BOSL2/threading.scad

//////////////////////////////////////////////////////////////////////
// LibFile: threading.scad
//   Provides generic threading support and specialized support for standard triangular (UTS/ISO) threading,
//   trapezoidal threading (ACME), pipe threading, buttress threading, square threading and ball screws.  
// Includes:
//   include <BOSL2/std.scad>
//   include <BOSL2/threading.scad>
// FileGroup: Threaded Parts
// FileSummary: Various types of threaded rods and nuts.
//////////////////////////////////////////////////////////////////////

// Section: Standard (UTS/ISO) Threading

// Module: threaded_rod()
// Usage:
//   threaded_rod(d, l|length, pitch, [internal=], ...) [ATTACHMENTS];
// Description:
//   Constructs a standard ISO (metric) or UTS (English) threaded rod.  These threads are close to triangular,
//   with a 60 degree thread angle.  You can give the outer diameter and get the "basic form" or you can
//   set d to a triplet [d_min, d_pitch, d_major] where are parameters determined by the ISO and UTS specifications
//   that define clearance sizing for the threading.  See screws.scad for how to make screws
//   using the specification parameters.  
// Arguments:
//   d = Outer diameter of threaded rod, or a triplet of [d_min, d_pitch, d_major]. 
//   l / length = length of threaded rod.
//   pitch = Length between threads.
//   ---
//   left_handed = if true, create left-handed threads.  Default = false
//   starts = The number of lead starts.  Default: 1
//   bevel = if true, bevel the thread ends.  Default: false
//   bevel1 = if true bevel the bottom end.
//   bevel2 = if true bevel the top end.
//   internal = If true, make this a mask for making internal threads.
//   d1 = Bottom outside diameter of threads.
//   d2 = Top outside diameter of threads.
//   higbee = If true apply higbee thread truncation at both ends, or set to an angle to adjust higbee cut point.  Default: false
//   higbee1 = If true apply higbee thread truncation at bottom end, or set to an angle to adjust higbee cut point.
//   higbee2 = If true apply higbee thread truncation at top end, or set to an angle to adjust higbee cut point.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
//   orient = Vector to rotate top towards, after spin.  See [orient](attachments.scad#subsection-orient).  Default: `UP`
//   $slop = The printer-specific slop value, which adds clearance (`4*$slop`) to internal threads.
// Example(2D):
//   projection(cut=true)
//       threaded_rod(d=10, l=15, pitch=1.5, orient=BACK);
// Examples(Med):
//   threaded_rod(d=10, l=20, pitch=1.25, left_handed=true, $fa=1, $fs=1);
//   threaded_rod(d=25, l=20, pitch=2, $fa=1, $fs=1);
//   threaded_rod(d=25, l=20, pitch=2, $fa=1, $fs=1, bevel=true);
//   rot(90)threaded_rod(d=25, l=20, pitch=2, $fa=1, $fs=1, higbee=true);
// Example: Diamond threading where both left-handed and right-handed nuts travel (in the same direction) on the threaded rod:
//   $slop = 0.075;
//   d = 3/8*INCH;
//   pitch = 1/16*INCH;
//   starts=3;
//   xdistribute(19){
//       intersection(){
//         threaded_rod(l=40, pitch=pitch, d=d,starts=starts,anchor=BOTTOM);
//         threaded_rod(l=40, pitch=pitch, d=d, left_handed=true,starts=starts,anchor=BOTTOM);
//       }
//       threaded_nut(nutwidth=4.5/8*INCH,id=d,h=3/8*INCH,pitch=pitch,starts=starts,anchor=BOTTOM);
//       threaded_nut(nutwidth=4.5/8*INCH,id=d,h=3/8*INCH,pitch=pitch,starts=starts,left_handed=true,anchor=BOTTOM);
//   }
function threaded_rod(
    d, l, pitch,
    left_handed=false,
    bevel,bevel1,bevel2,starts=1,
    internal=false,
    d1, d2,
    higbee, higbee1, higbee2,
    anchor, spin, orient
) = no_function("threaded_rod");

module threaded_rod(
    d, l, pitch,
    left_handed=false,
    bevel,bevel1,bevel2,starts=1,
    internal=false,
    d1, d2, length, 
    higbee, higbee1, higbee2,
    anchor, spin, orient
) {
    dummy1=
      assert(all_positive(pitch))
      assert(all_positive(d))
      assert(all_positive(l));
    basic = is_num(d) || is_undef(d) || is_def(d1) || is_def(d2);
    dummy2 = assert(basic || is_vector(d,3));
    depth = basic ? cos(30) * 5/8
                  : (d[2] - d[0])/2/pitch;
    crestwidth = basic ? 1/8 : 1/2 - (d[2]-d[1])/sqrt(3)/pitch;
    profile =    [
                  [-depth/sqrt(3)-crestwidth/2, -depth],
                  [              -crestwidth/2,      0],
                  [               crestwidth/2,      0],
                  [ depth/sqrt(3)+crestwidth/2, -depth]
                 ];
    oprofile = internal? [
        [-6/16, -depth],
        [-1/16,  0],
        [-1/32,  0.02],
        [ 1/32,  0.02],
        [ 1/16,  0],
        [ 6/16, -depth]
    ] : [
        [-7/16, -depth*1.07],
        [-6/16, -depth],
        [-1/16,  0],
        [ 1/16,  0],
        [ 6/16, -depth],
        [ 7/16, -depth*1.07]
    ];
    generic_threaded_rod(
        d=basic ? d : d[2], d1=d1, d2=d2, l=l,
        pitch=pitch,
        profile=profile,starts=starts,
        left_handed=left_handed,
        bevel=bevel,bevel1=bevel1,bevel2=bevel2,
        internal=internal, length=length, 
        higbee=higbee,
        higbee1=higbee1,
        higbee2=higbee2,
        anchor=anchor,
        spin=spin,
        orient=orient
    ) children();
}



// Module: threaded_nut()
// Usage:
//   threaded_nut(nutwidth, id, h|height|thickness, pitch,...) [ATTACHMENTS];
// Description:
//   Constructs a hex nut or square nut for an ISO (metric) or UTS (English) threaded rod. 
// Arguments:
//   nutwidth = flat to flat width of nut
//   id = diameter of threaded rod to screw onto.
//   h / height / thickness = height/thickness of nut.
//   pitch = Distance between threads, or zero for no threads. 
//   ---
//   shape = specifies shape of nut, either "hex" or "square".  Default: "hex"
//   left_handed = if true, create left-handed threads.  Default = false
//   starts = The number of lead starts.  Default: 1
//   bevel = if true, bevel the outside of the nut.  Default: true for hex nuts, false for square nuts
//   bevel1 = if true, bevel the outside of the nut bottom.
//   bevel2 = if true, bevel the outside of the nut top. 
//   bevang = set the angle for the outside nut bevel.  Default: 30
//   ibevel = if true, bevel the inside (the hole).   Default: true
//   ibevel1 = if true bevel the inside, bottom end.
//   ibevel2 = if true bevel the inside, top end.
//   higbee = If true apply higbee thread truncation at both ends, or set to an angle to adjust higbee cut point.  Default: false
//   higbee1 = If true apply higbee thread truncation at bottom end, or set to an angle to adjust higbee cut point.
//   higbee2 = If true apply higbee thread truncation at top end, or set to an angle to adjust higbee cut point.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
//   orient = Vector to rotate top towards, after spin.  See [orient](attachments.scad#subsection-orient).  Default: `UP`
//   $slop = The printer-specific slop value, which adds clearance (`4*$slop`) to internal threads.
// Examples(Med):
//   threaded_nut(nutwidth=16, id=8, h=8, pitch=1.25, $slop=0.05, $fa=1, $fs=1);
//   threaded_nut(nutwidth=16, id=8, h=8, pitch=1.25, left_handed=true, bevel=false, $slop=0.1, $fa=1, $fs=1);
//   threaded_nut(shape="square", nutwidth=16, id=8, h=8, pitch=1.25, $slop=0.1, $fa=1, $fs=1);
//   threaded_nut(shape="square", nutwidth=16, id=8, h=8, pitch=1.25, bevel2=true, $slop=0.1, $fa=1, $fs=1);
//   rot(90)threaded_nut(nutwidth=16, id=8, h=8, pitch=1.25,higbee=true, $slop=0.1, $fa=1, $fs=1);
function threaded_nut(
    nutwidth, id, h,
    pitch, starts=1, shape="hex", left_handed=false, bevel, bevel1, bevel2, id1,id2,
    ibevel1, ibevel2, ibevel, bevang=30, thickness, height,     
    anchor, spin, orient
)=no_function("threaded_nut");
module threaded_nut(
    nutwidth, id, h,
    pitch, starts=1, shape="hex", left_handed=false, bevel, bevel1, bevel2, id1,id2,
    ibevel1, ibevel2, ibevel, bevang=30, thickness, height,
    higbee, higbee1, higbee2,
    anchor, spin, orient
) {
    dummy1=
          assert(all_nonnegative(pitch), "Nut pitch must be nonnegative")
          assert(all_positive(id), "Nut inner diameter must be positive")
          assert(all_positive(h),"Nut thickness must be positive");
    basic = is_num(id) || is_undef(id) || is_def(id1) || is_def(id2);
    dummy2 = assert(basic || is_vector(id,3));
    depth = basic ? cos(30) * 5/8
                  : (id[2] - id[0])/2/pitch;
    crestwidth = basic ? 1/8 : 1/2 - (id[2]-id[1])/sqrt(3)/pitch;
    profile =    [
                  [-depth/sqrt(3)-crestwidth/2, -depth],
                  [              -crestwidth/2,      0],
                  [               crestwidth/2,      0],
                  [ depth/sqrt(3)+crestwidth/2, -depth]
                 ];
    oprofile = [
        [-6/16, -depth/pitch],
        [-1/16,  0],
        [-1/32,  0.02],
        [ 1/32,  0.02],
        [ 1/16,  0],
        [ 6/16, -depth/pitch]
    ];
    generic_threaded_nut(
        nutwidth=nutwidth,
        id=basic ? id : id[2], id1=id1, id2=id2,
        h=h,
        pitch=pitch,
        profile=profile,starts=starts,shape=shape, 
        left_handed=left_handed,
        bevel=bevel,bevel1=bevel1,bevel2=bevel2,
        ibevel1=ibevel1, ibevel2=ibevel2, ibevel=ibevel,
        height=height, thickness=thickness, bevang=bevang,
        higbee=higbee, higbee1=higbee1, higbee2=higbee2,
        anchor=anchor, spin=spin,
        orient=orient
    ) children();
}

