diff --git a/color.scad b/color.scad index 5338728..3c6a51b 100644 --- a/color.scad +++ b/color.scad @@ -123,6 +123,45 @@ module rainbow(list, stride=1, maxhues, shuffle=false, seed) } +// Module: color_overlaps() +// Synopsis: Shows ghostly children, with overlaps highlighted in color. +// SynTags: Trans +// Topics: Debugging +// See Also: rainbow(), debug_vnf() +// Usage: +// color_overlaps([color]) CHILDREN; +// Description: +// Displays the given children in ghostly transparent gray, while the places where the +// they overlap are highlighted with the given color. +// Arguments: +// color = The color to highlight overlaps with. Default: "red" +// Example(2D): 2D Overlaps +// color_overlaps() { +// circle(d=50); +// left(20) circle(d=50); +// right(20) circle(d=50); +// } +// Example(): 3D Overlaps +// color_overlaps() { +// cuboid(50); +// left(30) sphere(d=50); +// right(30) sphere(d=50); +// xcyl(d=10,l=120); +// } +module color_overlaps(color="red") { + pairs = [for (i=[0:1:$children-1], j=[i+1:1:$children-1]) [i,j]]; + for (p = pairs) { + color(color) { + intersection() { + children(p.x); + children(p.y); + } + } + } + %children(); +} + + // Section: Colorspace Conversion // Function&Module: hsl() diff --git a/gears.scad b/gears.scad index 9b966db..736012c 100644 --- a/gears.scad +++ b/gears.scad @@ -10,6 +10,60 @@ ////////////////////////////////////////////////////////////////////////////////////////////// +_GEAR_PITCH = 5; +_GEAR_HELICAL = 0; +_GEAR_THICKNESS = 10; +_GEAR_PA = 20; + + +$parent_gear_type = undef; +$parent_gear_pitch = undef; +$parent_gear_teeth = undef; +$parent_gear_pa = undef; +$parent_gear_helical = undef; +$parent_gear_thickness = undef; +$parent_gear_dir = undef; +$parent_gear_travel = 0; + + +function _inherit_gear_param(name, val, pval, dflt, invert=false) = + is_undef(val) + ? is_undef(pval) + ? dflt + : (invert?-1:1)*pval + : is_undef(pval) + ? assert(is_finite(val), str("Invalid ",name," value: ",val)) + val + : (invert?-1:1)*val; + + +function _inherit_gear_pitch(pitch,circ_pitch,diam_pitch,mod) = + pitch != undef? + echo("WARNING: The use of the argument pitch= in gear code is deprecated. Please use circ_pitch= instead.") + assert(is_finite(pitch) && pitch>0) + pitch : + circ_pitch != undef? + assert(is_finite(circ_pitch) && circ_pitch>0) + circ_pitch : + diam_pitch != undef? + assert(is_finite(diam_pitch) && diam_pitch>0) + pitch_value(diam_pitch=diam_pitch) : + mod != undef? + assert(is_finite(mod) && mod>0) + pitch_value(mod) : + $parent_gear_pitch != undef? $parent_gear_pitch : + 5; + +function _inherit_gear_pa(pressure_angle) = + _inherit_gear_param("pressure_angle", pressure_angle, $parent_gear_pa, dflt=20); + +function _inherit_gear_helical(helical,invert=false) = + _inherit_gear_param("helical", helical, $parent_gear_helical, dflt=0, invert=invert); + +function _inherit_gear_thickness(thickness) = + _inherit_gear_param("thickness", thickness, $parent_gear_thickness, dflt=10); + + // Section: Terminology // The outline of a gear is a smooth circle (the "pitch circle") which has // mountains and valleys added so it is toothed. There is an inner @@ -31,13 +85,13 @@ // Topics: Gears, Parts // See Also: rack(), spur_gear(), spur_gear2d(), bevel_gear() // Usage: As a Module -// spur_gear(pitch, teeth, thickness, [shaft_diam], [hide=], [pressure_angle=], [clearance=], [backlash=], [helical=], [slices=], [internal=]) [ATTACHMENTS]; +// spur_gear(circ_pitch, teeth, thickness, [shaft_diam], [hide=], [pressure_angle=], [clearance=], [backlash=], [helical=], [slices=], [internal=], [herringbone=]) [ATTACHMENTS]; // spur_gear(mod=, teeth=, thickness=, [shaft_diam=], ...) [ATTACHMENTS]; // Usage: As a Function -// vnf = spur_gear(pitch, teeth, thickness, [shaft_diam=], ...); +// vnf = spur_gear(circ_pitch, teeth, thickness, [shaft_diam=], ...); // vnf = spur_gear(mod=, teeth=, thickness=, [shaft_diam=], ...); // Description: -// Creates a involute spur gear, helical gear, or internal ring gear. The module `spur_gear()` gives an involute +// Creates a involute spur gear, helical gear, or a mask for an internal ring 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. Spur gears have straight teeth and // mesh together on parallel shafts without creating any axial thrust. The teeth engage suddenly across their @@ -45,27 +99,31 @@ // run more smoothly and quietly, however they do produce thrust along the gear axis. This can be // circumvented using herringbone or double helical gears, which have no axial thrust and also self-align. // Helical gears can mesh along shafts that are not parallel, where the angle between the shafts is -// the sum of the helical angles of the two gears. -// . +// the sum of the helical angles of the two gears. +// . // 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 +// important function is `mesh_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 +// distance between their centers should be `mesh_radius()` for one, plus `mesh_radius()` for the +// other, which gives the overall meshing distance. 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. +// 14.5 degrees and 20 degrees, and occasionally 25. The default here is 20 degrees. // 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. +// Normally, If the number of teeth is too few, gear tooth shapes may be undercut to allow meshing +// with other gears. If this is the case, profile shifting will automatically be applies to enlarge +// the teeth, removing the undercut. This may add to the distance needed between gears. +// If you with to override this correction, you can use `profile_shift=0`, or set it to a specific +// value like 0.5. // Arguments: -// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. +// circ_pitch = The circular pitch, or distance in mm between teeth around the pitch circle. // 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) @@ -76,95 +134,113 @@ // backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle // 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. +// 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. // internal = If true, create a mask for difference()ing from something else. -// mod = The metric module/modulus of the gear. +// profile_shift = Profile shift factor x. +// 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` // 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` // Side Effects: // If internal is true then the default tag is "remove" // Example: Spur Gear -// spur_gear(pitch=5, teeth=20, thickness=8, shaft_diam=5); +// spur_gear(circ_pitch=5, teeth=20, thickness=8, shaft_diam=5); // Example: Metric Gear // spur_gear(mod=2, teeth=20, thickness=8, shaft_diam=5); // Example: Helical Gear // spur_gear( -// pitch=5, teeth=20, thickness=10, +// circ_pitch=5, teeth=20, thickness=10, // shaft_diam=5, helical=-30, slices=12, // $fa=1, $fs=1 // ); // Example: Herringbone Gear // spur_gear( -// pitch=5, teeth=20, thickness=5, -// shaft_diam=5, helical=-30, slices=5, -// anchor=BOT -// ) attach(BOT,TOP,overlap=0.01) -// spur_gear( -// pitch=5, teeth=20, thickness=5, -// shaft_diam=5, helical=30, slices=5, -// anchor=TOP -// ); +// circ_pitch=5, teeth=20, thickness=10, shaft_diam=5, +// helical=30, herringbone=true, slices=5 +// ); +// Example(Big): Effects of Profile Shifting. +// circ_pitch=5; teeth=7; thick=10; shaft=5; strokewidth=0.2; +// pr = pitch_radius(circ_pitch, teeth); +// left(10) { +// profile_shift = 0; +// mr = mesh_radius(circ_pitch,teeth,profile_shift=profile_shift); +// back(mr) spur_gear(circ_pitch, teeth, thick, shaft, profile_shift=profile_shift); +// rack(circ_pitch, teeth=3, thickness=thick, height=5, orient=BACK); +// color("black") up(thick/2) linear_extrude(height=0.1) { +// back(mr) dashed_stroke(circle(r=pr), width=strokewidth, closed=true); +// dashed_stroke([[-7.5,0],[7.5,0]], width=strokewidth); +// } +// } +// right(10) { +// spur_gear(circ_pitch, teeth, thick, shaft, profile_shift=0.59); +// fwd(pr+0.59*circ_pitch/PI) +// rack(circ_pitch, teeth=3, thickness=thick, height=5, orient=BACK); +// color("black") up(thick/2) linear_extrude(height=0.1) { +// dashed_stroke(circle(r=pr), width=strokewidth, closed=true); +// fwd(pr+0.59*circ_pitch/PI) +// dashed_stroke([[-7.5,0],[7.5,0]], width=strokewidth); +// } +// } // Example(Anim,Frames=8,VPT=[0,30,0],VPR=[0,0,0],VPD=300): Assembly of Gears // n1 = 11; //red gear number of teeth // n2 = 20; //green gear // n3 = 5; //blue gear // n4 = 16; //orange gear // n5 = 9; //gray rack -// pitch = 9; //all meshing gears need the same `pitch` (and the same `pressure_angle`) +// circ_pitch = 9; //all meshing gears need the same `circ_pitch` (and the same `pressure_angle`) // thickness = 6; // hole = 3; // rack_base = 12; -// r1 = pitch_radius(pitch,n1); -// r2 = pitch_radius(pitch,n2); -// r3 = pitch_radius(pitch,n3); -// r4 = pitch_radius(pitch,n4); -// r5 = pitch_radius(pitch,n5); +// r1 = mesh_radius(circ_pitch,n1); +// r2 = mesh_radius(circ_pitch,n2); +// r3 = mesh_radius(circ_pitch,n3); +// r4 = mesh_radius(circ_pitch,n4); +// r5 = mesh_radius(circ_pitch,n5); // a1 = $t * 360 / n1; // a2 = -$t * 360 / n2 + 180/n2; // a3 = -$t * 360 / n3; // a4 = -$t * 360 / n4 - 7.5*180/n4; -// 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*$t) -// rack(pitch=pitch,teeth=n5,thickness=thickness,height=rack_base,anchor=CENTER,orient=BACK); +// color("#f77") zrot(a1) spur_gear(circ_pitch,n1,thickness,hole); +// color("#7f7") back(r1+r2) zrot(a2) spur_gear(circ_pitch,n2,thickness,hole); +// color("#77f") right(r1+r3) zrot(a3) spur_gear(circ_pitch,n3,thickness,hole); +// color("#fc7") left(r1+r4) zrot(a4) spur_gear(circ_pitch,n4,thickness,hole,hide=n4-3); +// color("#ccc") fwd(r1) right(circ_pitch*$t) +// rack(pitch=circ_pitch,teeth=n5,thickness=thickness,height=rack_base,anchor=CENTER,orient=BACK); // Example: Helical gears meshing with non-parallel shafts // ang1 = 30; // ang2 = 10; -// pitch = 5; +// circ_pitch = 5; // n = 20; -// r = pitch_radius(pitch,n); +// r = mesh_radius(circ_pitch,n); // left(r) spur_gear( -// pitch=pitch, teeth=n, thickness=10, +// circ_pitch, n, thickness=10, // shaft_diam=5, helical=ang1, slices=12, // $fa=1, $fs=1 // ); // right(r) // xrot(ang1+ang2) // zrot(360/n/2-5) spur_gear( -// pitch=pitch, teeth=n, thickness=10, +// circ_pitch=circ_pitch, teeth=n, thickness=10, // shaft_diam=5, helical=ang2, slices=12, // $fa=1, $fs=1 // ); // Example(Anim,Frames=36,VPT=[0,0,0],VPR=[55,0,25],VPD=375): Planetary Gear Assembly // rteeth=56; pteeth=16; cteeth=24; -// pitch=5; thick=10; pa=20; -// prad = (pitch_radius(pitch,rteeth) + -// pitch_radius(pitch,cteeth)) / 2; -// rrad = outer_radius(pitch,rteeth,internal=true) + 5; -// diff() -// cyl(r=rrad,l=thick) -// tag("remove") -// spur_gear( -// pitch=pitch, teeth=rteeth, thickness=thick+1, -// pressure_angle=pa, internal=true); +// circ_pitch=5; thick=10; pa=20; +// cr = mesh_radius(circ_pitch,cteeth); +// pr = mesh_radius(circ_pitch,pteeth); +// ring_gear( +// circ_pitch=circ_pitch, +// teeth=rteeth, +// thickness=thick, +// pressure_angle=pa); // for (a=[0:3]) { -// zrot($t*90+a*90) back(prad) { +// zrot($t*90+a*90) back(cr+pr) { // color("green") // spur_gear( -// pitch=pitch, teeth=pteeth, +// circ_pitch=circ_pitch, +// teeth=pteeth, // thickness=thick, // shaft_diam=5, // pressure_angle=pa, @@ -174,237 +250,545 @@ // color("orange") // zrot($t*90*rteeth/cteeth+$t*90+180/cteeth) // spur_gear( -// pitch=pitch, teeth=cteeth, +// circ_pitch=circ_pitch, +// teeth=cteeth, // thickness=thick, // shaft_diam=5, // pressure_angle=pa); + function spur_gear( - pitch = 3, - teeth = 11, - thickness = 6, + circ_pitch, + teeth=11, + thickness, shaft_diam = 0, hide = 0, - pressure_angle = 28, - clearance = undef, + pressure_angle, + clearance, backlash = 0.0, - helical = 0, - slices = 2, + helical, interior, internal, + profile_shift, + slices, + herringbone=false, + diam_pitch, mod, + pitch, + gear_spin = 0, anchor = CENTER, spin = 0, orient = UP ) = let( - dummy = !is_undef(interior) ? echo("The interior paramter to spur_gear has been replaced by internal and will be removed."):0, + dummy = !is_undef(interior) ? echo("In spur_gear(), the argument 'interior=' has been deprecated, and may be removed in the future. Please use 'internal=' instead."):0, internal = first_defined([internal,interior,false]), - pitch = is_undef(mod) ? pitch : pitch_value(mod), - p = pitch_radius(pitch, teeth), - c = outer_radius(pitch, teeth, clearance, internal), - r = _root_radius(pitch, teeth, clearance, internal), - twist = 360*thickness*tan(helical)/(2*PI*p), - rgn = [ - spur_gear2d( - pitch = pitch, + circ_pitch = _inherit_gear_pitch(pitch, circ_pitch, diam_pitch, mod), + PA = _inherit_gear_pa(pressure_angle), + helical = _inherit_gear_helical(helical, invert=!internal), + thickness = _inherit_gear_thickness(thickness), + profile_shift = default(profile_shift, auto_profile_shift(teeth,PA)), + pr = pitch_radius(circ_pitch, teeth, helical), + circum = 2 * PI * pr, + twist = 360*thickness*tan(helical)/circum, + slices = default(slices, ceil(twist/360*segs(pr)+1)), + rgn = spur_gear2d( + circ_pitch = circ_pitch, teeth = teeth, - pressure_angle = pressure_angle, + pressure_angle = PA, hide = hide, + helical = helical, clearance = clearance, backlash = backlash, - internal = internal + internal = internal, + profile_shift = profile_shift, + hub_diam = shaft_diam ), - if (shaft_diam > 0) circle(d=shaft_diam, $fn=max(12,segs(shaft_diam/2))) - ], - rvnf = linear_sweep(rgn, height=thickness, twist=twist, slices=slices, center=true), - vnf = zrot(twist/2, p=rvnf) - ) reorient(anchor,spin,orient, h=thickness, r=p, p=vnf); + rvnf = herringbone + ? zrot(twist/2, p=linear_sweep(rgn, height=thickness, twist=twist, slices=slices, center=true)) + : let( + wall_vnf = linear_sweep(rgn, height=thickness/2, twist=twist/2, slices=ceil(slices/2), center=false, caps=false), + cap_vnf = vnf_from_region(rgn, transform=up(thickness/2)*zrot(twist/2)) + ) + vnf_join([ + wall_vnf, zflip(p=wall_vnf), + cap_vnf, zflip(p=cap_vnf), + ]), + vnf = zrot(gear_spin, p=rvnf) + ) reorient(anchor,spin,orient, h=thickness, r=pr, p=vnf); module spur_gear( - pitch = 3, - teeth = 11, - thickness = 6, + circ_pitch, + teeth=11, + thickness, shaft_diam = 0, hide = 0, - pressure_angle = 28, - clearance = undef, + pressure_angle, + clearance, backlash = 0.0, - helical = 0, - slices = 2, + helical, internal, interior, + profile_shift, + slices, + herringbone=false, + pitch, + diam_pitch, mod, + gear_spin = 0, anchor = CENTER, spin = 0, orient = UP ) { - if (!is_undef(interior)) echo("The interior paramter to spur_gear has been replaced by internal and will be removed."); + dummy = !is_undef(interior) ? echo("In spur_gear(), the argument 'interior=' has been deprecated, and may be removed in the future. Please use 'internal=' instead."):0; internal = first_defined([internal,interior,false]); - pitch = is_undef(mod) ? pitch : pitch_value(mod); - p = pitch_radius(pitch, teeth); - c = outer_radius(pitch, teeth, clearance, internal); - r = _root_radius(pitch, teeth, clearance, internal); - twist = 360*thickness*tan(helical)/(2*PI*p); - default_tag("remove", internal) - attachable(anchor,spin,orient, r=p, l=thickness) { - zrot(twist/2) - linear_extrude( - height=thickness, center=true, - twist=twist, slices=slices, - convexity=teeth/2 - ) { - difference() { + circ_pitch = _inherit_gear_pitch(pitch, circ_pitch, diam_pitch, mod); + PA = _inherit_gear_pa(pressure_angle); + helical = _inherit_gear_helical(helical, invert=!internal); + thickness = _inherit_gear_thickness(thickness); + profile_shift = default(profile_shift, auto_profile_shift(teeth,PA)); + pr = pitch_radius(circ_pitch, teeth, helical); + circum = 2 * PI * pr; + twist = 360*thickness*tan(helical)/circum; + slices = default(slices, ceil(twist/360*segs(pr)+1)); + default_tag("remove", internal) { + attachable(anchor,spin,orient, r=pr, l=thickness) { + zrot(gear_spin) + if (herringbone) { + zflip_copy() down(0.01) + linear_extrude( + height=thickness/2+0.01, center=false, + twist=twist/2, slices=ceil(slices/2), + convexity=teeth/2 + ) { spur_gear2d( - pitch = pitch, + circ_pitch = circ_pitch, teeth = teeth, - pressure_angle = pressure_angle, + pressure_angle = PA, hide = hide, + helical = helical, clearance = clearance, backlash = backlash, - interior = interior + internal = internal, + profile_shift = profile_shift, + hub_diam = shaft_diam + ); + } + } else { + zrot(twist/2) + linear_extrude( + height=thickness, center=true, + twist=twist, slices=slices, + convexity=teeth/2 + ) { + spur_gear2d( + circ_pitch = circ_pitch, + teeth = teeth, + pressure_angle = PA, + hide = hide, + helical = helical, + clearance = clearance, + backlash = backlash, + internal = internal, + profile_shift = profile_shift, + hub_diam = shaft_diam ); - if (shaft_diam > 0) { - circle(r=shaft_diam/2, $fn=max(12,segs(shaft_diam/2))); - } } } - children(); + union() { + $parent_gear_type = "spur"; + $parent_gear_pitch = circ_pitch; + $parent_gear_teeth = teeth; + $parent_gear_pa = PA; + $parent_gear_helical = helical; + $parent_gear_thickness = thickness; + union() children(); + } } + } } // Function&Module: spur_gear2d() // Synopsis: Creates a 2D spur gear or internal ring gear. -// SynTags: Geom, Path +// SynTags: Geom, Region // Topics: Gears, Parts // See Also: rack(), spur_gear(), spur_gear2d(), bevel_gear() // Usage: As Module -// spur_gear2d(pitch, teeth, [hide=], [pressure_angle=], [clearance=], [backlash=], [internal=]) [ATTACHMENTS]; +// spur_gear2d(circ_pitch, teeth, [hide=], [pressure_angle=], [clearance=], [backlash=], [internal=]) [ATTACHMENTS]; // spur_gear2d(mod=, teeth=, [hide=], [pressure_angle=], [clearance=], [backlash=], [internal=]) [ATTACHMENTS]; // Usage: As Function -// poly = spur_gear2d(pitch, teeth, [hide=], [pressure_angle=], [clearance=], [backlash=], [internal=]); -// poly = spur_gear2d(mod=, teeth=, [hide=], [pressure_angle=], [clearance=], [backlash=], [internal=]); +// rgn = spur_gear2d(circ_pitch, teeth, [hide=], [pressure_angle=], [clearance=], [backlash=], [internal=]); +// rgn = spur_gear2d(mod=, teeth=, [hide=], [pressure_angle=], [clearance=], [backlash=], [internal=]); // 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 -// first 2 parameters `pitch` and `teeth`, and let the rest be default values. -// Meshing gears must match in `pitch`, `pressure_angle`, and `helical`, and be separated by -// the sum of their pitch radii, which can be found with `pitch_radius()`. +// When called as a module, creates a 2D involute spur gear. When called as a function, +// returns a 2D region for the 2D involute spur gear. Normally, you should just specify the +// first 2 parameters `circ_pitch` and `teeth`, and let the rest be default values. +// Meshing gears must match in `circ_pitch`, `pressure_angle`, and `helical`, and be separated by +// the sum of their meshing radii, which can be found with `mesh_radius()`. // Arguments: -// 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 = Total number of teeth around the spur gear. // 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. +// --- +// hide = Number of teeth to delete to make this only a fraction of a circle // 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 +// 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. -// mod = The metric module/modulus of the gear. +// profile_shift = Profile shift factor x. +// hub_diam = If given, the diameter of the central hub 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. +// 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` // spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#subsection-spin). Default: `0` // Example(2D): Typical Gear Shape -// spur_gear2d(pitch=5, teeth=20); +// spur_gear2d(circ_pitch=5, teeth=20); // Example(2D): Metric Gear // spur_gear2d(mod=2, teeth=20); // Example(2D): Lower Pressure Angle -// spur_gear2d(pitch=5, teeth=20, pressure_angle=20); +// spur_gear2d(circ_pitch=5, teeth=20, pressure_angle=20); // Example(2D): Partial Gear -// spur_gear2d(pitch=5, teeth=20, hide=15, pressure_angle=20); +// spur_gear2d(circ_pitch=5, teeth=20, hide=15, pressure_angle=20); +// Example(2D): Effects of Profile Shifting. +// circ_pitch=5; teeth=7; shaft=5; strokewidth=0.2; +// module the_gear(profile_shift=0) { +// pr = pitch_radius(circ_pitch,teeth); +// mr = mesh_radius(circ_pitch,teeth,profile_shift=profile_shift); +// back(mr) { +// spur_gear2d(circ_pitch, teeth, hub_diam=shaft, profile_shift=profile_shift); +// up(0.1) color("black") +// dashed_stroke(circle(r=pr), width=strokewidth, closed=true); +// } +// } +// module the_rack() { +// rack2d(circ_pitch, teeth=3, height=5); +// up(0.1) color("black") +// dashed_stroke([[-7.5,0],[7.5,0]], width=strokewidth); +// } +// left(10) { the_gear(0); the_rack(); } +// right(10) { the_gear(0.59); the_rack(); } // Example(2D): Planetary Gear Assembly // rteeth=56; pteeth=16; cteeth=24; -// pitch=5; pa=20; -// prad = (pitch_radius(pitch,rteeth) + -// pitch_radius(pitch,cteeth)) / 2; -// rrad = outer_radius(pitch,rteeth,internal=true) + 5; -// difference() { -// circle(r=rrad); -// spur_gear2d( -// pitch=pitch, teeth=rteeth, -// pressure_angle=pa, interior=true); -// } +// circ_pitch=5; pa=20; +// cr = mesh_radius(circ_pitch, cteeth); +// pr = mesh_radius(circ_pitch, pteeth); +// ring_gear2d( +// circ_pitch=circ_pitch, +// teeth=rteeth, +// pressure_angle=pa); // for (a=[0:3]) { -// zrot(a*90) back(prad) { +// zrot(a*90) back(cr+pr) { // color("green") // spur_gear2d( -// pitch=pitch, teeth=pteeth, +// circ_pitch=circ_pitch, +// teeth=pteeth, // pressure_angle=pa); // } // } // color("orange") // zrot(180/cteeth) -// spur_gear2d(pitch=pitch, teeth=cteeth, pressure_angle=pa); +// spur_gear2d( +// circ_pitch=circ_pitch, +// teeth=cteeth, +// pressure_angle=pa); // Example(2D): Called as a Function -// path = spur_gear2d(pitch=8, teeth=16); -// polygon(path); +// rgn = spur_gear2d(circ_pitch=8, teeth=16, hub_diam=5); +// region(rgn); + function spur_gear2d( - pitch = 3, + circ_pitch, teeth = 11, hide = 0, - pressure_angle = 28, - clearance = undef, + pressure_angle, + clearance, backlash = 0.0, internal, interior, + profile_shift, + helical, + hub_diam, + pitch, + diam_pitch, mod, + gear_spin = 0, anchor = CENTER, spin = 0 -) = - let( - dummy = !is_undef(interior) ? echo("The interior paramter to spur_gear2d has been replaced by internal and will be removed."):0, - internal = first_defined([internal,internal,false]), - pitch = is_undef(mod) ? pitch : pitch_value(mod), - pr = pitch_radius(pitch=pitch, teeth=teeth), - tooth_profile = _gear_tooth_profile( - pitch = pitch, - teeth = teeth, - pressure_angle = pressure_angle, - clearance = clearance, - backlash = backlash, - internal = internal, - valleys = false - ), - pts = concat( - [for (tooth = [0:1:teeth-hide-1]) - each rot(tooth*360/teeth, p=tooth_profile) - ], - hide>0? [[0,0]] : [] - ) -) reorient(anchor,spin, two_d=true, r=pr, p=pts); +) = let( + dummy = !is_undef(interior) ? echo("In spur_gear2d(), the argument 'interior=' has been deprecated, and may be removed in the future. Please use 'internal=' instead."):0, + internal = first_defined([internal,interior,false]), + circ_pitch = _inherit_gear_pitch(pitch, circ_pitch, diam_pitch, mod), + PA = _inherit_gear_pa(pressure_angle), + helical = _inherit_gear_helical(helical, invert=!internal), + profile_shift = default(profile_shift, auto_profile_shift(teeth,PA)), + pr = pitch_radius(circ_pitch, teeth, helical=helical), + tooth = _gear_tooth_profile( + circ_pitch=circ_pitch, + teeth=teeth, + pressure_angle=PA, + clearance=clearance, + backlash=backlash, + profile_shift=profile_shift, + helical=helical, + internal=internal + ), + perim = [ + for (i = [0:1:teeth-1-hide]) + each zrot(-i*360/teeth+gear_spin, p=tooth), + if (hide>0) [0,0], + ], + rgn = [ + list_unwrap(deduplicate(perim)), + if (is_finite(hub_diam) && hub_diam>0 && !hide) + reverse(circle(d=hub_diam)), + ] +) reorient(anchor,spin, two_d=true, r=pr, p=rgn); module spur_gear2d( - pitch = 3, + circ_pitch, teeth = 11, hide = 0, - pressure_angle = 28, - clearance = undef, + pressure_angle, + clearance, backlash = 0.0, internal, interior, + profile_shift, + helical, + hub_diam=0, + pitch, + diam_pitch, mod, + gear_spin = 0, anchor = CENTER, spin = 0 ) { - if (!is_undef(interior)) echo("The interior paramter to spur_gear2d has been replaced by internal and will be removed."); + dummy = !is_undef(interior) ? echo("In spur_gear2d(), the argument 'interior=' has been deprecated, and may be removed in the future. Please use 'internal=' instead."):0; internal = first_defined([internal,interior,false]); - pitch = is_undef(mod) ? pitch : pitch_value(mod); - path = spur_gear2d( - pitch = pitch, + circ_pitch = _inherit_gear_pitch(pitch, circ_pitch, diam_pitch, mod); + PA = _inherit_gear_pa(pressure_angle); + helical = _inherit_gear_helical(helical, invert=!internal); + profile_shift = default(profile_shift, auto_profile_shift(teeth,PA)); + rgn = spur_gear2d( + circ_pitch = circ_pitch, teeth = teeth, hide = hide, - pressure_angle = pressure_angle, + pressure_angle = PA, clearance = clearance, + helical = helical, backlash = backlash, - internal = internal + profile_shift = profile_shift, + internal = internal, + hub_diam = hub_diam ); - pr = pitch_radius(pitch=pitch, teeth=teeth); + pr = pitch_radius(circ_pitch, teeth, helical=helical); attachable(anchor,spin, two_d=true, r=pr) { - polygon(path); + zrot(gear_spin) region(rgn); + union() { + $parent_gear_type = "spur2D"; + $parent_gear_pitch = circ_pitch; + $parent_gear_teeth = teeth; + $parent_gear_pa = PA; + $parent_gear_helical = helical; + $parent_gear_thickness = 0; + union() children(); + } + } +} + + +// Module: ring_gear() +// Synopsis: Creates a 3D ring gear. +// SynTags: Geom +// Topics: Gears, Parts +// See Also: rack(), ring_gear2d(), spur_gear(), spur_gear2d(), bevel_gear() +// Usage: +// ring_gear(circ_pitch, teeth, thickness, [backing], [pressure_angle=], [helical=], [herringbone=], [profile_shift=], [clearance=], [backlash=]) [ATTACHMENTS]; +// ring_gear(mod=, teeth=, thickness=, backing=, [pressure_angle=], [helical=], [herringbone=], [profile_shift=], [clearance=], [backlash=]) [ATTACHMENTS]; +// ring_gear(diam_pitch=, teeth=, thickness=, backing=, [pressure_angle=], [helical=], [herringbone=], [profile_shift=], [clearance=], [backlash=]) [ATTACHMENTS]; +// Description: +// Creates a 3D involute ring gear. Normally, you should just specify the +// first 3 parameters `circ_pitch`, `teeth`, and `thickness`, and let the rest be default values. +// Meshing gears must match in `circ_pitch`, `pressure_angle`, and `helical`, and be separated by +// the sum of their profile shifts and pitch radii, which can be found with `mesh_radius()`. +// Arguments: +// circ_pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. +// teeth = Total number of teeth around the spur gear. +// thickness = Thickness of ring gear in mm +// backing = The width of the ring gear backing, in mm. +// 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 +// herringbone = If true, and helical is set, creates a herringbone gear. +// profile_shift = Profile shift factor x for tooth profile. +// 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 +// 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. +// 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: +// ring_gear(circ_pitch=5, teeth=48, thickness=10); +// Example: Adjusting Backing +// ring_gear(circ_pitch=5, teeth=48, thickness=10, backing=20); +// Example: Adjusting Pressure Angle +// ring_gear(circ_pitch=5, teeth=48, thickness=10, pressure_angle=28); +// Example: Tooth Profile Shifting +// ring_gear(circ_pitch=5, teeth=48, thickness=10, profile_shift=0.5); +// Example: Helical Ring Gear +// ring_gear(circ_pitch=5, teeth=48, thickness=10, helical=30); +// Example: Herringbone Ring Gear +// ring_gear(circ_pitch=5, teeth=48, thickness=10, helical=30, herringbone=true); +module ring_gear( + circ_pitch, + teeth = 50, + thickness = 10, + backing = 10, + pressure_angle, + helical, + herringbone = false, + profile_shift, + clearance, + backlash = 0.0, + pitch, + diam_pitch, + mod, + slices, + gear_spin = 0, + anchor = CENTER, + spin = 0, + orient = UP +) { + circ_pitch = _inherit_gear_pitch(pitch, circ_pitch, diam_pitch, mod); + PA = _inherit_gear_pa(pressure_angle); + helical = _inherit_gear_helical(helical); + thickness = _inherit_gear_thickness(thickness); + profile_shift = default(profile_shift, auto_profile_shift(teeth,PA)); + pr = pitch_radius(circ_pitch, teeth, helical=helical); + ar = outer_radius(circ_pitch, teeth, helical=helical, profile_shift=profile_shift, internal=true); + circum = 2 * PI * pr; + twist = 360*thickness*tan(helical)/circum; + slices = default(slices, ceil(twist/360*segs(pr)+1)); + attachable(anchor,spin,orient, h=thickness, r=pr) { + zrot(gear_spin) + if (herringbone) { + zflip_copy() down(0.01) + linear_extrude(height=thickness/2, center=false, twist=twist/2, slices=ceil(slices/2), convexity=teeth/4) { + difference() { + circle(r=ar+backing); + spur_gear2d( + circ_pitch = circ_pitch, + teeth = teeth, + pressure_angle = PA, + helical = helical, + clearance = clearance, + backlash = backlash, + profile_shift = profile_shift, + internal = true + ); + } + } + } else { + zrot(twist/2) + linear_extrude(height=thickness,center=true, twist=twist, convexity=teeth/4) { + difference() { + circle(r=ar+backing); + spur_gear2d( + circ_pitch = circ_pitch, + teeth = teeth, + pressure_angle = PA, + helical = helical, + clearance = clearance, + backlash = backlash, + profile_shift = profile_shift, + internal = true + ); + } + } + } children(); } } +// Module: ring_gear2d() +// Synopsis: Creates a 2D ring gear. +// SynTags: Geom +// Topics: Gears, Parts +// See Also: rack(), spur_gear(), spur_gear2d(), bevel_gear() +// Usage: +// ring_gear2d(circ_pitch, teeth, [backing], [pressure_angle=], [helical=], [profile_shift=], [clearance=], [backlash=]) [ATTACHMENTS]; +// ring_gear2d(mod=, teeth=, [backing=], [pressure_angle=], [helical=], [profile_shift=], [clearance=], [backlash=]) [ATTACHMENTS]; +// ring_gear2d(diam_pitch=, teeth=, [backing=], [pressure_angle=], [helical=], [profile_shift=], [clearance=], [backlash=]) [ATTACHMENTS]; +// Description: +// Creates a 2D involute ring gear. Normally, you should just specify the +// first 2 parameters `circ_pitch` and `teeth`, and let the rest be default values. +// Meshing gears must match in `circ_pitch`, `pressure_angle`, and `helical`, and be separated by +// the sum of their profile shifts and pitch radii, which can be found with `mesh_radius()`. +// Arguments: +// circ_pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. +// teeth = Total number of teeth around the spur gear. +// backing = The width of the ring gear backing, in mm. +// 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 +// profile_shift = Profile shift factor x for tooth profile. +// 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 +// 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. +// 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` +// Example(2D;Big): +// circ_pitch=5; teeth1=50; teeth2=16; +// pr1 = pitch_radius(circ_pitch, teeth1); +// pr2 = pitch_radius(circ_pitch, teeth2); +// ring_gear2d(circ_pitch=circ_pitch, teeth=teeth1); +// back(pr1-pr2) spur_gear2d(circ_pitch=circ_pitch, teeth=teeth2); +module ring_gear2d( + circ_pitch, + teeth = 50, + backing = 10, + pressure_angle, + helical, + profile_shift, + clearance, + backlash = 0.0, + pitch, + diam_pitch, + mod, + gear_spin = 0, + anchor = CENTER, + spin = 0 +) { + circ_pitch = _inherit_gear_pitch(pitch, circ_pitch, diam_pitch, mod); + PA = _inherit_gear_pa(pressure_angle); + helical = _inherit_gear_helical(helical); + profile_shift = default(profile_shift, auto_profile_shift(teeth,PA)); + pr = pitch_radius(circ_pitch, teeth, helical=helical); + ar = outer_radius(circ_pitch, teeth, helical=helical, profile_shift=profile_shift, internal=true); + attachable(anchor,spin, two_d=true, r=pr) { + zrot(gear_spin) + difference() { + circle(r=ar+backing); + spur_gear2d( + circ_pitch = circ_pitch, + teeth = teeth, + pressure_angle = PA, + helical = helical, + clearance = clearance, + backlash = backlash, + profile_shift = profile_shift, + internal = true + ); + } + children(); + } +} + // Function&Module: rack() // Synopsis: Creates a straight or helical gear rack. @@ -423,16 +807,18 @@ module spur_gear2d( // When called as a function, returns a 3D [VNF](vnf.scad) for the rack. // When called as a module, creates a 3D rack shape. // Arguments: -// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. Default: 5 +// pitch = The pitch, or distance in mm between teeth along the rack. Matches up with circular pitch on a spur gear. Default: 5 // 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 +// 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 // 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. +// profile_shift = Profile shift factor x. +// 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. // 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` @@ -458,28 +844,38 @@ module spur_gear2d( // 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); +// pr = pitch_radius(pitch, teeth2, helical=helical); +// right(pr*2*PI/teeth2*$t) +// rack(pitch, teeth1, thickness=thick, height=5, helical=helical); // up(pr) yrot(186.5-$t*360/teeth2) -// spur_gear(pitch=pitch, teeth=teeth2, thickness=thick, helical=helical, shaft_diam=5, orient=BACK); +// spur_gear(pitch, teeth2, thickness=thick, helical=helical, shaft_diam=5, orient=BACK); + module rack( - pitch = 5, + pitch, teeth = 20, - thickness = 5, + thickness, height = 10, - pressure_angle = 28, + pressure_angle, backlash = 0.0, clearance, - helical=0, + helical, + profile_shift = 0, + gear_travel=0, + circ_pitch, + diam_pitch, mod, anchor = CENTER, spin = 0, orient = UP ) { - pitch = is_undef(mod) ? pitch : pitch_value(mod); - a = _adendum(pitch); - d = _dedendum(pitch, clearance); - l = teeth * pitch; + pitch = _inherit_gear_pitch(pitch, circ_pitch, diam_pitch, mod); + PA = _inherit_gear_pa(pressure_angle); + helical = _inherit_gear_helical(helical); + thickness = _inherit_gear_thickness(thickness); + trans_pitch = pitch / cos(helical); + a = _adendum(pitch, profile_shift); + d = _dedendum(pitch, clearance, profile_shift); + l = teeth * trans_pitch; anchors = [ named_anchor("adendum", [0,0,a], BACK), named_anchor("adendum-left", [-l/2,0,a], LEFT), @@ -492,16 +888,20 @@ module rack( named_anchor("dedendum-front", [0,-thickness/2,-d], DOWN), named_anchor("dedendum-back", [0, thickness/2,-d], UP), ]; - attachable(anchor,spin,orient, size=[l, thickness, 2*abs(a-height)], anchors=anchors) { + size = [l, thickness, 2*height]; + attachable(anchor,spin,orient, size=size, anchors=anchors) { + right(gear_travel) skew(sxy=tan(helical)) xrot(90) { linear_extrude(height=thickness, center=true, convexity=teeth*2) { rack2d( pitch = pitch, teeth = teeth, height = height, - pressure_angle = pressure_angle, + pressure_angle = PA, backlash = backlash, - clearance = clearance + clearance = clearance, + helical = helical, + profile_shift = profile_shift ); } } @@ -511,24 +911,49 @@ module rack( function rack( - pitch = 5, + pitch, teeth = 20, - thickness = 5, + thickness, height = 10, - pressure_angle = 28, + pressure_angle, backlash = 0.0, clearance, - helical=0, + helical, + profile_shift = 0, + circ_pitch, + diam_pitch, mod, + gear_travel=0, anchor = CENTER, spin = 0, orient = UP ) = let( - pitch = is_undef(mod) ? pitch : pitch_value(mod), - a = _adendum(pitch), - d = _dedendum(pitch, clearance), - l = teeth * pitch, + pitch = _inherit_gear_pitch(pitch, circ_pitch, diam_pitch, mod), + PA = _inherit_gear_pa(pressure_angle), + helical = _inherit_gear_helical(helical), + thickness = _inherit_gear_thickness(thickness), + trans_pitch = pitch / cos(helical), + a = _adendum(pitch, profile_shift), + d = _dedendum(pitch, clearance, profile_shift), + l = teeth * trans_pitch, + path = rack2d( + pitch = pitch, + teeth = teeth, + height = height, + pressure_angle = PA, + backlash = backlash, + clearance = clearance, + helical = helical, + profile_shift = profile_shift + ), + vnf = linear_sweep(path, height=thickness, anchor="origin", orient=FWD), + m = product([ + right(gear_travel), + if (helical) skew(sxy=tan(helical)), + ]), + out = apply(m, vnf), + size = [l, thickness, 2*height], anchors = [ named_anchor("adendum", [0,0,a], BACK), named_anchor("adendum-left", [-l/2,0,a], LEFT), @@ -540,18 +965,8 @@ function rack( named_anchor("dedendum-right", [ l/2,0,-d], RIGHT), named_anchor("dedendum-front", [0,-thickness/2,-d], DOWN), named_anchor("dedendum-back", [0, thickness/2,-d], UP), - ], - path = rack2d( - pitch = pitch, - teeth = teeth, - height = height, - pressure_angle = pressure_angle, - backlash = backlash, - clearance = clearance - ), - 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); + ] + ) reorient(anchor,spin,orient, size=size, anchors=anchors, p=out); @@ -573,13 +988,17 @@ function rack( // When called as a function, returns a 2D path for the outline of the rack. // When called as a module, creates a 2D rack shape. // Arguments: -// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. +// pitch = The pitch, or distance in mm between teeth along the rack. Matches up with circular pitch on a spur gear. Default: 5 // teeth = Total number of teeth along the rack -// height = Height of rack in mm, from tooth top to back of rack. +// height = Height of rack in mm, from pitch line to back of rack. // --- // pressure_angle = Controls how straight or bulged the tooth sides are. In degrees. // backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle -// mod = The metric module/modulus of the gear. +// 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. Stretches out the tooth shapes. Used to match helical spur gear pinions. Default: 0 +// profile_shift = Profile shift factor x. +// 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. // 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` // Extra Anchors: @@ -592,69 +1011,120 @@ function rack( // Example(2D): // rack2d(pitch=5, teeth=10, height=10, pressure_angle=20); // Example(2D): Called as a Function -// path = rack2d(pitch=8, teeth=8, height=10, pressure_angle=28); +// path = rack2d(pitch=8, teeth=8, height=10, pressure_angle=20); // polygon(path); + function rack2d( - pitch = 5, + pitch, teeth = 20, height = 10, - pressure_angle = 28, - backlash = 0.0, - clearance = undef, + pressure_angle, + backlash = 0, + clearance, + helical, + profile_shift = 0, + circ_pitch, + diam_pitch, mod, + gear_travel = 0, anchor = CENTER, spin = 0 -) = - let( - pitch = is_undef(mod) ? pitch : pitch_value(mod), - a = _adendum(pitch), - d = _dedendum(pitch, clearance) +) = let( + pitch = _inherit_gear_pitch(pitch, circ_pitch, diam_pitch, mod), + PA = _inherit_gear_pa(pressure_angle), + helical = _inherit_gear_helical(helical), + adendum = _adendum(pitch, profile_shift), + dedendum = _dedendum(pitch, clearance, profile_shift) ) - assert(a+d < height) + assert(dedendum < height) let( - xa = a * sin(pressure_angle), - xd = d * sin(pressure_angle), - l = teeth * pitch, - anchors = [ - named_anchor("adendum", [ 0, a,0], BACK), - named_anchor("adendum-left", [-l/2, a,0], LEFT), - named_anchor("adendum-right", [ l/2, a,0], RIGHT), - named_anchor("dedendum", [ 0,-d,0], BACK), - named_anchor("dedendum-left", [-l/2,-d,0], LEFT), - named_anchor("dedendum-right", [ l/2,-d,0], RIGHT), + trans_pitch = pitch / cos(helical), + trans_pa = atan(tan(PA)/cos(helical)), + tthick = trans_pitch/PI * (PI/2 + 2*profile_shift * tan(PA)) - backlash, + l = teeth * trans_pitch, + ax = ang_adj_to_opp(trans_pa, adendum), + dx = ang_adj_to_opp(trans_pa, dedendum), + poff = tthick/2 - backlash, + tooth = [ + [-trans_pitch/2, -dedendum], + each arc(n=4, r=dedendum-adendum, corner=[ + [-trans_pitch/2, -dedendum], + [-poff-dx, -dedendum], + [-poff+ax, +adendum], + ]), + each arc(n=4, r=trans_pitch/16, corner=[ + [-poff-dx, -dedendum], + [-poff+ax, +adendum], + [+poff-ax, +adendum], + ]), + each arc(n=4, r=trans_pitch/16, corner=[ + [-poff+ax, +adendum], + [+poff-ax, +adendum], + [+poff+dx, -dedendum], + ]), + each arc(n=4, r=dedendum-adendum, corner=[ + [+poff-ax, +adendum], + [+poff+dx, -dedendum], + [+trans_pitch/2, -dedendum], + ]), + [+trans_pitch/2, -dedendum], ], - path = [ - [-(teeth-1)/2 * pitch + -1/2 * pitch, a-height], - [-(teeth-1)/2 * pitch + -1/2 * pitch, -d], - for (i = [0:1:teeth-1]) let( - off = (i-(teeth-1)/2) * pitch - ) each [ - [off + -1/4 * pitch + backlash - xd, -d], - [off + -1/4 * pitch + backlash + xa, a], - [off + 1/4 * pitch - backlash - xa, a], - [off + 1/4 * pitch - backlash + xd, -d], - ], - [ (teeth-1)/2 * pitch + 1/2 * pitch, -d], - [ (teeth-1)/2 * pitch + 1/2 * pitch, a-height], + path2 = [ + for(m = xcopies(trans_pitch,n=teeth)) + each apply(m,tooth) + ], + path = right(gear_travel, p=[ + [path2[0].x, -height], + each path2, + [last(path2).x, -height], + ]), + size=[l,2*height], + anchors = [ + named_anchor("adendum", [ 0, adendum,0], BACK), + named_anchor("adendum-left", [-l/2, adendum,0], LEFT), + named_anchor("adendum-right", [ l/2, adendum,0], RIGHT), + named_anchor("dedendum", [ 0,-dedendum,0], BACK), + named_anchor("dedendum-left", [-l/2,-dedendum,0], LEFT), + named_anchor("dedendum-right", [ l/2,-dedendum,0], RIGHT), ] - ) reorient(anchor,spin, two_d=true, size=[l,2*abs(a-height)], anchors=anchors, p=path); + ) reorient(anchor,spin, two_d=true, size=size, anchors=anchors, p=path); + module rack2d( - pitch = 5, + pitch, teeth = 20, height = 10, - pressure_angle = 28, + pressure_angle, backlash = 0.0, - clearance = undef, + clearance, + helical, + profile_shift = 0, + gear_travel = 0, + circ_pitch, + diam_pitch, mod, anchor = CENTER, spin = 0 ) { - pitch = is_undef(mod) ? pitch : pitch_value(mod); - a = _adendum(pitch); - d = _dedendum(pitch, clearance); - l = teeth * pitch; + pitch = _inherit_gear_pitch(pitch, circ_pitch, diam_pitch, mod); + PA = _inherit_gear_pa(pressure_angle); + helical = _inherit_gear_helical(helical); + trans_pitch = pitch / cos(helical); + a = _adendum(pitch, profile_shift); + d = _dedendum(pitch, clearance, profile_shift); + l = teeth * trans_pitch; + path = rack2d( + pitch = pitch, + teeth = teeth, + height = height, + pressure_angle = PA, + backlash = backlash, + clearance = clearance, + helical = helical, + profile_shift= profile_shift + ); + size = [l, 2*height]; anchors = [ named_anchor("adendum", [ 0, a,0], BACK), named_anchor("adendum-left", [-l/2, a,0], LEFT), @@ -663,16 +1133,8 @@ module rack2d( named_anchor("dedendum-left", [-l/2,-d,0], LEFT), named_anchor("dedendum-right", [ l/2,-d,0], RIGHT), ]; - path = rack2d( - pitch = pitch, - teeth = teeth, - height = height, - pressure_angle = pressure_angle, - backlash = backlash, - clearance = clearance - ); - attachable(anchor,spin, two_d=true, size=[l, 2*abs(a-height)], anchors=anchors) { - polygon(path); + attachable(anchor,spin, two_d=true, size=size, anchors=anchors) { + right(gear_travel) polygon(path); children(); } } @@ -686,10 +1148,10 @@ module rack2d( // Topics: Gears, Parts // See Also: rack(), rack2d(), spur_gear(), spur_gear2d(), bevel_pitch_angle(), bevel_gear() // Usage: As a Module -// bevel_gear(pitch, teeth, face_width, [pitch_angle=]|[mate_teeth=], [shaft_diam=], [hide=], [pressure_angle=], [clearance=], [backlash=], [cutter_radius=], [spiral_angle=], [left_handed=], [slices=], [internal=]); +// bevel_gear(circ_pitch, teeth, face_width, [pitch_angle=]|[mate_teeth=], [shaft_diam=], [hide=], [pressure_angle=], [clearance=], [backlash=], [cutter_radius=], [spiral_angle=], [left_handed=], [slices=], [internal=]); // bevel_gear(mod=, teeth=, face_width=, [pitch_angle=]|[mate_teeth=], [shaft_diam=], [hide=], [pressure_angle=], [clearance=], [backlash=], [cutter_radius=], [spiral_angle=], [left_handed=], [slices=], [internal=]); // Usage: As a Function -// vnf = bevel_gear(pitch, teeth, face_width, [pitch_angle=]|[mate_teeth=], [hide=], [pressure_angle=], [clearance=], [backlash=], [cutter_radius=], [spiral_angle=], [left_handed=], [slices=], [internal=]); +// vnf = bevel_gear(circ_pitch, teeth, face_width, [pitch_angle=]|[mate_teeth=], [hide=], [pressure_angle=], [clearance=], [backlash=], [cutter_radius=], [spiral_angle=], [left_handed=], [slices=], [internal=]); // vnf = bevel_gear(mod=, teeth=, face_width=, [pitch_angle=]|[mate_teeth=], [hide=], [pressure_angle=], [clearance=], [backlash=], [cutter_radius=], [spiral_angle=], [left_handed=], [slices=], [internal=]); // Description: // Creates a (potentially spiral) bevel gear. The module `bevel_gear()` gives a bevel gear, with @@ -700,26 +1162,25 @@ module rack2d( // they engage more gradually, resulting in a less abrupt transfer of force, so they are quieter // in operation and less likely to break. // . -// The module `bevel_gear()` gives a gear in the XY -// plane, centered on the origin, with one tooth centered on the positive Y axis. The various -// functions below it take the same parameters, and return various measurements for the gear. 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. +// The module `bevel_gear()` gives a gear in the XY plane, centered on the origin, with one tooth +// centered on the positive Y axis. The various functions below it take the same parameters, and +// return various measurements for the gear. The most important function is `mesh_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, if no profile shifting is done). So the distance between +// their centers should be `mesh_radius()` for one, plus `mesh_radius()` for the other, which gives +// the radii of their pitch circles and profile shifts. In order for two gears to mesh, they must +// have the same `circ_pitch` and `pressure_angle` parameters. `circ_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. The default here is 20 degrees. Larger numbers bulge out more, +// giving stronger teeth. 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. Default: 5 +// circ_pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. Default: 5 // teeth = Total number of teeth around the entire perimeter. Default: 20 // face_width = Width of the toothed surface in mm, from inside to outside. Default: 10 // --- @@ -727,7 +1188,7 @@ module rack2d( // mate_teeth = The number of teeth in the gear that this gear will mate with. Overrides `pitch_angle` if given. // shaft_diam = Diameter of the hole in the center, in mm. Module use only. Default: 0 (no shaft hole) // hide = Number of teeth to delete to make this only a fraction of a circle. Default: 0 -// pressure_angle = Controls how straight or bulged the tooth sides are. In degrees. Default: 28 +// pressure_angle = Controls how straight or bulged the tooth sides are. In degrees. Default: 20 // 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. Default: 0 // cutter_radius = Radius of spiral arc for teeth. If 0, then gear will not be spiral. Default: 0 @@ -735,7 +1196,8 @@ module rack2d( // left_handed = If true, the gear returned will have a left-handed spiral. Default: false // slices = Number of vertical layers to divide gear into. Useful for refining gears with `spiral`. Default: 1 // internal = If true, create a mask for difference()ing from something else. -// mod = The metric module/modulus of the gear. +// 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. // 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` @@ -747,44 +1209,45 @@ module rack2d( // If internal is true then the default tag is "remove" // Example: Beveled Gear // bevel_gear( -// pitch=5, teeth=36, face_width=10, shaft_diam=5, +// circ_pitch=5, teeth=36, face_width=10, shaft_diam=5, // pitch_angle=45, spiral_angle=0 // ); // Example: Spiral Beveled Gear and Pinion // t1 = 16; t2 = 28; // bevel_gear( -// pitch=5, teeth=t1, mate_teeth=t2, +// circ_pitch=5, teeth=t1, mate_teeth=t2, // slices=12, anchor="apex", orient=FWD // ); // bevel_gear( -// pitch=5, teeth=t2, mate_teeth=t1, left_handed=true, +// circ_pitch=5, teeth=t2, mate_teeth=t1, left_handed=true, // slices=12, anchor="apex", spin=180/t2 // ); // Example(Anim,Frames=4,VPD=175): Manual Spacing of Pinion and Gear -// t1 = 14; t2 = 28; pitch=5; -// back(pitch_radius(pitch=pitch, teeth=t2)) { +// t1 = 14; t2 = 28; circ_pitch=5; +// back(pitch_radius(circ_pitch, t2)) { // yrot($t*360/t1) // bevel_gear( -// pitch=pitch, teeth=t1, mate_teeth=t2, shaft_diam=5, +// circ_pitch=circ_pitch, teeth=t1, mate_teeth=t2, shaft_diam=5, // slices=12, orient=FWD // ); // } -// down(pitch_radius(pitch=pitch, teeth=t1)) { +// down(pitch_radius(circ_pitch, t1)) { // zrot($t*360/t2) // bevel_gear( -// pitch=pitch, teeth=t2, mate_teeth=t1, left_handed=true, +// circ_pitch=circ_pitch, teeth=t2, mate_teeth=t1, left_handed=true, // shaft_diam=5, slices=12, spin=180/t2 // ); // } + function bevel_gear( - pitch = 5, + circ_pitch = 5, teeth = 20, face_width = 10, pitch_angle = 45, mate_teeth, hide = 0, pressure_angle = 20, - clearance = undef, + clearance, backlash = 0.0, cutter_radius = 30, spiral_angle = 35, @@ -792,19 +1255,23 @@ function bevel_gear( slices = 5, internal, interior, + pitch, + diam_pitch, mod, anchor = "pitchbase", spin = 0, orient = UP -) = - let( - dummy = !is_undef(interior) ? echo("The interior paramter to bevel_gear has been replaced by internal and will be removed."):0, +) = let( + dummy = !is_undef(interior) ? echo("In bevel_gear(), the argument 'interior=' has been deprecated, and may be removed in the future. Please use 'internal=' instead."):0, internal = first_defined([internal,interior,false]), - pitch = is_undef(mod) ? pitch : pitch_value(mod), + circ_pitch = _inherit_gear_pitch(pitch, circ_pitch, diam_pitch, mod), + PA = _inherit_gear_pa(pressure_angle), + spiral_angle = _inherit_gear_helical(spiral_angle, invert=!internal), + face_width = _inherit_gear_thickness(face_width), slices = cutter_radius==0? 