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involute_gears.scad -> gears.scad

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Garth Minette 2021-03-01 01:29:41 -08:00
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README.md
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@ -124,7 +124,7 @@ The library files are as follows:
- [`polyhedra.scad`](polyhedra.scad): Modules to create various regular and stellated polyhedra.
- [`walls.scad`](walls.scad): Modules to create walls and structural elements for 3D printing.
- [`cubetruss.scad`](cubetruss.scad): Modules to create modular open-framed trusses and joiners.
- [`involute_gears.scad`](involute_gears.scad): Modules and functions to make involute gears and racks.
- [`gears.scad`](gears.scad): Modules and functions to make gears, racks, worm, and worm gears.
- [`joiners.scad`](joiners.scad): Modules to make joiner shapes for connecting separately printed objects.
- [`sliders.scad`](sliders.scad): Modules for creating simple sliders and rails.
- [`metric_screws.scad`](metric_screws.scad): Functions and modules to make metric screws, nuts, and screwholes.

214
involute_gears.scad → gears.scad
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@ -1,24 +1,11 @@
//////////////////////////////////////////////////////////////////////////////////////////////
// LibFile: involute_gears.scad
// Involute Spur Gears and Racks
// .
// by Leemon Baird, 2011, Leemon@Leemon.com
// http://www.thingiverse.com/thing:5505
// .
// Additional fixes and improvements by Revar Desmera, 2017-2019, revarbat@gmail.com
// .
// This file is public domain. Use it for any purpose, including commercial
// applications. Attribution would be nice, but is not required. There is
// no warranty of any kind, including its correctness, usefulness, or safety.
// .
// This is parameterized involute spur (or helical) gear. It is much simpler
// and less powerful than others on Thingiverse. But it is public domain. I
// implemented it from scratch from the descriptions and equations on Wikipedia
// and the web, using Mathematica for calculations and testing, and I now
// release it into the public domain.
// LibFile: gears.scad
// Spur Gears, Bevel Gears, Racks, Worms and Worm Gears.
// Originally based on code by Leemon Baird, 2011, Leemon@Leemon.com
// Almost completely rewritten for BOSL2 by Revar Desmera, 2017-2019, revarbat@gmail.com
// Includes:
// include <BOSL2/std.scad>
// include <BOSL2/involute_gears.scad>
// include <BOSL2/gears.scad>
//////////////////////////////////////////////////////////////////////////////////////////////
@ -77,7 +64,8 @@ function diametral_pitch(pitch=5, mod) =
// Usage:
// pitch = pitch_value(mod);
// Description:
// Get circular pitch in mm from module/modulus.
// Get circular pitch in mm from module/modulus. The circular pitch of a gear is the number of
// millimeters per tooth around the pitch radius circle.
// Arguments:
// mod = The module/modulus of the gear.
function pitch_value(mod) = mod * PI;
@ -87,7 +75,9 @@ function pitch_value(mod) = mod * PI;
// Usage:
// mod = module_value(pitch);
// Description:
// Get tooth density expressed as "module" or "modulus" in millimeters
// Get tooth density expressed as "module" or "modulus" in millimeters. The module is the pitch
// diameter of the gear divided by the number of teeth on it. For example, a gear with a pitch
// diameter of 40mm, with 20 teeth on it will have a modulus of 2.
// Arguments:
// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
function module_value(pitch=5) = pitch / PI;
@ -97,13 +87,22 @@ function module_value(pitch=5) = pitch / PI;
// Usage:
// ad = adendum(pitch|mod);
// Description:
// The height of the gear tooth above the pitch radius.
// The height of the top of a gear tooth above the pitch radius circle.
// Arguments:
// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
// mod = The metric module/modulus of the gear.