// Section: Trapezoidal Threading


// Module: trapezoidal_threaded_rod()
// Usage:
//   trapezoidal_threaded_rod(d, l|length, pitch, [thread_angle], [thread_depth], [internal=], ...) [ATTACHMENTS];
// Description:
//   Constructs a threaded rod with a symmetric trapezoidal thread.  Trapezoidal threads are used for lead screws because
//   they are one of the strongest symmetric profiles.  This tooth shape is stronger than a similarly
//   sized square thread becuase of its wider base.  However, it does place a radial load on the nut, unlike the square thread.
//   For loads in only one direction the asymmetric buttress thread profile can bear greater loads.  
//   .
//   By default produces the nominal dimensions
//   for metric trapezoidal threads: a thread angle of 30 degrees and a depth set to half the pitch.
//   You can also specify your own trapezoid parameters.  For ACME threads see acme_threaded_rod().
// Figure(2D,Med,NoAxes):
//   pa_delta = tan(15)/4;
//   rr1 = -1/2;
//   z1 = 1/4-pa_delta;
//   z2 = 1/4+pa_delta;
//   profile = [
//               [-z2, rr1],
//               [-z1,  0],
//               [ z1,  0],
//               [ z2, rr1],
//             ];
//   fullprofile = 50*left(1/2,p=concat(profile, right(1, p=profile)));
//   stroke(fullprofile,width=1);
//   dir = fullprofile[2]-fullprofile[3];
//   dir2 = fullprofile[5]-fullprofile[4];
//   curve = arc(32,angle=[75,105],r=67.5);
//   avgpt = mean([fullprofile[5]+.1*dir2, fullprofile[5]+.4*dir2]);
//   color("red"){
//    stroke([fullprofile[2]+.1*dir, fullprofile[2]+.4*dir], width=1);
//    stroke([fullprofile[5]+.1*dir2, fullprofile[5]+.4*dir2], width=1);
//    stroke(move(-curve[0]+avgpt,p=curve), width=1,endcaps="arrow2");
//    back(10)text("thread",size=4,halign="center");
//    back(3)text("angle",size=4,halign="center");
//   }
// Arguments:
//   d = Outer diameter of threaded rod.
//   l / length = Length of threaded rod.
//   pitch = Thread spacing. 
//   thread_angle = Angle between two thread faces.  Default: 30
//   thread_depth = Depth of threads.  Default: pitch/2
//   ---
//   left_handed = If true, create left-handed threads.  Default: false
//   starts = The number of lead starts.  Default: 1
//   bevel = if true, bevel the thread ends.  Default: false
//   bevel1 = if true bevel the bottom end.
//   bevel2 = if true bevel the top end. 
//   internal = If true, make this a mask for making internal threads.  Default: false
//   d1 = Bottom outside diameter of threads.
//   d2 = Top outside diameter of threads.
//   higbee = If true apply higbee thread truncation at both ends, or set to an angle to adjust higbee cut point.  Default: false
//   higbee1 = If true apply higbee thread truncation at bottom end, or set to an angle to adjust higbee cut point.
//   higbee2 = If true apply higbee thread truncation at top end, or set to an angle to adjust higbee cut point.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
//   orient = Vector to rotate top towards, after spin.  See [orient](attachments.scad#subsection-orient).  Default: `UP`
//   $slop = The printer-specific slop value, which adds clearance (`4*$slop`) to internal threads.
// Example(2D):
//   projection(cut=true)
//       trapezoidal_threaded_rod(d=10, l=15, pitch=2, orient=BACK);
// Examples(Med): 
//   trapezoidal_threaded_rod(d=10, l=40, pitch=2, $fn=32);  // Standard metric threading
//   rot(-65)trapezoidal_threaded_rod(d=10, l=17, pitch=2, higbee=25, $fn=32);  // Standard metric threading
//   trapezoidal_threaded_rod(d=10, l=17, pitch=2, bevel=true, $fn=32);  // Standard metric threading
//   trapezoidal_threaded_rod(d=10, l=30, pitch=2, left_handed=true, $fa=1, $fs=1);  // Standard metric threading
//   trapezoidal_threaded_rod(d=10, l=40, pitch=3, left_handed=true, starts=3, $fn=36);
//   trapezoidal_threaded_rod(l=25, d=10, pitch=2, starts=3, $fa=1, $fs=1, bevel=true, orient=RIGHT, anchor=BOTTOM);
//   trapezoidal_threaded_rod(d=60, l=16, pitch=8, thread_depth=3, thread_angle=90, left_handed=true, $fa=2, $fs=2);
//   trapezoidal_threaded_rod(d=60, l=16, pitch=8, thread_depth=3, thread_angle=90, left_handed=true, starts=4, $fa=2, $fs=2);
//   trapezoidal_threaded_rod(d=16, l=40, pitch=2, thread_angle=60);
//   trapezoidal_threaded_rod(d=25, l=40, pitch=10, thread_depth=8/3, thread_angle=100, starts=4, anchor=BOT, $fa=2, $fs=2);
//   trapezoidal_threaded_rod(d=50, l=35, pitch=8, thread_angle=60, starts=11, higbee=true,$fn=120);
// Example(Med): Using as a Mask to Make Internal Threads
//   bottom_half() difference() {
//       cube(50, center=true);
//       trapezoidal_threaded_rod(d=40, l=51, pitch=5, thread_angle=30, internal=true, bevel=true, orient=RIGHT, $fn=36);
//   }
function trapezoidal_threaded_rod(
    d, l, pitch,
    thread_angle=30,
    thread_depth=undef,
    left_handed=false,
    bevel,bevel1,bevel2,
    starts=1, length,
    internal=false,
    higbee, higbee1, higbee2,d1,d2,
    anchor, spin, orient
) = no_function("trapezoidal_threaded_rod");
module trapezoidal_threaded_rod(
    d, l, pitch,
    thread_angle=30,
    thread_depth=undef,
    left_handed=false,
    bevel,bevel1,bevel2,
    starts=1, length,
    internal=false,
    higbee, higbee1, higbee2,d1,d2,
    anchor, spin, orient
) {
    dummy0 = assert(all_positive(pitch));
    dummy1 = assert(thread_angle>=0 && thread_angle<180);
    depth = first_defined([thread_depth, pitch/2]);
    pa_delta = 0.5*depth*tan(thread_angle/2) / pitch;
    dummy2 = assert(pa_delta<1/4, "Specified thread geometry is impossible");
    rr1 = -depth/pitch;
    z1 = 1/4-pa_delta;
    z2 = 1/4+pa_delta;
    profile = [
               [-z2, rr1],
               [-z1,  0],
               [ z1,  0],
               [ z2, rr1],
              ];
    generic_threaded_rod(d=d,l=l,pitch=pitch,profile=profile,
                         left_handed=left_handed,bevel=bevel,bevel1=bevel1,bevel2=bevel2,starts=starts,internal=internal,d1=d1,d2=d2,
                         higbee=higbee,higbee1=higbee1,higbee2=higbee2,anchor=anchor,spin=spin,orient=orient,length=length)
      children();
}