1 : slices, pitch_angle = is_undef(mate_teeth)? pitch_angle : atan(teeth/mate_teeth), - pr = pitch_radius(pitch, teeth), - rr = _root_radius(pitch, teeth, clearance, internal), + pr = pitch_radius(circ_pitch, teeth), + rr = _root_radius(circ_pitch, teeth, clearance, internal), pitchoff = (pr-rr) * sin(pitch_angle), ocone_rad = opp_ang_to_hyp(pr, pitch_angle), icone_rad = ocone_rad - face_width, @@ -817,13 +1284,12 @@ function bevel_gear( sang = radcpang - (180-angC1), eang = radcpang - (180-angC2), profile = _gear_tooth_profile( - pitch = pitch, + circ_pitch = circ_pitch, teeth = teeth, - pressure_angle = pressure_angle, + pressure_angle = PA, clearance = clearance, backlash = backlash, internal = internal, - valleys = false, center = true ), verts1 = [ @@ -887,13 +1353,12 @@ function bevel_gear( module bevel_gear( - pitch = 5, + circ_pitch = 5, teeth = 20, face_width = 10, pitch_angle = 45, mate_teeth, shaft_diam = 0, - hide = 0, pressure_angle = 20, clearance = undef, backlash = 0.0, @@ -903,27 +1368,31 @@ module bevel_gear( slices = 5, internal, interior, + pitch, + diam_pitch, mod, anchor = "pitchbase", spin = 0, orient = UP ) { - if (!is_undef(interior)) echo("The interior paramter to bevel_gear has been replaced by internal and will be removed."); + dummy = !is_undef(interior) ? echo("In bevel_gear(), the argument 'interior=' has been deprecated, and may be removed in the future. Please use 'internal=' instead."):0; internal = first_defined([internal,interior,false]); - pitch = is_undef(mod) ? pitch : pitch_value(mod); + circ_pitch = _inherit_gear_pitch(pitch, circ_pitch, diam_pitch, mod); + PA = _inherit_gear_pa(pressure_angle); + spiral_angle = _inherit_gear_helical(spiral_angle, invert=!internal); + face_width = _inherit_gear_thickness(face_width); slices = cutter_radius==0? 1 : slices; pitch_angle = is_undef(mate_teeth)? pitch_angle : atan(teeth/mate_teeth); - pr = pitch_radius(pitch, teeth); + pr = pitch_radius(circ_pitch, teeth); ipr = pr - face_width*sin(pitch_angle); - rr = _root_radius(pitch, teeth, clearance, internal); + rr = _root_radius(circ_pitch, teeth, clearance, internal); pitchoff = (pr-rr) * sin(pitch_angle); vnf = bevel_gear( - pitch = pitch, + circ_pitch = circ_pitch, teeth = teeth, face_width = face_width, pitch_angle = pitch_angle, - hide = hide, - pressure_angle = pressure_angle, + pressure_angle = PA, clearance = clearance, backlash = backlash, cutter_radius = cutter_radius, @@ -940,7 +1409,7 @@ module bevel_gear( named_anchor("flattop", [0,0,thickness/2]), named_anchor("apex", [0,0,adj_ang_to_opp(pr,90-pitch_angle)+pitchoff-thickness/2]) ]; - default_tag("remove",internal) + default_tag("remove",internal) { attachable(anchor,spin,orient, r1=pr, r2=ipr, h=thickness, anchors=anchors) { difference() { vnf_polyhedron(vnf, convexity=teeth/2); @@ -950,6 +1419,7 @@ module bevel_gear( } children(); } + } } @@ -962,15 +1432,15 @@ module bevel_gear( // Topics: Gears, Parts // See Also: worm(), worm_gear(), rack(), rack2d(), spur_gear(), spur_gear2d(), bevel_pitch_angle(), bevel_gear() // Usage: As a Module -// worm(pitch, d, l, [starts=], [left_handed=], [pressure_angle=], [backlash=], [clearance=]); +// worm(circ_pitch, d, l, [starts=], [left_handed=], [pressure_angle=], [backlash=], [clearance=]); // worm(mod=, d=, l=, [starts=], [left_handed=], [pressure_angle=], [backlash=], [clearance=]); // Usage: As a Function -// vnf = worm(pitch, d, l, [starts=], [left_handed=], [pressure_angle=], [backlash=], [clearance=]); +// vnf = worm(circ_pitch, d, l, [starts=], [left_handed=], [pressure_angle=], [backlash=], [clearance=]); // vnf = worm(mod=, d=, l=, [starts=], [left_handed=], [pressure_angle=], [backlash=], [clearance=]); // Description: // 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 +// circ_pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. Default: 5 // d = The diameter of the worm. Default: 30 // l = The length of the worm. Default: 100 // starts = The number of lead starts. Default: 1 @@ -978,100 +1448,113 @@ module bevel_gear( // 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 // clearance = Clearance gap at the bottom of the inter-tooth valleys. -// mod = The metric module/modulus of the gear. +// profile_shift = Profile shift factor x. +// 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. // 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: -// worm(pitch=8, d=30, l=50, $fn=72); +// worm(circ_pitch=8, d=30, l=50, $fn=72); // Example: Multiple Starts. -// worm(pitch=8, d=30, l=50, starts=3, $fn=72); +// worm(circ_pitch=8, d=30, l=50, starts=3, $fn=72); // Example: Left Handed -// worm(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 -// vnf = worm(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); + function worm( - pitch=5, + circ_pitch, d=30, l=100, starts=1, left_handed=false, - pressure_angle=20, + pressure_angle, backlash=0, clearance, + profile_shift, + diam_pitch, mod, + pitch, anchor=CENTER, spin=0, orient=UP ) = let( - pitch = is_undef(mod) ? pitch : pitch_value(mod), - rack_profile = select(rack2d( - pitch = pitch, - teeth = starts, - height = d, - pressure_angle = pressure_angle, - backlash = backlash, - clearance = clearance - ), 1, -2), - polars = [ - for (i=idx(rack_profile)) let( - p = rack_profile[i], - a = 360 * p.x / pitch / starts - ) [a, p.y + d/2] + circ_pitch = _inherit_gear_pitch(pitch, circ_pitch, diam_pitch, mod), + PA = _inherit_gear_pa(pressure_angle), + profile_shift = default(profile_shift, 0), + helical = asin(starts * circ_pitch / PI / d), + trans_pitch = circ_pitch / cos(helical), + tooth = xflip( + p=select(rack2d( + pitch=circ_pitch, + teeth=1, + pressure_angle=PA, + clearance=clearance, + backlash=backlash, + helical=helical, + profile_shift=profile_shift + ), 1, -2) + ), + rack_profile = [ + for (t = xcopies(trans_pitch, n=2*ceil(l/trans_pitch)+1)) + each apply(t, tooth) ], - maxang = 360 / segs(d/2), - refined_polars = [ - for (i=idx(polars,e=-2)) let( - delta = polars[i+1].x - polars[i].x, - steps = ceil(delta/maxang), - step = delta/steps - ) for (j = [0:1:steps-1]) - [polars[i].x + j*step, lerp(polars[i].y,polars[i+1].y, j/steps)] - ], - cross_sect = [ for (p = refined_polars) polar_to_xy(p.y, p.x) ], - revs = l/pitch/starts, - zsteps = ceil(revs*360/maxang), - zstep = l/zsteps, - astep = revs*360/zsteps, + steps = max(36, segs(d/2)), + step = 360 / steps, + zsteps = ceil(l / circ_pitch * cos(helical) / starts * steps), + zstep = l / zsteps, profiles = [ - for (i=[0:1:zsteps]) let( - z = i*zstep - l/2, - a = i*astep - 360*revs/2 - ) - apply(zrot(a)*up(z), path3d(cross_sect)) + for (j = [0:1:zsteps]) [ + for (i = [0:1:steps-1]) let( + u = i / steps - 0.5, + ang = 360 * (1 - u) + 90, + z = j*zstep - l/2, + zoff = circ_pitch * starts * u / cos(helical), + h = lookup(z+zoff, rack_profile) + ) + cylindrical_to_xyz(d/2+h, ang, z) + ] ], - rprofiles = [ for (prof=profiles) reverse(prof) ], - vnf1 = vnf_vertex_array(rprofiles, caps=true, col_wrap=true, style="min_edge"), + vnf1 = vnf_vertex_array(profiles, caps=true, col_wrap=true, style="alt"), vnf = left_handed? xflip(p=vnf1) : vnf1 ) reorient(anchor,spin,orient, d=d, l=l, p=vnf); module worm( - pitch=5, + circ_pitch, d=15, l=100, starts=1, left_handed=false, - pressure_angle=20, + pressure_angle, backlash=0, clearance, + profile_shift=0, + pitch, + diam_pitch, mod, + gear_spin=0, anchor=CENTER, spin=0, orient=UP ) { + circ_pitch = _inherit_gear_pitch(pitch, circ_pitch, diam_pitch, mod); + PA = _inherit_gear_pa(pressure_angle); + profile_shift = default(profile_shift, auto_profile_shift(starts,PA)); vnf = worm( - pitch=pitch, + circ_pitch=circ_pitch, starts=starts, d=d, l=l, left_handed=left_handed, - pressure_angle=pressure_angle, + pressure_angle=PA, backlash=backlash, clearance=clearance, + profile_shift=profile_shift, mod=mod ); attachable(anchor,spin,orient, d=d, l=l) { - vnf_polyhedron(vnf, convexity=ceil(l/pitch)*2); + zrot(gear_spin) vnf_polyhedron(vnf, convexity=ceil(l/circ_pitch)*2); children(); } } @@ -1083,15 +1566,15 @@ module worm( // Topics: Gears, Parts // See Also: worm(), worm_gear(), rack(), rack2d(), spur_gear(), spur_gear2d(), bevel_pitch_angle(), bevel_gear() // Usage: As a Module -// worm_gear(pitch, teeth, worm_diam, [worm_starts=], [worm_arc=], [crowning=], [left_handed=], [pressure_angle=], [backlash=], [clearance=], [slices=], [shaft_diam=]) [ATTACHMENTS]; +// worm_gear(circ_pitch, teeth, worm_diam, [worm_starts=], [worm_arc=], [crowning=], [left_handed=], [pressure_angle=], [backlash=], [clearance=], [slices=], [shaft_diam=]) [ATTACHMENTS]; // worm_gear(mod=, teeth=, worm_diam=, [worm_starts=], [worm_arc=], [crowning=], [left_handed=], [pressure_angle=], [backlash=], [clearance=], [slices=], [shaft_diam=]) [ATTACHMENTS]; // Usage: As a Function -// vnf = worm_gear(pitch, teeth, worm_diam, [worm_starts=], [worm_arc=], [crowning=], [left_handed=], [pressure_angle=], [backlash=], [clearance=], [slices=]); +// vnf = worm_gear(circ_pitch, teeth, worm_diam, [worm_starts=], [worm_arc=], [crowning=], [left_handed=], [pressure_angle=], [backlash=], [clearance=], [slices=]); // vnf = worm_gear(mod=, teeth=, worm_diam=, [worm_starts=], [worm_arc=], [crowning=], [left_handed=], [pressure_angle=], [backlash=], [clearance=], [slices=]); // Description: // Creates a worm gear to match with a worm. // Arguments: -// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. Default: 5 +// circ_pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. Default: 5 // teeth = Total number of teeth along the rack. Default: 30 // worm_diam = The pitch diameter of the worm gear to match to. Default: 30 // worm_starts = The number of lead starts on the worm gear to match to. Default: 1 @@ -1101,30 +1584,41 @@ module worm( // 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 // clearance = Clearance