BOSL2/screws.scad

//////////////////////////////////////////////////////////////////////
// LibFile: screws.scad
//   Functions and modules for creating metric (ISO) and English (UTS) standard screws and nuts.
//   Included is a function for calculating the standard dimensions of screws including the
//   tolerance values that are required to make screws mate properly when they are formed
//   precisely.  If you can fabricate objects accurately then the modeled screws will mate
//   with standard hardware without the need to introduce extra gaps for clearance.
// Includes:
//   include <BOSL2/std.scad>
//   include <BOSL2/screws.scad>
// FileGroup: Threaded Parts
// FileSummary: ISO (metric) and UTS screws and nuts.
//////////////////////////////////////////////////////////////////////

include <BOSL2/structs.scad>
include <BOSL2/threading.scad>
include <BOSL2/screw_drive.scad>

// Section: Screw Parameters
//    This modules in this file create standard ISO (metric) and UTS (English) threaded screws.
//    The {{screw()}} and {{nut()}} modules produce
//    screws and nuts that comply with the relevant ISO and ASME standards,
//    including tolerances for screw fit.  You can also create screws with
//    various head types and drive types that should match standard hardware.
// Subsection: Screw Naming
//    You can specify screws using a string that specifies the screw.  
//    For ISO (metric) screws the specification has the form: "M`<size>`x`<pitch>`,`<length>`,
//    so "M6x1,10" specifies a 6mm diameter screw with a thread pitch of 1mm and length of 10mm.
//    You can omit the pitch or length, e.g. "M6x1", or "M6,10", or just "M6".
//    .
//    For UTS (English) screws the specification has the form `<size>`-`<threadcount>`,`<length>`, e.g. 
//    "#8-32,1/2", or "1/4-20,1".  The units are in inches, including the length.  Size can be a
//    number from 0 to 12 with or without a leading # to specify a screw gauge size, or any other
//    value to specify a diameter in inches, either as a float or a fraction, so "0.5-13" and
//    "1/2-13" are equivalent.  To force interpretation of the value as inches add '' (two
//    single-quotes) to the end, e.g. "1''-4" is a one inch screw and "1-80" is a very small
//    1-gauge screw.  The pitch is specified using a thread count, the number of threads per inch.
//    As with the ISO screws, you can omit the pitch or length and specify "#6-32", "#6,3/4", or simply #6.
// Subsection: Standard Screw Pitch
//    If you omit the pitch when specifying a screw or nut then the library supplies a standard screw pitch based
//    on the screw diameter.  For each screw diameter, multiple standard pitches are possible.
//    The available thread pitch types are different for ISO and UTS:
//    .
//    | ISO      |    UTS   |
//    | -------- | -------- |
//    | "coarse" |  "coarse" or "UNC" |
//    | "fine"   |   "fine" or "UNF"  |
//    | "extrafine" or "extra fine" | "extrafine", "extra fine", or "UNEF"  |
//    | "superfine" or "super fine" |   |
//    | "none"   |  "none"  |
//    .
//    The default pitch selection is "coarse".  Note that this selection is case insensitive.
//    To set the pitch using these pitch strings you use the `thread=` argument to the modules.
//    You cannot incorporate a named pitch into the thread name.  The finer pitch categories
//    are defined only for larger screw diameters.  You can also use the `thread=` argument to
//    directly specify a pitch, so `thread=2` produces a thread pitch of 2mm.  Setting the
//    pitch to zero produces an unthreaded screws, the same as setting it to "none".  Specifying
//    a numeric value this way overrides a value given in the specification.  You can also set
//    `thread=true` or `thread=false` to turn threading on and off, with the same default coarse
//    threading when you set it to true.  
// Subsection: Screw Heads
//    By default screws do not have heads.  
//    You can request a screw head using `head=` parameter to specify the desired head type.  If you want the
//    head to have a recess for driving the screw you must also specify a drive type using `drive=`.  
//    The table below lists the head options.  Only some combinations of head and drive
//    type are supported.  Different sized flat heads exist for the same screw type.
//    Sometimes this depends on the type of recess.  If you specify "flat" then the size will be chosen
//    appropriately for the recess you specify.
//    .
//    The `drive=` argument can be set to "none", "hex", "slot", 
//    "phillips", "ph0" to "ph4" (for phillips of the specified size), "torx" or
//    "t<size>" (for Torx at a specified size, e.g. "t20").  If you have no head but still
//    give a drive type you will get a set screw.  The table below lists all of the head types and
//    shows which drive type is compatible with each head types.  Different head types work in ISO and UTS,
//    as marked in the first column.  
//    .
//    |ISO|UTS|Head            | Drive  |
//    |---|---|--------------- | ----------------------------|
//    |X|X|"none"          | hex, torx, slot |
//    |X|X|"hex"           | *none*|
//    |X|X|"socket"        | hex, torx|
//    |X|X|"button"        | hex, torx|
//    |X|X|"flat"          | slot, phillips, hex, torx|
//    |X|X|"flat sharp"    | slot, phillips, hex, torx|
//    | |X|"flat small"    | slot, phillips|
//    | |X|"flat large"    | hex, torx |
//    | |X|"flat undercut" | slot, phillips |
//    | |X|"flat 82"       | slot, phillips |
//    | |X|"flat 100"      | slot, phillips |
//    | |X|"round"         | slot, phillips |
//    | |X|"fillister"     | slot, phillips |
//    |X|X|"pan"           | slot, phillips, torx (ISO only) |
//    |X| |"cheese"        | slot, phillips, torx |
//    .
//    The drive size is specified appropriately for the drive type: drive number for phillips or torx,
//    and recess width in mm or inches (as appropriate) for hex.  Drive size is determined automatically
//    from the screw size, but by passing the `drive_size=` argument you can override the default, or
//    in cases where no default exists you can specify it.  Flat head screws have variations such as 100 degree
//    angle for UTS, or undercut heads.  You can also request a "sharp" screw which will set the screw diameter 
//    the theoretical maximum and produce sharp corners instead of a flat edge on the head.  The flat head options
//    can be mixed in any order, for example, "flat sharp undercut" or "flat undercut sharp".  
// Subsection: Tolerance
//    Without tolerance requirements, screws would not fit together.  The screw standards specify a
//    nominal size, but the tolerance determines a range of allowed sizes based on that nominal size.
//    So for example, an M10 screw with the default tolerance has an outside (major) diameter between 9.74 mm and 9.97 mm.
//    The library will use the center point in the allowed range and create a screw with a diameter of 9.86 mm.
//    A M10 nut at the default tolerance has a major diameter (which is the inside diameter) between 10 mm and 10.4 mm.
//    Shrinking the major diameter of a screw makes the screw loose.  Shrinking the major diameter of a nut, on the other hand,
//    makes the hole smaller and hence makes the nut tighter.  For this reason, we need a difference tolerance
//    for a screw than for a nut.  Screw tolerances shrink the diameter to make the screw looser whereas nut tolerances
//    increase the diameter to make the nut looser.  Screws modeled using this library will have dimensions consistent with the
//    standards they are based on, so that they will interface properly if fabricated by an accurate method.  The ISO and UTS
//    systems use different tolerance designations.
//    .
//    For UTS screw threads the tolerance is one of "1A", "2A" or "3A", in
//    order of increasing tightness.  The default tolerance is "2A", which
//    is the general standard for manufactured bolts.
//    .
//    For UTS nut threads, the tolerance is one of "1B", "2B" or "3B", in
//    order of increasing tightness.  The default tolerance is "2B", which
//    is the general standard for manufactured nuts.
//    .
//    The ISO tolerances are more complicated.  For both screws and nuts the ISO tolerance has the form of a number
//    and letter.  The letter specifies the "fundamental deviation", also called the "tolerance position", the gap
//    from the nominal size.  The number specifies the allowed range (variability) of the thread heights.  For
//    screws, the letter must be "e", "f", "g", or "h", where "e" is the loosest and "h" means no gap.  The number
//    for a screw tolerance must be a value from 3-9 for crest diameter and one of 4, 6, or 8 for pitch diameter.
//    A tolerance "6g" specifies both pitch and crest diameter to be the same, but they can be different, with a
//    tolerance like "5g6g" specifies a pitch diameter tolerance of "5g" and a crest diameter tolerance of "6g".
//    Smaller numbers give a tighter tolerance.  The default ISO screw tolerance is "6g".
//    .
//    For ISO nuts the letters specifying the fundamental deviation are upper case and must be "G" or "H" where "G"
//    is loose and "H" means no gap. The number specifying the variability must range from 4-8.  An allowed (loose)
//    nut tolerance is "7G".  The default ISO tolerance is "6H".


// Section: Making Screws


/*
http://mdmetric.com/thddata.htm#idx

Seems to show JIS has same nominal thread as others
https://www.nbk1560.com/~/media/Images/en/Product%20Site/en_technical/11_ISO%20General%20Purpose%20Metric%20Screw%20Threads.ashx?la=en

Various ISO standards here:  https://www.fasteners.eu/standards/ISO/4026/

Torx values:  https://www.stanleyengineeredfastening.com/-/media/web/sef/resources/docs/other/socket_screw_tech_manual_1.ashx