// Module: trapezoidal_threaded_nut()
// Usage:
//   trapezoidal_threaded_nut(nutwidth, id, h|height|thickness, pitch, [thread_angle], [thread_depth], ...) [ATTACHMENTS];
// Description:
//   Constructs a hex nut or square nut for a symmetric trapzoidal threaded rod.
//   By default produces the nominal dimensions
//   for metric trapezoidal threads: a thread angle of 30 degrees and a depth set to half the pitch.
//   You can also specify your own trapezoid parameters.  For ACME threads see acme_threaded_nut(). 
// Arguments:
//   nutwidth = flat to flat width of nut
//   id = diameter of threaded rod to screw onto.
//   h / height / thickness = height/thickness of nut.
//   pitch = Thread spacing.
//   thread_angle = Angle between two thread faces.  Default: 30
//   thread_depth = Depth of the threads.  Default: pitch/2
//   ---
//   shape = specifies shape of nut, either "hex" or "square".  Default: "hex"
//   left_handed = if true, create left-handed threads.  Default = false
//   starts = The number of lead starts.  Default = 1
//   bevel = if true, bevel the outside of the nut.  Default: true for hex nuts, false for square nuts
//   bevel1 = if true, bevel the outside of the nut bottom.
//   bevel2 = if true, bevel the outside of the nut top. 
//   bevang = set the angle for the outside nut bevel.  Default: 30
//   ibevel = if true, bevel the inside (the hole).   Default: true
//   ibevel1 = if true bevel the inside, bottom end.
//   ibevel2 = if true bevel the inside, top end.
//   higbee = If true apply higbee thread truncation at both ends, or set to an angle to adjust higbee cut point.  Default: false
//   higbee1 = If true apply higbee thread truncation at bottom end, or set to an angle to adjust higbee cut point.
//   higbee2 = If true apply higbee thread truncation at top end, or set to an angle to adjust higbee cut point.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
//   orient = Vector to rotate top towards, after spin.  See [orient](attachments.scad#subsection-orient).  Default: `UP`
//   $slop = The printer-specific slop value, which adds clearance (`4*$slop`) to internal threads.
// Examples(Med):
//   trapezoidal_threaded_nut(nutwidth=16, id=8, h=8, pitch=2, $slop=0.1, anchor=UP);
//   trapezoidal_threaded_nut(nutwidth=16, id=8, h=8, pitch=2, bevel=true, $slop=0.05, anchor=UP);
//   trapezoidal_threaded_nut(nutwidth=17.4, id=10, h=10, pitch=2, $slop=0.1, left_handed=true);
//   trapezoidal_threaded_nut(nutwidth=17.4, id=10, h=10, pitch=2, starts=3, $fa=1, $fs=1, $slop=0.15);
//   trapezoidal_threaded_nut(nutwidth=17.4, id=10, h=10, pitch=2, starts=3, $fa=1, $fs=1, $slop=0.15, higbee=true);
//   trapezoidal_threaded_nut(nutwidth=17.4, id=10, h=10, pitch=0, $slop=0.2);   // No threads
function trapezoidal_threaded_nut(
    nutwidth,
    id,
    h,
    pitch,
    thread_angle=30,
    thread_depth, shape="hex",
    left_handed=false,
    starts=1,
    bevel,bevel1,bevel2,bevang=30,
    ibevel1,ibevel2,ibevel,
    thickness,height,
    id1,id2,
    higbee,higbee1,higbee2,
    anchor, spin, orient
) = no_function("trapezoidal_threaded_nut");
module trapezoidal_threaded_nut(
    nutwidth,
    id,
    h,
    pitch,
    thread_angle=30,
    thread_depth, shape="hex",
    left_handed=false,
    starts=1,
    bevel,bevel1,bevel2,bevang=30,
    ibevel1,ibevel2,ibevel,
    thickness,height,
    id1,id2,
    higbee,higbee1,higbee2,
    anchor, spin, orient
) {
    dummy1 = assert(is_num(pitch) && pitch>=0 && thread_angle>=0 && thread_angle<180);
    depth = first_defined([thread_depth, pitch/2]);
    pa_delta = 0.5*depth*tan(thread_angle/2) / pitch;
    dummy2 = assert(pitch==0 || pa_delta<1/4, "Specified thread geometry is impossible");
    rr1 = -depth/pitch;
    z1 = 1/4-pa_delta;
    z2 = 1/4+pa_delta;
    profile = [
               [-z2, rr1],
               [-z1,  0],
               [ z1,  0],
               [ z2, rr1],
              ];
    generic_threaded_nut(nutwidth=nutwidth,id=id,h=h,pitch=pitch,profile=profile,id1=id1,id2=id2,
                         shape=shape,left_handed=left_handed,bevel=bevel,bevel1=bevel1,bevel2=bevel2,starts=starts,
                         ibevel=ibevel,ibevel1=ibevel1,ibevel2=ibevel2,bevang=bevang,height=height,thickness=thickness,
                         higbee=higbee, higbee1=higbee1, higbee2=higbee2,
                         anchor=anchor,spin=spin,orient=orient)
      children();
}


// Module: acme_threaded_rod()
// Usage:
//   acme_threaded_rod(d, l|length, tpi|pitch=, [internal=], ...) [ATTACHMENTS];
// Description:
//   Constructs an ACME trapezoidal threaded screw rod.  This form has a 29 degree thread angle with a
//   symmetric trapezoidal thread.  
// Arguments:
//   d = Outer diameter of threaded rod.
//   l / length = length of threaded rod.
//   tpi = threads per inch.
//   ---
//   pitch = thread spacing (alternative to tpi)
//   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
//   bevel1 = if true bevel the bottom end.
//   bevel2 = if true bevel the top end. 
//   internal = If true, this is a mask for making internal threads.
//   higbee = If true apply higbee thread truncation at both ends, or set to an angle to adjust higbee cut point.  Default: false
//   higbee1 = If true apply higbee thread truncation at bottom end, or set to an angle to adjust higbee cut point.
//   higbee2 = If true apply higbee thread truncation at top end, or set to an angle to adjust higbee cut point.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
//   orient = Vector to rotate top towards, after spin.  See [orient](attachments.scad#subsection-orient).  Default: `UP`
//   $slop = The printer-specific slop value, which adds clearance (`4*$slop`) to internal threads.
// Example(2D):
//   projection(cut=true)
//       acme_threaded_rod(d=10, l=15, pitch=2, orient=BACK);
// Examples(Med):
//   acme_threaded_rod(d=3/8*INCH, l=20, pitch=1/8*INCH, $fn=32);
//   acme_threaded_rod(d=10, l=30, pitch=2, starts=3, $fa=1, $fs=1);
function acme_threaded_rod(
    d, l, tpi, pitch,
    starts=1,
    left_handed=false,
    bevel,bevel1,bevel2,
    internal=false, length, 
    higbee, higbee1, higbee2,
    anchor, spin, orient
) = no_function("acme_threaded_rod");
module acme_threaded_rod(
    d, l, tpi, pitch,
    starts=1,
    left_handed=false,
    bevel,bevel1,bevel2,
    internal=false, length, 
    higbee, higbee1, higbee2,
    anchor, spin, orient
) {
    dummy = assert(num_defined([pitch,tpi])==1,"Must give exactly one of pitch and tpi");
    pitch = is_undef(pitch) ? INCH/tpi : pitch;
    trapezoidal_threaded_rod(
        d=d, l=l, pitch=pitch,
        thread_angle=29,
        thread_depth=pitch/2,
        starts=starts,
        left_handed=left_handed,
        bevel=bevel,bevel1=bevel1,bevel2=bevel2,
        internal=internal, length=length,
        higbee=higbee,
        anchor=anchor,
        spin=spin,
        orient=orient
    ) children();
}



// Module: acme_threaded_nut()
// Usage:
//   acme_threaded_nut(nutwidth, id, h|height|thickness, tpi|pitch=, [shape=], ...) [ATTACHMENTS];
// Description:
//   Constructs a hexagonal or square nut for an ACME threaded screw rod. 
// Arguments:
//   nutwidth = flat to flat width of nut. 
//   id = diameter of threaded rod to screw onto.
//   h / height / thickness = height/thickness of nut.
//   tpi = threads per inch
//   ---
//   pitch = Thread spacing (alternative to tpi)
//   shape = specifies shape of nut, either "hex" or "square".  Default: "hex"
//   left_handed = if true, create left-handed threads.  Default = false
//   starts = Number of lead starts.  Default: 1
//   bevel = if true, bevel the outside of the nut.  Default: true for hex nuts, false for square nuts
//   bevel1 = if true, bevel the outside of the nut bottom.
//   bevel2 = if true, bevel the outside of the nut top. 
//   bevang = set the angle for the outside nut bevel.  Default: 30
//   ibevel = if true, bevel the inside (the hole).   Default: true
//   ibevel1 = if true bevel the inside, bottom end.
//   ibevel2 = if true bevel the inside, top end.
//   higbee = If true apply higbee thread truncation at both ends, or set to an angle to adjust higbee cut point.  Default: false
//   higbee1 = If true apply higbee thread truncation at bottom end, or set to an angle to adjust higbee cut point.
//   higbee2 = If true apply higbee thread truncation at top end, or set to an angle to adjust higbee cut point.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
//   orient = Vector to rotate top towards, after spin.  See [orient](attachments.scad#subsection-orient).  Default: `UP`
//   $slop = The printer-specific slop value, which adds clearance (`4*$slop`) to internal threads.
// Examples(Med):
//   acme_threaded_nut(nutwidth=16, id=3/8*INCH, h=8, tpi=8, $slop=0.05);
//   acme_threaded_nut(nutwidth=16, id=1/2*INCH, h=10, tpi=12, starts=3, $slop=0.1, $fa=1, $fs=1);
//   acme_threaded_nut(nutwidth=16, id=1/2*INCH, h=10, tpi=12, starts=3, $slop=0.1, $fa=1, $fs=1,ibevel=false,higbee=true);
function acme_threaded_nut(
    nutwidth, id, h, tpi, pitch,
    starts=1,
    left_handed=false,shape="hex",
    bevel,bevel1,bevel2,bevang=30,
    ibevel,ibevel1,ibevel2,
    height,thickness,
    higbee,higbee1,higbee2,
    anchor, spin, orient
) = no_function("acme_threaded_nut");
module acme_threaded_nut(
    nutwidth, id, h, tpi, pitch,
    starts=1,
    left_handed=false,shape="hex",
    bevel,bevel1,bevel2,bevang=30,
    ibevel,ibevel1,ibevel2,
    height,thickness,
    higbee,higbee1,higbee2,
    anchor, spin, orient
) {
    dummy = assert(num_defined([pitch,tpi])==1,"Must give exactly one of pitch and tpi");
    pitch = is_undef(pitch) ? INCH/tpi : pitch;
    dummy2=assert(is_num(pitch) && pitch>=0);
    trapezoidal_threaded_nut(
        nutwidth=nutwidth, id=id, h=h, pitch=pitch,
        thread_depth = pitch/2, 
        thread_angle=29,shape=shape, 
        left_handed=left_handed,
        bevel=bevel,bevel1=bevel1,bevel2=bevel2,
        ibevel=ibevel,ibevel1=ibevel1,ibevel2=ibevel2,
        height=height,thickness=thickness,
        starts=starts,
        higbee=higbee, higbee1=higbee1, higbee2=higbee2,
        anchor=anchor,
        spin=spin,
        orient=orient
    ) children();
}