// Examples:
// ad = adendum(pitch=5);
// ad = adendum(mod=2);
// Example(2D):
// pitch = 5; teeth = 17;
// pr = pitch_radius(pitch=pitch, teeth=teeth);
// adn = adendum(pitch=5);
// #spur_gear2d(pitch=pitch, teeth=teeth);
// color("black") {
// stroke(circle(r=pr),width=0.1,closed=true);
// stroke(circle(r=pr+adn),width=0.1,closed=true);
// }
function adendum(pitch=5, mod) =
let( pitch = is_undef(mod) ? pitch : pitch_value(mod) )
module_value(pitch) * 1.0;
@ -121,6 +120,15 @@ function adendum(pitch=5, mod) =
// Examples:
// ddn = dedendum(pitch=5);
// ddn = dedendum(mod=2);
// Example(2D):
// pitch = 5; teeth = 17;
// pr = pitch_radius(pitch=pitch, teeth=teeth);
// ddn = dedendum(pitch=5);
// #spur_gear2d(pitch=pitch, teeth=teeth);
// color("black") {
// stroke(circle(r=pr),width=0.1,closed=true);
// stroke(circle(r=pr-ddn),width=0.1,closed=true);
// }
function dedendum(pitch=5, clearance, mod) =
let( pitch = is_undef(mod) ? pitch : pitch_value(mod) )
is_undef(clearance)? (1.25 * module_value(pitch)) :
@ -140,6 +148,11 @@ function dedendum(pitch=5, clearance, mod) =
// Examples:
// pr = pitch_radius(pitch=5, teeth=11);
// pr = pitch_radius(mod=2, teeth=20);
// Example(2D):
// pr = pitch_radius(pitch=5, teeth=11);
// #spur_gear2d(pitch=5, teeth=11);
// color("black")
// stroke(circle(r=pr),width=0.1,closed=true);
function pitch_radius(pitch=5, teeth=11, mod) =
let( pitch = is_undef(mod) ? pitch : pitch_value(mod) )
pitch * teeth / PI / 2;
@ -159,6 +172,11 @@ function pitch_radius(pitch=5, teeth=11, mod) =
// Examples:
// or = outer_radius(pitch=5, teeth=20);
// or = outer_radius(mod=2, teeth=16);
// Example(2D):
// pr = outer_radius(pitch=5, teeth=11);
// #spur_gear2d(pitch=5, teeth=11);
// color("black")
// stroke(circle(r=pr),width=0.1,closed=true);
function outer_radius(pitch=5, teeth=11, clearance, interior=false, mod) =
let( pitch = is_undef(mod) ? pitch : pitch_value(mod) )
pitch_radius(pitch, teeth) +
@ -179,6 +197,11 @@ function outer_radius(pitch=5, teeth=11, clearance, interior=false, mod) =
// Examples:
// rr = root_radius(pitch=5, teeth=11);
// rr = root_radius(mod=2, teeth=16);
// Example(2D):
// pr = root_radius(pitch=5, teeth=11);
// #spur_gear2d(pitch=5, teeth=11);
// color("black")
// stroke(circle(r=pr),width=0.1,closed=true);
function root_radius(pitch=5, teeth=11, clearance, interior=false, mod) =
let( pitch = is_undef(mod) ? pitch : pitch_value(mod) )
pitch_radius(pitch, teeth) -
@ -198,6 +221,11 @@ function root_radius(pitch=5, teeth=11, clearance, interior=false, mod) =
// Examples:
// br = base_radius(pitch=5, teeth=20, pressure_angle=20);
// br = base_radius(mod=2, teeth=18, pressure_angle=20);
// Example(2D):
// pr = base_radius(pitch=5, teeth=11);
// #spur_gear2d(pitch=5, teeth=11);
// color("black")
// stroke(circle(r=pr),width=0.1,closed=true);
function base_radius(pitch=5, teeth=11, pressure_angle=28, mod) =
let( pitch = is_undef(mod) ? pitch : pitch_value(mod) )
pitch_radius(pitch, teeth) * cos(pressure_angle);
@ -215,6 +243,19 @@ function base_radius(pitch=5, teeth=11, pressure_angle=28, mod) =
// drive_angle = Angle between the drive shafts of each gear. Default: 90º.