*/



// Module: screw()
// Usage:
//   screw([spec], [head], [drive], [thread=], [drive_size=], [length=|l=], [thread_len=], [undersize=], [tolerance=], [details=], [anchor=], [atype=], [orient=], [spin=]) [ATTACHMENTS];
// Description:
//   Create a screw.  See [screw parameters](#section-screw-parameters) for details on the parameters that define a screw.
//   The tolerance determines the dimensions of the screw
//   based on ISO and ASME standards.  Screws fabricated at those dimensions will mate properly with standard hardware.
//   Note that the $slop argument does not affect the size of screws: it only adjusts screw holes.  This will work fine
//   if you are printing both parts, but if you need to mate printed screws to metal parts you may need to adjust the size
//   of the screws, which you can do with the undersize arguments.  
//   .
//   You can generate a screw specification from {{screw_info()}}, possibly create a modified version using {{struct_set()}}, and pass that in rather than giving the parameters.
//   .
//   The anchors and anchor types refer to various parts of the screw, which are labeled below.  The "screw" anchor type (the default) is simply 
//   the whole screw and the "head" anchor is the head.  These anchors will anchor to bounding cylinder for the specified screw part, so 
// Figure(2D,VPD = 113.4, VPT = [16.9671, 14.9021, -3.59741], VPR = [0, 0, 0],NoAxes)
//   rpos=33;
//   fsize=2.5;
//   projection(cut=true) xrot(-90)screw("M8", head="socket", length=25, thread_len=10);
//   right(rpos)projection(cut=true) xrot(-90)screw("M8", head="flat", length=25, thread_len=10);
//   color("black"){
//      stroke([[5,0],[5,10]],endcaps="arrow2",width=.3);
//      back(5)right(6)text("threads",size=fsize,anchor=LEFT);
//      stroke([[5,10],[5,25]],endcaps="arrow2",width=.3);
//      back(10+15/2)right(6)text("shank",size=fsize,anchor=LEFT);
//      stroke([[-5,0],[-5,25]],endcaps="arrow2",width=.3);
//      back(25/2)right(-6)text("shaft",size=fsize,anchor=RIGHT);
//   }
//   sh=10.2841;
//   right(rpos)
//   color("black"){
//      stroke([[5,0],[5,10]],endcaps="arrow2",width=.3);
//      back(5)right(6)text("threads",size=fsize,anchor=LEFT);
//      stroke([[5,10],[5,10+sh]],endcaps="arrow2",width=.3);
//      back(10+sh/2)right(6)text("shank",size=fsize,anchor=LEFT);
//      stroke([[-5,0],[-5,10+sh]],endcaps="arrow2",width=.3);
//      back((10+sh)/2)right(-6)text("shaft",size=fsize,anchor=RIGHT);
//   }
// Arguments:
//   spec = screw specification, e.g. "M5x1" or "#8-32".  See [screw naming](#subsection-screw-naming).  This can also be a screw specification structure of the form produced by {{screw_info()}}.  
//   head = head type.  See [screw heads](#subsection-screw-heads)  Default: none
//   drive = drive type.  See [screw heads](#subsection-screw-heads) Default: none
//   ---
//   length = length of screw (in mm)
//   thread = thread type or specification. See [screw pitch](#subsection-standard-screw-pitch). Default: "coarse"
//   drive_size = size of drive recess to override computed value
//   undersize = amount to decrease screw diameter, a scalar to apply to all parts, or a 3-vector to control threads, shank and head independently.  Default: 0
//   undersize_threads = amount to decrease diameter of the threaded part of screw
//   undersize_shoulder = amount to decrease the diameter of shoulder of screw
//   undersize_head = amount to decrease the head diameter of the screw
//   thread_len = length of threaded portoin of screw (in mm), for making partly threaded screws.  Default: fully threaded
//   details = toggle some details in rendering.  Default: true
//   tolerance = screw tolerance.  Determines actual screw thread geometry based on nominal sizing.  See [tolerance](#subsection-tolerance). Default is "2A" for UTS and "6g" for ISO.  
//   atype = anchor type, one of "screw", "head", "shaft", "threads", "shank"
//   anchor = Translate so anchor point on the shaft is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `BOTTOM`
//   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`
// Anchor Types:
//   screw = the entire screw (default)
//   head = screw head (invalid for headless screws)
//   shaft = screw shaft
//   shank = unthreaded section of shaft (invalid if screw is fully threaded)
//   threads = threaded section of screw     
// Extra Anchors:
//   top = top of screw
//   bot = bottom of screw
//   center = center of screw
//   head_top = top of head (invalid for headless screws)
//   head_bot = bottom of head (invalid for headless screws)
//   head_center = center of head (invalid for headless screws)
//   shaft_top = top of shaft
//   shaft_bot = bottom of shaft
//   shaft_center = center of shaft
//   shank_top = top of shank (invalid if screw is fully threaded)
//   shank_bot = bottom of shank (invalid if screw is fully threaded)
//   shank_center = center of shank (invalid if screw is fully threaded)
//   threads_top = top of threaded portion of screw (invalid if thread_len=0)
//   threads_bot = bottom of threaded portion of screw (invalid if thread_len=0)
//   threads_center = center of threaded portion of screw (invalid if thread_len=0)
// Example(Med): Selected UTS (English) screws
//   $fn=32;
//   xdistribute(spacing=8){
//     screw("#6", length=12);
//     screw("#6-32", head="button", drive="torx",length=12);
//     screw("#6-32,3/4", head="hex");
//     screw("#6", thread="fine", head="fillister",length=12, drive="phillips");
//     screw("#6", head="flat small",length=12,drive="slot");
//     screw("#6-32", head="flat large", length=12, drive="torx");
//     screw("#6-32", head="flat undercut",length=12);
//     screw("#6-24", head="socket",length=12);          // Non-standard threading
//     screw("#6-32", drive="hex", drive_size=1.5, length=12);
//   }
// Example(Med): A few examples of ISO (metric) screws
//   $fn=32;
//   xdistribute(spacing=8){
//     screw("M3", head="flat small",length=12);
//     screw("M3", head="button",drive="torx",length=12);
//     screw("M3", head="pan", drive="phillips",length=12);
//     screw("M3x1", head="pan", drive="slot",length=12);   // Non-standard threading!
//     screw("M3", head="flat large",length=12);
//     screw("M3", thread="none", head="flat", drive="hex",length=12);  // No threads
//     screw("M3", head="socket",length=12);
//     screw("M5", head="hex", length=12);
//   }
// Example(Med): Demonstration of all head types for UTS screws (using pitch zero for fast preview)
//   xdistribute(spacing=15){
//     ydistribute(spacing=15){
//        screw("1/4", thread=0,length=8, anchor=TOP, head="none", drive="hex");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="none", drive="torx");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="none", drive="slot");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="none");
//     }
//     screw("1/4", thread=0, length=8, anchor=TOP, head="hex");
//     ydistribute(spacing=15){
//        screw("1/4", thread=0,length=8, anchor=TOP, head="socket", drive="hex");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="socket", drive="torx");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="socket");
//     }
//     ydistribute(spacing=15){
//        screw("1/4", thread=0,length=8, anchor=TOP, head="socket ribbed", drive="hex",$fn=32);
//        screw("1/4", thread=0,length=8, anchor=TOP, head="socket ribbed", drive="torx",$fn=32);
//        screw("1/4", thread=0,length=8, anchor=TOP, head="socket ribbed",$fn=24);
//     }
//     ydistribute(spacing=15){
//        screw("1/4", thread=0,length=8, anchor=TOP, head="button", drive="hex");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="button", drive="torx");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="button");
//     }
//     ydistribute(spacing=15){
//        screw("1/4", thread=0,length=8, anchor=TOP, head="round", drive="slot");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="round", drive="phillips");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="round");
//     }     
//     ydistribute(spacing=15){
//        screw("1/4", thread=0,length=8, anchor=TOP, head="pan", drive="slot");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="pan", drive="phillips");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="pan");
//     }
//     ydistribute(spacing=15){
//        screw("1/4", thread=0,length=8, anchor=TOP, head="fillister", drive="slot");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="fillister", drive="phillips");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="fillister");
//     }
//     ydistribute(spacing=15){
//        screw("1/4", thread=0,length=8, anchor=TOP, head="flat", drive="slot");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="flat", drive="phillips");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="flat", drive="hex");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="flat", drive="torx");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="flat large");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="flat small");
//     }
//     ydistribute(spacing=15){
//        screw("1/4", thread=0,length=8, anchor=TOP, head="flat undercut", drive="slot");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="flat undercut", drive="phillips");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="flat undercut");
//     }
//     ydistribute(spacing=15){
//        screw("1/4", thread=0,length=8, anchor=TOP, head="flat 100", drive="slot");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="flat 100", drive="phillips");
//        screw("1/4", thread=0,length=8, anchor=TOP, head="flat 100");
//     }
//   }
// Example(Med): Demonstration of all head types for metric screws without threading.
//   xdistribute(spacing=15){
//     ydistribute(spacing=15){
//       screw("M6x0", length=8, anchor=TOP,  head="none", drive="hex");
//       screw("M6x0", length=8, anchor=TOP,  head="none", drive="torx");
//       screw("M6x0", length=8, anchor=TOP);
//     }
//     screw("M6x0", length=8, anchor=TOP,  head="hex");
//     ydistribute(spacing=15){
//       screw("M6x0", length=8, anchor=TOP,  head="socket", drive="hex");
//       screw("M6x0", length=8, anchor=TOP,  head="socket", drive="torx");
//       screw("M6x0", length=8, anchor=TOP,  head="socket");
//     }
//     ydistribute(spacing=15){
//       screw("M6x0", length=8, anchor=TOP,  head="socket ribbed", drive="hex", $fn=32);
//       screw("M6x0", length=8, anchor=TOP,  head="socket ribbed", drive="torx", $fn=32);
//       screw("M6x0", length=8, anchor=TOP,  head="socket ribbed", $fn=32);
//     }
//     ydistribute(spacing=15){
//       screw("M6x0", length=8, anchor=TOP,  head="pan", drive="slot");
//       screw("M6x0", length=8, anchor=TOP,  head="pan", drive="phillips");
//       screw("M6x0", length=8, anchor=TOP,  head="pan", drive="torx");
//       screw("M6x0", length=8, anchor=TOP,  head="pan");
//       screw("M6x0", length=8, anchor=TOP,  head="pan flat");
//     }
//     ydistribute(spacing=15){
//       screw("M6x0", length=8, anchor=TOP,  head="button", drive="hex");
//       screw("M6x0", length=8, anchor=TOP,  head="button", drive="torx");
//       screw("M6x0", length=8, anchor=TOP,  head="button");
//     }
//     ydistribute(spacing=15){
//       screw("M6x0", length=8, anchor=TOP,  head="cheese", drive="slot");
//       screw("M6x0", length=8, anchor=TOP,  head="cheese", drive="phillips");
//       screw("M6x0", length=8, anchor=TOP,  head="cheese", drive="torx");
//       screw("M6x0", length=8, anchor=TOP,  head="cheese");
//     }
//     ydistribute(spacing=15){
//       screw("M6x0", length=8, anchor=TOP,  head="flat", drive="phillips");
//       screw("M6x0", length=8, anchor=TOP,  head="flat", drive="slot");
//       screw("M6x0", length=8, anchor=TOP,  head="flat", drive="hex");
//       screw("M6x0", length=8, anchor=TOP,  head="flat", drive="torx");
//       screw("M6x0", length=8, anchor=TOP,  head="flat small");
//       screw("M6x0", length=8, anchor=TOP,  head="flat large");
//     }
//   }
// Example: The three different English (UTS) screw tolerances
//   module label(val)
//   {
//     difference(){
//        children();
//        yflip()linear_extrude(height=.35) text(val,valign="center",halign="center",size=8);
//     }
//   }
//   $fn=64;
//   xdistribute(spacing=15){
//     label("1") screw("1/4-20,5/8", head="hex",orient=DOWN,atype="head", anchor=TOP,tolerance="1A");  // Loose
//     label("2") screw("1/4-20,5/8", head="hex",orient=DOWN,atype="head", anchor=TOP,tolerance="2A");  // Standard
//     label("3") screw("1/4-20,5/8", head="hex",orient=DOWN,atype="head", anchor=TOP,tolerance="3A");  // Tight
//   }
// Example(2D): This example shows the gap between nut and bolt at the loosest tolerance for UTS.  This gap is what enables the parts to mesh without binding and is part of the definition for standard metal hardware.  Note that this gap is part of the standard definition for the metal hardware, not the 3D printing adjustment provided by the $slop parameter.  
//   $slop=0;
//   $fn=32;
//   projection(cut=true)xrot(-90){
//       screw("1/4-20,1/4", head="hex",orient=UP,anchor=BOTTOM,tolerance="1A");
//       down(INCH*1/20*2.145) nut("1/4-20", thickness=8, diameter=0.5*INCH,tolerance="1B");
//   }
// Example: Here is a screw with nonstadard threading and a weird head size, which we create by modifying the screw structure:
//  spec = screw_info("M6x2,12",head="socket");
//  newspec = struct_set(spec,["head_size",30,"head_height",3]);
//  screw(newspec);
// Example: A bizarre custom screw with nothing standard about it.  If your screw is very strange, consider setting tolerance to zero so you get exactly the screw you defined.  You'll need to create your own clearance between mating threads in this case.  
//  spec = [["system","ISO"],
//          ["pitch", 2.3],
//          ["head", "flat"],
//          ["head_size", 20],
//          ["head_size_sharp", 22],
//          ["head_angle", 60],
//          ["diameter",12],
//          ["length",22]];
//  screw(spec,tolerance=0);


// redo this once the dust settles!
function screw(spec, head="none", drive, thread="coarse", drive_size, oversize, length, l, shank=0, tolerance=undef, details=true, anchor=undef,anchor_head=undef,spin=0, orient=UP) = no_function("screw");

module screw(spec, head="none", drive, thread="coarse", drive_size, 
             length, l, tolerance=undef, details=true, shoulder_diam=0, shoulder_len=0, thread_len,
             undersize=0, threads_undersize, shoulder_undersize, head_undersize,
             atype="shaft",anchor=BOTTOM, spin=0, orient=UP,
             _internal=false, _counterbore=0)
{
   internal = _internal;
   counterbore = _counterbore;
   dummyA=assert(is_def(undersize) || num_defined([threads_undersize, shoulder_undersize, head_undersize])==0, "Cannot combine undersize with other more specific undersize parameters");
   undersize = scalar_vec3(undersize);
   threads_undersize = first_defined([threads_undersize, undersize[0], 0]);
   shoulder_undersize = first_defined([shoulder_undersize, undersize[1], 0]);
   head_undersize = first_defined([head_undersize, undersize[2], 0]);   
   dummyB=assert(is_string(spec) || is_struct(spec), "Screw spec must be a string or struct");
   spec = _validate_screw_spec(
                               is_struct(spec) ? spec
                             : screw_info(spec, head, drive, thread=thread, drive_size=drive_size, threads_oversize=-threads_undersize, head_oversize=-head_undersize) );
   head = struct_val(spec,"head");
   pitch = struct_val(spec, "pitch");
   nominal_diam = struct_val(spec, "diameter");
   threadspec = pitch==0 ? undef : thread_specification(spec, internal=internal, tolerance=tolerance);
   d_major = pitch==0 ? nominal_diam : mean(struct_val(threadspec, "d_major"));
   headless = head=="none";
   flathead = starts_with(head,"flat");
   screwlen = one_defined([l,length],"l,length",dflt=undef);
   length = first_defined([screwlen,struct_val(spec,"length")]);
   dummyC = assert(in_list(atype,["shaft","head","shank","threads","screw","shoulder"]),str("Unknown anchor type: \"",atype,"\""));
   dummyD = assert(is_finite(length) && length>0, "Must specify positive screw length");
   dummyE = assert(is_finite(shoulder_len) && shoulder_len>=0, "Must specify a nonegative shoulder length");
   dummyF = assert(is_finite(shoulder_diam) && shoulder_diam>=0, "Must specify nonnegative shoulder diameter");
   dummyG = assert(is_undef(thread_len) || all_nonnegative(thread_len), "Must specify nonnegative thread length");
   shoulder_diam = shoulder_diam-shoulder_undersize;
   sides = max(12, segs(nominal_diam/2));
   head_height = headless || flathead ? 0 
               : counterbore==true || is_undef(counterbore) || counterbore==0 ? struct_val(spec, "head_height")
               : counterbore;
   head_diam = struct_val(spec, "head_size");
   flat_height = !flathead ? 0 
               : let( given_height = struct_val(spec, "head_height"))
                 all_positive(given_height) ? given_height
               : (struct_val(spec,"head_size_sharp")-d_major)/2/tan(struct_val(spec,"head_angle")/2);
   flat_cbore_height = flathead && is_num(counterbore) ? counterbore : 0;

   shoulder_adj = shoulder_len>0 ? flat_height:0;  // Adjustment because flathead height doesn't count toward shoulder length
   shoulder_full = shoulder_len==0 ? 0 : shoulder_len + flat_height;
   shank_len = is_def(thread_len) ? length - thread_len - (shoulder_len==0?flat_height:0) : 0;
   thread_len = is_def(thread_len) ? thread_len
              : length - (shoulder_len==0?flat_height:0);
   dummyH = assert(!(atype=="shank" && shank_len==0), "Specified atype of \"shank\" but screw has no shank (thread_len not given or it equals shaft length)");
   dummyI = assert(!(atype=="shoulder" && shoulder_len==0), "Specified atype of \"shoulder\" but screw has no shoulder");
   dummyJ = assert(!(atype=="threads" && thread_len==0), "Specified atype of \"threads\" but screw has no threaded part (thread_len=0)");
   dummyK = assert(!(atype=="head" && headless), "You cannot anchor headless screws with atype=\"head\"");
   eps_gen = 0.01;
   eps_shoulder = headless && !internal ? 0 : eps_gen;
   eps_shank = headless && !internal && shoulder_len==0 ? 0 : eps_gen;
   eps_thread = headless && !internal && shank_len==0 && shoulder_len==0 ? 0 : eps_gen;
   echo(shank_len=shank_len, thread_len=thread_len);
   echo(eps_shoulder=eps_shoulder, eps_shank=eps_shank, eps_thread=eps_thread);
   dummyL = assert(is_undef(flat_height) || flat_height < length, str("Length of screw (",length,") is shorter than the flat head height (",flat_height,")"));
   offset = atype=="head" ? (-head_height+flat_height-flat_cbore_height)/2
          : atype=="shoulder" ? shoulder_len/2 + flat_height
          : atype=="shaft" ? shoulder_len + (length+flat_height+shoulder_adj)/2
          : atype=="shank" ? shoulder_len + (length-thread_len+flat_height+shoulder_adj)/2
          : atype=="threads" ? shoulder_len + shoulder_adj + length-thread_len + thread_len/2
          : atype=="screw" ? (length-head_height+shoulder_len+shoulder_adj)/2
          : assert(false,"Unknown atype");
   echo(atype=atype, offset=offset, hh=head_height,length=length);
   anchor_list = [
          named_anchor("top", [0,0,offset+head_height+flat_cbore_height]),
          named_anchor("bot", [0,0,-length-shoulder_full+offset]),
          named_anchor("center", [0,0, -length/2 - shoulder_full/2 + head_height/2 + offset]),
          if (!headless) named_anchor("head_top", [0,0,head_height+offset]),
          if (!headless) named_anchor("head_bot", [0,0,-flat_height+offset]),
          if (!headless) named_anchor("head_center", [0,0,(head_height-flat_height)/2+offset]),
          if (shoulder_len>0) named_anchor("shoulder_top", [0,0,offset-flat_height]),
          if (shoulder_len>0) named_anchor("shoulder_bot", [0,0,offset-shoulder_full]),
          if (shoulder_len>0) named_anchor("shoulder_center", [0,0,offset-flat_height-shoulder_len/2]),
          named_anchor("shaft_top", [0,0,-shoulder_len-flat_height+offset]),
          named_anchor("shaft_bot", [0,0,-length-shoulder_full+offset]),
          named_anchor("shaft_center", [0,0,(-shoulder_len-flat_height-length-shoulder_full)/2+offset]),
          if (shank_len>0) named_anchor("shank_top", [0,0,-shoulder_len-flat_height+offset]),
          if (shank_len>0) named_anchor("shank_bot", [0,0,-shank_len-shoulder_len-flat_height+offset]),
          if (shank_len>0) named_anchor("shank_center", [0,0,-shank_len/2-shoulder_len-flat_height+offset]),
          named_anchor("threads_top", [0,0,-shank_len-shoulder_len-flat_height+offset]),
          named_anchor("threads_bot", [0,0,-length-shoulder_full+offset]),
          named_anchor("threads_center", [0,0,(-shank_len-length-shoulder_len-shoulder_full-flat_height)/2+offset])
   ];
   vnf = head=="hex" && counterbore==0 ? linear_sweep(hexagon(id=head_diam),height=head_height,center=true) : undef;
   head_diam_full = head=="hex" ? 2*head_diam/sqrt(3) : head_diam;
   attach_d = in_list(atype,["threads","shank","shaft"]) ? d_major 
            : atype=="screw" ? max(d_major,shoulder_diam,default(head_diam_full,0))
            : atype=="shoulder" ? shoulder_diam
            : is_def(vnf) ? undef
            : head_diam_full;
   attach_l = atype=="shaft" ? length-(shoulder_len>0?0:flat_height)
            : atype=="shoulder" ? shoulder_len
            : atype=="shank" ? shank_len
            : atype=="threads" ? thread_len
            : atype=="screw" ? length+head_height+shoulder_full + flat_cbore_height
            : is_def(vnf) ? undef
            : head_height+flat_height+flat_cbore_height;
   echo(attach_l=attach_l);
   attachable(
              vnf = vnf, 
              d = attach_d, 
              l = attach_l,
              orient = orient,
              anchor = anchor,
              spin = spin,
              anchors=anchor_list)
   {
     up(offset)
       difference(){
         union(){
           screw_head(spec,details,counterbore=counterbore,flat_height=flat_height);
           if (shoulder_len>0)
             up(eps_shoulder-flat_height) 
               cyl(d=shoulder_diam, h=shoulder_len+eps_shoulder, anchor=TOP, $fn=sides, chamfer1=details ? shoulder_diam/30:0);
           if (shank_len>0 || pitch==0){
             L = pitch==0 ? length - (shoulder_len==0?flat_height:0) : shank_len;
             down(shoulder_len+flat_height-eps_shank) 
               cyl(d=d_major, h=L+eps_shank, anchor=TOP, $fn=sides);
           }
           if (thread_len>0 && pitch>0)
             down(shoulder_len+flat_height+shank_len-eps_thread)
                   threaded_rod([mean(struct_val(threadspec, "d_minor")),
                                 mean(struct_val(threadspec, "d_pitch")),
                                 d_major], 
                      pitch = struct_val(threadspec, "pitch"),
                      l=thread_len+eps_thread, left_handed=false, internal=internal, 
                      bevel1=details,bevel2=details && (flathead || shoulder_len>0 || headless) && !_internal,
                      $fn=sides, anchor=TOP);
         }
         if (!internal) _driver(spec);
       }
     children();
   }  
}