// Section: Pipe Threading

// Module: npt_threaded_rod()
// Usage:
//   npt_threaded_rod(size, [internal=], ...) [ATTACHMENTS];
// Description:
//   Constructs a standard NPT pipe end threading. If `internal=true`, creates a mask for making
//   internal pipe threads.  Tapers smaller upwards if `internal=false`.  Tapers smaller downwards
//   if `internal=true`.  If `hollow=true` and `internal=false`, then the pipe threads will be
//   hollowed out into a pipe with the apropriate internal diameter.
// Arguments:
//   size = NPT standard pipe size in inches.  1/16", 1/8", 1/4", 3/8", 1/2", 3/4", 1", 1+1/4", 1+1/2", or 2".  Default: 1/2"
//   ---
//   left_handed = If true, create left-handed threads.  Default = false
//   bevel = if true, bevel the thread ends.  Default: false
//   bevel1 = if true bevel the bottom end.
//   bevel2 = if true bevel the top end. 
//   hollow = If true, create a pipe with the correct internal diameter.
//   internal = If true, make this a mask for making internal threads.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
//   orient = Vector to rotate top towards, after spin.  See [orient](attachments.scad#subsection-orient).  Default: `UP`
//   $slop = The printer-specific slop value, which adds clearance (`4*$slop`) to internal threads.
// Example(2D): The straight gray rectangle reveals the tapered threads.  
//   projection(cut=true) npt_threaded_rod(size=1/4, orient=BACK);
//   right(.533*INCH/2) color("gray") rect([2,0.5946*INCH],anchor=LEFT);
// Examples(Med):
//   npt_threaded_rod(size=3/8, $fn=72);
//   npt_threaded_rod(size=1/2, $fn=72, bevel=true);
//   npt_threaded_rod(size=1/2, left_handed=true, $fn=72);
//   npt_threaded_rod(size=3/4, hollow=true, $fn=96);
// Example:
//   diff("remove"){
//      cuboid([40,40,40])
//      tag("remove"){
//        up(.01)position(TOP)
//            npt_threaded_rod(size=3/4, $fn=96, internal=true, $slop=0.1, anchor=TOP);
//        cyl(d=3/4*INCH, l=42, $fn=32);
//      }
//   }
function npt_threaded_rod(
    size=1/2,
    left_handed=false,
    bevel,bevel1,bevel2,
    hollow=false,
    internal=false,
    anchor, spin, orient
)=no_function("npt_threaded_rod");
module npt_threaded_rod(
    size=1/2,
    left_handed=false,
    bevel,bevel1,bevel2,
    hollow=false,
    internal=false,
    anchor, spin, orient
) {
    assert(is_finite(size));
    assert(is_bool(left_handed));
    assert(is_undef(bevel) || is_bool(bevel));
    assert(is_bool(hollow));
    assert(is_bool(internal));
    assert(!(internal&&hollow), "Cannot created a hollow internal threads mask.");
    info_table = [
        // Size    len      OD    TPI
        [ 1/16,  [ 0.3896, 0.308, 27  ]],
        [ 1/8,   [ 0.3924, 0.401, 27  ]],
        [ 1/4,   [ 0.5946, 0.533, 18  ]],
        [ 3/8,   [ 0.6006, 0.668, 18  ]],
        [ 1/2,   [ 0.7815, 0.832, 14  ]],
        [ 3/4,   [ 0.7935, 1.043, 14  ]],
        [ 1,     [ 0.9845, 1.305, 11.5]],
        [ 1+1/4, [ 1.0085, 1.649, 11.5]],
        [ 1+1/2, [ 1.0252, 1.888, 11.5]],
        [ 2,     [ 1.0582, 2.362, 11.5]],
    ];
    info = [for (data=info_table) if(approx(size,data[0])) data[1]][0];
    dummy1 = assert(is_def(info), "Unsupported NPT size.  Try one of 1/16, 1/8, 1/4, 3/8, 1/2, 3/4, 1, 1+1/4, 1+1/2, 2");
    l = INCH * info[0];
    d = INCH * info[1];
    pitch = INCH / info[2];
    rr = d/2;
    rr2 = rr - l/32;
    r1 = internal? rr2 : rr;
    r2 = internal? rr : rr2;
    depth = pitch * cos(30) * 5/8;
    profile = internal? [
        [-6/16, -depth/pitch],
        [-1/16,  0],
        [-1/32,  0.02],
        [ 1/32,  0.02],
        [ 1/16,  0],
        [ 6/16, -depth/pitch]
    ] : [
        [-7/16, -depth/pitch*1.07],
        [-6/16, -depth/pitch],
        [-1/16,  0],
        [ 1/16,  0],
        [ 6/16, -depth/pitch],
        [ 7/16, -depth/pitch*1.07]
    ];
    attachable(anchor,spin,orient, l=l, r1=r1, r2=r2) {
        difference() {
            generic_threaded_rod(
                d1=2*r1, d2=2*r2, l=l,
                pitch=pitch,
                profile=profile,
                left_handed=left_handed,
                bevel=bevel,bevel1=bevel1,bevel2=bevel2,
                internal=internal,
                higbee=true
            );
            if (hollow) cylinder(l=l+1, d=size*INCH, center=true);
        }
        children();
    }
}



// Section: Buttress Threading

// Module: buttress_threaded_rod()
// Usage:
//   buttress_threaded_rod(d, l|length, pitch, [internal=], ...) [ATTACHMENTS];
// Description:
//   Constructs a simple buttress threaded rod with a 45 degree angle.  The buttress thread or sawtooth thread has low friction and high loading
//   in one direction at the cost of higher friction and inferior loading in the other direction.  Buttress threads are sometimes used on
//   vises, which are loaded only in one direction.  
// Arguments:
//   d = Outer diameter of threaded rod.
//   l / length = length of threaded rod.
//   pitch = Thread spacing.
//   ---
//   left_handed = if true, create left-handed threads.  Default = false
//   starts = Number of lead starts.  Default: 1
//   bevel = if true, bevel the thread ends.  Default: false
//   bevel1 = if true bevel the bottom end.
//   bevel2 = if true bevel the top end. 
//   internal = If true, this is a mask for making internal threads.
//   higbee = If true apply higbee thread truncation at both ends, or set to an angle to adjust higbee cut point.  Default: false
//   higbee1 = If true apply higbee thread truncation at bottom end, or set to an angle to adjust higbee cut point.
//   higbee2 = If true apply higbee thread truncation at top end, or set to an angle to adjust higbee cut point.
//   d1 = Bottom outside diameter of threads.
//   d2 = Top outside diameter of threads.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
//   orient = Vector to rotate top towards, after spin.  See [orient](attachments.scad#subsection-orient).  Default: `UP`
//   $slop = The printer-specific slop value, which adds clearance (`4*$slop`) to internal threads.
// Example(2D):
//   projection(cut=true)
//       buttress_threaded_rod(d=10, l=15, pitch=2, orient=BACK);
// Examples(Med):
//   buttress_threaded_rod(d=10, l=20, pitch=1.25, left_handed=true, $fa=1, $fs=1);
//   buttress_threaded_rod(d=25, l=20, pitch=2, $fa=1, $fs=1);
function buttress_threaded_rod(
    d, l, pitch,
    left_handed=false,
    bevel,bevel1,bevel2,
    internal=false,
    higbee, higbee1, higbee2,
    d1,d2,starts=1,length, 
    anchor, spin, orient
) = no_function("buttress_threaded_rod");
module buttress_threaded_rod(
    d, l, pitch,
    left_handed=false,
    bevel,bevel1,bevel2,
    internal=false,
    higbee,higbee1,higbee2,
    d1,d2,starts=1,length, 
    anchor, spin, orient
) {
    depth = pitch * 3/4;
    profile = [
        [ -7/16, -0.75],
        [  5/16,  0],
        [  7/16,  0],
        [  7/16, -0.75],
        [  1/ 2, -0.77],
    ];
    higbee2 = !internal || (!higbee && !higbee2) ? higbee2
            : let (higval = first_defined([higbee2,higbee]))
              is_num(higval) ? higval + 270
            : 270;
    generic_threaded_rod(
        d=d, l=l, pitch=pitch,
        profile=profile, 
        left_handed=left_handed,
        bevel=bevel,bevel1=bevel1,bevel2=bevel2,
        internal=internal,
        higbee=higbee,
        higbee1=higbee1,
        higbee2=higbee2,
        d1=d1,d2=d2,
        anchor=anchor,length=length, 
        spin=spin,starts=starts,
        orient=orient
    ) children();
}



