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Merge pull request #1231 from adrianVmariano/master

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misc gear fixes
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Revar Desmera 2023-07-31 18:42:21 -07:00 committed by GitHub
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1 changed files with 66 additions and 95 deletions
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gears.scad
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@ -49,10 +49,10 @@ function _inherit_gear_pitch(fname,pitch,circ_pitch,diam_pitch,mod,warn=true) =
circ_pitch : circ_pitch :
diam_pitch != undef? diam_pitch != undef?
assert(is_finite(diam_pitch) && diam_pitch>0) assert(is_finite(diam_pitch) && diam_pitch>0)
pitch_value(diam_pitch=diam_pitch) : circular_pitch(diam_pitch=diam_pitch) :
mod != undef? mod != undef?
assert(is_finite(mod) && mod>0) assert(is_finite(mod) && mod>0)
pitch_value(mod) : circular_pitch(mod=mod) :
$parent_gear_pitch != undef? $parent_gear_pitch : $parent_gear_pitch != undef? $parent_gear_pitch :
5; 5;
@ -270,7 +270,7 @@ function _inherit_gear_thickness(thickness) =
// Subsection: Ring Gears (Internal Gears) // Subsection: Ring Gears (Internal Gears)
// A ring gear (or internal gear) is a gear where the teeth are on the inside of a circle. Such gears must be mated // A ring gear (or internal gear) is a gear where the teeth are on the inside of a circle. Such gears must be mated
// to a regular (external) gear, which rotates around the inside. // to a regular (external) gear, which rotates around the inside.
// Figure(2D,Med,NoAxes,VPT =[0.491171,1.07815,0.495977],VPD=292.705): A interior or ring gear (yellow) with a mating spur gear (blue) // Figure(2D,Med,NoAxes,VPT=[0.491171,1.07815,0.495977],VPD=292.705): A interior or ring gear (yellow) with a mating spur gear (blue)
// teeth1=18; // teeth1=18;
// teeth2=30; // teeth2=30;
// ps1=undef; // ps1=undef;
@ -348,7 +348,7 @@ function _inherit_gear_thickness(thickness) =
// ps2=auto_profile_shift(teeth=teeth1); // ps2=auto_profile_shift(teeth=teeth1);
// mod=3; // mod=3;
// d = gear_dist(mod=mod, teeth1=teeth1, teeth2=teeth2,profile_shift1=ps1, profile_shift2=ps2,helical=0, internal2=true); // d = gear_dist(mod=mod, teeth1=teeth1, teeth2=teeth2,profile_shift1=ps1, profile_shift2=ps2,helical=0, internal2=true);
// ang = 1; // ang = .5;
// color_overlaps(){ // color_overlaps(){
// ring_gear2d(mod=mod, teeth=teeth2,profile_shift=ps2,helical=0,backing=4); // ring_gear2d(mod=mod, teeth=teeth2,profile_shift=ps2,helical=0,backing=4);
// zrot(ang*360/teeth2) // zrot(ang*360/teeth2)
@ -417,7 +417,7 @@ function _inherit_gear_thickness(thickness) =
// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter. // diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter.
// mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth. // mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth.
// internal = If true, create a mask for difference()ing from something else. // internal = If true, create a mask for difference()ing from something else.
// profile_shift = Profile shift factor x. // profile_shift = Profile shift factor x. Default: "auto"
// herringbone = If true, and helical is set, creates a herringbone gear. // herringbone = If true, and helical is set, creates a herringbone gear.
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER` // 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` // spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#subsection-spin). Default: `0`
@ -551,7 +551,7 @@ function spur_gear(
helical, helical,
interior, interior,
internal, internal,
profile_shift, profile_shift="auto",
slices, slices,
herringbone=false, herringbone=false,
diam_pitch, diam_pitch,
@ -569,7 +569,7 @@ function spur_gear(
PA = _inherit_gear_pa(pressure_angle), PA = _inherit_gear_pa(pressure_angle),
helical = _inherit_gear_helical(helical, invert=!internal), helical = _inherit_gear_helical(helical, invert=!internal),
thickness = _inherit_gear_thickness(thickness), thickness = _inherit_gear_thickness(thickness),
profile_shift = default(profile_shift, auto_profile_shift(teeth,PA,helical)) profile_shift = auto_profile_shift(teeth,PA,helical,profile_shift=profile_shift)
) )
assert(is_integer(teeth) && teeth>3) assert(is_integer(teeth) && teeth>3)
assert(is_finite(thickness) && thickness>0) assert(is_finite(thickness) && thickness>0)
@ -581,7 +581,6 @@ function spur_gear(
assert(is_finite(helical) && abs(helical)<90) assert(is_finite(helical) && abs(helical)<90)
assert(is_bool(herringbone)) assert(is_bool(herringbone))
assert(slices==undef || (is_integer(slices) && slices>0)) assert(slices==undef || (is_integer(slices) && slices>0))
assert(is_finite(profile_shift) && abs(profile_shift)<1)
assert(is_finite(gear_spin)) assert(is_finite(gear_spin))
let( let(
pr = pitch_radius(circ_pitch, teeth, helical), pr = pitch_radius(circ_pitch, teeth, helical),
@ -626,7 +625,7 @@ module spur_gear(
helical, helical,
internal, internal,
interior, interior,
profile_shift, profile_shift="auto",
slices, slices,
herringbone=false, herringbone=false,
pitch, pitch,
@ -643,7 +642,7 @@ module spur_gear(
PA = _inherit_gear_pa(pressure_angle); PA = _inherit_gear_pa(pressure_angle);
helical = _inherit_gear_helical(helical, invert=!internal); helical = _inherit_gear_helical(helical, invert=!internal);
thickness = _inherit_gear_thickness(thickness); thickness = _inherit_gear_thickness(thickness);