// Examples:
// ang = bevel_pitch_angle(teeth=18, mate_teeth=30);
// Example(2D):
// t1 = 13; t2 = 19; pitch=5;
// pang = bevel_pitch_angle(teeth=t1, mate_teeth=t2, drive_angle=90);
// color("black") {
// zrot_copies([0,pang])
// stroke([[0,0,0], [0,-20,0]],width=0.2);
// stroke(arc(r=3, angle=[270,270+pang]),width=0.2);
// }
// #bevel_gear(
// pitch=5, teeth=t1, mate_teeth=t2,
// spiral_angle=0, cutter_radius=1000,
// slices=12, anchor="apex", orient=BACK
// );
function bevel_pitch_angle(teeth, mate_teeth, drive_angle=90) =
atan(sin(drive_angle)/((mate_teeth/teeth)+cos(drive_angle)));
@ -235,6 +276,20 @@ function bevel_pitch_angle(teeth, mate_teeth, drive_angle=90) =
// Examples:
// thick = worm_gear_thickness(pitch=5, teeth=36, worm_diam=30);
// thick = worm_gear_thickness(mod=2, teeth=28, worm_diam=25);
// Example(2D):
// pitch = 5; teeth=17;
// worm_diam = 30; starts=2;
// y = worm_gear_thickness(pitch=pitch, teeth=teeth, worm_diam=worm_diam);
// #worm_gear(
// pitch=pitch, teeth=teeth,
// worm_diam=worm_diam,
// worm_starts=starts,
// orient=BACK
// );
// color("black") {
// ycopies(y) stroke([[-25,0],[25,0]], width=0.5);
// stroke([[-20,-y/2],[-20,y/2]],width=0.5,endcaps="arrow");
// }
function worm_gear_thickness(pitch=5, teeth=30, worm_diam=30, worm_arc=60, crowning=1, clearance, mod) =
let(
pitch = is_undef(mod) ? pitch : pitch_value(mod),
@ -354,11 +409,11 @@ module gear_tooth_profile(
}
// Function&Module: gear2d()
// Function&Module: spur_gear2d()
// Usage: As Module
// gear2d(pitch|mod, teeth, <hide>, <pressure_angle>, <clearance>, <backlash>, <interior>);
// spur_gear2d(pitch|mod, teeth, <hide>, <pressure_angle>, <clearance>, <backlash>, <interior>);
// Usage: As Function
// poly = gear2d(pitch|mod, teeth, <hide>, <pressure_angle>, <clearance>, <backlash>, <interior>);
// poly = spur_gear2d(pitch|mod, teeth, <hide>, <pressure_angle>, <clearance>, <backlash>, <interior>);
// Description:
// When called as a module, creates a 2D involute spur gear. When called as a function, returns a
// 2D path for the perimeter of a 2D involute spur gear. Normally, you should just specify the
@ -377,17 +432,17 @@ module gear_tooth_profile(
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
// Example(2D): Typical Gear Shape
// gear2d(pitch=5, teeth=20);
// spur_gear2d(pitch=5, teeth=20);
// Example(2D): Metric Gear
// gear2d(mod=2, teeth=20);
// spur_gear2d(mod=2, teeth=20);
// Example(2D): Lower Pressure Angle
// gear2d(pitch=5, teeth=20, pressure_angle=20);
// spur_gear2d(pitch=5, teeth=20, pressure_angle=20);
// Example(2D): Partial Gear
// gear2d(pitch=5, teeth=20, hide=15, pressure_angle=20);
// spur_gear2d(pitch=5, teeth=20, hide=15, pressure_angle=20);
// Example(2D): Called as a Function
// path = gear2d(pitch=8, teeth=16);
// path = spur_gear2d(pitch=8, teeth=16);
// polygon(path);
function gear2d(
function spur_gear2d(
pitch = 3,
teeth = 11,
hide = 0,
@ -421,7 +476,7 @@ function gear2d(
) reorient(anchor,spin, two_d=true, r=pr, p=pts);
module gear2d(
module spur_gear2d(
pitch = 3,
teeth = 11,
hide = 0,
@ -434,7 +489,7 @@ module gear2d(
spin = 0
) {
pitch = is_undef(mod) ? pitch : pitch_value(mod);
path = gear2d(
path = spur_gear2d(
pitch = pitch,
teeth = teeth,
hide = hide,
@ -570,41 +625,44 @@ module rack2d(
// Section: 3D Gears and Racks
// Function&Module: gear()
// Function&Module: spur_gear()
// Usage: As a Module
// gear(pitch|mod, teeth, thickness, <shaft_diam>, <hide>, <pressure_angle>, <clearance>, <backlash>, <helical>, <slices>, <interior>);
// spur_gear(pitch, teeth, thickness, <shaft_diam=>, <hide>, <pressure_angle>, <clearance>, <backlash>, <helical>, <slices>, <interior>);
// spur_gear(mod=, teeth=, thickness=, <shaft_diam=>, ...);
// Usage: As a Function
// vnf = gear(pitch|mod, teeth, thickness, <shaft_diam>, <hide>, <pressure_angle>, <clearance>, <backlash>, <helical>, <slices>, <interior>);