// Module: buttress_threaded_nut()
// Usage:
//   buttress_threaded_nut(nutwidth, id, h|height|thickness, pitch, ...) [ATTACHMENTS];
// Description:
//   Constructs a hexagonal or square nut for a simple buttress threaded screw rod.  
// Arguments:
//   nutwidth = diameter of the nut.
//   id = diameter of threaded rod to screw onto.
//   h = height/thickness of nut.
//   pitch = Thread spacing. 
//   ---
//   shape = specifies shape of nut, either "hex" or "square".  Default: "hex"
//   left_handed = if true, create left-handed threads.  Default = false
//   starts = The number of lead starts.  Default: 1
//   bevel = if true, bevel the outside of the nut.  Default: true for hex nuts, false for square nuts
//   bevel1 = if true, bevel the outside of the nut bottom.
//   bevel2 = if true, bevel the outside of the nut top. 
//   bevang = set the angle for the outside nut bevel.  Default: 30
//   ibevel = if true, bevel the inside (the hole).   Default: true
//   ibevel1 = if true bevel the inside, bottom end.
//   ibevel2 = if true bevel the inside, top end.
//   higbee = If true apply higbee thread truncation at both ends, or set to an angle to adjust higbee cut point.  Default: false
//   higbee1 = If true apply higbee thread truncation at bottom end, or set to an angle to adjust higbee cut point.
//   higbee2 = If true apply higbee thread truncation at top end, or set to an angle to adjust higbee cut point.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
//   orient = Vector to rotate top towards, after spin.  See [orient](attachments.scad#subsection-orient).  Default: `UP`
//   $slop = The printer-specific slop value, which adds clearance (`4*$slop`) to internal threads.
// Examples(Med):
//   buttress_threaded_nut(nutwidth=16, id=8, h=8, pitch=1.25, left_handed=true, $slop=0.05, $fa=1, $fs=1);
function buttress_threaded_nut(
    nutwidth, id, h,
    pitch, shape="hex", left_handed=false,
    bevel,bevel1,bevel2,bevang=30,starts=1,
    ibevel,ibevel1,ibevel2,height,thickness,
    higbee,higbee1,higbee2,
    anchor, spin, orient
) = no_function("buttress_threaded_nut");
module buttress_threaded_nut(
    nutwidth, id, h,
    pitch, shape="hex", left_handed=false,
    bevel,bevel1,bevel2,bevang=30,starts=1,
    ibevel,ibevel1,ibevel2,height,thickness,
    higbee,higbee1,higbee2,
    anchor, spin, orient
) {
    depth = pitch * 3/4;
    profile = [
        [ -7/16, -0.75],
        [  5/16,  0],
        [  7/16,  0],
        [  7/16, -0.75],
        [  1/ 2, -0.77],
    ];
    higbee2 = !higbee && !higbee2 ? higbee2
            : let (higval = first_defined([higbee2,higbee]))
              is_num(higval) ? higval + 270
            : 270;
    generic_threaded_nut(
        nutwidth=nutwidth, id=id, h=h,
        pitch=pitch,
        profile=profile,
        shape=shape,
        left_handed=left_handed,starts=starts,
        bevel=bevel,bevel1=bevel1,bevel2=bevel2,bevang=bevang,
        ibevel=ibevel,ibevel1=ibevel1,ibevel2=ibevel2,
        higbee=higbee, higbee1=higbee1, higbee2=higbee2,
        anchor=anchor, spin=spin, height=height, thickness=thickness, 
        orient=orient
    ) children();
}



// Section: Square Threading

// Module: square_threaded_rod()
// Usage:
//   square_threaded_rod(d, l|length, pitch, [internal=], ...) [ATTACHMENTS];
// Description:
//   Constructs a square profile threaded screw rod.  The greatest advantage of square threads is that they have the least friction and a much higher intrinsic efficiency than trapezoidal threads.
//   They produce no radial load on the nut.  However, square threads cannot carry as much load as trapezoidal threads. 
// Arguments:
//   d = Outer diameter of threaded rod.
//   l / length = length of threaded rod.
//   pitch = Thread spacing.
//   ---
//   left_handed = if true, create left-handed threads.  Default = false
//   starts = The number of lead starts.  Default = 1
//   bevel = if true, bevel the thread ends.  Default: false
//   bevel1 = if true bevel the bottom end.
//   bevel2 = if true bevel the top end. 
//   internal = If true, this is a mask for making internal threads.
//   higbee = If true apply higbee thread truncation at both ends, or set to an angle to adjust higbee cut point.  Default: false
//   higbee1 = If true apply higbee thread truncation at bottom end, or set to an angle to adjust higbee cut point.
//   higbee2 = If true apply higbee thread truncation at top end, or set to an angle to adjust higbee cut point.
//   d1 = Bottom outside diameter of threads.
//   d2 = Top outside diameter of threads.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
//   orient = Vector to rotate top towards, after spin.  See [orient](attachments.scad#subsection-orient).  Default: `UP`
//   $slop = The printer-specific slop value, which adds clearance (`4*$slop`) to internal threads.
// Example(2D):
//   projection(cut=true)
//       square_threaded_rod(d=10, l=15, pitch=2, orient=BACK);
// Examples(Med):
//   square_threaded_rod(d=10, l=20, pitch=2, starts=2, $fn=32);
function square_threaded_rod(
    d, l, pitch,
    left_handed=false,
    bevel,bevel1,bevel2,
    starts=1,
    internal=false,
    higbee, higbee1, higbee2,
    d1,d2,
    anchor, spin, orient
) = no_function("square_threaded_rod");
module square_threaded_rod(
    d, l, pitch,
    left_handed=false,
    bevel,bevel1,bevel2,
    starts=1,
    internal=false,
    higbee=0, higbee1, higbee2,
    d1,d2,length,
    anchor, spin, orient
) {
    trapezoidal_threaded_rod(
        d=d, l=l, pitch=pitch,
        thread_angle=0.1,
        left_handed=left_handed,
        bevel=bevel,bevel1=bevel1,bevel2=bevel2,
        starts=starts,
        internal=internal,
        higbee=higbee,
        higbee1=higbee1,
        higbee2=higbee2,
        d1=d1,
        d2=d2,
        length=length,
        anchor=anchor,
        spin=spin,
        orient=orient
    ) children();
}



// Module: square_threaded_nut()
// Usage:
//   square_threaded_nut(nutwidth, id, h|height|thickness, pitch, ...) [ATTACHMENTS];
// Description:
//   Constructs a hexagonal or square nut for a square profile threaded screw rod.  
// Arguments:
//   nutwidth = diameter of the nut.
//   id = diameter of threaded rod to screw onto.
//   h / height / thickness = height/thickness of nut.
//   pitch = Length between threads.
//   ---
//   shape = specifies shape of nut, either "hex" or "square".  Default: "hex"
//   left_handed = if true, create left-handed threads.  Default = false
//   starts = The number of lead starts.  Default = 1
//   bevel = if true, bevel the outside of the nut.  Default: true for hex nuts, false for square nuts
//   bevel1 = if true, bevel the outside of the nut bottom.
//   bevel2 = if true, bevel the outside of the nut top. 
//   bevang = set the angle for the outside nut bevel.  Default: 30
//   ibevel = if true, bevel the inside (the hole).   Default: true
//   ibevel1 = if true bevel the inside, bottom end.
//   ibevel2 = if true bevel the inside, top end.
//   higbee = If true apply higbee thread truncation at both ends, or set to an angle to adjust higbee cut point.  Default: false
//   higbee1 = If true apply higbee thread truncation at bottom end, or set to an angle to adjust higbee cut point.
//   higbee2 = If true apply higbee thread truncation at top end, or set to an angle to adjust higbee cut point.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
//   orient = Vector to rotate top towards, after spin.  See [orient](attachments.scad#subsection-orient).  Default: `UP`
//   $slop = The printer-specific slop value, which adds clearance (`4*$slop`) to internal threads.
// Examples(Med):
//   square_threaded_nut(nutwidth=16, id=10, h=10, pitch=2, starts=2, $slop=0.1, $fn=32);
function square_threaded_nut(
    nutwidth, id, h,
    pitch,
    left_handed=false,
    bevel,bevel1,bevel2,bevang=30,
    ibevel,ibevel1,ibevel2,
    height,thickness,    
    starts=1,
    higbee,higbee1,higbee2,
    anchor, spin, orient
) = no_function("square_threaded_nut");
module square_threaded_nut(
    nutwidth, id, h,
    pitch,
    left_handed=false,
    bevel,bevel1,bevel2,bevang=30,
    ibevel,ibevel1,ibevel2,
    height,thickness,    
    higbee,higbee1,higbee2,
    starts=1,
    anchor, spin, orient
) {
    assert(is_num(pitch) && pitch>=0)
    trapezoidal_threaded_nut(
        nutwidth=nutwidth, id=id, h=h, pitch=pitch,
        thread_angle=0,
        left_handed=left_handed,
        bevel=bevel,bevel1=bevel1,bevel2=bevel2, bevang=bevang,
        ibevel=ibevel, ibevel1=ibevel1, ibevel2=ibevel2,
        height=height,thickness=thickness,
        starts=starts,
        higbee=higbee, higbee1=higbee1, higbee2=higbee2,
        anchor=anchor,
        spin=spin,
        orient=orient
    ) children();
}