profile_shift = default(profile_shift, auto_profile_shift(teeth,PA,helical)); profile_shift = auto_profile_shift(teeth,PA,helical,profile_shift=profile_shift);
checks = checks =
assert(is_integer(teeth) && teeth>3) assert(is_integer(teeth) && teeth>3)
assert(is_finite(thickness) && thickness>0) assert(is_finite(thickness) && thickness>0)
@ -654,7 +653,6 @@ module spur_gear(
assert(is_finite(backlash) && backlash>=0) assert(is_finite(backlash) && backlash>=0)
assert(is_finite(helical) && abs(helical)<90) assert(is_finite(helical) && abs(helical)<90)
assert(is_bool(herringbone)) assert(is_bool(herringbone))
assert(is_finite(profile_shift) && abs(profile_shift)<1)
assert(slices==undef || (is_integer(slices) && slices>0)) assert(slices==undef || (is_integer(slices) && slices>0))
assert(is_finite(gear_spin)); assert(is_finite(gear_spin));
pr = pitch_radius(circ_pitch, teeth, helical); pr = pitch_radius(circ_pitch, teeth, helical);
@ -747,7 +745,7 @@ module spur_gear(
// backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle // backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle
// helical = The angle of the rack teeth away from perpendicular to the gear axis of rotation. Stretches out the tooth shapes. Used to match helical spur gear pinions. Default: 0 // helical = The angle of the rack teeth away from perpendicular to the gear axis of rotation. Stretches out the tooth shapes. Used to match helical spur gear pinions. Default: 0
// internal = If true, create a mask for difference()ing from something else. // internal = If true, create a mask for difference()ing from something else.
// profile_shift = Profile shift factor x. // profile_shift = Profile shift factor x. Default: "auto"
// shaft_diam = If given, the diameter of the central shaft hole. // shaft_diam = If given, the diameter of the central shaft hole.
// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter. // diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter.
// mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth. // mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth.
@ -819,7 +817,7 @@ function spur_gear2d(
backlash = 0.0, backlash = 0.0,
internal, internal,
interior, interior,
profile_shift, profile_shift="auto",
helical, helical,
shaft_diam = 0, shaft_diam = 0,
pitch, pitch,
@ -834,7 +832,7 @@ function spur_gear2d(
circ_pitch = _inherit_gear_pitch("spur_gear2d()", pitch, circ_pitch, diam_pitch, mod), circ_pitch = _inherit_gear_pitch("spur_gear2d()", pitch, circ_pitch, diam_pitch, mod),
PA = _inherit_gear_pa(pressure_angle), PA = _inherit_gear_pa(pressure_angle),
helical = _inherit_gear_helical(helical, invert=!internal), helical = _inherit_gear_helical(helical, invert=!internal),
profile_shift = default(profile_shift, auto_profile_shift(teeth,PA,helical)) profile_shift = auto_profile_shift(teeth,PA,helical,profile_shift=profile_shift)
) )
assert(is_integer(teeth) && teeth>3) assert(is_integer(teeth) && teeth>3)
assert(is_finite(shaft_diam) && shaft_diam>=0) assert(is_finite(shaft_diam) && shaft_diam>=0)
@ -842,7 +840,6 @@ function spur_gear2d(
assert(is_finite(PA) && PA>=0 && PA<90, "Bad pressure_angle value.") assert(is_finite(PA) && PA>=0 && PA<90, "Bad pressure_angle value.")
assert(clearance==undef || (is_finite(clearance) && clearance>=0)) assert(clearance==undef || (is_finite(clearance) && clearance>=0))
assert(is_finite(backlash) && backlash>=0) assert(is_finite(backlash) && backlash>=0)
assert(is_finite(profile_shift) && abs(profile_shift)<1)
assert(is_finite(helical) && abs(helical)<90) assert(is_finite(helical) && abs(helical)<90)
assert(is_finite(gear_spin)) assert(is_finite(gear_spin))
let( let(
@ -879,7 +876,7 @@ module spur_gear2d(
backlash = 0.0, backlash = 0.0,
internal, internal,
interior, interior,
profile_shift, profile_shift="auto",
helical, helical,
shaft_diam = 0, shaft_diam = 0,
pitch, pitch,
@ -894,7 +891,7 @@ module spur_gear2d(
circ_pitch = _inherit_gear_pitch("spur_gear2d()", pitch, circ_pitch, diam_pitch, mod); circ_pitch = _inherit_gear_pitch("spur_gear2d()", pitch, circ_pitch, diam_pitch, mod);
PA = _inherit_gear_pa(pressure_angle); PA = _inherit_gear_pa(pressure_angle);
helical = _inherit_gear_helical(helical, invert=!internal); helical = _inherit_gear_helical(helical, invert=!internal);
profile_shift = default(profile_shift, auto_profile_shift(teeth,PA,helical)); profile_shift = auto_profile_shift(teeth,PA,helical,profile_shift=profile_shift);
checks = checks =
assert(is_integer(teeth) && teeth>3) assert(is_integer(teeth) && teeth>3)
assert(is_finite(shaft_diam) && shaft_diam>=0) assert(is_finite(shaft_diam) && shaft_diam>=0)
@ -902,7 +899,6 @@ module spur_gear2d(
assert(is_finite(PA) && PA>=0 && PA<90, "Bad pressure_angle value.") assert(is_finite(PA) && PA>=0 && PA<90, "Bad pressure_angle value.")
assert(clearance==undef || (is_finite(clearance) && clearance>=0)) assert(clearance==undef || (is_finite(clearance) && clearance>=0))
assert(is_finite(backlash) && backlash>=0) assert(is_finite(backlash) && backlash>=0)
assert(is_finite(profile_shift) && abs(profile_shift)<1)
assert(is_finite(helical) && abs(helical)<90) assert(is_finite(helical) && abs(helical)<90)
assert(is_finite(gear_spin)); assert(is_finite(gear_spin));
rgn = spur_gear2d( rgn = spur_gear2d(
@ -961,7 +957,7 @@ module spur_gear2d(
// pressure_angle = Controls how straight or bulged the tooth sides are. In degrees. // pressure_angle = Controls how straight or bulged the tooth sides are. In degrees.