// vnf = spur_gear(pitch, teeth, thickness, <shaft_diam>, ...);
// vnf = spur_gear(mod=, teeth=, thickness=, <shaft_diam>, ...);
// Description:
// Creates a (potentially helical) involute spur gear. The module `gear()` gives an involute spur
// gear, with reasonable defaults for all the parameters. Normally, you should just choose the
// first 4 parameters, and let the rest be default values. The module `gear()` gives a gear in the
// XY plane, centered on the origin, with one tooth centered on the positive Y axis. The
// most important is `pitch_radius()`, which tells how far apart to space gears that are meshing,
// and `outer_radius()`, which gives the size of the region filled by the gear. A gear has a "pitch
// Creates a (potentially helical) involute spur gear. The module `spur_gear()` gives an involute
// spur gear, with reasonable defaults for all the parameters. Normally, you should just choose the
// first 4 parameters, and let the rest be default values. The module `spur_gear()` gives a gear in
// the XY plane, centered on the origin, with one tooth centered on the positive Y axis. The most
// important is `pitch_radius()`, which tells how far apart to space gears that are meshing, and
// `outer_radius()`, which gives the size of the region filled by the gear. A gear has a "pitch
// circle", which is an invisible circle that cuts through the middle of each tooth (though not the
// exact center). In order for two gears to mesh, their pitch circles should just touch. So the
// distance between their centers should be `pitch_radius()` for one, plus `pitch_radius()` for the
// other, which gives the radii of their pitch circles. In order for two gears to mesh, they must
// have the same `pitch` and `pressure_angle` parameters. `pitch` gives the number of millimeters of arc around
// the pitch circle covered by one tooth and one space between teeth. The `pressure_angle` controls how flat or
// bulged the sides of the teeth are. Common values include 14.5 degrees and 20 degrees, and
// occasionally 25. Though I've seen 28 recommended for plastic gears. Larger numbers bulge out
// more, giving stronger teeth, so 28 degrees is the default here. The ratio of `teeth` for two
// meshing gears gives how many times one will make a full revolution when the the other makes one
// full revolution. If the two numbers are coprime (i.e. are not both divisible by the same number
// greater than 1), then every tooth on one gear will meet every tooth on the other, for more even
// wear. So coprime numbers of teeth are good.
// have the same `pitch` and `pressure_angle` parameters. `pitch` gives the number of millimeters
// of arc around the pitch circle covered by one tooth and one space between teeth. The
// `pressure_angle` controls how flat or bulged the sides of the teeth are. Common values include
// 14.5 degrees and 20 degrees, and occasionally 25. Though I've seen 28 recommended for plastic
// gears. Larger numbers bulge out more, giving stronger teeth, so 28 degrees is the default here.
// The ratio of `teeth` for two meshing gears gives how many times one will make a full revolution
// when the the other makes one full revolution. If the two numbers are coprime (i.e. are not both
// divisible by the same number greater than 1), then every tooth on one gear will meet every tooth
// on the other, for more even wear. So coprime numbers of teeth are good.
// Arguments:
// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
// teeth = Total number of teeth around the entire perimeter
// thickness = Thickness of gear in mm
// shaft_diam = Diameter of the hole in the center, in mm. Default: 0 (no shaft hole)
// ---
// hide = Number of teeth to delete to make this only a fraction of a circle
// pressure_angle = Controls how straight or bulged the tooth sides are. In degrees.
// clearance = Clearance gap at the bottom of the inter-tooth valleys.
// backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle
// helical = Teeth rotate this many degrees from bottom of gear to top. 360 makes the gear a screw with each thread going around once.
// helical = Teeth are slanted around the spur gear at this angle away from the gear axis of rotation.
// slices = Number of vertical layers to divide gear into. Useful for refining gears with `helical`.
// scale = Scale of top of gear compared to bottom. Useful for making crown gears.
// interior = If true, create a mask for difference()ing from something else.
@ -613,11 +671,11 @@ module rack2d(
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
// orient = Vector to rotate top towards, after spin. See [orient](attachments.scad#orient). Default: `UP`
// Example: Spur Gear
// gear(pitch=5, teeth=20, thickness=8, shaft_diam=5);
// spur_gear(pitch=5, teeth=20, thickness=8, shaft_diam=5);
// Example: Metric Gear
// gear(mod=2, teeth=20, thickness=8, shaft_diam=5);
// spur_gear(mod=2, teeth=20, thickness=8, shaft_diam=5);
// Example: Helical Gear
// gear(
// spur_gear(
// pitch=5, teeth=20, thickness=10,
// shaft_diam=5, helical=-30, slices=12,
// $fa=1, $fs=1
@ -641,13 +699,13 @@ module rack2d(
// a2 = -$t * 360 / n2 + 180/n2;
// a3 = -$t * 360 / n3;
// a4 = -$t * 360 / n4 - 7.5*180/n4;
// color("#f77") zrot(a1) gear(pitch,n1,thickness,hole);
// color("#7f7") back(r1+r2) zrot(a2) gear(pitch,n2,thickness,hole);
// color("#77f") right(r1+r3) zrot(a3) gear(pitch,n3,thickness,hole);
// color("#fc7") left(r1+r4) zrot(a4) gear(pitch,n4,thickness,hole,hide=n4-3);
// color("#f77") zrot(a1) spur_gear(pitch,n1,thickness,hole);
// color("#7f7") back(r1+r2) zrot(a2) spur_gear(pitch,n2,thickness,hole);
// color("#77f") right(r1+r3) zrot(a3) spur_gear(pitch,n3,thickness,hole);
// color("#fc7") left(r1+r4) zrot(a4) spur_gear(pitch,n4,thickness,hole,hide=n4-3);
// color("#ccc") fwd(r1) right(pitch*$t)
// rack(pitch=pitch,teeth=n5,thickness=thickness,height=rack_base,anchor=CENTER,orient=BACK);
function gear(
function spur_gear(
pitch = 3,
teeth = 11,
thickness = 6,
@ -671,7 +729,7 @@ function gear(
r = root_radius(pitch, teeth, clearance, interior),
twist = atan2(thickness*tan(helical),p),
rgn = [
gear2d(
spur_gear2d(
pitch = pitch,
teeth = teeth,
pressure_angle = pressure_angle,
@ -686,7 +744,7 @@ function gear(
) reorient(anchor,spin,orient, h=thickness, r=p, p=vnf);
module gear(
module spur_gear(
pitch = 3,
teeth = 11,
thickness = 6,
@ -711,7 +769,7 @@ module gear(
attachable(anchor,spin,orient, r=p, l=thickness) {
difference() {
linear_extrude(height=thickness, center=true, convexity=teeth/2, twist=twist) {
gear2d(
spur_gear2d(
pitch = pitch,
teeth = teeth,
pressure_angle = pressure_angle,
@ -979,9 +1037,11 @@ module bevel_gear(
// Function&Module: rack()
// Usage: As a Module
// rack(pitch|mod, teeth, thickness, height, <pressure_angle>, <backlash>);
// rack(pitch, teeth, thickness, height, <pressure_angle=>, <backlash=>);
// rack(mod=, teeth=, thickness=, height=, <pressure_angle=>, <backlash>=);
// Usage: As a Function
// vnf = rack(pitch|mod, teeth, thickness, height, <pressure_angle>, <backlash>);
// vnf = rack(pitch, teeth, thickness, height, <pressure_angle=>, <backlash=>);
// vnf = rack(mod=, teeth=, thickness=, height=, <pressure_angle=>, <backlash=>);
// Description:
// This is used to create a 3D rack, which is a linear bar with teeth that a gear can roll along.