// Module: screw_hole()
// Usage:
//   screw_hole([name], [head], [thread=], [length=|l=], [shank=], [oversize=], [tolerance=], [$slop=], [anchor=], [atype=], [orient=], [spin=]) [ATTACHMENTS];
// Description:
//   Create a screw hole mask.  See [screw parameters](#section-screw-parameters) for details on the parameters that define a screw.
//   The screw hole can be threaded to receive a screw or it can be an unthreaded clearance hole.  
//   The tolerance determines the dimensions of the screw
//   based on ISO and ASME standards.  Screws fabricated at those dimensions will mate properly with standard hardware.
//   The $slop argument makes the hole larger by 4*$slop to account for printing overextrusion.  It defaults to 0.
//   .
//   You can generate a screw specification from {{screw_info()}}, possibly create a modified version, and pass that in rather than giving the parameters.
//   .
//   The tolerance should be a nut tolerance for a threaded hole or a clearance hole tolerance for clearance holes.
//   For clearance holes, the UTS tolerances are "normal", "loose" and "close".  ASME also specifies the same naming for metric clearance holes.
//   However, ISO gives "fine", "medium" and "coarse" instead.  This function accepts all of these in either system.  It also takes "tight" to be equivalent to "close",
//   even though no standard suggests it, because it's a natural opposite of "loose".  The official tolerance designations for ISO are "H12" for "fine", "H13" for "medium"
//   and "H14" for "coarse".  These designations will also work, but only for metric holes.  
//   .
//   The counterbore parameter adds a cylindrical clearance hole above the screw shaft.  For flat heads it extends above the flathead and for other screw types it 
//   replaces the head with a cylinder large enough for the head to fit.  For a flat head you must specify the length of the counterbore.  For other heads you can
//   set counterbore to true and it will be sized to match the head height.  The counterbore will extend 0.01 above the TOP of the hole mask to ensure no
//   problems with differences.  
// Arguments:
//   spec = screw specification, e.g. "M5x1" or "#8-32".  See [screw naming](#subsection-screw-naming).  This can also be a screw specification structure of the form produced by {{screw_info()}}.  
//   head = head type.  See [screw heads](#subsection-screw-heads)  Default: none
//   ---
//   thread = thread type or specification for threaded masks, or false to make an unthreaded mask.  See [screw pitch](#subsection-standard-screw-pitch). Default: false
//   oversize = amount to increase diameter of all screw parts, a scalar or length 3 vector.  Default: 0
//   oversize_hole = amount to increase diameter of the hole.
//   oversize_shank = amount to increase diameter of shank.
//   oversize_head = amount to increase diameter of head.  
//   length = length of screw (in mm)
//   shank = length of unthreaded portion of screw (in mm).  Default: 0
//   counterbore = set to length of counterbore, or true to make a counterbore equal to head height.  Default: no counterbore
//   tolerance = threading or clearance hole tolerance.  For internal threads, detrmines actual thread geometry based on nominal sizing.  See [tolerance](#subsection-tolerance). Default is "2B" for UTS and 6H for ISO.  For clearance holes, determines how much clearance to add.  Default is "normal".  
//   $slop = add extra gap to account for printer overextrusion.  Default: 0
//   atype = anchor type, one of "screw", "head", "shaft", "threads", "shank"
//   anchor = Translate so anchor point on the shaft is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `BOTTOM`
//   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:
//   diff()
//     cuboid(20)
//       position(TOP)
//         down(4)screw_hole("1/4-20,.5",head="socket",counterbore=5,anchor=TOP);

module screw_hole(spec, head="none", thread=false, oversize, hole_oversize, head_oversize, 
             length, l, shank=0, tolerance=undef, shank_diam, counterbore=0, 
             atype="shaft",anchor=BOTTOM,spin=0, orient=UP)
{
   // Force flatheads to sharp for proper countersink shape
  
   head = starts_with(head,"flat") ? str(head," sharp")
                                   : head;
   if ((thread && thread!="none") || is_def(oversize) || is_def(hole_oversize)) {
     undersize = is_def(oversize) ? -oversize
               : -[hole_oversize, 0, default(head_oversize,0)];
     default_tag("remove")
       screw(spec,head=head,thread=thread,undersize=undersize,
             length=length,l=l,tolerance=tolerance, _counterbore=counterbore,
             atype=atype, anchor=anchor, spin=spin, orient=orient, _internal=true)
         children();
   }
   else {
     tolerance = default(tolerance, "normal");
     dummyA=assert(is_string(spec) || is_struct(spec), "Screw spec must be a string or struct");
     screw_spec = _validate_screw_spec(
                                        is_struct(spec) ? spec
                                      : screw_info(spec, head,  thread=thread));
     // UTS clearances from ASME B18.2.8
     UTS_clearance = [
       [ // Close fit
         0.1120 * INCH,0.008*INCH,
         0.1250 * INCH, 1/64*INCH,
         7/16   * INCH, 1/64*INCH,
         1/2    * INCH, 1/32*INCH,
         1.25   * INCH, 1/32*INCH,
         1.375  * INCH, 1/16*INCH
       ],
       [ // Normal fit
         0.1120 * INCH, 1/64*INCH,
         0.1250 * INCH, 1/32*INCH,
         7/16   * INCH, 1/32*INCH,
         1/2    * INCH, 1/16*INCH,
         7/8    * INCH, 1/16*INCH,
         1      * INCH, 3/32*INCH,
         1.25   * INCH, 3/32*INCH,
         1.375  * INCH,  1/8*INCH
       ],
       [ // Loose fit
         0.1120 * INCH, 1/32*INCH,
         0.1250 * INCH, 3/64*INCH,
         7/16   * INCH, 3/64*INCH,
         1/2    * INCH, 7/64*INCH,
         5/8    * INCH, 7/64*INCH,
         3/4    * INCH, 5/32*INCH,
         1      * INCH, 5/32*INCH,
         1.125  * INCH, 3/16*INCH,
         1.25   * INCH, 3/16*INCH,
         1.375  * INCH,15/64*INCH
       ]
     ];
     // ISO clearances appear in ASME B18.2.8 and ISO 273
     ISO_clearance = [
       [ // Close, Fine, H12 
         [2.5, 0.1],
         [3.5, 0.2],
         [4,   0.3],
         [5,   0.3],
         [6,   0.4],
         [8,   0.4],
         [10,  0.5],
         [12,  1],
         [42,  1],
         [48,  2],
         [80,  2],
         [90,  3],
         [100, 4],
       ],
       [  // Normal, Medium, H13
         [1.6, 0.2],
         [2,   0.4],
         [3.5, 0.4],
         [4,   0.5],
         [5,   0.5],
         [6,   0.6],
         [8,   1],
         [10,  1],
         [12,  1.5],
         [16,  1.5],
         [20,  2],
         [24,  2],
         [30,  3],
         [42,  3],
         [48,  4],
         [56,  6],
         [90,  6],
         [100, 7],
       ],
       [  // Loose, Coarse, H14
         [1.6, 0.25],
         [2,   0.3],
         [3,   0.6],
         [3.5, 0.7],
         [4,   0.8],
         [5,   0.8],
         [6,   1],
         [8,   2],
         [10,  2],
         [12,  2.5],
         [16,  2.5],
         [20,  4],
         [24,  4],
         [30,  5],
         [36,  6],
         [42,  6],
         [48,  8],
         [56, 10],
         [72, 10],
         [80, 11],
         [90, 11],
         [100,12],
       ]
     ];
     tol_ind = in_list(downcase(tolerance), ["close", "fine", "tight"]) ? 0
             : in_list(downcase(tolerance), ["normal", "medium"]) ? 1
             : in_list(downcase(tolerance), ["loose", "coarse"]) ? 2
             : in_list(tolerance, ["H12","H13","H14"]) ?
                   assert(struct_val(spec,"systerm")=="ISO", str("Hole tolerance ", tolerance, " only allowed with ISO screws"))
                   parse_int(substr(tolerance,1))
             : assert(false,str("Unknown tolerance ",tolerance, " for clearance hole"));
     tol_table = struct_val(spec,"system")=="UTS" ? UTS_clearance[tol_ind] : ISO_clearance[tol_ind];
     hole_oversize = lookup(struct_val(screw_spec, "diameter"), tol_table) + 4*get_slop();
     head_oversize = first_defined([head_oversize,hole_oversize]) + 4*get_slop();
     shank_oversize = 0;
echo(hole_oversize, shank_oversize, head_oversize, oversize);
     default_tag("remove")     
       screw(spec,head=head,thread=thread,threads_undersize=-hole_oversize, head_undersize=-head_oversize, 
             length=length,l=l,tolerance=tolerance, _counterbore=counterbore,
             atype=atype, anchor=anchor, spin=spin, orient=orient, _internal=true)
         children();
   }
}  


module _driver(spec)
{
  drive = struct_val(spec,"drive");
  if (is_def(drive) && drive!="none") {
    head = struct_val(spec,"head");
    diameter = struct_val(spec,"diameter");
    drive_size = struct_val(spec,"drive_size");
    drive_width = struct_val(spec,"drive_width");
    drive_diameter = struct_val(spec, "drive_diameter");
    drive_depth = first_defined([struct_val(spec, "drive_depth"), .7*diameter]); // Note hack for unspecified depth
    head_top = starts_with(head,"flat") || head=="none" ? 0 :
               struct_val(spec,"head_height");
    up(head_top-drive_depth){
      // recess should be positioned with its bottom center at (0,0) and the correct recess depth given above
      if (drive=="phillips") phillips_mask(drive_size,anchor=BOTTOM);
      if (drive=="torx") torx_mask(size=drive_size, l=drive_depth+1, center=false);
      if (drive=="hex") hex_drive_mask(drive_size,drive_depth+1,anchor=BOT);
      if (drive=="slot") {
          head_width = first_defined([struct_val(spec, "head_size"), diameter]);
          cuboid([2*head_width, drive_width, drive_depth+1],anchor=BOTTOM);
      }
    }
  }
}


function _ISO_thread_tolerance(diameter, pitch, internal=false, tolerance=undef) =
  let(
    P = pitch,
    H = P*sqrt(3)/2,
    tolerance = first_defined([tolerance, internal?"6H":"6g"]),

    pdiam = diameter - 2*3/8*H,          // nominal pitch diameter
    mindiam = diameter - 2*5/8*H,        // nominal minimum diameter

    EI = [   // Fundamental deviations for nut thread
          ["G", 15+11*P],
          ["H", 0],            // Standard practice
         ],

    es = [    // Fundamental deviations for bolt thread
          ["e", -(50+11*P)],   // Exceptions if P<=0.45mm
          ["f", -(30+11*P)],
          ["g", -(15+11*P)],   // Standard practice
          ["h", 0]             // Standard practice for tight fit
         ],

    T_d6 = 180*pow(P,2/3)-3.15/sqrt(P),
    T_d = [  // Crest diameter tolerance for major diameter of bolt thread
           [4, 0.63*T_d6],
           [6, T_d6],
           [8, 1.6*T_d6]
          ],

    T_D1_6 = 0.2 <= P && P <= 0.8 ? 433*P - 190*pow(P,1.22) :
             P > .8 ? 230 * pow(P,0.7) : undef,
    T_D1 = [ // Crest diameter tolerance for minor diameter of nut thread
             [4, 0.63*T_D1_6],
             [5, 0.8*T_D1_6],
             [6, T_D1_6],
             [7, 1.25*T_D1_6],
             [8, 1.6*T_D1_6]
           ],

    rangepts = [0.99, 1.4, 2.8, 5.6, 11.2, 22.4, 45, 90, 180, 300],
    d_ind = floor(lookup(diameter,hstack(rangepts,count(len(rangepts))))),
    avgd = sqrt(rangepts[d_ind]* rangepts[d_ind+1]),

    T_d2_6 = 90*pow(P, 0.4)*pow(avgd,0.1),
    T_d2 = [ // Pitch diameter tolerance for bolt thread
             [3, 0.5*T_d2_6],
             [4, 0.63*T_d2_6],
             [5, 0.8*T_d2_6],
             [6, T_d2_6],
             [7, 1.25*T_d2_6],
             [8, 1.6*T_d2_6],
             [9, 2*T_d2_6],
           ],