// helical = The angle of the rack teeth away from perpendicular to the gear axis of rotation. Stretches out the tooth shapes. Used to match helical spur gear pinions. Default: 0 // helical = The angle of the rack teeth away from perpendicular to the gear axis of rotation. Stretches out the tooth shapes. Used to match helical spur gear pinions. Default: 0
// herringbone = If true, and helical is set, creates a herringbone gear. // herringbone = If true, and helical is set, creates a herringbone gear.
// profile_shift = Profile shift factor x for tooth profile. // profile_shift = Profile shift factor x for tooth profile. Default: 0
// clearance = Gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters) // clearance = Gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters)
// backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle // backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle
// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter. // diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter.
@ -990,7 +986,7 @@ module ring_gear(
pressure_angle, pressure_angle,
helical, helical,
herringbone = false, herringbone = false,
profile_shift, profile_shift=0,
clearance, clearance,
backlash = 0.0, backlash = 0.0,
or,od,width, or,od,width,
@ -1007,8 +1003,8 @@ module ring_gear(
PA = _inherit_gear_pa(pressure_angle); PA = _inherit_gear_pa(pressure_angle);
helical = _inherit_gear_helical(helical); helical = _inherit_gear_helical(helical);
thickness = _inherit_gear_thickness(thickness); thickness = _inherit_gear_thickness(thickness);
profile_shift = default(profile_shift, auto_profile_shift(teeth,PA,helical));
checks = checks =
assert(is_finite(profile_shift), "Profile shift for ring gears must be numerical")
assert(is_integer(teeth) && teeth>3) assert(is_integer(teeth) && teeth>3)
assert(is_finite(thickness) && thickness>0) assert(is_finite(thickness) && thickness>0)
assert(is_finite(PA) && PA>=0 && PA<90, "Bad pressure_angle value.") assert(is_finite(PA) && PA>=0 && PA<90, "Bad pressure_angle value.")
@ -1016,7 +1012,6 @@ module ring_gear(
assert(is_bool(herringbone)) assert(is_bool(herringbone))
assert(clearance==undef || (is_finite(clearance) && clearance>=0)) assert(clearance==undef || (is_finite(clearance) && clearance>=0))
assert(is_finite(backlash) && backlash>=0) assert(is_finite(backlash) && backlash>=0)
assert(is_finite(profile_shift) && abs(profile_shift)<1)
assert(slices==undef || (is_integer(slices) && slices>0)) assert(slices==undef || (is_integer(slices) && slices>0))
assert(num_defined([backing,or,od,width])<=1, "Cannot define more than one of backing, or, od and width") assert(num_defined([backing,or,od,width])<=1, "Cannot define more than one of backing, or, od and width")
assert(is_finite(gear_spin)); assert(is_finite(gear_spin));
@ -1107,7 +1102,7 @@ module ring_gear(
// width = width of the ring, measuring from tips of teeth to outside of ring. // width = width of the ring, measuring from tips of teeth to outside of ring.
// helical = The angle of the rack teeth away from perpendicular to the gear axis of rotation. Stretches out the tooth shapes. Used to match helical spur gear pinions. Default: 0 // helical = The angle of the rack teeth away from perpendicular to the gear axis of rotation. Stretches out the tooth shapes. Used to match helical spur gear pinions. Default: 0
// pressure_angle = Controls how straight or bulged the tooth sides are. In degrees. // pressure_angle = Controls how straight or bulged the tooth sides are. In degrees.
// profile_shift = Profile shift factor x for tooth profile. // profile_shift = Profile shift factor x for tooth profile. Default: 0
// clearance = Gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters) // clearance = Gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters)
// backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle // backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle
// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter. // diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter.
@ -1136,7 +1131,7 @@ module ring_gear2d(
backing, backing,
pressure_angle, pressure_angle,
helical, helical,
profile_shift, profile_shift=0,
clearance, clearance,
backlash = 0.0, backlash = 0.0,
or,od,width, or,od,width,
@ -1150,15 +1145,14 @@ module ring_gear2d(
circ_pitch = _inherit_gear_pitch("ring_gear2d()",pitch, circ_pitch, diam_pitch, mod); circ_pitch = _inherit_gear_pitch("ring_gear2d()",pitch, circ_pitch, diam_pitch, mod);
PA = _inherit_gear_pa(pressure_angle); PA = _inherit_gear_pa(pressure_angle);
helical = _inherit_gear_helical(helical); helical = _inherit_gear_helical(helical);
profile_shift = default(profile_shift, auto_profile_shift(teeth,PA,helical));
checks = checks =
assert(is_finite(profile_shift), "Profile shift for ring gears must be numerical")
assert(is_integer(teeth) && teeth>3) assert(is_integer(teeth) && teeth>3)
assert(num_defined([backing,or,od,width])<=1, "Cannot define more than one of backing, or, od and width") assert(num_defined([backing,or,od,width])<=1, "Cannot define more than one of backing, or, od and width")
assert(is_finite(PA) && PA>=0 && PA<90, "Bad pressure_angle value.") assert(is_finite(PA) && PA>=0 && PA<90, "Bad pressure_angle value.")