// A rack can mesh with any gear that has the same `pitch` and `pressure_angle`.
@ -992,9 +1052,11 @@ module bevel_gear(
// teeth = Total number of teeth along the rack. Default: 20
// thickness = Thickness of rack in mm (affects each tooth). Default: 5
// height = Height of rack in mm, from tooth top to back of rack. Default: 10
// ---
// pressure_angle = Controls how straight or bulged the tooth sides are. In degrees. Default: 28
// backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle. Default: 0
// clearance = Clearance gap at the bottom of the inter-tooth valleys.
// helical = The angle of the rack teeth away from perpendicular to the rack length. Used to match helical spur gear pinions. Default: 0
// mod = The metric module/modulus of the gear.
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
@ -1010,10 +1072,21 @@ module bevel_gear(
// "dedendum-right" = At the base of the teeth, at the right end of the rack.
// "dedendum-back" = At the base of the teeth, at the back of the rack.
// "dedendum-front" = At the base of the teeth, at the front of the rack.
// Example:
// Example(VPR=[60,0,325],VPD=130):
// rack(pitch=5, teeth=10, thickness=5, height=5, pressure_angle=20);
// Example: Rack for Helical Gear
// rack(pitch=5, teeth=10, thickness=5, height=5, pressure_angle=20, helical=30);
// Example: Alternate Helical Gear
// rack(pitch=5, teeth=10, thickness=5, height=5, pressure_angle=20, helical=-30);
// Example: Metric Rack
// rack(mod=2, teeth=10, thickness=5, height=5, pressure_angle=20);
// Example(Anim,VPT=[0,0,12],VPD=100,Frames=6): Rack and Pinion
// teeth1 = 16; teeth2 = 16;
// pitch = 5; thick = 5; helical = 30;
// pr = pitch_radius(pitch=pitch, teeth=teeth2);
// right(pr*2*PI/teeth2*$t) rack(pitch=pitch, teeth=teeth1, thickness=thick, height=5, helical=helical);
// up(pr) yrot(186.5-$t*360/teeth2)
// spur_gear(pitch=pitch, teeth=teeth2, thickness=thick, helical=helical, shaft_diam=5, orient=BACK);
module rack(
pitch = 5,
teeth = 20,
@ -1022,6 +1095,7 @@ module rack(
pressure_angle = 28,
backlash = 0.0,
clearance,
helical=0,
mod,
anchor = CENTER,
spin = 0,
@ -1044,7 +1118,7 @@ module rack(
anchorpt("dedendum-back", [0, thickness/2,-d], UP),
];
attachable(anchor,spin,orient, size=[l, thickness, 2*abs(a-height)], anchors=anchors) {
xrot(90) {
skew(sxy=tan(helical)) xrot(90) {
linear_extrude(height=thickness, center=true, convexity=teeth*2) {
rack2d(
pitch = pitch,
@ -1069,6 +1143,7 @@ function rack(
pressure_angle = 28,
backlash = 0.0,
clearance,
helical=0,
mod,
anchor = CENTER,
spin = 0,
@ -1099,8 +1174,9 @@ function rack(
backlash = backlash,
clearance = clearance
),
vnf = linear_sweep(path, height=thickness, anchor="origin", orient=FWD)
) reorient(anchor,spin,orient, size=[l, thickness, 2*abs(a-height)], anchors=anchors, p=vnf);
vnf = linear_sweep(path, height=thickness, anchor="origin", orient=FWD),
out = helical==0? vnf : skew(sxy=tan(helical), p=vnf)
) reorient(anchor,spin,orient, size=[l, thickness, 2*abs(a-height)], anchors=anchors, p=out);
@ -1110,7 +1186,7 @@ function rack(
// Usage: As a Function
// vnf = worm(pitch|mod, d, l, <starts>, <left_handed>, <pressure_angle>, <backlash>, <clearance>);
// Description:
// Creates a worm shape that can be matched to a work gear.
// Creates a worm shape that can be matched to a worm gear.
// Arguments:
// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. Default: 5
// d = The diameter of the worm. Default: 30