    T_D2 = [  // Tolerance for pitch diameter of nut thread
              [4, 0.85*T_d2_6],
              [5, 1.06*T_d2_6],
              [6, 1.32*T_d2_6],
              [7, 1.7*T_d2_6],
              [8, 2.12*T_d2_6]
           ],

    internal = is_def(internal) ? internal : tolerance[1] != downcase(tolerance[1]),
    internalok = !internal || (
                               len(tolerance)==2 && str_find("GH",tolerance[1])!=undef && str_find("45678",tolerance[0])!=undef),
    tol_str = str(tolerance,tolerance),
    externalok = internal || (
                              (len(tolerance)==2 || len(tolerance)==4)
                                                          && str_find("efgh", tol_str[1])!=undef
                                                          && str_find("efgh", tol_str[3])!=undef
                                                          && str_find("3456789", tol_str[0]) != undef
                                                          && str_find("468", tol_str[2]) !=undef)
  )
  assert(internalok,str("Invalid internal thread tolerance, ",tolerance,".  Must have form <digit><letter>"))
  assert(externalok,str("invalid external thread tolerance, ",tolerance,".  Must have form <digit><letter> or <digit><letter><digit><letter>"))
  let(
    tol_num_pitch = parse_num(tol_str[0]),
    tol_num_crest = parse_num(tol_str[2]),
    tol_letter = tol_str[1]
  )
  assert(tol_letter==tol_str[3],str("Invalid tolerance, ",tolerance,".  Cannot mix different letters"))
  internal ?
    let(  // Nut case
      //a=echo("nut", tol_letter, tol_num_pitch, tol_num_crest),
      fdev = struct_val(EI,tol_letter)/1000,
      Tdval = struct_val(T_D1, tol_num_crest)/1000,
      df=     echo(T_D1=T_D1),
      Td2val = struct_val(T_D2, tol_num_pitch)/1000,
      //fe=   echo("nut",P,fdev=fdev, Tdval=Tdval, Td2val=Td2val),
      bot=[diameter+fdev, diameter+fdev+Td2val+H/6],
      xdiam = [mindiam+fdev,mindiam+fdev+Tdval],
      pitchdiam = [pdiam + fdev, pdiam+fdev+Td2val]
    )
    [["pitch",P],["d_minor",xdiam], ["d_pitch",pitchdiam], ["d_major",bot],["basic",[mindiam,pdiam,diameter]]]
  :
    let( // Bolt case
      //a=echo("bolt"),
      fdev = struct_val(es,tol_letter)/1000,
      Tdval = struct_val(T_d, tol_num_crest)/1000,
      Td2val = struct_val(T_d2, tol_num_pitch)/1000,
      mintrunc = P/8,
      d1 = diameter-5*H/4,
      maxtrunc = H/4 - mintrunc * (1-cos(60-acos(1-Td2val/4/mintrunc)))+Td2val/2,
      //cc=echo("bolt",P,fdev=fdev, Tdval=Tdval, Td2val=Td2val),
      bot = [diameter-2*H+2*mintrunc+fdev, diameter-2*H+2*maxtrunc+fdev],
      xdiam = [diameter+fdev,diameter+fdev-Tdval],
      pitchdiam = [pdiam + fdev, pdiam+fdev-Td2val]
    )
    [["pitch",P],["d_major",xdiam], ["d_pitch",pitchdiam], ["d_minor",bot],["basic",[mindiam,pdiam,diameter]]];

function _UTS_thread_tolerance(diam, pitch, internal=false, tolerance=undef) =
  let(
    d = diam/INCH,   // diameter in inches
    P = pitch/INCH,  // pitch in inches
    H = P*sqrt(3)/2,
    tolerance = first_defined([tolerance, internal?"2B":"2A"]),
    tolOK = in_list(tolerance, ["1A","1B","2A","2B","3A","3B"]),
    internal = tolerance[1]=="B"
  )
  assert(tolOK,str("Tolerance was ",tolerance,". Must be one of 1A, 2A, 3A, 1B, 2B, 3B"))
  let(
    LE = 9*P,   // length of engagement.  Is this right?
    pitchtol_2A = 0.0015*pow(d,1/3) + 0.0015*sqrt(LE) + 0.015*pow(P,2/3),
    pitchtol_table = [
                 ["1A", 1.500*pitchtol_2A],
                 ["2A",       pitchtol_2A],
                 ["3A", 0.750*pitchtol_2A],
                 ["1B", 1.950*pitchtol_2A],
                 ["2B", 1.300*pitchtol_2A],
                 ["3B", 0.975*pitchtol_2A]
               ],
     pitchtol = struct_val(pitchtol_table, tolerance),
     allowance = tolerance=="1A" || tolerance=="2A" ? 0.3 * pitchtol_2A : 0,
     majortol = tolerance == "1A" ? 0.090*pow(P,2/3) :
                tolerance == "2A" || tolerance == "3A" ? 0.060*pow(P,2/3) :
                pitchtol+pitch/4/sqrt(3),    // Internal case
     minortol = tolerance=="1B" || tolerance=="2B" ?
                    (
                      d < 0.25 ? constrain(0.05*pow(P,2/3)+0.03*P/d - 0.002, 0.25*P-0.4*P*P, 0.394*P)
                               : (P > 0.25 ? 0.15*P : 0.25*P-0.4*P*P)
                    ) :
                tolerance=="3B" ? constrain(0.05*pow(P,2/3)+0.03*P/d - 0.002, P<1/13 ? 0.12*P : 0.23*P-1.5*P*P, 0.394*P)
                     :0, // not used for external threads
     //f=echo(allowance=allowance),
     //g=echo(pta2 = pitchtol_2A),
     // ff=echo(minortol=minortol, pitchtol=pitchtol, majortol=majortol),
     basic_minordiam = d - 5/4*H,
     basic_pitchdiam = d - 3/4*H,
     majordiam = internal ? [d,d] :          // A little confused here, paragraph 8.3.2
                          [d-allowance-majortol, d-allowance],
     //ffda=echo(allowance=allowance, majortol=majortol, "*****************************"),
     pitchdiam = internal ? [basic_pitchdiam, basic_pitchdiam + pitchtol]
                          : [majordiam[1] - 3/4*H-pitchtol, majordiam[1]-3/4*H],
     minordiam = internal ? [basic_minordiam, basic_minordiam + minortol]
                          : [pitchdiam[0] - 3/4*H, basic_minordiam - allowance - H/8]   // the -H/8 is for the UNR case, 0 for UN case
    )
    [["pitch",P*INCH],["d_major",majordiam*INCH], ["d_pitch", pitchdiam*INCH], ["d_minor",minordiam*INCH],
     ["basic", INCH*[basic_minordiam, basic_pitchdiam, d]]];

function _exact_thread_tolerance(d,P) =
   let(
       H = P*sqrt(3)/2,
       basic_minordiam = d - 5/4*H,
       basic_pitchdiam = d - 3/4*H
      )
    [["pitch", P], ["d_major", [d,d]], ["d_pitch", [basic_pitchdiam,basic_pitchdiam]], ["d_minor", [basic_minordiam,basic_minordiam]],
     ["basic", [basic_minordiam, basic_pitchdiam, d]]];


// Module: nut()
// Usage:
//   nut([name], diameter, thickness, [thread=], [oversize=], [spec=], [tolerance=], [$slop=]) [ATTACHMENTS];
// Description:
//   Generates a hexagonal nut.  See [screw parameters](#section-screw-parameters) for details on the parameters that define a nut.
//   As for screws, you can give the specification in `spec` and then omit the name.  The diameter is the flat-to-flat
//   size of the nut produced.  
//   .
//   The tolerance determines the actual thread sizing based on the nominal size in accordance with standards.  
//   The $slop parameter determines extra gaps left to account for printing overextrusion.  It defaults to 0.
// Arguments:
//   name = screw specification, e.g. "M5x1" or "#8-32".  See [screw naming](#subsection-screw-naming).
//   diameter = outside diameter of nut (flat to flat dimension)
//   thickness = thickness of nut (in mm)
//   ---
//   thread = thread type or specification. See [screw pitch](#subsection-standard-screw-pitch). Default: "coarse"
//   oversize = amount to increase screw diameter for clearance holes.  Default: 0
//   spec = screw specification from `screw_info()`.  If you specify this you can omit all the preceeding parameters.
//   bevel = bevel the nut.  Default: false
//   tolerance = nut tolerance.  Determines actual nut thread geometry based on nominal sizing.  See [tolerance](#subsection-tolerance). Default is "2B" for UTS and "6H" for ISO.
//   $slop = extra space left to account for printing over-extrusion.  Default: 0
//   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: A metric and UTS nut
//   nut("3/8", 5/8*INCH, 1/4*INCH);
//   right(25)
//      nut("M8", 16, 6);
// Example: The three different UTS nut tolerances
//   module mark(number)
//   {
//     difference(){
//        children();
//        ycopies(n=number, spacing=1.5)right(.25*INCH-2)up(8-.35)cyl(d=1, h=1);
//     }
//   }
//   $fn=64;
//   xdistribute(spacing=17){
//     mark(1) nut("1/4-20", thickness=8, diameter=0.5*INCH,tolerance="1B");
//     mark(2) nut("1/4-20", thickness=8, diameter=0.5*INCH,tolerance="2B");
//     mark(3) nut("1/4-20", thickness=8, diameter=0.5*INCH,tolerance="3B");
//   }

function nut(name, diameter, thickness, thread="coarse", spec, tolerance=undef,
           bevel=false, anchor=BOTTOM,spin=0, orient=UP) = no_function("nut");

module nut(name, diameter, thickness, thread="coarse", spec, tolerance=undef,
           bevel=false, anchor=BOTTOM,spin=0, orient=UP, oversize=0)
{
   assert(is_num(diameter) && diameter>0);
   assert(is_num(thickness) && thickness>0);
   spec = is_def(spec) ? spec : screw_info(name, thread=thread, threads_oversize=oversize);
   threadspec = thread_specification(spec, internal=true, tolerance=tolerance);
   echo(threadspec=threadspec,"for nut threads");
   echo(nut_minor_diam = mean(struct_val(threadspec,"d_minor")));
   threaded_nut(
        od=diameter,
        id=[mean(struct_val(threadspec, "d_minor")),
            mean(struct_val(threadspec, "d_pitch")),
            mean(struct_val(threadspec, "d_major"))],
        pitch = struct_val(threadspec, "pitch"),
        h=thickness,
        bevel=bevel,
        anchor=anchor,spin=spin,orient=orient) children();
}


// Takes a screw name as input and returns a list of the form
// [system, diameter, thread, length]
// where system is either "english" or "metric".  

function _parse_screw_name(name) =
    let( commasplit = str_split(name,","),
         length = parse_num(commasplit[1]),
         xdash = str_split(commasplit[0], "-x"),
         type = xdash[0],
         thread = parse_float(xdash[1])
    )
    assert(len(commasplit)<=2, str("More than one comma found in screw name, \"",name,"\""))
    assert(len(xdash)<=2, str("Screw name has too many '-' or 'x' characters, \"",name,"\""))
    assert(len(commasplit)==1 || is_num(length), str("Invalid length in screw name, \"",name,"\""))
    assert(len(xdash)==1 || all_nonnegative(thread),str("Thread pitch not a valid number in screw name, \"",name,"\""))
    type[0] == "M" || type[0] == "m" ? 
        let(diam = parse_float(substr(type,1)))
        assert(is_num(diam), str("Screw size must be a number in screw name, \"",name,"\""))
        ["metric", parse_float(substr(type,1)), thread, length] 
    :
    let(
        diam = type[0] == "#" ? type :
               suffix(type,2)=="''" ? parse_float(substr(type,0,len(type)-2)) :
               let(val=parse_num(type))
               assert(all_positive(val), str("Screw size must be a number in screw name, \"",name,"\""))
               val == floor(val) && val>=0 && val<=12 ? str("#",type) : val
    )
    assert(is_str(diam) || is_num(diam), str("Invalid screw diameter in screw name, \"",name,"\""))
    ["english", diam, thread, u_mul(25.4,length)];


// drive can be "hex", "phillips", "slot", "torx", or "none"
// or you can specify "ph0" up to "ph4" for phillips and "t20" for torx 20
function _parse_drive(drive=undef, drive_size=undef) =
    is_undef(drive) ? ["none",undef] 
  : assert(is_string(drive))
    let(drive = downcase(drive))
    in_list(drive,["hex","phillips", "slot", "torx", "phillips", "none"]) ? [drive, drive_size] 
  : drive[0]=="t" ? let(size = parse_int(substr(drive,1))) ["torx",size,torx_depth(size) ] 
  : starts_with(drive,"ph") && search(drive[2], "01234")!=[] ? ["phillips", ord(drive[2])-ord("0")] 
  : assert(false,str("Unknown screw drive type ",drive));


// Module: screw_head()
// Usage:
//    screw_head(screw_info, [details],[counterbore],[flat_height])
// Description:
//    Draws the screw head described by the data structure `screw_info`, which
//    should have the fields produced by {{screw_info()}}.  See that function for
//    details on the fields.  Standard orientation is with the head centered at (0,0)
//    and oriented in the +z direction.  Flat heads appear below the xy plane.
//    Other heads appear sitting on the xy plane.
// Arguments:
//    screw_info = structure produced by {{screw_info()}}
//    details = true for more detailed model.  Default: false
function screw_head(screw_info,details=false) = no_function("screw_head");
module screw_head(screw_info,details=false, counterbore=0,flat_height) {
   no_children($children);
   head = struct_val(screw_info, "head");
   head_size = struct_val(screw_info, "head_size");
   head_height = struct_val(screw_info, "head_height");
   dum0=assert(is_def(head_height) || in_list(head,["flat","none"]), "Undefined head height only allowed with flat head or headless screws");
   heightok = (is_undef(head_height) && in_list(head,["flat","none"])) || all_positive(head_height);
   dum1=assert(heightok, "Head hight must be a postive number");
   dum2=assert(counterbore==0 || counterbore==false || head!="none", "Cannot counterbore a headless screw");
   counterbore_temp = counterbore==false? 0 
                    : head!="flat" && counterbore==true ? head_height 
                    : counterbore;
   dum3=assert(is_finite(counterbore_temp) && counterbore_temp>=0, str(counterbore==true? "Must specify numerical counterbore height with flat head screw"
                                                             : "Counterbore must be a nonnegative number"));

   echo(counterboretemp=counterbore_temp);
   counterbore = counterbore_temp==0 && head!="flat" ? counterbore_temp : counterbore_temp + 0.01;
   if (head!="flat" && counterbore>0)  
     cyl(d=head=="hex"? 2*head_size/sqrt(3) : head_size, l=counterbore, anchor=BOTTOM);
   if (head=="flat") {   // For flat head, counterbore is integrated
     angle = struct_val(screw_info, "head_angle")/2;
     diam = struct_val(screw_info, "diameter");
     sharpsize = struct_val(screw_info, "head_size_sharp");
     echo(sharpsize=sharpsize, hs=head_size);
     sidewall_height = (sharpsize - head_size)/2 / tan(angle);
     cylheight = counterbore + sidewall_height;
     slopeheight = flat_height - sidewall_height;
     r1 = head_size/2;
     r2 = r1 - tan(angle)*slopeheight;
     echo(r1=r1,r2=r2,slopeheight=slopeheight, cylheight=cylheight, sideh=sidewall_height,flath=flat_height);
     rotate_extrude()
       polygon([[0,-flat_height],[r2,-flat_height],[r1,-flat_height+slopeheight],[r1,counterbore], [0,counterbore]]);
   }
   if (head!="flat" && counterbore==0) {
     if (in_list(head,["round","pan round","button","fillister","cheese"])) {
       base = head=="fillister" ? 0.75*head_height :
              head=="pan round" ? .6 * head_height :
              head=="cheese" ? .7 * head_height :
              0.1 * head_height;   // round and button
       head_size2 = head=="cheese" ?  head_size-2*tan(5)*head_height : head_size; // 5 deg slope on cheese head
       cyl(l=base, d1=head_size, d2=head_size2,anchor=BOTTOM)
         attach(TOP)
           rotate_extrude()
             intersection(){
               arc(points=[[-head_size2/2,0], [0,-base+head_height * (head=="button"?4/3:1)], [head_size2/2,0]]);
               square([head_size2, head_height-base]);
             }
     }
     if (head=="pan flat")
       cyl(l=head_height, d=head_size, rounding2=0.2*head_size, anchor=BOTTOM);
     if (head=="socket")
       cyl(l=head_height, d=head_size, anchor=BOTTOM, chamfer2=details?struct_val(screw_info,"diameter")/10:undef);
     if (head=="socket ribbed"){
       // These numbers are based on ISO specifications that dictate how much oversizsed a ribbed socket head can be
       // We are making our ribbed heads the same size as unribbed (by cutting the ribbing away), but these numbers are presumably a good guide
       rib_size = [[2, .09],
                   [3, .09],
                   [6, .11],
                   [12, .135],
                   [20, .165]];
       diam = struct_val(screw_info,"diameter");
       intersection() {
         cyl(h=head_height/4, d=head_size, anchor=BOT)
            attach(TOP) cyl(l=head_height*3/4, d=head_size, anchor=BOT, texture="trunc_ribs", tex_counts=[31,1], tex_scale=-lookup(diam,rib_size));
         cyl(h=head_height,d=head_size, chamfer2=diam/10, anchor=BOT);
       }
     }
     if (head=="hex")
       intersection(){
         linear_extrude(height=head_height) hexagon(id=head_size);
         if (details)
           down(.01)cyl(l=head_height+.02,d=2*head_size/sqrt(3), chamfer=head_size*(1/sqrt(3)-1/2), anchor=BOTTOM);
       }
   }
}



