rod(
	d=10, l=100, pitch=2,
	left_handed=false,
	bevel=false,
	starts=1,
	orient=ORIENT_Z,
	align=CENTER
) {
	trapezoidal_threaded_rod(
		d=d, l=l, pitch=pitch,
		thread_angle=0,
		left_handed=left_handed,
		bevel=bevel,
		starts=starts,
		orient=orient,
		align=align
	);
}



// Module: square_threaded_nut()
// Description:
//   Constructs a hex nut for a square profile threaded screw rod.  This method
//   makes much smoother threads than the naive linear_extrude method.
// Arguments:
//   od = diameter of the nut.
//   id = diameter of threaded rod to screw onto.
//   h = height/thickness of nut.
//   pitch = Length between threads.
//   left_handed = if true, create left-handed threads.  Default = false
//   bevel = if true, bevel the thread ends.  Default: false
//   starts = The number of lead starts.  Default = 1
//   slop = printer slop calibration to allow for tight fitting of parts.  default=0.2
//   orient = Orientation of the nut.  Use the `ORIENT_` constants from `constants.scad`.  Default: `ORIENT_Z`.
//   align = Alignment of the nut.  Use the constants from `constants.scad`.  Default: `CENTER`.
// Examples:
//   square_threaded_nut(od=16, id=10, h=10, pitch=2, starts=2, slop=0.15, $fn=32);
module square_threaded_nut(
	od=17.4, id=10.5, h=10,
	pitch=3.175,
	left_handed=false,
	bevel=false,
	starts=1,
	slop=PRINTER_SLOP,
	orient=ORIENT_Z,
	align=CENTER
) {
	trapezoidal_threaded_nut(
		od=od, id=id, h=h, pitch=pitch,
		thread_angle=0,
		left_handed=left_handed,
		bevel=bevel,
		starts=starts,
		slop=slop,
		orient=orient,
		align=align
	);
}



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