assert(is_finite(helical) && abs(helical)<90) assert(is_finite(helical) && abs(helical)<90)
assert(clearance==undef || (is_finite(clearance) && clearance>=0)) assert(clearance==undef || (is_finite(clearance) && clearance>=0))
assert(is_finite(backlash) && backlash>=0) assert(is_finite(backlash) && backlash>=0)
assert(is_finite(profile_shift) && abs(profile_shift)<1)
assert(is_finite(gear_spin)); assert(is_finite(gear_spin));
pr = pitch_radius(circ_pitch, teeth, helical=helical); pr = pitch_radius(circ_pitch, teeth, helical=helical);
ar = outer_radius(circ_pitch, teeth, helical=helical, profile_shift=profile_shift, internal=true); ar = outer_radius(circ_pitch, teeth, helical=helical, profile_shift=profile_shift, internal=true);
@ -1232,7 +1226,7 @@ module ring_gear2d(
// mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth. // mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth.
// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter. // diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter.
// helical = The angle of the rack teeth away from perpendicular to the rack length. Used to match helical spur gear pinions. Default: 0 // helical = The angle of the rack teeth away from perpendicular to the rack length. Used to match helical spur gear pinions. Default: 0
// profile_shift = Profile shift factor x. // profile_shift = Profile shift factor x. Default: 0
// pressure_angle = Controls how straight or bulged the tooth sides are. In degrees. Default: 20 // pressure_angle = Controls how straight or bulged the tooth sides are. In degrees. Default: 20
// backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle. Default: 0 // 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. Default: module/4 // clearance = Clearance gap at the bottom of the inter-tooth valleys. Default: module/4
@ -1310,7 +1304,6 @@ module rack(
assert(is_finite(backlash) && backlash>=0) assert(is_finite(backlash) && backlash>=0)
assert(is_finite(helical) && abs(helical)<90) assert(is_finite(helical) && abs(helical)<90)
//assert(is_bool(herringbone)) //assert(is_bool(herringbone))
assert(is_finite(profile_shift) && abs(profile_shift)<1)
assert(is_finite(gear_travel)); assert(is_finite(gear_travel));
trans_pitch = pitch / cos(helical); trans_pitch = pitch / cos(helical);
a = _adendum(pitch, profile_shift); a = _adendum(pitch, profile_shift);
@ -1391,7 +1384,6 @@ function rack(
assert(is_finite(backlash) && backlash>=0) assert(is_finite(backlash) && backlash>=0)
assert(is_finite(helical) && abs(helical)<90) assert(is_finite(helical) && abs(helical)<90)
//assert(is_bool(herringbone)) //assert(is_bool(herringbone))
assert(is_finite(profile_shift) && abs(profile_shift)<1)
assert(is_finite(gear_travel)) assert(is_finite(gear_travel))
let( let(
trans_pitch = pitch / cos(helical), trans_pitch = pitch / cos(helical),
@ -1473,7 +1465,7 @@ function rack(
// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter. // diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter.
// helical = The angle of the rack teeth away from perpendicular to the rack length. Stretches out the tooth shapes. Used to match helical spur gear pinions. Default: 0 // helical = The angle of the rack teeth away from perpendicular to the rack length. Stretches out the tooth shapes. Used to match helical spur gear pinions. Default: 0
// pressure_angle = Controls how straight or bulged the tooth sides are. In degrees. // pressure_angle = Controls how straight or bulged the tooth sides are. In degrees.
// profile_shift = Profile shift factor x for tooth shape. // profile_shift = Profile shift factor x for tooth shape. Default: 0
// backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle // backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle
// clearance = Clearance gap at the bottom of the inter-tooth valleys. Default: module/4 // clearance = Clearance gap at the bottom of the inter-tooth valleys. Default: module/4
// gear_travel = The distance the rack should be moved by linearly. Default: 0 // gear_travel = The distance the rack should be moved by linearly. Default: 0
@ -1521,7 +1513,6 @@ function rack2d(
assert(clearance==undef || (is_finite(clearance) && clearance>=0)) assert(clearance==undef || (is_finite(clearance) && clearance>=0))
assert(is_finite(backlash) && backlash>=0) assert(is_finite(backlash) && backlash>=0)
assert(is_finite(helical) && abs(helical)<90) assert(is_finite(helical) && abs(helical)<90)
assert(is_finite(profile_shift) && abs(profile_shift)<1)
assert(is_finite(gear_travel)) assert(is_finite(gear_travel))
assert(num_defined([width,backing,bottom])<=1, "Can define only one of width, backing and bottom") assert(num_defined([width,backing,bottom])<=1, "Can define only one of width, backing and bottom")
let( let(
@ -1619,7 +1610,6 @@ module rack2d(
assert(clearance==undef || (is_finite(clearance) && clearance>=0)) assert(clearance==undef || (is_finite(clearance) && clearance>=0))
assert(is_finite(backlash) && backlash>=0) assert(is_finite(backlash) && backlash>=0)
assert(is_finite(helical) && abs(helical)<90) assert(is_finite(helical) && abs(helical)<90)
assert(is_finite(profile_shift) && abs(profile_shift)<1)
assert(is_finite(gear_travel)) assert(is_finite(gear_travel))
assert(num_defined([width,backing,bottom])<=1, "Can define only one of width, backing and bottom"); assert(num_defined([width,backing,bottom])<=1, "Can define only one of width, backing and bottom");
trans_pitch = pitch / cos(helical); trans_pitch = pitch / cos(helical);
@ -1967,7 +1957,7 @@ module bevel_gear(
// pressure_angle = Controls how straight or bulged the tooth sides are. In degrees. Default: 20 // pressure_angle = Controls how straight or bulged the tooth sides are. In degrees. Default: 20
// backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle. Default: 0 // 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. Default: module/4 // clearance = Clearance gap at the bottom of the inter-tooth valleys. Default: module/4
// profile_shift = Profile shift factor x. // profile_shift = Profile shift factor x. Default: 0
// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter. // diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter.
// mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth. // mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth.
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER` // anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER`
@ -1980,8 +1970,8 @@ module bevel_gear(
// Example: Left Handed // Example: Left Handed
// worm(circ_pitch=8, d=30, l=50, starts=3, left_handed=true, $fn=72); // worm(circ_pitch=8, d=30, l=50, starts=3, left_handed=true, $fn=72);
// Example: Called as Function // Example: Called as Function
// vnf = worm(circ_pitch=8, d=35, l=50, starts=2, left_handed=true, pressure_angle=20, $fn=72); vnf = worm(circ_pitch=8, d=35, l=50, starts=2, left_handed=true, pressure_angle=20, $fn=72);
// vnf_polyhedron(vnf); vnf_polyhedron(vnf);
function worm( function worm(
circ_pitch, circ_pitch,
@ -1991,7 +1981,7 @@ function worm(
pressure_angle, pressure_angle,
backlash=0, backlash=0,
clearance, clearance,
profile_shift, profile_shift=0,
diam_pitch, diam_pitch,
mod, mod,
pitch, pitch,
@ -2002,8 +1992,7 @@ function worm(
) = ) =
let( let(
circ_pitch = _inherit_gear_pitch("worm()", pitch, circ_pitch, diam_pitch, mod), circ_pitch = _inherit_gear_pitch("worm()", pitch, circ_pitch, diam_pitch, mod),
PA = _inherit_gear_pa(pressure_angle), PA = _inherit_gear_pa(pressure_angle)
profile_shift = default(profile_shift, 0)
) )
assert(is_integer(starts) && starts>0) assert(is_integer(starts) && starts>0)
assert(is_finite(l) && l>0) assert(is_finite(l) && l>0)
@ -2012,7 +2001,6 @@ function worm(
assert(clearance==undef || (is_finite(clearance) && clearance>=0)) assert(clearance==undef || (is_finite(clearance) && clearance>=0))
assert(is_finite(backlash) && backlash>=0) assert(is_finite(backlash) && backlash>=0)
assert(is_bool(left_handed)) assert(is_bool(left_handed))
assert(is_finite(profile_shift) && abs(profile_shift)<1)
assert(is_finite(gear_spin)) assert(is_finite(gear_spin))
let( let(
helical = asin(starts * circ_pitch / PI / d), helical = asin(starts * circ_pitch / PI / d),
@ -2076,7 +2064,7 @@ module worm(
) { ) {
circ_pitch = _inherit_gear_pitch("worm()", pitch, circ_pitch, diam_pitch, mod); circ_pitch = _inherit_gear_pitch("worm()", pitch, circ_pitch, diam_pitch, mod);
PA = _inherit_gear_pa(pressure_angle); PA = _inherit_gear_pa(pressure_angle);
profile_shift = default(profile_shift, auto_profile_shift(starts,PA)); profile_shift = auto_profile_shift(starts,PA,profile_shift=profile_shift);
checks = checks =
assert(is_integer(starts) && starts>0) assert(is_integer(starts) && starts>0)
assert(is_finite(l) && l>0) assert(is_finite(l) && l>0)
@ -2131,7 +2119,7 @@ module worm(
// pressure_angle = Controls how straight or bulged the tooth sides are. In degrees. Default: 20 // pressure_angle = Controls how straight or bulged the tooth sides are. In degrees. Default: 20
// backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle. Default: 0 // 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. Default: module/4 // clearance = Clearance gap at the bottom of the inter-tooth valleys. Default: module/4
// profile_shift = Profile shift factor x. // profile_shift = Profile shift factor x. Default: "auto"
// slices = The number of vertical slices to refine the curve of the worm throat. Default: 10 // slices = The number of vertical slices to refine the curve of the worm throat. Default: 10
// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter. // diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter.
// mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth. // mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth.