// Function: screw_info()
// Usage:
//   info = screw_info(name, [head], [drive], [thread=], [drive_size=], [oversize=])
//
// Description:
//   Look up screw characteristics for the specified screw type.
//   See [screw parameters](#section-screw-parameters) for details on the parameters that define a screw.
//   .
//   The `oversize=` parameter adds the specified amount to the screw and head diameter to make an
//   oversized screw.  This is intended for generating clearance holes, not for dealing with printer
//   inaccuracy.  Does not affect length, thread pitch or head height.
//   .
//   The output is a [[struct|structs.scad]] with the following fields:
//   .
//   Field              | What it is
//   ------------------ | ---------------
//   `"system"`         | Either `"UTS"` or `"ISO"` (used for correct tolerance computation).
//   `"diameter"`       | The nominal diameter of the screw shaft in mm.
//   `"pitch"`          | The thread pitch in mm.  (0 for no threads)
//   `"head"`           | The type of head (a string from the list above).
//   `"head_size"`      | Size of the head in mm.
//   `"head_size_sharp"`| Theoretical head diameter for a flat head screw if it is made with sharp edges (or for countersinks)
//   `"head_angle"`     | Countersink angle for flat heads.
//   `"head_height"`    | Height of the head (when needed to specify the head).
//   `"drive"`          | The drive type (`"phillips"`, `"torx"`, `"slot"`, `"hex"`, `"none"`)
//   `"drive_size"`     | The drive size, either a drive number (phillips or torx) or a dimension in mm (hex).  Not defined for slot drive.
//   `"drive_diameter"` | Diameter of a phillips drive.
//   `"drive_width"`    | Width of the arms of the cross in a phillips drive or the slot for a slot drive.
//   `"drive_depth"`    | Depth of the drive recess.
//   `"length"`         | Length of the screw in mm measured in the customary fashion.  For flat head screws the total length and for other screws, the length from the bottom of the head to the screw tip.
//
// Arguments:
//   name = screw specification, e.g. "M5x1" or "#8-32".  See [screw naming](#subsection-screw-naming).
//   head = head type.  See [screw heads](#subsection-screw-heads)  Default: none
//   drive = drive type.  See [screw heads](#subsection-screw-heads) Default: none
//   ---
//   thread = thread type or specification. See [screw pitch](#subsection-standard-screw-pitch). Default: "coarse"
//   drive_size = size of drive recess to override computed value
//   oversize = amount to increase screw diameter for clearance holes.  Default: 0
//   head_oversize = amount to increase head diameter for countersink holes.  Default: 0 
function screw_info(name, head="none", drive, thread="coarse", drive_size=undef, threads_oversize=0, head_oversize=0) =
  let(type=_parse_screw_name(name),
      drive_info = _parse_drive(drive, drive_size),
      drive=drive_info[0],
      thread = thread==true ? "coarse"
             : thread==false || thread=="none" ? 0
             : thread,
      screwdata =   type[0] == "english" ? _screw_info_english(type[1],type[2], head, thread, drive) 
                  : type[0] == "metric" ? _screw_info_metric(type[1], type[2], head, thread, drive) 
                  : [],
      over_ride = concat(
                        len(drive_info)>=3 ? ["drive_depth", drive_info[2]] : [], 
                        is_def(type[3]) ? ["length",type[3]] : [],
                        is_def(drive_info[1]) ? ["drive_size", drive_info[1]] : []
                      )
,ff=echo(sd=screwdata,head=head)
  )
  _oversize_screw(struct_set(screwdata, over_ride), threads_oversize=threads_oversize, head_oversize=head_oversize);


function _oversize_screw(spec, threads_oversize, head_oversize) = spec;

function _xoversize_screw(spec, threads_oversize, head_oversize) = 
  threads_oversize==0 && head_oversize==0 ? spec 
  : 
  let(
      head_size =  struct_val(spec,"head_size"),
      sharp_size = struct_val(spec,"head_size_sharp"),
      diameter = struct_val(spec,"diameter")
  )
  struct_set(spec, concat(
                            is_def(diameter) ? ["diameter", diameter+threads_oversize] : [],
                            is_def(sharp_size) ? ["head_size_sharp", sharp_size+head_oversize] : [],
                            is_def(head_size) ? ["head_size", head_size+head_oversize] : []
                           ));