// Section: Ball Screws

// Module: ball_screw_rod()
// Usage:
//   ball_screw_rod(d, l|length, pitch, [ball_diam], [ball_arc], [internal=], ...) [ATTACHMENTS];
// Description:
//   Constructs a ball screw rod.  This type of rod is used with ball bearings.  
// Arguments:
//   d = Outer diameter of threaded rod.
//   l / length = length of threaded rod.
//   pitch = Thread spacing. Also, the diameter of the ball bearings used.
//   ball_diam = The diameter of the ball bearings to use with this ball screw.
//   ball_arc = The arc portion that should touch the ball bearings. Default: 120 degrees.
//   ---
//   left_handed = if true, create left-handed threads.  Default = false
//   starts = The number of lead starts.  Default = 1
//   bevel = if true, bevel the thread ends.  Default: false
//   bevel1 = if true bevel the bottom end.
//   bevel2 = if true bevel the top end. 
//   internal = If true, make this a mask for making internal threads.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
//   orient = Vector to rotate top towards, after spin.  See [orient](attachments.scad#subsection-orient).  Default: `UP`
//   $slop = The printer-specific slop value, which adds clearance (`4*$slop`) to internal threads.
// Example(2D): Thread Profile, ball_diam=4, ball_arc=100
//   projection(cut=true) ball_screw_rod(d=10, l=15, pitch=5, ball_diam=4, ball_arc=100, orient=BACK, $fn=24);
// Example(2D): Thread Profile, ball_diam=4, ball_arc=120
//   projection(cut=true) ball_screw_rod(d=10, l=15, pitch=5, ball_diam=4, ball_arc=120, orient=BACK, $fn=24);
// Example(2D): Thread Profile, ball_diam=3, ball_arc=120
//   projection(cut=true) ball_screw_rod(d=10, l=15, pitch=5, ball_diam=3, ball_arc=120, orient=BACK, $fn=24);
// Examples(Med):
//   ball_screw_rod(d=15, l=20, pitch=8, ball_diam=5, ball_arc=120, $fa=1, $fs=0.5);
//   ball_screw_rod(d=15, l=20, pitch=5, ball_diam=4, ball_arc=120, $fa=1, $fs=0.5);
//   ball_screw_rod(d=15, l=20, pitch=5, ball_diam=4, ball_arc=120, left_handed=true, $fa=1, $fs=0.5);
function ball_screw_rod(
    d, l, pitch, 
    ball_diam=5, ball_arc=100,
    starts=1,
    left_handed=false,
    internal=false,
    bevel,bevel1,bevel2, length, 
    anchor, spin, orient
) = no_function("ball_screw_rod");
module ball_screw_rod(
    d, l, pitch, 
    ball_diam=5, ball_arc=100,
    starts=1,
    left_handed=false,
    internal=false,
    bevel,bevel1,bevel2, length, 
    anchor, spin, orient
) {
    n = max(3,ceil(segs(ball_diam/2)*ball_arc/2/360));
    depth = ball_diam * (1-cos(ball_arc/2))/2;
    cpy = ball_diam/2/pitch*cos(ball_arc/2);
    profile = [
        each arc(n=n, d=ball_diam/pitch, cp=[-0.5,cpy], start=270, angle=ball_arc/2),
        each arc(n=n, d=ball_diam/pitch, cp=[+0.5,cpy], start=270-ball_arc/2, angle=ball_arc/2)
    ];
    generic_threaded_rod(
        d=d, l=l, pitch=pitch,
        profile=profile,
        left_handed=left_handed,
        starts=starts,
        bevel=bevel,bevel1=bevel1,bevel2=bevel2,
        internal=internal,
        higbee=0, length=length, 
        anchor=anchor,
        spin=spin,
        orient=orient
    ) children();
}



// Section: Generic Threading

// Module: generic_threaded_rod()
// Usage:
//   generic_threaded_rod(d, l|length, pitch, profile, [internal=], ...) [ATTACHMENTS];
// Description:
//   Constructs a generic threaded rod using an arbitrary thread profile that you supply.  The rod can be tapered (e.g. for pipe threads).
//   For specific thread types use other modules that supply the appropriate profile.
//   .
//   You give the profile as a 2D path that will be scaled by the pitch to produce the final thread shape.  The profile X values
//   must be between -1/2 and 1/2.  The Y=0 point will align with the specified rod diameter, so generally you want a Y value of zero at the peak (which
//   makes your specified diameter the outer diameter of the threads).  
//   The value in the valleys of the thread should then be `-depth/pitch` due to the scaling by the thread pitch.  The segment between the end
//   of one thread and the start of the next is added automatically, so you should not have the path start and end at equivalent points (X = ±1/2 with the same Y value).
//   Generally you should center the profile horizontally in the interval [-1/2, 1/2].
//   .
//   If internal is true then produce a thread mask to difference from an object.
//   When internal is true the rod diameter is enlarged to correct for the polygonal nature of circles to ensure that the internal diameter is the specified size.
//   The diameter is also increased by `4 * $slop` to create clearance for threading by allowing a `2 * $slop` gap on each side. 
//   If bevel is set to true and internal is false then the ends of the rod will be beveled.  When bevel is true and internal is true the ends of the rod will
//   be filled in so that the rod mask will create a bevel when subtracted from an object.  The bevel is at 45 deg and is the depth of the threads.
//   .
//   Higbee or blunt start threading specifies that the thread ends abruptly at its full width instead of running off the end of the shaft and leaving a sharp edged partial
//   thread at the end of the screw.  This makes screws easier to start and
//   prevents cross threading.  If you set `higbee=true` then the blunt start applies to both ends.  The blunt start cuts the thread end in a single facet, 
//   so if you use lots of facets it will be close to perpendicular to the screw surface, but if you use fewer facets, it will be a more sloped cut.  
//   The place to cut the threads is calculated to try to leave a 1/4 thread gap from the end of the screw, but depending on your profile, you may
//   wish to adjust this.  If you set higbee to a numerical value it will be added to the computed higbee angle, so a positive value will cut the thread back farther
//   giving more space at the end.  Higbee works on both internal and external threads.  
// Arguments:
//   d = Outer diameter of threaded rod.
//   l / length = Length of threaded rod.
//   pitch = Thread spacing.
//   profile = A 2D path giving the shape of a thread
//   ---
//   left_handed = If true, create left-handed threads.  Default: false
//   starts = The number of lead starts.  Default: 1
//   bevel = if true, bevel the thread ends.  Default: false
//   bevel1 = if true bevel the bottom end.
//   bevel2 = if true bevel the top end. 
//   internal = If true, make this a mask for making internal threads.  Default: false
//   d1 = Bottom outside diameter of threads.
//   d2 = Top outside diameter of threads.
//   higbee = If true apply higbee thread truncation at both ends, or set to an angle to adjust higbee cut point.  Default: false
//   higbee1 = If true apply higbee thread truncation at bottom end, or set to an angle to adjust higbee cut point.
//   higbee2 = If true apply higbee thread truncation at top end, or set to an angle to adjust higbee cut point.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
//   orient = Vector to rotate top towards, after spin.  See [orient](attachments.scad#subsection-orient).  Default: `UP`
//   $slop = The printer-specific slop value, which adds clearance (`4*$slop`) to internal threads.
// Example(2DMed): Example Tooth Profile
//   pitch = 2;
//   depth = pitch * cos(30) * 5/8;
//   profile = [
//       [-7/16, -depth/pitch*1.07],
//       [-6/16, -depth/pitch],
//       [-1/16,  0],
//       [ 1/16,  0],
//       [ 6/16, -depth/pitch],
//       [ 7/16, -depth/pitch*1.07]
//   ];
//   stroke(profile, width=0.02);
// Example:
//   pitch = 2;
//   depth = pitch * cos(30) * 5/8;
//   profile = [
//       [-7/16, -depth/pitch*1.07],
//       [-6/16, -depth/pitch],
//       [-1/16,  0],
//       [ 1/16,  0],
//       [ 6/16, -depth/pitch],
//       [ 7/16, -depth/pitch*1.07]
//   ];
//   generic_threaded_rod(d=10, l=40, pitch=2, profile=profile);
function generic_threaded_rod(
    d, l, pitch, profile,
    left_handed=false,
    bevel,
    bevel1, bevel2, 
    starts=1,
    internal=false,
    d1, d2, length,
    higbee, higbee1, higbee2,
    anchor, spin, orient
) = no_function("generic_threaded_rod");
module generic_threaded_rod(
    d, l, pitch, profile,
    left_handed=false,
    bevel,
    bevel1, bevel2, 
    starts=1,
    internal=false,
    d1, d2, length,
    higbee, higbee1, higbee2,
    anchor, spin, orient
) {
    l = one_defined([l,length],"l,length");
    bevel1 = first_defined([bevel1,bevel,false]);
    bevel2 = first_defined([bevel2,bevel,false]);
    thigbee1 = first_defined([higbee1,higbee,false]);
    thigbee2 = first_defined([higbee2,higbee,false]);
    // Zero higbee should be treated as "true", default angle, but it tests as false so adjust
    higbee1 = thigbee1==0 ? true : thigbee1;
    higbee2 = thigbee2==0 ? true : thigbee2;
    dummy0 = 
      assert(all_positive([pitch]),"Thread pitch must be a positive value")
      assert(all_positive([l]),"Length must be a postive value")
      assert(is_path(profile),"Profile must be a path")
      assert(is_finite(higbee1) || is_bool(higbee1), str("higbee",is_undef(higbee)?"1":""," must be boolean or a number"))
      assert(is_finite(higbee2) || is_bool(higbee2), str("higbee",is_undef(higbee)?"1":""," must be boolean or a number"))
      assert(is_bool(left_handed));
    r1 = get_radius(d1=d1, d=d);
    r2 = get_radius(d1=d2, d=d);
    sides = quantup(segs(max(r1,r2)), starts);
    rsc = internal? (1/cos(180/sides)) : 1;
    islop = internal? 2*get_slop() : 0;
    _r1 = r1 * rsc + islop;
    _r2 = r2 * rsc + islop;
    threads = quantup(l/pitch+2,1); // Was quantup(1/pitch+2,2*starts);
    dir = left_handed? -1 : 1;
    twist = 360 * l / pitch / starts;
    profile = !internal ? profile
            : [
                 for(entry=profile) if (entry.x>=0) [entry.x-1/2,entry.y], 
                 for(entry=profile) if (entry.x<0) [entry.x+1/2,entry.y]
              ];
    gap = 0.25;
    thread_minx = min(column(profile,0));
    thread_maxx = max(column(profile,0));
    // Compute higbee cut angles, or set to large negative value if higbee is not enabled
    higang1 = !higbee1 ? -1000
                       : (180+(gap-(thread_minx+.5))*360)/starts + (is_num(higbee1) ? higbee1 : 0);
    higang2 = !higbee2 ? -1000
                       : (180+(gap-(.5-thread_maxx))*360)/starts + (is_num(higbee2) ? higbee2 : 0);
    prof3d = path3d(profile);
    pdepth = -min(column(profile,1));
    pmax = pitch * max(column(profile,1));
    rmax = max(_r1,_r2)+pmax;
    depth = pdepth * pitch;
    dummy1 = assert(_r1>depth && _r2>depth, "Screw profile deeper than rod radius");
    map_threads = right((_r1 + _r2) / 2)                   // Shift profile out to thread radius
                * affine3d_skew(sxz=(_r2-_r1)/l)           // Skew correction for tapered threads
                * frame_map(x=[0,0,1], y=[1,0,0])          // Map profile to 3d, parallel to z axis
                * scale(pitch);                            // scale profile by pitch
    start_steps = sides / starts;
    thread_verts = [
         // Outer loop constructs a vertical column of the screw at each angle
         // covering 1/starts * 360 degrees of the cylinder.  
         for (step = [0:1:start_steps]) let(
             ang = 360 * step/sides,
             dz = step / start_steps,    // z offset for threads at this angle
             rot_prof = zrot(ang*dir)*map_threads,   // Rotate profile to correct angular location
             full_profile =  [   // profile for the entire rod
                 for (thread = [-threads/2:1:threads/2-1]) let(
                     tang = (thread/starts) * 360 + ang,
                     adjusted_prof3d = tang < -twist/2+higang1 || tang > twist/2-higang2 
                                           ? [for(v=prof3d) [v.x,internal?pmax/pitch:-pdepth,v.z]] 
                                     : prof3d
                 )
                 // The right movement finds the position of the thread along
                 // what will be the z axis after the profile is mapped to 3d                                           
                 each apply(right(dz + thread) , adjusted_prof3d)
             ]
         ) [
             [0, 0, -l/2-pitch],
             each apply(rot_prof , full_profile),
             [0, 0, +l/2+pitch]
         ]
    ];
    style=internal?"concave":"convex";
    