@ -2190,7 +2178,7 @@ function worm_gear(
pressure_angle, pressure_angle,
backlash = 0, backlash = 0,
clearance, clearance,
profile_shift, profile_shift="auto",
slices = 10, slices = 10,
gear_spin=0, gear_spin=0,
pitch, pitch,
@ -2204,7 +2192,7 @@ function worm_gear(
let( let(
circ_pitch = _inherit_gear_pitch("worm_gear()", pitch, circ_pitch, diam_pitch, mod), circ_pitch = _inherit_gear_pitch("worm_gear()", pitch, circ_pitch, diam_pitch, mod),
PA = _inherit_gear_pa(pressure_angle), PA = _inherit_gear_pa(pressure_angle),
profile_shift = default(profile_shift, auto_profile_shift(teeth,PA)) profile_shift = auto_profile_shift(teeth,PA,profile_shift=profile_shift)
) )
assert(is_integer(teeth) && teeth>10) assert(is_integer(teeth) && teeth>10)
assert(is_finite(worm_diam) && worm_diam>0) assert(is_finite(worm_diam) && worm_diam>0)
@ -2302,7 +2290,7 @@ module worm_gear(
backlash = 0, backlash = 0,
shaft_diam = 0, shaft_diam = 0,
slices = 10, slices = 10,
profile_shift, profile_shift="auto",
gear_spin=0, gear_spin=0,
pitch, pitch,
diam_pitch, diam_pitch,
@ -2313,7 +2301,7 @@ module worm_gear(
) { ) {
circ_pitch = _inherit_gear_pitch("worm_gear()", pitch, circ_pitch, diam_pitch, mod); circ_pitch = _inherit_gear_pitch("worm_gear()", pitch, circ_pitch, diam_pitch, mod);
PA = _inherit_gear_pa(pressure_angle); PA = _inherit_gear_pa(pressure_angle);
profile_shift = default(profile_shift, auto_profile_shift(teeth,PA)); profile_shift = auto_profile_shift(teeth,PA,profile_shift=profile_shift);
checks = checks =
assert(is_integer(teeth) && teeth>10) assert(is_integer(teeth) && teeth>10)
assert(is_finite(worm_diam) && worm_diam>0) assert(is_finite(worm_diam) && worm_diam>0)
@ -2566,7 +2554,7 @@ function _gear_tooth_profile(
// Function: circular_pitch() // Function: circular_pitch()
// Synopsis: Returns tooth density expressed as "circular pitch". // Synopsis: Returns tooth density expressed as "circular pitch".
// Topics: Gears, Parts // Topics: Gears, Parts
// See Also: spur_gear(), diametral_pitch(), circular_pitch(), pitch_value(), module_value() // See Also: spur_gear(), diametral_pitch(), circular_pitch(), module_value()
// Usage: // Usage:
// circ_pitch = circular_pitch(circ_pitch); // circ_pitch = circular_pitch(circ_pitch);
// circ_pitch = circular_pitch(mod=); // circ_pitch = circular_pitch(mod=);
@ -2611,7 +2599,7 @@ function circular_pitch(circ_pitch, mod, pitch, diam_pitch) =
// Function: diametral_pitch() // Function: diametral_pitch()
// Synopsis: Returns tooth density expressed as "diametral pitch". // Synopsis: Returns tooth density expressed as "diametral pitch".
// Topics: Gears, Parts // Topics: Gears, Parts
// See Also: spur_gear(), diametral_pitch(), circular_pitch(), pitch_value(), module_value() // See Also: spur_gear(), diametral_pitch(), circular_pitch(), module_value()
// Usage: // Usage:
// dp = diametral_pitch(circ_pitch); // dp = diametral_pitch(circ_pitch);
// dp = diametral_pitch(mod=); // dp = diametral_pitch(mod=);
@ -2635,37 +2623,10 @@ function diametral_pitch(circ_pitch, mod, pitch, diam_pitch) =
PI / circ_pitch / INCH; PI / circ_pitch / INCH;
// Function: pitch_value()
// Synopsis: Returns tooth density expressed as "circular pitch".
// Topics: Gears, Parts
// See Also: spur_gear(), diametral_pitch(), circular_pitch(), pitch_value(), module_value()
// Usage:
// circ_pitch = pitch_value(mod);
// circ_pitch = pitch_value(circ_pitch=);
// circ_pitch = pitch_value(diam_pitch=);
// Description:
// Returns the circular pitch in mm from module/modulus or diametral pitch.
// The circular pitch of a gear is the number of millimeters per tooth around the pitch radius circle.
// For example, if you have a gear with 11 teeth, and the pitch diameter is 35mm, then the circumfrence
// of the pitch diameter is really close to 110mm, making the circular pitch of that gear about 10mm/tooth.
// Arguments:
// mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth.
// ---
// circ_pitch = The circular pitch, or distance in mm between teeth around the pitch circle.
// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter.
// Example:
// circ_pitch = pitch_value(mod=2);
// circ_pitch = pitch_value(circ_pitch=8);
// circ_pitch = pitch_value(diam_pitch=16);
function pitch_value(mod, circ_pitch, diam_pitch) =
circular_pitch(mod=mod, circ_pitch=circ_pitch, diam_pitch=diam_pitch);
// Function: module_value() // Function: module_value()
// Synopsis: Returns tooth density expressed as "module" or "modulus" in millimeters. // Synopsis: Returns tooth density expressed as "module" or "modulus" in millimeters.
// Topics: Gears, Parts // Topics: Gears, Parts
// See Also: spur_gear(), diametral_pitch(), circular_pitch(), pitch_value(), module_value() // See Also: spur_gear(), diametral_pitch(), circular_pitch(), module_value()
// Usage: // Usage:
// mod = module_value(circ_pitch); // mod = module_value(circ_pitch);
// mod = module_value(mod=); // mod = module_value(mod=);
@ -2699,7 +2660,7 @@ function module_value(circ_pitch, mod, pitch, diam_pitch) =
/// The height of the top of a gear tooth above the pitch radius circle. /// The height of the top of a gear tooth above the pitch radius circle.
/// Arguments: /// Arguments:
/// circ_pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. /// circ_pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
/// profile_shift = Profile shift factor x. /// profile_shift = Profile shift factor x. Default: 0
/// --- /// ---
/// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter. /// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter.
/// mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth. /// mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth.
@ -2738,7 +2699,7 @@ function _adendum(
/// Arguments: /// Arguments:
/// circ_pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. /// circ_pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
/// clearance = If given, sets the clearance between meshing teeth. Default: module/4 /// clearance = If given, sets the clearance between meshing teeth. Default: module/4
/// profile_shift = Profile shift factor x. /// profile_shift = Profile shift factor x. Default: 0
/// --- /// ---
/// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter. /// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter.
/// mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth. /// mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth.
@ -2772,7 +2733,7 @@ function _dedendum(
// Function: pitch_radius() // Function: pitch_radius()
// Synopsis: Returns the pitch radius for a gear. // Synopsis: Returns the pitch radius for a gear.
// Topics: Gears, Parts // Topics: Gears, Parts
// See Also: spur_gear(), diametral_pitch(), circular_pitch(), pitch_value(), module_value(), outer_radius() // See Also: spur_gear(), diametral_pitch(), circular_pitch(), module_value(), outer_radius()
// Usage: // Usage:
// pr = pitch_radius(pitch, teeth, [helical]); // pr = pitch_radius(pitch, teeth, [helical]);
// pr = pitch_radius(mod=, teeth=, [helical=]); // pr = pitch_radius(mod=, teeth=, [helical=]);
@ -2821,21 +2782,24 @@ function pitch_radius(
// Function: outer_radius() // Function: outer_radius()
// Synopsis: Returns the outer radius for a gear. // Synopsis: Returns the outer radius for a gear.
// Topics: Gears, Parts // Topics: Gears, Parts
// See Also: spur_gear(), diametral_pitch(), circular_pitch(), pitch_value(), module_value(), pitch_radius(), outer_radius() // See Also: spur_gear(), diametral_pitch(), circular_pitch(), module_value(), pitch_radius(), outer_radius()
// Usage: // Usage:
// or = outer_radius(circ_pitch, teeth, [helical=], [clearance=], [internal=], [profile_shift=]); // or = outer_radius(circ_pitch, teeth, [helical=], [clearance=], [internal=], [profile_shift=]);
// or = outer_radius(mod=, teeth=, [helical=], [clearance=], [internal=], [profile_shift=]); // or = outer_radius(mod=, teeth=, [helical=], [clearance=], [internal=], [profile_shift=]);
// or = outer_radius(diam_pitch=, teeth=, [helical=], [clearance=], [internal=], [profile_shift=]); // or = outer_radius(diam_pitch=, teeth=, [helical=], [clearance=], [internal=], [profile_shift=]);
// Description: // Description:
// Calculates the outer radius for the gear. The gear fits entirely within a cylinder of this radius. // Calculates the outer radius for the gear. The gear fits entirely within a cylinder of this radius, unless
// it has been strongly profile shifted, in which case it will be undersized due to tip clipping.
// This function does not apply automatic profile shifting.
// Arguments: // Arguments:
// circ_pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. // circ_pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
// teeth = The number of teeth on the gear. // teeth = The number of teeth on the gear.
// --- // ---
// clearance = If given, sets the clearance between meshing teeth. Default: module/4 // clearance = If given, sets the clearance between meshing teeth. Default: module/4
// profile_shift = Profile shift factor x. // profile_shift = Profile shift factor x. Default: "auto"
// internal = If true, calculate for an internal gear. // pressure_angle = Pressure angle. Default: 20
// helical = The helical angle (from vertical) of the teeth on the gear. Default: 0 // helical = The helical angle (from vertical) of the teeth on the gear. Default: 0
// internal = If true, calculate for an internal gear.
// mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth. // mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth.
// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter. // diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter.
// Example: // Example:
@ -2857,8 +2821,11 @@ function pitch_radius(
// halign="center", valign="top"); // halign="center", valign="top");
// } // }
function outer_radius(circ_pitch, teeth, clearance, internal=false, helical=0, profile_shift=0, mod, pitch, diam_pitch) = function outer_radius(circ_pitch, teeth, clearance, internal=false, helical=0, profile_shift=0, pressure_angle=20, mod, pitch, diam_pitch) =
let( circ_pitch = circular_pitch(pitch, mod, circ_pitch, diam_pitch) ) let(
circ_pitch = circular_pitch(pitch, mod, circ_pitch, diam_pitch),
profile_shift = auto_profile_shift(teeth, pressure_angle, helical, profile_shift=profile_shift)
)
pitch_radius(circ_pitch, teeth, helical) + ( pitch_radius(circ_pitch, teeth, helical) + (
internal internal
? _dedendum(circ_pitch, clearance, profile_shift=-profile_shift) ? _dedendum(circ_pitch, clearance, profile_shift=-profile_shift)
@ -2873,7 +2840,7 @@ function outer_radius(circ_pitch, teeth, clearance, internal=false, helical=0, p
/// rr = _root_radius(mod=, teeth=, [helical=], [clearance=], [internal=], [profile_shift=]); /// rr = _root_radius(mod=, teeth=, [helical=], [clearance=], [internal=], [profile_shift=]);
/// Topics: Gears /// Topics: Gears
/// Description: /// Description:
/// Calculates the root radius for the gear, at the base of the dedendum. /// Calculates the root radius for the gear, at the base of the dedendum. Does not apply auto profile shifting.
/// Arguments: /// Arguments:
/// circ_pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. /// circ_pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
/// teeth = The number of teeth on the gear. /// teeth = The number of teeth on the gear.
@ -2881,7 +2848,7 @@ function outer_radius(circ_pitch, teeth, clearance, internal=false, helical=0, p
/// clearance = If given, sets the clearance between meshing teeth. Default: module/4 /// clearance = If given, sets the clearance between meshing teeth. Default: module/4
/// internal = If true, calculate for an internal gear. /// internal = If true, calculate for an internal gear.