function _screw_info_english(diam, threadcount, head, thread, drive) =
 let(
   diameter = is_string(diam) ? parse_int(substr(diam,1))*0.013 +0.06 
                              : diam,
   diamgroup = diameter<7/16 ? 0
             : diameter==7/16 ? 1
             : 2,
   pitch =
     is_num(thread) ? thread :
     is_def(threadcount) ? INCH/threadcount :
     let(
        tind=struct_val([["coarse",0],["unc",0],
                         ["fine",1],["unf",1],
                         ["extra fine",2],["extrafine",2],["unef",2]],
                         downcase(thread)),
        dummy = assert(is_def(tind), str("Unknown thread type, \"",thread,"\"")),
                 // coarse  fine  xfine
                 // UNC     UNF   UNEF
        UTS_thread = [
            ["#0", [undef,    80, undef]],
            ["#1", [   64,    72, undef]],
            ["#2", [   56,    64, undef]],
            ["#3", [   48,    56, undef]],
            ["#4", [   40,    48, undef]],
            ["#5", [   40,    44, undef]],
            ["#6", [   32,    40, undef]],
            ["#8", [   32,    36, undef]],
            ["#10",[   24,    32, undef]],
            ["#12",[   24,    28,    32]],
            [1/4,  [   20,    28,    32]],
            [5/16, [   18,    24,    32]],
            [3/8,  [   16,    24,    32]],
            [7/16, [   14,    20,    28]],
            [1/2,  [   13,    20,    28]],
            [9/16, [   12,    18,    24]],
            [5/8,  [   11,    18,    24]],
            [3/4,  [   10,    16,    20]],
            [7/8,  [    9,    14,    20]],
            [1,    [    8,    12,    20]],
            [1.125,[    7,    12,    18]],
            [1.25, [    7,    12,    18]],
            [1.375,[    6,    12,    18]],
            [1.5,  [    6,    12,    18]],
            [1.75, [    5, undef, undef]],
            [2,    [  4.5, undef, undef]],
         ],
       tentry = struct_val(UTS_thread, diam)
     )
     assert(is_def(tentry), str("Unknown screw size, \"",diam,"\""))
     INCH / tentry[tind],
   head_data =
       head=="none" ? let (
          UTS_setscrew = [
               // hex width, hex depth torx,  torx depth    slot width   slot depth 
            ["#0", [0.028,   0.050,   undef,     undef,       0.012,       0.018]],
            ["#1", [0.035,   0.060,   undef,     undef,       0.014,       0.018]],
            ["#2", [0.035,   0.060,   undef,     undef,       0.016,       0.022]],
            ["#3", [0.05 ,   0.070,   undef,     undef,       0.018,       0.025]],
            ["#4", [0.05 ,   0.045,      6,      0.027,       0.021,       0.028]],
            ["#5", [1/16 ,   0.080,      7,      0.036,       0.023,       0.031]],
            ["#6", [1/16 ,   0.080,      7,      0.036,       0.025,       0.035]],
            ["#8", [5/64 ,   0.090,      8,      0.041,       0.029,       0.041]],
            ["#10",[3/32 ,   0.100,      10,     0.049,       0.032,       0.048]],
            ["#12",[undef,   undef,   undef,    undef,        0.038,       0.056]],
            [1/4,  [1/8  ,   0.125,      15,     0.068,       0.045,       0.063]],
            [5/16, [5/32 ,   0.156,      25,     0.088,       0.051,       0.078]],
            [3/8,  [3/16 ,   0.188,      30,     0.097,       0.064,       0.094]],
            [7/16, [7/32 ,   0.219,      40,     0.117,       0.072,       0.109]],
            [1/2,  [1/4  ,   0.250,      45,     0.137,       0.081,       0.125]],
            [9/16, [undef,   undef,   undef,    undef,        0.091,       0.141]],
            [5/8,  [5/16 ,   0.312,      55,     0.202,       0.102,       0.156]],
            [3/4,  [3/8  ,   0.375,      60,     0.202,       0.129,       0.188]],
            [7/8,  [1/2  ,   0.500,      70,     0.291]],     
            [1,    [9/16 ,   0.562,      70,     0.291]],     
            [1.125,[9/16 ,   0.562]],
            [1.25, [5/8  ,   0.625]],
            [1.375,[5/8  ,   0.625]],
            [1.5,  [3/4  ,   0.750]],
            [1.75, [1    ,   1.000]],
            [2,    [1    ,   1.000]],
            ],
          entry = struct_val(UTS_setscrew, diam),
          dummy=assert(is_def(entry), str("Screw size ",diam," unsupported for headless screws")),
          drive_dims = drive == "hex" ? [["drive_size", INCH*entry[0]], ["drive_depth", INCH*entry[1]]]
                     : drive == "torx" ? [["drive_size", entry[2]], ["drive_depth", INCH*entry[3]]] 
                     : drive == "slot" ? [["drive_width", INCH*entry[4]], ["drive_depth", INCH*entry[5]]]
                     : []
         ) concat([["head","none"]], drive_dims) 
     : head=="hex" ? let( 
            UTS_hex = [
               // flat to flat width, height
               ["#2", [    1/8,   1/16]],
               ["#4", [   3/16,   1/16]],
               ["#6", [    1/4,   3/32]],
               ["#8", [    1/4,   7/64]],
               ["#10",[   5/16,    1/8]],
               ["#12",[   5/16,   5/32]],
               [1/4,  [   7/16,   5/32]],
               [5/16, [    1/2,  13/64]],
               [3/8,  [   9/16,    1/4]],
               [7/16, [    5/8,  19/64]],
               [1/2,  [    3/4,  11/32]],
               [9/16, [  13/16,  23/64]],
               [5/8,  [  15/16,  27/64]],
               [3/4,  [  1.125,    1/2]],
               [7/8,  [ 1+5/16,  37/64]],
               [1,    [    1.5,  43/64]],
               [1.125,[1+11/16,  11/16]],
               [1.25, [  1+7/8,  27/32]],
               [1.5,  [   2.25,  15/16]],
               [1.75, [  2+5/8, 1+3/32]],
               [2,    [      3, 1+7/32]],
            ],
            entry = struct_val(UTS_hex, diam)
           )
           assert(is_def(entry), str("Screw size ",diam," unsupported for head type \"",head,"\""))
           [["head", "hex"], ["head_size", INCH*entry[0]], ["head_height", INCH*entry[1]]] 
     : in_list(head,["socket","socket ribbed"]) ? let(
            UTS_socket = [    // height = screw diameter
                       //diam,   hex, torx size, hex depth, torx depth
               ["#0", [  0.096,  0.05, 6,         0.025,      0.027]],
               ["#1", [  0.118,  1/16, 7,         0.031,      0.036]],
               ["#2", [   9/64,  5/64, 8,         0.038,      0.037]],
               ["#3", [  0.161,  5/64, 8,         0.044,      0.041]],   // For larger sizes, hex recess depth is
               ["#4", [  0.183,  3/32, 10,        0.051,      0.049]],   // half the screw diameter
               ["#5", [  0.205,  3/32, 10,        0.057,      0.049]],
               ["#6", [  0.226,  7/64, 15,        0.064,      0.058]],
               ["#8", [  0.270,  9/64, 25,        0.077,      0.078]],
               ["#10",[   5/16,  5/32, 27,        undef,      0.088]],
               ["#12",[  0.324,  5/32, 27,        undef,      0.088]],
               [1/4,  [    3/8,  3/16, 30,        undef,      0.097]],
               [5/16, [  15/32,   1/4, 45,        undef,      0.137]],
               [3/8,  [   9/16,  5/16, 50,        undef,      0.155]],
               [7/16, [  21/32,   3/8, 55,        undef,      0.202]],
               [1/2,  [    3/4,   3/8, 55,        undef,      0.202]],
               [9/16, [  27/32,  7/16, 60,        undef,      0.240]],
               [5/8,  [  15/16,   1/2, 70,        undef,      0.291]],
               [3/4,  [  1.125,   5/8, 80,        undef,      0.332]],
               [7/8,  [ 1+5/16,   3/4, 100,       undef,      0.425]],
               [1,    [    1.5,   3/4, 100,       undef,      0.425]],
               [1.125,[1+11/16,   7/8, undef,     undef,      undef]],
               [1.25, [  1+7/8,   7/8, undef,     undef,      undef]],
               [1.375,[ 2+1/16,     1, undef,     undef,      undef]],
               [1.5,  [   2.25,     1, undef,     undef,      undef]],
               [1.75, [  2+5/8,  1.25, undef,     undef,      undef]],
               [2,    [      3,   1.5, undef,     undef,      undef]],
            ],
            entry = struct_val(UTS_socket, diam),
            dummy=assert(is_def(entry), str("Screw size ",diam," unsupported for head type \"",head,"\"")),
            hexdepth = is_def(entry[3]) ? entry[3]
                     : is_def(diam) ? diam/2
                     : undef,
            drive_size =  drive=="hex" ? [["drive_size",INCH*entry[1]], ["drive_depth",INCH*hexdepth]] :
                          drive=="torx" ? [["drive_size",entry[2]],["drive_depth",INCH*entry[4]]] : []
            )
            concat([["head",head],["head_size",INCH*entry[0]], ["head_height", INCH*diameter]],drive_size) 
     : head=="pan" ? let (
           UTS_pan = [  // pan head for phillips or slotted
                 //              head height 
                 //    diam,   slotted  phillips  phillips drive, phillips diam, phillips width, phillips depth, slot width, slot depth  torx size
               ["#0", [0.116,   0.039,   0.044,        0,          0.067,          0.013,           0.039,       0.023,         0.022]],
               ["#1", [0.142,   0.046,   0.053,        0,          0.085,          0.015,           0.049,       0.027,         0.027]],
               ["#2", [0.167,   0.053,   0.063,        1,          0.104,          0.017,           0.059,       0.031,         0.031,      8]],
               ["#3", [0.193,   0.060,   0.071,        1,          0.112,          0.019,           0.068,       0.035,         0.036]],
               ["#4", [0.219,   0.068,   0.080,        1,          0.122,          0.019,           0.078,       0.039,         0.040,     10]],
               ["#5", [0.245,   0.075,   0.089,        2,          0.158,          0.028,           0.083,       0.043,         0.045]],
               ["#6", [0.270,   0.082,   0.097,        2,          0.166,          0.028,           0.091,       0.048,         0.050,     15]],
               ["#8", [0.322,   0.096,   0.115,        2,          0.182,          0.030,           0.108,       0.054,         0.058,     20]],
               ["#10",[0.373,   0.110,   0.133,        2,          0.199,          0.031,           0.124,       0.060,         0.068,     25]],
               ["#12",[0.425,   0.125,   0.151,        3,          0.259,          0.034,           0.141,       0.067,         0.077]],
               [1/4,  [0.492,   0.144,   0.175,        3,          0.281,          0.036,           0.161,       0.075,         0.087,     30]],
               [5/16, [0.615,   0.178,   0.218,        4,          0.350,          0.059,           0.193,       0.084,         0.106]],
               [3/8,  [0.740,   0.212,   0.261,        4,          0.389,          0.065,           0.233,       0.094,         0.124]],
            ],
            htind = drive=="slot" ? 1 : 2,
            entry = struct_val(UTS_pan, diam),
            dummy=assert(is_def(entry), str("Screw size ",diam," unsupported for head type \"",head,"\"")),
            drive_size = drive=="phillips" ? [["drive_size", entry[3]], ["drive_diameter",INCH*entry[4]],["drive_width",INCH*entry[5]],["drive_depth",INCH*entry[6]]] :
                                            [["drive_width", INCH*entry[7]], ["drive_depth",INCH*entry[8]]])
           concat([["head","pan round"], ["head_size", INCH*entry[0]], ["head_height", INCH*entry[htind]]], drive_size) 
     : head=="button" || head=="round" ? let(
            UTS_button = [    // button, hex or torx drive
                 //   head diam, height, phillips, hex,   torx, hex depth
               ["#0", [0.114,    0.032,   undef,   0.035,  5    , 0.020, 0.015]],
               ["#1", [0.139,    0.039,   undef,   3/64,   5    , 0.028, 0.022]],
               ["#2", [0.164,    0.046,   undef,   3/64,   6    , 0.028, 0.023]],
               ["#3", [0.188,    0.052,   undef,   1/16,   undef, 0.035, undef]],
               ["#4", [0.213,    0.059,   undef,   1/16,   8    , 0.035, 0.032]],
               ["#5", [0.238,    0.066,   undef,   5/64,   10   , 0.044, 0.038]],
               ["#6", [0.262,    0.073,   undef,   5/64,   10   , 0.044, 0.038]],
               ["#8", [0.312,    0.087,   undef,   3/32,   15   , 0.052, 0.045]],
               ["#10",[0.361,    0.101,   undef,   1/8,    25   , 0.070, 0.052]],
               ["#12",[0.413,    0.114,   undef,   1/8,    undef, 0.070, undef]],   // also 0.410, .115, 9/64, hex depth guessed
               [1/4,  [0.437,    0.132,   undef,   5/32,   27   , 0.087, 0.068]],
               [5/16, [0.547,    0.166,   undef,   3/16,   40   , 0.105, 0.090]],
               [3/8,  [0.656,    0.199,   undef,   7/32,   45   , 0.122, 0.106]],
               [7/16, [0.750,    0.220,   undef,   1/4,    undef, 0.193, undef]],  // hex depth interpolated
               [1/2,  [0.875,    0.265,   undef,   5/16,   55   , 0.175, 0.158]],
               [5/8,  [1.000,    0.331,   undef,   3/8,    60   , 0.210, 0.192]],
               [3/4,  [1.1,      0.375,   undef,   7/16,   undef, 0.241]],  // hex depth extrapolated
             ],
             UTS_round = [   // slotted, phillips
                  // head diam, head height, phillips drive, hex, torx, ph diam, ph width, ph depth, slot width, slot depth
               ["#0", [0.113, 0.053, 0, undef, undef]],
               ["#1", [0.138, 0.061, 0, undef, undef]],
               ["#2", [0.162, 0.069, 1, undef, undef, 0.100, 0.017, 0.053, 0.031, 0.048]],
               ["#3", [0.187, 0.078, 1, undef, undef, 0.109, 0.018, 0.062, 0.035, 0.053]],
               ["#4", [0.211, 0.086, 1, undef, undef, 0.118, 0.019, 0.072, 0.039, 0.058]],
               ["#5", [0.236, 0.095, 2, undef, undef, 0.154, 0.027, 0.074, 0.043, 0.063]],
               ["#6", [0.260, 0.103, 2, undef, undef, 0.162, 0.027, 0.084, 0.048, 0.068]],
               ["#8", [0.309, 0.120, 2, undef, undef, 0.178, 0.030, 0.101, 0.054, 0.077]],
               ["#10",[0.359, 0.137, 2, undef, undef, 0.195, 0.031, 0.119, 0.060, 0.087]],
               ["#12",[0.408, 0.153, 3, undef, undef, 0.249, 0.032, 0.125, 0.067, 0.096]],
               [1/4,  [0.472, 0.175, 3, undef, undef, 0.268, 0.034, 0.147, 0.075, 0.109]],
               [5/16, [0.590, 0.216, 3, undef, undef, 0.308, 0.040, 0.187, 0.084, 0.132]],
               [3/8,  [0.708, 0.256, 4, undef, undef, 0.387, 0.064, 0.228, 0.094, 0.155]],
               [1/2,  [0.813, 0.355, 4, undef, undef, 0.416, 0.068, 0.256, 0.106, 0.211]]
             ],
             entry = struct_val(head=="button" ? UTS_button : UTS_round, diam),
             dummy=assert(is_def(entry), str("Screw size ",diam," unsupported for head type \"",head,"\"")),
             drive_index = drive=="phillips" ? 2 :
                           drive=="hex" ? 3 :
                           drive=="torx" ? 4 : undef,
             drive_size = drive=="phillips" && head=="round" ? [["drive_size", entry[2]], ["drive_diameter",u_mul(INCH,entry[5])],
                                              ["drive_width",INCH*entry[6]],["drive_depth",INCH*entry[7]]] :
                          drive=="slot" && head=="round" ?  [["drive_width", INCH*entry[8]], ["drive_depth",u_mul(INCH,entry[9])]] :
                          drive=="hex" && head=="button" ? [["drive_size", INCH*entry[drive_index]], ["drive_depth", u_mul(INCH,entry[5])]]:
                          drive=="torx" && head=="button" ? [["drive_size", entry[drive_index]], ["drive_depth", u_mul(INCH,entry[6])]]:
                          is_def(drive_index) && head=="button" ? [["drive_size", entry[drive_index]]] : []
             )
             concat([["head",head],["head_size",INCH*entry[0]], ["head_height", INCH*entry[1]]],drive_size) 
     : head=="fillister" ? let(
             UTS_fillister = [ // head diam, head height, slot width, slot depth, phillips diam, phillips depth, phillips width, phillips #
                   ["#0", [0.096, 0.055, 0.023, 0.025, 0.067, 0.039, 0.013, 0]],
                   ["#1", [0.118, 0.069, 0.027, 0.031, 0.085, 0.049, 0.015,  ]],
                   ["#2", [0.140, 0.083, 0.031, 0.037, 0.104, 0.059, 0.017,  ]],
                   ["#3", [0.161, 0.095, 0.035, 0.043, 0.112, 0.068, 0.019, 1]],
                   ["#4", [0.183, 0.107, 0.039, 0.048, 0.122, 0.078, 0.019, 1]],
                   ["#5", [0.205, 0.120, 0.043, 0.054, 0.143, 0.067, 0.027, 2]],
                   ["#6", [0.226, 0.132, 0.048, 0.060, 0.166, 0.091, 0.028, 2]],
                   ["#8", [0.270, 0.156, 0.054, 0.071, 0.182, 0.108, 0.030, 2]],
                   ["#10",[0.313, 0.180, 0.060, 0.083, 0.199, 0.124, 0.031, 2]],
                   ["#12",[0.357, 0.205, 0.067, 0.094, 0.259, 0.141, 0.034, 3]],
                   [1/4,  [0.414, 0.237, 0.075, 0.109, 0.281, 0.161, 0.036, 3]],
                   [5/16, [0.518, 0.295, 0.084, 0.137, 0.322, 0.203, 0.042, 3]],
                   [3/8,  [0.622, 0.355, 0.094, 0.164, 0.389, 0.233, 0.065, 4]],
             ],
             entry = struct_val(UTS_fillister, diam),
             dummy=assert(is_def(entry), str("Screw size ",diam," unsupported for head type \"",head,"\"")),
             drive_size = drive=="phillips" ? [["drive_size", entry[7]], ["drive_diameter",INCH*entry[4]],
                                              ["drive_width",INCH*entry[6]],["drive_depth",INCH*entry[5]]] :
                          drive=="slot"?  [["drive_width", INCH*entry[2]], ["drive_depth",INCH*entry[3]]] : []
             )
             concat([["head", "fillister"], ["head_size", INCH*entry[0]], ["head_height", INCH*entry[1]]], drive_size) 
     : starts_with(head,"flat ") || head=="flat" ? 
         let(
             headparts = str_split(head," ",keep_nulls=false),
             partsok = [for (part=headparts) if (!in_list(part, ["flat","undercut","100","82","small","large","sharp"])) part], 
             dummy1=assert(partsok==[], str("Unknown flat head parameter(s) ",partsok)),
             dummy2=assert(!(in_list("small",headparts) && in_list("large",headparts)), "Cannot specify large and small flat head at the same time"),
             undercut = in_list("undercut", headparts),
             small = in_list("small",headparts) || (!in_list("large",headparts) && drive!="hex" && drive!="torx"),
             angle = in_list("100", headparts) ? 100 : 82,
             dummy3=assert(!undercut || angle==82, "Cannot make undercut 100 degree screw"),
             dummy4=assert(small || angle==82, "Only 82 deg large screws are supported"),
             dummy5=assert(small || !undercut, "Undercut only supported for small flatheads"),
             UTS_flat_small = [  // for phillips drive, slotted, and torx   ASME B18.6.3
                    //                     ----- Phillips ----              undercut phillips
                    //    ph drive, torx , diam,  depth, width, slotwidth,  diam, depth, width
                    //       0       1       2      3      4        5           6        7  
                   ["#0", [  0,     undef, 0.062, 0.035, 0.014,   0.023,   0.062, 0.035, 0.014]],
                   ["#1", [  0,     undef, 0.070, 0.043, 0.015,   0.026,   0.070, 0.043, 0.015]],
                   ["#2", [  1,     6    , 0.096, 0.055, 0.017,   0.031,   0.088, 0.048, 0.017]],
                   ["#3", [  1,     undef, 0.100, 0.060, 0.018,   0.035,   0.099, 0.059, 0.018]],
                   ["#4", [  1,     8    , 0.122, 0.081, 0.018,   0.039,   0.110, 0.070, 0.018]],
                   ["#5", [  2,     undef, 0.148, 0.074, 0.027,   0.043,   0.122, 0.081, 0.018]], //ph#1 for undercut
                   ["#6", [  2,     10   , 0.168, 0.094, 0.029,   0.048,   0.140, 0.066, 0.025]],
                   ["#8", [  2,     15   , 0.182, 0.110, 0.030,   0.054,   0.168, 0.094, 0.029]],
                   ["#10",[  2,     20   , 0.198, 0.124, 0.032,   0.060,   0.182, 0.110, 0.030]],
                   ["#12",[  3,     undef, 0.262, 0.144, 0.035,   0.067,   0.226, 0.110, 0.030]],
                   [1/4,  [  3,     27   , 0.276, 0.160, 0.036,   0.075,   0.244, 0.124, 0.032]],
                   [5/16, [  4,     40   , 0.358, 0.205, 0.061,   0.084,   0.310, 0.157, 0.053]],
                   [3/8,  [  4,     40   , 0.386, 0.234, 0.065,   0.094,   0.358, 0.205, 0.061]],
                   [1/2,  [  4,     undef, 0.418, 0.265, 0.069,   0.106,   0.402, 0.252, 0.068]]
             ],
             UTS_flat_small_100 = [  // for phillips drive, slotted, 100 deg angle  ASME B18.6.3
                    //                     ----- Phillips ----            
                    //    ph drive, torx , diam,  depth, width, slotwidth
                    //       0       1       2      3      4        5    
                   ["#0", [  0,     undef, 0.054, 0.027, 0.013,   0.023]],
                   ["#1", [  0,     undef, 0.062, 0.035, 0.014,   0.026]],
                   ["#2", [  1,     6    , 0.088, 0.048, 0.012,   0.031]],
                   ["#3", [  1,     undef, 0.096, 0.055, 0.014,   0.035]],
                   ["#4", [  1,     8    , 0.110, 0.070, 0.018,   0.039]],
                   ["#6", [  2,     10   , 0.148, 0.074, 0.027,   0.048]],
                   ["#8", [  2,     15   , 0.162, 0.090, 0.028,   0.054]],
                   ["#10",[  2,     20   , 0.178, 0.104, 0.030,   0.060]],
                   [1/4,  [  3,     27   , 0.240, 0.124, 0.033,   0.075]],
                   [5/16, [  4,     40   , 0.310, 0.157, 0.053,   0.084]],
                   [3/8,  [  4,     40   , 0.336, 0.182, 0.056,   0.094]],
             ],
             UTS_flat_large = [   // for hex drive, torx     ASME B18.3
                       // minimum
                       // head diam, hex drive size, torx size, hex depth, torx depth
                   ["#0", [ 0.117,   1/32,            3    ,     0.025,    0.016]],
                   ["#1", [ 0.143,   3/64,            6    ,     0.031,    0.036]],
                   ["#2", [ 0.168,   3/64,            6    ,     0.038,    0.036]],
                   ["#3", [ 0.193,   1/16,            8    ,     0.044,    0.041]],
                   ["#4", [ 0.218,   1/16,            10   ,     0.055,    0.038]],
                   ["#5", [ 0.240,   5/64,            10   ,     0.061,    0.038]],
                   ["#6", [ 0.263,   5/64,            15   ,     0.066,    0.045]],
                   ["#8", [ 0.311,   3/32,            20   ,     0.076,    0.053]],
                   ["#10",[ 0.359,    1/8,            25   ,     0.087,    0.061]],
                   [1/4,  [ 0.480,   5/32,            30   ,     0.111,    0.075]],
                   [5/16, [ 0.600,   3/16,            40   ,     0.135,    0.090]],
                   [3/8,  [ 0.720,   7/32,            45   ,     0.159,    0.106]],
                   [7/16, [ 0.781,    1/4,            50   ,     0.172,    0.120]],
                   [1/2,  [ 0.872,   5/16,            50   ,     0.220,    0.120]],
                   [5/8,  [ 1.112,    3/8,            55   ,     0.220,    0.158]],
                   [3/4,  [ 1.355,    1/2,            60   ,     0.248,    0.192]],
                   [7/8,  [ 1.604,   9/16,            undef,     0.297,    undef]],
                   [1,    [ 1.841,    5/8,            undef,     0.325,    undef]],
                   [1.125,[ 2.079,    3/4,            undef,     0.358,    undef]],
                   [1.25, [ 2.316,    7/8,            undef,     0.402,    undef]],
                   [1.375,[ 2.688,    7/8,            undef,     0.402,    undef]],
                   [1.5,  [ 2.938,      1,            undef,     0.435,    undef]],
             ],
             entry = struct_val(    angle==100 ? UTS_flat_small_100 
                                  : small ? UTS_flat_small 
                                  : UTS_flat_large, 
                                diam),
             dummy=assert(is_def(entry), str("Screw size ",diam," unsupported for head type \"",head,"\"")),
             a=[1.92+1.82, 1.88+1.8, 1.88+1.8]/2,
             b=[.003+.013, .063+.073, .125+.135]/2,
             smallsize = a[diamgroup]*diameter-b[diamgroup],
     
             csmall=[2.04, 2, 2],
             dsmall=[.003, .063, .125], 
             dlarge = [-.031, .031, .062],
             sharpsize = small ? csmall[diamgroup]*diameter-dsmall[diamgroup] // max theoretical (sharp) head diam
                                     : diameter < 0.1 ? [0.138,0.168,0.0822,0.0949][(diameter - 0.06)/.013] 
                                     : 2*diameter-dlarge[diamgroup],
             largesize = lerp(entry[0],sharpsize,.20),   // Have min size and max theory size.  Use point 20% up from min size
             undercut_height = let(
                                   a=[.432+.386, .417+.37, .417+.37]/2,
                                   b=[.001+.005, .026+.029, .052+.055]/2
                               )
                               a[diamgroup]*diameter + b[diamgroup],
             e=undercut ? [.202+.134, .192+.129, .192+.129]/2 
              : angle==100 ? [.222+.184]/2 
              : [.288+.192, .274+.184, .274+.184]/2,
             f=undercut ? [.002, .012+.011, .024+.019]/2
              : angle==100 ? [.0005+.004]/2 
              : [.004, .015+.017, .034+.027],
             tipdepth_small = e[diamgroup]*diameter + f[diamgroup],
             driveind = small && drive=="phillips" ? 0
                      : !small && drive=="hex" ? 1 
                      : drive=="torx" ? 2 
                      : undef,
             drive_dims = small ? (
                            drive=="phillips" && !undercut ? [["drive_diameter",INCH*entry[2]],
                                                              ["drive_width",INCH*entry[4]],
                                                              ["drive_depth",INCH*entry[3]]] :
                            drive=="phillips" && undercut ?  [["drive_diameter",INCH*entry[6]],
                                                              ["drive_width",INCH*entry[8]],
                                                              ["drive_depth",INCH*entry[7]]] :
                            drive=="slot" ? [["drive_width", INCH*entry[5]], 
                                             ["drive_depth", INCH*tipdepth_small]] :
                            