    thread_vnfs = vnf_join([
        // Main thread faces
        for (i=[0:1:starts-1])
            zrot(i*360/starts, p=vnf_vertex_array(thread_verts, reverse=left_handed, style=style)),
        // Top closing face(s) of thread                                 
        for (i=[0:1:starts-1]) let(
            rmat = zrot(i*360/starts),
            pts = deduplicate(list_head(thread_verts[0], len(prof3d)+1)),
            faces = [for (i=idx(pts,e=-2)) left_handed ? [0, i, i+1] : [0, i+1, i]]
        ) [apply(rmat,pts), faces],
        // Bottom closing face(s) of thread                                 
        for (i=[0:1:starts-1]) let(
            rmat = zrot(i*360/starts),
            pts = deduplicate(list_tail(last(thread_verts), -len(prof3d)-2)),
            faces = [for (i=idx(pts,e=-2)) left_handed ? [len(pts)-1, i+1, i] : [len(pts)-1, i, i+1]]
        ) [apply(rmat,pts), faces]
    ]);

    slope = (_r1-_r2)/l;
    maxlen = 2*pitch;

    attachable(anchor,spin,orient, r1=_r1, r2=_r2, l=l) {
        union(){

          // This method is faster but more complex code and it produces green tops
          difference() {
              vnf_polyhedron(vnf_quantize(thread_vnfs),convexity=10);

              if (!internal){
                  if (bevel1 || bevel2)
                      rotate_extrude(){
                         if (bevel2) polygon([[             0, l/2],
                                              [_r2+pmax-depth, l/2],
                                              [_r2+pmax+slope*depth, l/2-depth],
                                              [              rmax+1, l/2-depth],
                                              [rmax+1, l/2+maxlen],
                                              [     0, l/2+maxlen]]);
                         if (bevel1) polygon([[             0,-l/2],
                                              [_r1+pmax-depth, -l/2],
                                              [_r1+pmax-slope*depth, -l/2+depth],
                                              [              rmax+1, -l/2+depth],
                                              [rmax+1, -l/2-maxlen],
                                              [     0, -l/2-maxlen]]);
                      }
              }
              if (!bevel1 || internal)
                  down(l/2) cuboid([2*rmax+1,2*rmax+1, maxlen], anchor=TOP);                     
              if (!bevel2 || internal)
                  up(l/2) cuboid([2*rmax+1,2*rmax+1, maxlen], anchor=BOTTOM);
          }

          /*  // slower, simpler approach for beveling
          intersection(){
              //vnf_validate(vnf_quantize(thread_vnfs), size=0.1);
              vnf_polyhedron(vnf_quantize(thread_vnfs), convexity=10);
              cyl(l=l, r1=_r1+pmax, r2=_r2+pmax, chamfer1=bevel1?depth:undef, chamfer2=bevel2?depth:undef);                  
          }
          */

          // Add bevel for internal thread mask
          if (internal) {
            if (bevel1)
              down(l/2+.001)cyl(l=depth, r1=_r1+pmax, r2=_r1+pmax-slope*depth-depth,anchor=BOTTOM);
            if (bevel2)
              up(l/2+.001)cyl(l=depth, r2=_r2+pmax, r1=_r2+pmax+slope*depth-depth,anchor=TOP);
          }
        }
        children();
    }
}



// Module: generic_threaded_nut()
// Usage:
//   generic_threaded_nut(nutwidth, id, h|height|thickness, pitch, profile, [$slop], ...) [ATTACHMENTS];
// Description:
//   Constructs a hexagonal or square nut for an generic threaded rod using a user-supplied thread profile.
//   See {{generic_threaded_rod()}} for details on the profile specification.  
// Arguments:
//   nutwidth = outer dimension of nut from flat to flat. 
//   id = diameter of threaded rod to screw onto.
//   h / height / thickness = height/thickness of nut.
//   pitch = Thread spacing.
//   profile = Thread profile.
//   ---
//   shape = specifies shape of nut, either "hex" or "square".  Default: "hex"
//   left_handed = if true, create left-handed threads.  Default = false
//   starts = The number of lead starts.  Default = 1
//   bevel = if true, bevel the outside of the nut.  Default: true for hex nuts, false for square nuts
//   bevel1 = if true, bevel the outside of the nut bottom.
//   bevel2 = if true, bevel the outside of the nut top. 
//   bevang = set the angle for the outside nut bevel.  Default: 30
//   ibevel = if true, bevel the inside (the hole).   Default: true
//   ibevel1 = if true bevel the inside, bottom end.
//   ibevel2 = if true bevel the inside, top end.
//   higbee = If true apply higbee thread truncation at both ends, or set to an angle to adjust higbee cut point.  Default: false
//   higbee1 = If true apply higbee thread truncation at bottom end, or set to an angle to adjust higbee cut point.
//   higbee2 = If true apply higbee thread truncation at top end, or set to an angle to adjust higbee cut point.
//   id1 = inner diameter at the bottom
//   id2 = inner diameter at the top
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
//   orient = Vector to rotate top towards, after spin.  See [orient](attachments.scad#subsection-orient).  Default: `UP`
//   $slop = The printer-specific slop value, which adds clearance (`4*$slop`) to internal threads.
function generic_threaded_nut(
    nutwidth,
    id,
    h,
    pitch,
    profile,
    shape="hex",
    left_handed=false,
    starts=1,
    bevel,bevel1,bevel2,bevang=30,
    ibevel, ibevel1, ibevel2,
    id1,id2, height, thickness, 
    higbee,higbee1,higbee2,
    anchor, spin, orient
) = no_function("generic_threaded_nut");
module generic_threaded_nut(
    nutwidth,
    id,
    h,
    pitch,
    profile,
    shape="hex",
    left_handed=false,
    starts=1,
    bevel,bevel1,bevel2,bevang=30,
    ibevel, ibevel1, ibevel2,
    id1,id2, height, thickness, 
    higbee,higbee1,higbee2,
    anchor, spin, orient
) {
    