/// helical = The helical angle (from vertical) of the teeth on the gear. Default: 0 /// helical = The helical angle (from vertical) of the teeth on the gear. Default: 0
/// profile_shift = Profile shift factor x. /// profile_shift = Profile shift factor x. Default:0
/// mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth. /// mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth.
/// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter. /// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter.
/// Example: /// Example:
@ -3100,8 +3067,8 @@ function gear_dist(
assert(!(internal1 || internal2) || (teeth1>0 && teeth2>0), "Cannot specify internal gear with rack (zero tooth count)") assert(!(internal1 || internal2) || (teeth1>0 && teeth2>0), "Cannot specify internal gear with rack (zero tooth count)")
let( let(
mod = module_value(mod=mod,circ_pitch= circ_pitch, diam_pitch=diam_pitch), mod = module_value(mod=mod,circ_pitch= circ_pitch, diam_pitch=diam_pitch),
profile_shift1 = default(profile_shift1, auto_profile_shift(teeth1,pressure_angle,helical)), profile_shift1 = auto_profile_shift(teeth1,pressure_angle,helical,profile_shift=profile_shift1),
profile_shift2 = default(profile_shift2, auto_profile_shift(teeth2,pressure_angle,helical)), profile_shift2 = auto_profile_shift(teeth2,pressure_angle,helical,profile_shift=profile_shift2),
teeth1 = internal2? -teeth1 : teeth1, teeth1 = internal2? -teeth1 : teeth1,
teeth2 = internal1? -teeth2 : teeth2 teeth2 = internal1? -teeth2 : teeth2
) )
@ -3182,8 +3149,8 @@ function gear_dist_skew(teeth1,teeth2,helical1,helical2,profile_shift1,profile_s
assert(all_nonnegative([teeth1,teeth2]),"Must give nonnegative values for teeth") assert(all_nonnegative([teeth1,teeth2]),"Must give nonnegative values for teeth")
assert(teeth1>0 || teeth2>0, "One of the teeth counts must be nonzero") assert(teeth1>0 || teeth2>0, "One of the teeth counts must be nonzero")
let( let(
profile_shift1 = default(profile_shift1, auto_profile_shift(teeth1,pressure_angle,helical1)), profile_shift1 = auto_profile_shift(teeth1,pressure_angle,helical1,profile_shift=profile_shift1),
profile_shift2 = default(profile_shift2, auto_profile_shift(teeth2,pressure_angle,helical2)), profile_shift2 = auto_profile_shift(teeth2,pressure_angle,helical2,profile_shift=profile_shift2),
mod = module_value(circ_pitch=circ_pitch, diam_pitch=diam_pitch, mod=mod) mod = module_value(circ_pitch=circ_pitch, diam_pitch=diam_pitch, mod=mod)
) )
teeth1==0 || teeth2==0? pitch_radius(mod=mod, teeth=teeth1+teeth2, helical=teeth1?helical1:helical2) + (profile_shift1+profile_shift2)*mod teeth1==0 || teeth2==0? pitch_radius(mod=mod, teeth=teeth1+teeth2, helical=teeth1?helical1:helical2) + (profile_shift1+profile_shift2)*mod
@ -3223,8 +3190,8 @@ function gear_skew_angle(teeth1,teeth2,helical1,helical2,profile_shift1,profile_
assert(all_nonnegative([teeth1,teeth2]),"Must give nonnegative values for teeth") assert(all_nonnegative([teeth1,teeth2]),"Must give nonnegative values for teeth")
assert(teeth1>0 || teeth2>0, "One of the teeth counts must be nonzero") assert(teeth1>0 || teeth2>0, "One of the teeth counts must be nonzero")
let( let(
profile_shift1 = default(profile_shift1, auto_profile_shift(teeth1,pressure_angle,helical1)), profile_shift1 = auto_profile_shift(teeth1,pressure_angle,helical1,profile_shift=profile_shift1),
profile_shift2 = default(profile_shift2, auto_profile_shift(teeth2,pressure_angle,helical2)) profile_shift2 = auto_profile_shift(teeth2,pressure_angle,helical2,profile_shift=profile_shift2)
) )
profile_shift1==0 && profile_shift2==0 ? helical1+helical2 profile_shift1==0 && profile_shift2==0 ? helical1+helical2
: teeth1==0 || teeth2==0 ? helical1+helical2 : teeth1==0 || teeth2==0 ? helical1+helical2
@ -3279,10 +3246,14 @@ function get_profile_shift(desired,circ_pitch,teeth1,teeth2,pressure_angle=20,mo
// helical = helical angle // helical = helical angle
// --- // ---
// min_teeth = If given, the minimum number of teeth on a gear that has acceptable undercut. // min_teeth = If given, the minimum number of teeth on a gear that has acceptable undercut.
// profile_shift = If numerical then just return this value; if "auto" or not given then compute the automatic profile shift.
function auto_profile_shift(teeth, pressure_angle=20, helical=0, min_teeth) =
teeth==0 ? 0: function auto_profile_shift(teeth, pressure_angle=20, helical=0, min_teeth, profile_shift) =
let( assert(is_undef(profile_shift) || is_finite(profile_shift) || profile_shift=="auto", "Profile shift must be \"auto\" or a number")
is_num(profile_shift) ? profile_shift
: teeth==0 ? 0
: let(
pressure_angle=atan(tan(pressure_angle)/cos(helical)), pressure_angle=atan(tan(pressure_angle)/cos(helical)),
min_teeth = is_undef(min_teeth) min_teeth = is_undef(min_teeth)
? 2 / pow(sin(pressure_angle),2) ? 2 / pow(sin(pressure_angle),2)