                            []
                            )
                         :
                           (
                             drive=="hex" ? [["drive_depth", INCH*entry[3]]] :
                             drive=="torx" ? [["drive_depth", INCH*entry[4]]] : []
                           )
         )
         [
           ["head","flat"],
           ["head_angle",angle],
           ["head_size", in_list("sharp",headparts) ? sharpsize*INCH
                        : small ? smallsize*INCH : largesize*INCH], //entry[0]*INCH],
           ["head_size_sharp", sharpsize*INCH],
           if (is_def(driveind)) ["drive_size", (drive=="hex"?INCH:1)*entry[driveind]],
           if (undercut) ["head_height", undercut_height*INCH],
           each drive_dims
         ]
     : []
 )
 concat([["system","UTS"],["diameter",INCH*diameter],["pitch", pitch],["drive",drive]],
          head_data
 );


function _screw_info_metric(diam, pitch, head, thread, drive) =
 let(
   pitch =
     is_num(thread) ? thread :
     is_def(pitch) ? pitch :
     let(
        tind=struct_val([["coarse",0],
                         ["fine",1],
                         ["extra fine",2],["extrafine",2],
             ["super fine",3],["superfine",3]],
                         downcase(thread)),
        dummy = assert(is_def(tind), str("Unknown thread type, \"",thread,"\"")),
                            // coarse  fine  xfine superfine
        ISO_thread = [
                      [1  , [0.25,    0.2 ,   undef, undef,]],
                      [1.2, [0.25,    0.2 ,   undef, undef,]],
                      [1.4, [0.3 ,    0.2 ,   undef, undef,]],
                      [1.6, [0.35,    0.2 ,   undef, undef,]],
                      [1.7, [0.35,   undef,   undef, undef,]],
                      [1.8, [0.35,    0.2 ,   undef, undef,]],
                      [2  , [0.4 ,    0.25,   undef, undef,]],
                      [2.2, [0.45,    0.25,   undef, undef,]],
                      [2.3, [0.4 ,   undef,   undef, undef,]],
                      [2.5, [0.45,    0.35,   undef, undef,]],
                      [2.6, [0.45,   undef,   undef, undef,]],
                      [3  , [0.5 ,    0.35,   undef, undef,]],
                      [3.5, [0.6 ,    0.35,   undef, undef,]],
                      [4  , [0.7 ,    0.5 ,   undef, undef,]],
                      [5  , [0.8 ,    0.5 ,   undef, undef,]],
                      [6  , [1   ,    0.75,   undef, undef,]],
                      [7  , [1   ,    0.75,   undef, undef,]],
                      [8  , [1.25,    1   ,    0.75, undef,]],
                      [9  , [1.25,    1   ,    0.75, undef,]],
                      [10 , [1.5 ,    1.25,    1   ,  0.75,]],
                      [11 , [1.5 ,    1   ,    0.75, undef,]],
                      [12 , [1.75,    1.5 ,    1.25,  1,   ]],
                      [14 , [2   ,    1.5 ,    1.25,  1,   ]],
                      [16 , [2   ,    1.5 ,    1   , undef,]],
                      [18 , [2.5 ,    2   ,    1.5 ,  1,   ]],
                      [20 , [2.5 ,    2   ,    1.5 ,  1,   ]],
                      [22 , [2.5 ,    2   ,    1.5 ,  1,]],
                      [24 , [3   ,    2   ,    1.5 ,  1,]],
                      [27 , [3   ,    2   ,    1.5 ,  1,]],
                      [30 , [3.5 ,    3   ,    2   ,  1.5,]],
                      [33 , [3.5 ,    3   ,    2   ,  1.5,]],
                      [36 , [4   ,    3   ,    2   ,  1.5,]],
                      [39 , [4   ,    3   ,    2   ,  1.5,]],
                      [42 , [4.5 ,    4   ,    3   ,  2,]],
                      [45 , [4.5 ,    4   ,    3   ,  2,]],
                      [48 , [5   ,    4   ,    3   ,  2,]],
                      [52 , [5   ,    4   ,    3   ,  2,]],
                      [56 , [5.5 ,    4   ,    3   ,  2,]],
                      [60 , [5.5 ,    4   ,    3   ,  2,]],
                      [64 , [6   ,    4   ,    3   ,  2,]],
                      [68 , [6   ,    4   ,    3   ,  2,]],
                      [72 , [6   ,    4   ,    3   ,  2,]],
                      [80 , [6   ,    4   ,    3   ,  2,]],
                      [90 , [6   ,    4   ,    3   ,  2,]],
                      [100, [6   ,    4   ,    3   ,  2,]],
        ],
        tentry = struct_val(ISO_thread, diam)
     )
     assert(is_def(tentry), str("Unknown screw size, M",diam,""))
     tentry[tind],
   head_data =
       head=="none" ? let(
           metric_setscrew =
               [
                  //   hex    torx, torx depth, slot width, slot depth 
                [1.2, [undef, undef,   undef,    0.330,        0.460]],
                [1.4, [0.7,   undef,   undef,    undef,        undef]],
                [1.6, [0.7,   undef,   undef,    0.380,        0.650]],
                [1.8, [0.7,   undef,   undef,    undef,        undef]],
                [2,   [0.9,   undef,   undef,    0.380,        0.740]],
                [2.5, [1.3,   undef,   undef,    0.530,        0.835]],
                [3,   [1.5,     6,     0.77,     0.530,        0.925]],
                [3.5, [undef, undef,   undef,    0.630,        1.085]],
                [4,   [2,       8,     1.05,     0.730,        1.270]],
                [5,   [2.5,    10,     1.24,     0.930,        1.455]],
                [6,   [3,      15,     1.74,     1.130,        1.800]],
                [8,   [4,      25,     2.24,     1.385,        2.250]],
                [10,  [5,      40,     2.97,     1.785,        2.700]],
                [12,  [6,      45,     3.48,     2.185,        3.200]],
                [16,  [8,      55,     5.15]],
                [20,  [10,   undef,    undef]],    
               ],
            entry = struct_val(metric_setscrew, diam),
            dummy=assert(is_def(entry), str("Screw size M",diam," unsupported for headless screws")),
            drive_dim = drive=="hex" ? [["drive_size", entry[0]], ["drive_depth", diam/2]]
                      : drive=="torx" ? [["drive_size", entry[1]], ["drive_depth", entry[2]]]
                      : drive=="slot" ? [["drive_width", entry[3]], ["drive_depth", entry[4]]]
                      : []
           )
           concat([["head","none"]], drive_dim) 
     : head=="hex" ? let(
            metric_hex = [
              // flat to flat width, height
              [5, [8, 3.5]],
              [6, [10,4]],
              [8, [13, 5.3]],
              [10, [17, 6.4]],
              [12, [19, 7.5]],
              [14, [22, 8.8]],
              [16, [24, 10]],
              [18, [27,11.5]],
              [20, [30, 12.5]],
              [24, [36, 15]],
              [30, [46, 18.7]],
            ],
            entry = struct_val(metric_hex, diam)
           )
           assert(is_def(entry), str("Screw size M",diam," unsupported for head type \"",head,"\""))
           [["head", "hex"], ["head_size", entry[0]], ["head_height", entry[1]]] 
     : in_list(head,["socket","socket ribbed"]) ? let(
            // ISO 14579 gives dimensions for Torx (hexalobular) socket heads
            metric_socket = [    // height = screw diameter
                      //diam, hex, torx size, torx depth
                [1.4, [2.5,   1.3]],
                [1.6, [3,     1.5]],
                [2,   [3.8,   1.5,    6,        0.775]],
                [2.5, [4.5,     2,    8,        0.975]],
                [2.6, [5,       2,    8,        1.05]],
                [3,   [5.5,   2.5,    10,       1.14]],
                [3.5, [6.2,   2.5]]   ,
                [4,   [7,       3,    25,       1.61]],
                [5,   [8.5,     4,    27,       1.84]],
                [6,   [10,      5,    30,       2.22]],
                [7,   [12,      6]],
                [8,   [13,      6,    45,       3.115]],
                [10,  [16,      8,    50,       3.82]],
                [12,  [18,     10,    55,       5.015]],
                [14,  [21,     12,    60,       5.805]],
                [16,  [24,     14,    70,       6.815]],
                [18,  [27,     14,    80,       7.75]],
                [20,  [30,     17,    90,       8.945]],
                [22,  [33,     17]],
                [24,  [36,     19,    100,     10.79]],
                [27,  [40,     19]],
                [30,  [45,     22]],
                [33,  [50,     24]],
                [36,  [54,     27]],
                [42,  [63,     32]],
                [48,  [72,     36]],
            ],
            entry = struct_val(metric_socket, diam),
            dummy=assert(is_def(entry), str("Screw size M",diam," unsupported for headless screws")),
            drive_size =  drive=="hex" ? [["drive_size",entry[1]],["drive_depth",diam/2]] :
                          drive=="torx" ? [["drive_size", entry[2]], ["drive_depth", entry[3]]] :
                          []
            )
            concat([["head",head],["head_size",entry[0]], ["head_height", diam]],drive_size) 
     : in_list(head,["pan","pan round","pan flat"]) ? let (
           metric_pan = [  // pan head for phillips or slotted, torx from ISO 14583
                      //          head height
                      // diam, slotted  phillips phillips size  phillips diam, phillips depth, ph width, slot width,slot depth, torx size, torx depth
                 [1.6,   [3.2,   1  ,     1.3,        0,          undef,         undef,        undef,       0.4,      0.35]],
                 [2,     [4,     1.3,     1.6,        1,          1.82,          1.19,         0.48,        0.5,      0.5,        6,         0.7]],
                 [2.5,   [5,     1.5,     2,          1,          2.68,          1.53,         0.70,        0.6,      0.6,        8,         0.975]],
                 [3,     [5.6,   1.8,     2.4,        1,          2.90,          1.76,         0.74,        0.8,      0.7,        10,        1.14]],
                 [3.5,   [7,     2.1,     3.1,        2,          3.92,          1.95,         0.87,        1.0,      0.8,        15,        1.2]],
                 [4,     [8,     2.4 ,    3.1,        2,          4.40,          2.45,         0.93,        1.2,      1.0,        20,        1.465]],
                 [5,     [9.5,   3,       3.8,        2,          4.90,          2.95,         1.00,        1.2,      1.2,        25,        1.715]],
                 [6,     [12,    3.6,     4.6,        3,          6.92,          3.81,         1.14,        1.6,      1.4,        30,        2.22]],
                 [8,     [16,    4.8,     6,          4,          9.02,          4.88,         1.69,        2.0,      1.9,        45,        2.985]],
                 [10,    [20,    6.0,     7.5,        4,          10.18,         5.09,         1.84,        2.5,      2.4,        50,        3.82]], 
            ],
            type = head=="pan" ? (drive=="slot" ? "pan flat" : "pan round") : head,
            htind = drive=="slot" ? 1 : 2,
            entry = struct_val(metric_pan, diam),
            dummy=assert(is_def(entry), str("Screw size M",diam," unsupported for headless screws")),
            drive_size = drive=="phillips" ? [["drive_size", entry[3]], ["drive_diameter", entry[4]], ["drive_depth",entry[5]], ["drive_width",entry[6]]] 
                       : drive=="torx" ? [["drive_size", entry[9]], ["drive_depth", entry[10]]]
                       : drive=="slot" ? [["drive_width", entry[7]], ["drive_depth", entry[8]]] 
                       : []
           )
           concat([["head",type], ["head_size", entry[0]], ["head_height", entry[htind]]], drive_size) 
     : head=="button" || head=="cheese" ? let(
            // hex drive depth from ISO 7380-1
            metric_button = [    // button, hex drive
                 //   head diam, height, hex, phillips, hex drive depth, torx size, torx depth
                 [1.6, [2.9,     0.8,    0.9, undef,    0.55]], // These four cases,
                 [2,   [3.5,     1.3,    1.3, undef,    0.69]], // extrapolated hex depth
                 [2.2, [3.8,     0.9,    1.3, undef,    0.76]], //
                 [2.5, [4.6,     1.5,    1.5, undef,    0.87]], //
                 [3,   [5.7,     1.65,   2,   undef,    1.04,                8,      0.81]],
                 [3.5, [5.7,     1.65,   2,   undef,    1.21]], // interpolated hex depth
                 [4,   [7.6,     2.2,    2.5, undef,    1.30,                15,     1.3]],
                 [5,   [9.5,     2.75,   3,   undef,    1.56,                25,     1.56]],
                 [6,   [10.5,    3.3,    4,   undef,    2.08,                27,     2.08]],
                 [8,   [14,      4.4,    5,   undef,    2.60,                40,     2.3]],
                 [10,  [17.5,    5.5,    6,   undef,    3.12,                45,     2.69]],
                 [12,  [21,      6.6,    8,   undef,    4.16,                55,     4.02]],    
                 [16,  [28,      8.8,    10,  undef,    5.2]], 
             ],
             metric_cheese = [   // slotted, phillips     ISO 1207, ISO 7048
                                 // hex drive is not supported (hence undefs)
                // head diam, head height, hex drive, phillips drive, slot width, slot depth, ph diam
                [1,   [2,     0.7,         undef,      undef]],
                [1.2, [2.3,   0.8,         undef,      undef]],
                [1.4, [2.6,   0.9,         undef,      undef]],
                [1.6, [3,     1,           undef,      undef,         0.4,        0.45]],
                [2,   [3.8,   1.3,         undef,      1    ,         0.5,        0.6,        undef,       undef]],
                [2.5, [4.5,   1.6,         undef,      1    ,         0.6,        0.7,          2.7,        1.20]],
                [3,   [5.5,   2,           undef,      2    ,         0.8,        0.85,         3.5,        0.86]],
                [3.5, [6,     2.4,         undef,      2    ,         1.0,        1.0,          3.8,        1.15]],
                [4,   [7,     2.6,         undef,      2    ,         1.2,        1.1,          4.1,        1.45]],
                [5,   [8.5,   3.3,         undef,      2    ,         1.2,        1.3,          4.8,        2.14]],
                [6,   [10,    3.9,         undef,      3    ,         1.6,        1.6,          6.2,        2.25]],
                [8,   [13,    5,           undef,      3    ,         2.0,        2.0,          7.7,        3.73]],
                [10,  [16,    6,           undef,      undef,         2.5,        2.4,        undef,       undef]]
             ],
             metric_cheese_torx = [ // torx cheese, ISO 14580, the heads are taller than other cheese screws
                      //head diam, head height, torx size, torx depth
                [2,   [3.8,        1.55,         6,         0.775]],
                [2.5, [4.5,        1.85,         8,         0.845]],
                [3,   [5.5,        2.4,         10,         1.14]],
                [3.5, [6,          2.6,         15,         1.2]],
                [4,   [7,          3.1,         20,         1.465]],
                [5,   [8.5,        3.65,        25,         1.715]],
                [6,   [10,         4.4,         30,         2.095]],
                [8,   [13,         5.8,         45,         2.855]],
                [10,  [16,         6.9,         59,         3.235]]
             ],