    extra = 0.01;
    id1 = first_defined([id1,id]);
    id2 = first_defined([id2,id]);
    h = one_defined([h,height,thickness],"h,height,thickness");
    dummyA = assert(is_num(pitch) && pitch>=0, "pitch must be a nonnegative number")
             assert(is_num(h) && h>0, "height/thickness must be a positive number")
             assert(in_list(shape,["square","hex"]), "shape must be \"hex\" or \"square\"")
             assert(all_positive([id1,id2]), "Inner diameter(s) of nut must be positive number(s)");
    slope = (id2-id1)/h;
    full_id1 = id1-slope*extra/2;
    full_id2 = id2+slope*extra/2;
    ibevel1 = first_defined([ibevel1,ibevel,true]);
    ibevel2 = first_defined([ibevel2,ibevel,true]);
    bevel1 = first_defined([bevel1,bevel,shape=="hex"?true:false]);
    bevel2 = first_defined([bevel2,bevel,shape=="hex"?true:false]);
    depth = -pitch*min(column(profile,1));
    IBEV=0.05;
    vnf = linear_sweep(hexagon(id=nutwidth), height=h, center=true);
    attachable(anchor,spin,orient, size=shape=="square" ? [nutwidth,nutwidth,h] : undef, vnf=shape=="hex" ? vnf : undef) {
        difference() {
            _nutshape(nutwidth,h, shape,bevel1,bevel2);
            if (pitch==0) 
               cyl(l=h+extra, d1=full_id1+4*get_slop(), d2=full_id2+4*get_slop(), chamfer1=ibevel1?-IBEV*full_id1:undef, chamfer2=ibevel2?-IBEV*full_id2:undef);
            else
               generic_threaded_rod(
                     d1=full_id1,d2=full_id2,
                     l=h+extra,
                     pitch=pitch,
                     profile=profile,
                     left_handed=left_handed,
                     starts=starts,
                     internal=true,
                     bevel1=ibevel1,bevel2=ibevel2,
                     higbee=higbee, higbee1=higbee1, higbee2=higbee2
                );
        }
        children();
    }
}


module _nutshape(nutwidth, h, shape, bevel1, bevel2)
{
   bevel_d=0.9;
   intersection(){
       if (shape=="hex")
         cyl(d=nutwidth, circum=true, $fn=6, l=h, chamfer1=bevel1?0:nutwidth*.01, chamfer2=bevel2?0:nutwidth*.01);
        //vnf_polyhedron(vnf);
       else
         cuboid([nutwidth,nutwidth,h],chamfer=nutwidth*.01, except=[if (bevel1) BOT, if(bevel2) TOP]);
       fn = quantup(segs(r=nutwidth/2),shape=="hex"?6:4);
       d = shape=="hex" ? 2*nutwidth/sqrt(3) : sqrt(2)*nutwidth;
       chamfsize = (d-nutwidth)/2/bevel_d;
       cyl(d=d*.99,h=h+.01,realign=true,circum=true,$fn=fn,chamfer1=bevel1?chamfsize:0,chamfer2=bevel2?chamfsize:0,chamfang=30);
   }
}


// Module: thread_helix()
// Usage:
//   thread_helix(d, pitch, [thread_depth], [flank_angle], [turns], [profile=], [left_handed=], [higbee=], [internal=]);
// Description:
//   Creates a right-handed helical thread with optional end tapering.  Unlike
//   {{generic_threaded_rod()}, this module just generates the thread, and you specify the total
//   angle of threading that you want, which makes it easy to put complete threads onto a longer
//   shaft.  It also optionally makes a finely divided taper at the thread ends.  However, it takes
//   2-3 times as long to render compared to {{generic_threaded_rod()}}.  This module was designed
//   to handle threads found in plastic and glass bottles.
//   .
//   You can specify a thread_depth and flank_angle, in which case you get a symmetric trapezoidal
//   thread, whose inner diameter (the base of the threads for external threading) is d (so the
//   total diameter will be d + thread_depth).  This differs from the threaded_rod modules, where
//   the specified diameter is the outer diameter.  Alternatively you can give a profile, following
//   the same rules as for general_threaded_rod.  The Y=0 point will align with the specified
//   diameter, and the profile should range in X from -1/2 to 1/2.  You cannot specify both the
//   profile and the thread_depth or flank_angle.
//   .
//   Unlike {{generic_threaded_rod()}, when internal=true this module generates the threads, not a thread mask.
//   The profile needs to be inverted to produce the proper thread form.  If you use the built-in trapezoidal
//   thread you get the inverted thread, designed so that the inner diameter is d.  If you supply a custom profile
//   you must invert it yourself to get internal threads.  With adequate clearance
//   this thread will mate with the thread that uses the same parameters but has internal=false.  Note that
//   unlike the threaded_rod modules, thread_helix does not adjust the diameter for faceting, nor does it
//   subtract any $slop for clearance.  
//   .
//   The taper options specify tapering at of the threads at each end, and is given as the linear distance
//   over which to taper.  If taper is positive the threads are lengthened by the specified distance; if taper
//   is negative, the taper is included in the thread length specified by `turns`.  Tapering works on both internal and external threads.  
// Arguments:
//   d = Inside base diameter of threads.  Default: 10
//   pitch = Distance between threads.  Default: 2
//   thread_depth = Depth of threads from top to bottom.
//   flank_angle = Angle of thread faces to plane perpendicular to screw.  Default: 15 degrees.
//   turns = Number of revolutions to rotate thread around. 
//   ---
//   profile = If an asymmetrical thread profile is needed, it can be specified here.
//   starts = The number of thread starts.  Default: 1
//   left_handed = If true, thread has a left-handed winding.
//   internal = if true make internal threads.  The only effect this has is to change how the threads taper if tapering is selected. When true, threads taper towards the outside; when false, they taper towards the inside.  Default: false
//   d1 = Bottom inside base diameter of threads.
//   d2 = Top inside base diameter of threads.
//   taper = Length of tapers for thread ends.  Positive to add taper to threads, negative to taper within specified length.  Default: 0
//   taper1 = Length of taper for bottom thread end
//   taper2 = Length of taper for top thread end
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
//   orient = Vector to rotate top towards, after spin.  See [orient](attachments.scad#subsection-orient).  Default: `UP`
// Example(2DMed): Typical Tooth Profile
//   pitch = 2;
//   depth = pitch * cos(30) * 5/8;
//   profile = [
//       [-6/16, 0           ],
//       [-1/16, depth/pitch ],
//       [ 1/16, depth/pitch ],
//       [ 6/16, 0           ],
//   ];
//   stroke(profile, width=0.02);
// Figure(2D,Med):
//   pa_delta = tan(15)/4;
//      rr1 = -1/2;
//      z1 = 1/4-pa_delta;
//      z2 = 1/4+pa_delta;
//      profile = [
//                  [-z2, rr1],
//                  [-z1,  0],
//                  [ z1,  0],
//                  [ z2, rr1],
//                ];
//      fullprofile = 50*left(1/2,p=concat(profile, right(1, p=profile)));
//      stroke(fullprofile,width=1);
//      dir = fullprofile[2]-fullprofile[3];
//      dir2 = fullprofile[5]-fullprofile[4];
//      curve = arc(15,angle=[75,87],r=40 /*67.5*/);
//      avgpt = mean([fullprofile[5]+.1*dir2, fullprofile[5]+.4*dir2]);
//      color("red"){
//       stroke([fullprofile[4]+[0,1], fullprofile[4]+[0,37]], width=1);
//       stroke([fullprofile[5]+.1*dir2, fullprofile[5]+.4*dir2], width=1);
//       stroke(move(-curve[0]+avgpt,p=curve), width=0.71,endcaps="arrow2");
//       right(14)back(19)text("flank",size=4,halign="center");
//       right(14)back(14)text("angle",size=4,halign="center");
//      }
// Examples:
//   thread_helix(d=10, pitch=2, thread_depth=0.75, flank_angle=15, turns=2.5, $fn=72);
//   thread_helix(d=10, pitch=2, thread_depth=0.75, flank_angle=15, turns=2.5, taper=1, $fn=72);
//   thread_helix(d=10, pitch=2, thread_depth=0.75, flank_angle=15, turns=2, taper=2, internal=true, $fn=72);
//   thread_helix(d=10, pitch=2, thread_depth=0.75, flank_angle=15, turns=1, left_handed=true, taper=1, $fn=36);
function thread_helix(
    d, pitch, thread_depth, flank_angle, turns,
    profile, starts=1, left_handed=false, internal=false,
    d1, d2, taper, taper1, taper2,
    anchor, spin, orient
) = no_function("thread_helix");
module thread_helix(
    d, pitch, thread_depth, flank_angle, turns=2,
    profile, starts=1, left_handed=false, internal=false,
    d1, d2, taper, taper1, taper2,
    anchor, spin, orient
) {
    dummy1=assert(is_undef(profile) || !any_defined([thread_depth, flank_angle]),"Cannot give thread_depth or flank_angle with a profile");
    h = pitch*starts*turns;
    r1 = get_radius(d1=d1, d=d, dflt=10);
    r2 = get_radius(d1=d2, d=d, dflt=10);
    profile = is_def(profile) ? profile :
        let(
            tdp = thread_depth / pitch,
            dz = tdp * tan(flank_angle),
            cap = (1 - 2*dz)/2
        )
        internal?
          [
            [-cap/2-dz, tdp],
            [-cap/2,    0  ],
            [+cap/2,    0  ],
            [+cap/2+dz, tdp],
          ]
        :
          [
            [+cap/2+dz, 0  ],
            [+cap/2,    tdp],
            [-cap/2,    tdp],
            [-cap/2-dz, 0  ],
          ];
    pline = mirror([-1,1],  p = profile * pitch);
    dir = left_handed? -1 : 1;
    attachable(anchor,spin,orient, r1=r1, r2=r2, l=h) {
        zrot_copies(n=starts) {
            spiral_sweep(pline, h=h, r1=r1, r2=r2, turns=turns*dir, taper=taper, taper1=taper1, taper2=taper2, internal=internal, anchor=CENTER);
        }
        children();
    }
}



// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap

// Questions
//   Should nut modules take d1/d2 for tapered nuts?
//
// Need explanation of what exactly the diff is between threaded_rod and helix_threads.
// Higbee is different, angle in one and length in another.  Need to reconcile