             entry = struct_val( head=="button" ? metric_button 
                               : drive=="torx"? metric_cheese_torx 
                               : metric_cheese, 
                            diam),
             dummy=assert(is_def(entry), str("Screw size M",diam," unsupported for headless screws")),
             drive_index = drive=="phillips" ? 3 
                         : drive=="hex" ? 2 
                         : undef,
             drive_dim = head=="button" && drive=="hex" ? [["drive_depth", entry[4]]] 
                       : head=="button" && drive=="torx" ? [["drive_size", entry[5]],["drive_depth", entry[6]]] 
                       : head=="cheese" && drive=="torx" ? [["drive_size", entry[2]],["drive_depth", entry[3]]] 
                       : head=="cheese" && drive=="slot" ? [["drive_width", entry[4]], ["drive_depth", entry[5]]] 
                       : head=="cheese" && drive=="phillips" ? [["drive_diameter", entry[6]], ["drive_depth", entry[7]],
                                                                ["drive_width", entry[6]/4]]  // Fabricated this width value to fill in missing field
                       :[],
             drive_size = is_def(drive_index) ? [["drive_size", entry[drive_index]]] : []
             )
             concat([["head",head],["head_size",entry[0]], ["head_height", entry[1]]],drive_size, drive_dim) 
     : starts_with(head,"flat ") || head=="flat" ?
         let(
             headparts = str_split(head," ",keep_nulls=false),
             partsok = [for (part=headparts) if (!in_list(part, ["flat","small","large","sharp","90"])) part], 
             dummy1=assert(partsok==[], str("Unknown flat head parameter(s) ",partsok)),
             dummy2=assert(!(in_list("small",headparts) && in_list("large",headparts)), "Cannot specify large and small flat head at the same time"),
             small = in_list("small",headparts) || (!in_list("large",headparts) && drive!="hex"),
             metric_flat_large = [ // for hex drive from ISO-10642, don't know where torx came from
                     // -- diam -----   hex size    hex depth     torx   torx depth
                     // theory  actual
                     //  max     min
                  [3,  [6.72,     5.54,      2  ,       1.1,        10,   0.96]],
                  [4,  [8.96,     7.53,      2.5,       1.5,        20,   1.34]],
                  [5,  [11.20,    9.43,      3  ,       1.9,        25,   1.54]],
                  [6,  [13.44,    11.34,     4  ,       2.2,        30,   1.91]],
                  [8,  [17.92,    15.24,     5  ,       3.0,        40,   2.3]],
                  [10, [22.4,     19.22,     6  ,       3.6,        50,   3.04]],
                  [12, [26.88,    23.12,     8  ,       4.3]], 
                  [14, [30.8,     26.52,    10  ,       4.5]],
                  [16, [33.6,     29.01,    10  ,       4.8]],
                  [20, [40.32,    36.05,    12  ,       5.6]]    
             ],
             metric_flat_small = [ // Phillips from ISO 7046
                                   // Slots from ISO 2009
                                   // Torx from ISO 14581
                    // theory    mean                                             nominal       mean             torx
                    //  diam, actual diam  ph size, ph diam, ph depth, ph width, slot width, slot depth  torx   mean depth
                 [1.6, [ 3.6,    2.85,         0,     1.6,    0.75,    undef,     0.4,         0.41,     undef,  undef  ]],
                 [2,   [ 4.4,    3.65,         0,     1.9,    1.05,     0.53,     0.5,         0.5,         6,    0.575 ]],
                 [2.5, [ 5.5,    4.55,         1,     2.9,    1.6,      0.74,     0.6,         0.625,       8,    0.725 ]],
                 [3,   [ 6.3,    5.35,         1,     3.2,    1.90,     0.79,     0.8,         0.725,      10,    0.765 ]],
                 [3.5, [ 8.2,    7.12,         2,     4.4,    2.15,     0.91,     1.0,         1.05,       15,    1.240 ]],
                 [4,   [ 9.4,    8.22,         2,     4.6,    2.35,     0.96,     1.2,         1.15,       10,    1.335 ]],
                 [5,   [10.4,    9.12,         2,     5.2,    2.95,     1.04,     1.2,         1.25,       25,    1.315 ]],
                 [6,   [12.6,   11.085,        3,     6.8,    3.25,     1.12,     1.6,         1.4,        30,    1.585 ]],
                 [8,   [17.3,   15.585,        4,     8.9,    4.30,     1.80,     2.0,         2.05,       45,    2.345 ]],
                 [10,  [20  ,   18.04,         4,    10.0,    5.40,    undef,     2.5,         2.3,        50,    2.605 ]],
                 [12,  [24  ,   21.75 ]],  // Additional screw head data from ISO 7721, but no driver data   
                 [14,  [28  ,   25.25 ]],
                 [16,  [32  ,   28.75 ]],
                 [18,  [36  ,   32.2  ]],
                 [20,  [40  ,   35.7  ]]
             ],
             entry = struct_val(small ? metric_flat_small : metric_flat_large, diam),
             dummy=assert(is_def(entry), str("Screw size M",diam," unsupported for headless screws")),
             driveind = small && drive=="phillips" ? 2
                      : !small && drive=="hex" ? 2
                      : !small && drive=="torx" ? 4
                      : small && drive=="torx" ? 8 : undef,
             drive_dim = small && drive=="phillips" ? [["drive_diameter", entry[3]], ["drive_depth",entry[4]], ["drive_width", entry[5]]] 
                       : small && drive=="slot" ? [["drive_width", entry[6]], ["drive_depth", entry[7]]] 
                       : drive=="torx" ? [["drive_depth", entry[driveind+1]]] 
                       : !small && drive=="hex" ? [["drive_depth", entry[3]]]
                       : [],
             sharpsize = entry[0]
         )
         [
           ["head","flat"],
           ["head_angle",90],
           ["head_size", in_list("sharp",headparts) ? sharpsize
                       : small ? entry[1]              // entry is mean diameter
                       : lerp(entry[1],entry[0],.2)],  // entry is min diameter, so enlarge it 20%
           ["head_size_sharp", sharpsize],
           if (is_def(driveind)) ["drive_size", entry[driveind]],
           each drive_dim
         ]
     : [] 
 )
 concat(
        [["system","ISO"],["diameter",diam],["pitch", pitch],["drive",drive]],
        head_data
 );




function _is_positive(x) = is_num(x) && x>0;

function _validate_screw_spec(spec) = let(
    dummy=echo_struct(spec,"Screw Specification"),
    systemOK = in_list(struct_val(spec,"system"), ["UTS","ISO"]),
    diamOK = _is_positive(struct_val(spec, "diameter")),
    pitch = struct_val(spec,"pitch"),
    pitchOK = is_undef(pitch) || (is_num(pitch) && pitch>=0),
    head = struct_val(spec,"head"),
    f=echo(head=head),
    headOK = head=="none" || 
                (in_list(head, ["cheese","pan flat","pan round", "flat", "button","socket","socket ribbed", "fillister","round","hex"]) &&
                 _is_positive(struct_val(spec, "head_size"))),
    flatheadOK = (head!="flat" || _is_positive(struct_val(spec,"head_size_sharp"))),
    drive = struct_val(spec, "drive"),
    driveOK = is_undef(drive) || drive=="none"
              || (
                  _is_positive(struct_val(spec, "drive_depth")) &&
                    (
                      in_list(drive, ["torx","hex"])
                        || (drive=="phillips" && _is_positive(struct_val(spec, "drive_diameter")) &&
                                                 _is_positive(struct_val(spec, "drive_width")) &&
                                                 _is_positive(struct_val(spec, "drive_width")))
                        || (drive=="slot" && _is_positive(struct_val(spec, "drive_width")))
                    )
                  )
    )
    assert(systemOK, str("Screw spec has invalid \"system\", ", struct_val(spec,"system"), ".  Must be \"ISO\" or \"UTS\""))
    assert(diamOK, str("Screw spec has invalid \"diameter\", ", struct_val(spec,"diameter")))
    assert(pitchOK, str("Screw spec has invalid \"pitch\", ", pitch))
    assert(headOK, "Screw head type invalid or unknown for your screw type and size")  // head is "undef" for invalid heads; we don't know what the user specified
    assert(flatheadOK, "Flat head screw invalid because no \"head_size_sharp\" value is present.")
    assert(driveOK, str("Screw drive type \"",drive,"\" invalid or unknown for your screw size or head type, \"",head,"\""))
    spec;




// Function: thread_specification()
// Usage:
//   thread_specification(screw_spec, [tolerance], [internal])
// Description:
//   Determines actual thread geometry for a given screw with specified tolerance and nominal size.  See [tolerance](#subsection-tolerance) for
//   information on tolerances.  If tolerance is omitted the default is used.  If tolerance
//   is "none" or 0 then return the nominal thread geometry.  When `internal=true` the nut tolerance is used.  
//   .
//   The return value is a structure with the following fields:
//   - pitch: the thread pitch
//   - d_major: major diameter range
//   - d_pitch: pitch diameter range
//   - d_minor: minor diameter range
//   - basic: vector `[minor, pitch, major]` of the nominal or "basic" diameters for the threads
// Arguments:
//   screw_spec = screw specification structure
//   ---
//   tolerance = thread geometry tolerance
//   internal = true for internal threads.  Default: false
function thread_specification(screw_spec, tolerance=undef, internal=false) =
  let( 
       diam = struct_val(screw_spec, "diameter"),
       pitch = struct_val(screw_spec, "pitch"),
       tspec = tolerance == 0 || tolerance=="none" ? _exact_thread_tolerance(diam, pitch)
             :  struct_val(screw_spec,"system") == "ISO" ? _ISO_thread_tolerance(diam, pitch, internal, tolerance)
             :  struct_val(screw_spec,"system") == "UTS" ? _UTS_thread_tolerance(diam, pitch, internal, tolerance)
             :  assert(false,"Unknown screw system ",struct_val(screw_spec,"system"))
  )
  assert(min(struct_val(tspec,"d_minor"))>0, "Thread specification is too coarse for the diameter")
  tspec;





// recess sizing:
// http://www.fasnetdirect.com/refguide/Machinepancombo.pdf
//
/*   ASME B 18.6.3
http://www.smithfast.com/newproducts/screws/msflathead/


/* phillips recess diagram

http://files.engineering.com/getfile.aspx?folder=76fb0d5e-1fff-4c49-87a5-05979477ca88&file=Noname.jpg&__hstc=212727627.6c577ef84c12d9cc69c819eea7be49d2.1563972499721.1563972499721.1563972499721.1&__hssc=212727627.1.1563972499721&__hsfp=165344926

*/


// To do list
//
// Is there no way to create a mask for making threaded holes?  This seems to be missing.
//
// Metric hex engagement:
// https://www.bayoucitybolt.com/socket-head-cap-screws-metric.html
//
// Torx drive depth for UTS and ISO (at least missing for "flat small", which means you can't select torx for this head type)
// Handle generic phillips (e.g. ph2) or remove it?

// https://www.fasteners.eu/tech-info/ISO/7721-2/
//
// How do you insert a threaded hole into a model?
// Default nut thickness
//
//    JIS 
//https://www.garagejournal.com/forum/media/jis-b-4633-vs-iso-8764-1-din-5260-ph.84492/

//square:
//https://www.aspenfasteners.com/content/pdf/square_drive_specification.pdf
//http://www.globalfastener.com/standards/index.php?narr58=149
//https://patents.google.com/patent/US1003657

// thread standards:
// https://www.gewinde-normen.de/en/index.html

///////////////////////////////////////////////////////
//
// how to make screw mask: examples (e.g. for clearance hole w/ countersink)
// how to make a screw hole (a mask function?)
// 

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

/*
TODO list:

anchoring for counterbores OK?:  counterbore ignored for flatheads
    counterbore is treated as the head for regular heads
    for flathead counterbore is ignored.  Need an anchor that gives
    access to counterbore for the flathead case but also the top of the head(?)
anchoring for other heads:  using bounding cylinder
    hex head anchoring OK?
need to make holes at actual size instead of nominal?
   or relative to actual size?
   That means I need to preserve thread= to specify this
shoulder screws: generally how to handle these?
torx depth for UTS pan head
$fn control
phillips driver spec with ph# is confusing since it still looks up depth in tables
   and can give an error if it's not found
phillips code just uses depth, not width and slot width; maybe remove excess data?  
torx depths missing for pan head
support for square drive?  (It's in the ASME standard)
proper support for nuts, nut traps

*/

/*
iso shoulder screws, hex drive socket head  ISO 7379
  Mcmaster has variations like 12mm shoulder for m10, 6mm shoulder for M5

   shld  thread  head  head  hex  hex dep
   diam  length  diam   ht                   shold tol
5, [6.5,    9.5,  10,  4.5,   3,  2.4         .03
6, [8  ,    11 ,  13,  5.5,   4,  3.3         .03
8, [10 ,    13 ,  16,  7  ,   5,  4.2         .03 
10,[13 ,    16 ,  18,  9  ,   6,  4.9         .037
12,[16 ,    18 ,  24, 11  ,   8,  6.6         .037
16,[20 ,    22 ,  30, 14  ,  10,  8.8         .046
20,[25 ,    27 ,  36, 16  ,  12,  10          .046


UTS shoulder screws, b18.3 (table 13)

       sh diam  thread len, head diam   hex size  hex depth
[#4,    [1/8  ,   5/32 ,    1/4      ,  5/64   ,  0.067
[#6,    [5/32 ,   3/16 ,    9/32     ,  3/32   ,  0.067
[#8,    [3/16 ,   3/16 ,    5/16     ,  3/32   ,  0.079
[#10,   [1/4  ,   3/8  ,    3/8      ,  1/8    ,  0.094
[1/4,   [5/16 ,   7/16 ,    7/16     ,  5/32   ,  0.117
[5/16,  [3/8  ,   1/2  ,    9/16     ,  3/16   ,  0.141
[3/8,   [1/2  ,   5/8  ,    3/4      ,  1/4    ,  0.188
[1/2,   [5/8  ,   3/4  ,    7/8      ,  5/16   ,  0.234
[5/8,   [3/4  ,   7/8  ,    1        ,  3/8    ,  0.281
[3/4,   [1    ,   1    ,    1+5/16   ,  1/2    ,  0.375
[7/8,   [1+1/4,   1+1/8,    1+3/4    ,  5/8    ,  0.469
[1+1/8, [1+1/2,   1+1/2,    2+1/8    ,  7/8    ,  0.656
[1+1/4, [1+3/4,   1+3/4,    2+3/8    ,  1      ,  0.750
[1+1/2, [2    ,   2    ,    2+3/4    ,  1+1/4  ,  0.937

         shoulder tol = .003

height = .5 (shoulder nom diam) + .0625
         .5 (shoulder nom diam) + .125  >= 3/4

         
*/