gap at the bottom of the inter-tooth valleys. +// profile_shift = Profile shift factor x. // slices = The number of vertical slices to refine the curve of the worm throat. Default: 10 -// mod = The metric module/modulus of the gear. +// 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. // 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: Right-Handed -// worm_gear(pitch=5, teeth=36, worm_diam=30, worm_starts=1); +// worm_gear(circ_pitch=5, teeth=36, worm_diam=30, worm_starts=1); // Example: Left-Handed -// worm_gear(pitch=5, teeth=36, worm_diam=30, worm_starts=1, left_handed=true); +// worm_gear(circ_pitch=5, teeth=36, worm_diam=30, worm_starts=1, left_handed=true); // Example: Multiple Starts -// worm_gear(pitch=5, teeth=36, worm_diam=30, worm_starts=4); +// worm_gear(circ_pitch=5, teeth=36, worm_diam=30, worm_starts=4); // Example: Metric Worm Gear // worm_gear(mod=2, teeth=32, worm_diam=30, worm_starts=1); // Example(Anim,Frames=4,FrameMS=125,VPD=220,VPT=[-15,0,0]): Meshing Worm and Gear // $fn=36; -// pitch = 5; starts = 4; +// circ_pitch = 5; starts = 4; // worm_diam = 30; worm_length = 50; // gear_teeth=36; // right(worm_diam/2) // yrot($t*360/starts) -// worm(d=worm_diam, l=worm_length, pitch=pitch, starts=starts, orient=BACK); -// left(pitch_radius(pitch=pitch, teeth=gear_teeth)) +// worm( +// d=worm_diam, +// l=worm_length, +// circ_pitch=circ_pitch, +// starts=starts, +// orient=BACK); +// left(pitch_radius(circ_pitch, gear_teeth)) // zrot(-$t*360/gear_teeth) -// worm_gear(pitch=pitch, teeth=gear_teeth, worm_diam=worm_diam, worm_starts=starts); +// worm_gear( +// circ_pitch=circ_pitch, +// teeth=gear_teeth, +// worm_diam=worm_diam, +// worm_starts=starts); // Example: Meshing Worm and Gear Metricly // $fn = 72; // modulus = 2; starts = 3; @@ -1135,20 +1629,25 @@ module worm( // left(pitch_radius(mod=modulus, teeth=gear_teeth)) // worm_gear(mod=modulus, teeth=gear_teeth, worm_diam=worm_diam, worm_starts=starts); // Example: Called as Function -// vnf = worm_gear(pitch=8, teeth=30, worm_diam=30, worm_starts=1); +// vnf = worm_gear(circ_pitch=8, teeth=30, worm_diam=30, worm_starts=1); // vnf_polyhedron(vnf); + function worm_gear( - pitch = 5, + circ_pitch, teeth = 36, worm_diam = 30, worm_starts = 1, worm_arc = 60, - crowning = 1, + crowning = 0.1, left_handed = false, - pressure_angle = 20, + pressure_angle, backlash = 0, clearance, + profile_shift, slices = 10, + gear_spin=0, + pitch, + diam_pitch, mod, anchor = CENTER, spin = 0, @@ -1156,35 +1655,40 @@ function worm_gear( ) = assert(worm_arc >= 10 && worm_arc <= 60) let( - pitch = is_undef(mod) ? pitch : pitch_value(mod), - p = pitch_radius(pitch, teeth), - circ = 2 * PI * p, - r1 = p + worm_diam/2 + crowning, - r2 = worm_diam/2 + crowning, - thickness = worm_gear_thickness(pitch=pitch, teeth=teeth, worm_diam=worm_diam, worm_arc=worm_arc, crowning=crowning, clearance=clearance), - helical = pitch * worm_starts * worm_arc / 360 * 360 / circ, - tooth_profile = reverse(_gear_tooth_profile( - pitch = pitch, - teeth = teeth, - pressure_angle = pressure_angle, - clearance = clearance, - backlash = backlash, - valleys = false, - center = true - )), + circ_pitch = _inherit_gear_pitch(pitch, circ_pitch, diam_pitch, mod), + PA = _inherit_gear_pa(pressure_angle), + profile_shift = default(profile_shift, auto_profile_shift(teeth,PA)), + helical = asin(worm_starts * circ_pitch / PI / worm_diam), + pr = pitch_radius(circ_pitch, teeth, helical), + hob_rad = worm_diam / 2 + crowning, + thickness = worm_gear_thickness(circ_pitch=circ_pitch, teeth=teeth, worm_diam=worm_diam, worm_arc=worm_arc, crowning=crowning, clearance=clearance), + tooth_profile = _gear_tooth_profile( + circ_pitch=circ_pitch, + teeth=teeth, + pressure_angle=PA, + clearance=clearance, + backlash=backlash, + helical=helical, + profile_shift=profile_shift, + center=true + ), + tbot = min(column(tooth_profile,1)), + arcthick = hob_rad * sin(worm_arc/2) * 2, + twist = sin(helical)*arcthick / (2*PI*pr) * 360, profiles = [ for (slice = [0:1:slices]) let( - u = slice/slices - 0.5, - zang = u * worm_arc, - tp = [0,r1,0] - spherical_to_xyz(r2, 90, 90+zang), - zang2 = u * helical + u = slice/slices - 0.5 ) [ for (i = [0:1:teeth-1]) each apply( - zrot(-i*360/teeth+zang2) * - move(tp) * - xrot(-zang) * - scale(cos(zang)), + zrot(-i*360/teeth + twist*u - 0.5) * + right(pr+hob_rad) * + yrot(u*worm_arc) * + left(hob_rad) * + zrot(-90) * + back(tbot) * + scale(cos(u*worm_arc)) * + fwd(tbot), path3d(tooth_profile) ) ] @@ -1215,45 +1719,58 @@ function worm_gear( ], sides_vnf ]), - vnf = left_handed? xflip(p=vnf1) : vnf1 - ) reorient(anchor,spin,orient, r=p, l=thickness, p=vnf); + m = product([ + zrot(gear_spin), + if (left_handed) xflip(), + ]), + vnf = apply(m,vnf1) + ) reorient(anchor,spin,orient, r=pr, l=thickness, p=vnf); module worm_gear( - pitch = 5, + circ_pitch, teeth = 36, worm_diam = 30, worm_starts = 1, worm_arc = 60, - crowning = 1, + crowning = 0.1, left_handed = false, - pressure_angle = 20, + pressure_angle, backlash = 0, slices = 10, clearance, + profile_shift, + gear_spin=0, + pitch, + diam_pitch, mod, shaft_diam = 0, anchor = CENTER, spin = 0, orient = UP ) { - pitch = is_undef(mod) ? pitch : pitch_value(mod); - p = pitch_radius(pitch, teeth); + circ_pitch = _inherit_gear_pitch(pitch, circ_pitch, diam_pitch, mod); + PA = _inherit_gear_pa(pressure_angle); + profile_shift = default(profile_shift, auto_profile_shift(teeth,PA)); + helical = asin(worm_starts * circ_pitch / PI / worm_diam); + pr = pitch_radius(circ_pitch, teeth, helical); vnf = worm_gear( - pitch = pitch, + circ_pitch = circ_pitch, teeth = teeth, worm_diam = worm_diam, worm_starts = worm_starts, worm_arc = worm_arc, crowning = crowning, left_handed = left_handed, - pressure_angle = pressure_angle, + pressure_angle = PA, backlash = backlash, - slices = slices, - clearance = clearance + clearance = clearance, + profile_shift = profile_shift, + slices = slices ); thickness = pointlist_bounds(vnf[0])[1].z; - attachable(anchor,spin,orient, r=p, l=thickness) { + attachable(anchor,spin,orient, r=pr, l=thickness) { + zrot(gear_spin) difference() { vnf_polyhedron(vnf, convexity=teeth/2); if (shaft_diam > 0) { @@ -1267,75 +1784,162 @@ module worm_gear( -/// Function&Module: _gear_tooth_profile() -/// Usage: As Module -/// _gear_tooth_profile(pitch|mod, teeth, [pressure_angle], [clearance], [backlash], [internal], [valleys]); +/// Function: _gear_tooth_profile() /// Usage: As Function -/// path = _gear_tooth_profile(pitch|mod, teeth, [pressure_angle], [clearance], [backlash], [internal], [valleys]); +/// path = _gear_tooth_profile(pitch, teeth, [pressure_angle], [clearance], [backlash], [internal]); /// Topics: Gears /// See Also: spur_gear2d() /// Description: /// When called as a function, returns the 2D profile path for an individual gear tooth. /// When called as a module, creates the 2D profile shape for an individual gear tooth. /// Arguments: -/// 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 = Total number of teeth on the spur gear that this is a tooth for. /// pressure_angle = Pressure Angle. Controls how straight or bulged the tooth sides are. In degrees. /// 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 /// internal = If true, create a mask for difference()ing from something else. -/// valleys = If true, add the valley bottoms on either side of the tooth. Default: true /// center = If true, centers the pitch circle of the tooth profile at the origin. Default: false. -/// mod = The metric module/modulus of the gear. +/// 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. /// Example(2D): -/// _gear_tooth_profile(pitch=5, teeth=20, pressure_angle=20); +/// _gear_tooth_profile(circ_pitch=5, teeth=20, pressure_angle=20); /// Example(2D): Metric Gear Tooth /// _gear_tooth_profile(mod=2, teeth=20, pressure_angle=20); /// Example(2D): /// _gear_tooth_profile( -/// pitch=5, teeth=20, pressure_angle=20, valleys=false +/// circ_pitch=5, teeth=20, pressure_angle=20 /// ); /// Example(2D): As a function /// path = _gear_tooth_profile( -/// pitch=5, teeth=20, pressure_angle=20, valleys=false +/// circ_pitch=5, teeth=20, pressure_angle=20 /// ); /// stroke(path, width=0.1); + function _gear_tooth_profile( - pitch = 3, - teeth = 11, - pressure_angle = 28, - clearance = undef, + circ_pitch, + teeth, + pressure_angle = 20, + clearance, backlash = 0.0, + helical = 0, internal = false, - valleys = true, - center = false, - mod + profile_shift = 0.0, + center = false ) = let( - pitch = is_undef(mod) ? pitch : pitch_value(mod), - p = pitch_radius(pitch, teeth), - c = outer_radius(pitch, teeth, clearance, internal), - r = _root_radius(pitch, teeth, clearance, internal), - b = _base_radius(pitch, teeth, pressure_angle), - t = pitch/2-backlash/2, //tooth thickness at pitch circle - k = -_gear_iang(b, p) - t/2/p/PI*180, //angle to where involute meets base circle on each side of tooth - kk = r=uc_min) undercut[i]], + + // The u values to use when generating the tooth. + us = [ + for (i=[0:1:20-1]) 0.2*sin(i/20*90), + for (i=[2:1:steps-1]) i/(steps-1), + ], + + // Generate the left half of the tooth. + tooth_half_raw = deduplicate([ + for (u = us) let( + r = lerp(rrad, ma_rad, u), + a1 = lookup(r, involute_lup) + soff, + a2 = lookup(r, undercut_lup), + a = internal || r < undercut_lup[0].x? a1 : min(a1,a2) + ) if(a<90+180/teeth) polar_to_xy(r, a), + for (i=[0:1:cap_steps-1]) let( + a = ma_ang + soff - i * (cap_step-1) + ) polar_to_xy(ma_rad, a), + ]), + + // Find undercut bottom "jaggie" if it exists. + minima = [ + for (i = idx(tooth_half_raw)) + let(p = tooth_half_raw[i]) + if (i > 0 && i < len(tooth_half_raw)-1 && norm(p) <= prad) + let( + pp = tooth_half_raw[i-1], + np = tooth_half_raw[i+1] + ) + if (p.x > pp.x && p.x > np.x) + i + ], + + // Strip "jaggies" if found. + tooth_half = len(minima)<2? tooth_half_raw : [ + for (i = idx(tooth_half_raw)) + let(p = tooth_half_raw[i]) + if (i <= minima[0] || i >= last(minima)) + p + ], + + // Mirror the tooth to complete it. + tooth = deduplicate([ + each tooth_half, + each reverse(xflip(tooth_half)), + ]), + out = center? fwd(prad, p=tooth) : tooth +) out; @@ -1348,55 +1952,85 @@ function _gear_tooth_profile( // Function: circular_pitch() // Synopsis: Returns tooth density expressed as "circular pitch". // Topics: Gears, Parts -// See Also: spur_gear(), diametral_pitch(), circular_pitch(), pitch_value() +// See Also: spur_gear(), diametral_pitch(), circular_pitch(), pitch_value(), module_value() // Usage: -// circp = circular_pitch(pitch); -// circp = circular_pitch(mod=); +// circ_pitch = circular_pitch(circ_pitch); +// circ_pitch = circular_pitch(mod=); +// circ_pitch = circular_pitch(diam_pitch=); // Description: -// Get tooth density expressed as "circular pitch". +// Get tooth density expressed as "circular pitch", or the distance in mm between teeth around the pitch 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: -// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. -// mod = The metric module/modulus of the gear. +// circ_pitch = The circular pitch, or distance in mm between teeth around the pitch circle. +// --- +// 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. // Example: -// circp = circular_pitch(pitch=5); -// circp = circular_pitch(mod=2); -function circular_pitch(pitch=5, mod) = - let( pitch = is_undef(mod) ? pitch : pitch_value(mod) ) - pitch; +// circ_pitch = circular_pitch(circ_pitch=5); +// circ_pitch = circular_pitch(diam_pitch=12); +// circ_pitch = circular_pitch(mod=2); + +function circular_pitch(circ_pitch, mod, pitch, diam_pitch) = + assert(one_defined([pitch, mod, circ_pitch, diam_pitch], "pitch,mod,circ_pitch,diam_pitch")) + pitch != undef? assert(is_finite(pitch) && pitch>0) pitch : + circ_pitch != undef? assert(is_finite(circ_pitch) && circ_pitch>0) circ_pitch : + diam_pitch != undef? assert(is_finite(diam_pitch) && diam_pitch>0) PI / diam_pitch * INCH : + assert(is_finite(mod) && mod>0) mod * PI; // Function: diametral_pitch() // Synopsis: Returns tooth density expressed as "diametral pitch". // Topics: Gears, Parts -// See Also: spur_gear(), diametral_pitch(), circular_pitch(), pitch_value() +// See Also: spur_gear(), diametral_pitch(), circular_pitch(), pitch_value(), module_value() // Usage: -// dp = diametral_pitch(pitch); +// dp = diametral_pitch(circ_pitch); // dp = diametral_pitch(mod=); +// dp = diametral_pitch(diam_pitch=); // Description: -// Get tooth density expressed as "diametral pitch". +// Returns tooth density expressed as "diametral pitch", the number of teeth per inch of pitch diameter. +// For example, if you have a gear with 30 teeth, with a 1.5 inch pitch diameter, then you have a +// diametral pitch of 20 teeth/inch. // Arguments: -// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. -// mod = The metric module/modulus of the gear. +// circ_pitch = The circular pitch, or distance in mm between teeth around the pitch circle. +// --- +// 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. // Example: -// dp = diametral_pitch(pitch=5); -// dp = diametral_pitch(mod=2); -function diametral_pitch(pitch=5, mod) = - let( pitch = is_undef(mod) ? pitch : pitch_value(mod) ) - PI / pitch; +// diam_pitch = diametral_pitch(mod=2); +// diam_pitch = diametral_pitch(circ_pitch=8); +// diam_pitch = diametral_pitch(diam_pitch=16); + +function diametral_pitch(circ_pitch, mod, pitch, diam_pitch) = + let( circ_pitch = circular_pitch(pitch, mod, circ_pitch, diam_pitch) ) + PI / circ_pitch / INCH; // Function: pitch_value() -// Synopsis: Returns circular pitch in mm from module/modulus. +// Synopsis: Returns tooth density expressed as "circular pitch". // Topics: Gears, Parts // See Also: spur_gear(), diametral_pitch(), circular_pitch(), pitch_value(), module_value() // Usage: -// pitch = pitch_value(mod); +// circ_pitch = pitch_value(mod); +// circ_pitch = pitch_value(circ_pitch=); +// circ_pitch = pitch_value(diam_pitch=); // Description: -// 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. +// 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 module/modulus of the gear. -function pitch_value(mod) = mod * PI; +// 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() @@ -1404,68 +2038,106 @@ function pitch_value(mod) = mod * PI; // Topics: Gears, Parts // See Also: spur_gear(), diametral_pitch(), circular_pitch(), pitch_value(), module_value() // Usage: -// mod = module_value(pitch); +// mod = module_value(circ_pitch); +// mod = module_value(mod=); +// mod = module_value(diam_pitch=); // Description: // 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; +// circ_pitch = The circular pitch, or distance in mm between teeth around the pitch circle. +// --- +// 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. +// Example: +// mod = module_value(circ_pitch=8); +// mod = module_value(mod=2); +// mod = module_value(diam_pitch=16); + +function module_value(circ_pitch, mod, pitch, diam_pitch) = + let( circ_pitch = circular_pitch(pitch, mod, circ_pitch, diam_pitch) ) + circ_pitch / PI; /// Function: _adendum() /// Usage: -/// ad = _adendum(pitch|mod); +/// ad = _adendum(circ_pitch, [profile_shift]); +/// ad = _adendum(diam_pitch=, [profile_shift=]); +/// ad = _adendum(mod=, [profile_shift=]); /// Topics: Gears /// Description: /// 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. +/// circ_pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. +/// profile_shift = Profile shift factor x. +/// --- +/// 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. /// Example: -/// ad = _adendum(pitch=5); +/// ad = _adendum(circ_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); +/// circ_pitch = 5; teeth = 17; +/// pr = pitch_radius(circ_pitch, teeth); +/// adn = _adendum(circ_pitch=5); +/// #spur_gear2d(circ_pitch=circ_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; + +function _adendum( + circ_pitch, + profile_shift=0, + diam_pitch, + mod, + pitch +) = + let( mod = module_value(circ_pitch, mod, pitch, diam_pitch) ) + mod * (1 + profile_shift); /// Function: _dedendum() /// Usage: -/// ddn = _dedendum(pitch|mod, [clearance]); +/// ddn = _dedendum(circ_pitch=, [clearance], [profile_shift]); +/// ddn = _dedendum(diam_pitch=, [clearance=], [profile_shift=]); +/// ddn = _dedendum(mod=, [clearance=], [profile_shift=]); /// Topics: Gears /// Description: /// The depth of the gear tooth valley, below the pitch radius. /// Arguments: -/// 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. -/// mod = The metric module/modulus of the gear. +/// profile_shift = Profile shift factor x. +/// --- +/// 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. /// Example: -/// ddn = _dedendum(pitch=5); +/// ddn = _dedendum(circ_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); +/// circ_pitch = 5; teeth = 17; +/// pr = pitch_radius(circ_pitch, teeth); +/// ddn = _dedendum(circ_pitch=5); +/// #spur_gear2d(circ_pitch=circ_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)) : - (module_value(pitch) + clearance); + +function _dedendum( + circ_pitch, + clearance, + profile_shift=0, + diam_pitch, + mod, + pitch +) = let( + mod = module_value(circ_pitch, mod, pitch, diam_pitch), + clearance = default(clearance, 0.25 * mod) + ) + mod * (1 - profile_shift) + clearance; // Function: pitch_radius() @@ -1473,26 +2145,40 @@ function _dedendum(pitch=5, clearance, mod) = // Topics: Gears, Parts // See Also: spur_gear(), diametral_pitch(), circular_pitch(), pitch_value(), module_value(), outer_radius() // Usage: -// pr = pitch_radius(pitch, teeth); -// pr = pitch_radius(mod=, teeth=); +// pr = pitch_radius(pitch, teeth, [helical]); +// pr = pitch_radius(mod=, teeth=, [helical=]); // Description: // Calculates the pitch radius for the gear. Two mated gears will have their centers spaced apart // by the sum of the two gear's pitch radii. // Arguments: -// 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. -// mod = The metric module/modulus of the gear. +// helical = The helical angle (from vertical) of the teeth on the gear. Default: 0 +// --- +// 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. // Example: -// pr = pitch_radius(pitch=5, teeth=11); +// pr = pitch_radius(circ_pitch=5, teeth=11); +// pr = pitch_radius(circ_pitch=5, teeth=11, helical=30); +// pr = pitch_radius(diam_pitch=10, teeth=11); // pr = pitch_radius(mod=2, teeth=20); +// pr = pitch_radius(mod=2, teeth=20, helical=30); // Example(2D): -// pr = pitch_radius(pitch=5, teeth=11); -// #spur_gear2d(pitch=5, teeth=11); +// pr = pitch_radius(circ_pitch=5, teeth=11); +// #spur_gear2d(circ_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; + +function pitch_radius( + circ_pitch, + teeth, + helical=0, + mod, + diam_pitch, + pitch +) = + let( circ_pitch = circular_pitch(pitch, mod, circ_pitch, diam_pitch) ) + circ_pitch * teeth / PI / 2 / cos(helical); // Function: outer_radius() @@ -1500,59 +2186,84 @@ function pitch_radius(pitch=5, teeth=11, mod) = // Topics: Gears, Parts // See Also: spur_gear(), diametral_pitch(), circular_pitch(), pitch_value(), module_value(), pitch_radius(), outer_radius() // Usage: -// or = outer_radius(pitch, teeth, [clearance=], [internal=]); -// or = outer_radius(mod=, teeth=, [clearance=], [internal=]); +// or = outer_radius(circ_pitch, 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=]); // Description: // Calculates the outer radius for the gear. The gear fits entirely within a cylinder of this radius. // Arguments: -// 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. +// --- // clearance = If given, sets the clearance between meshing teeth. +// profile_shift = Profile shift factor x. // internal = If true, calculate for an internal gear. -// mod = The metric module/modulus of the gear. +// helical = The helical angle (from vertical) of the teeth on the gear. Default: 0 +// 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. // Example: -// or = outer_radius(pitch=5, teeth=20); +// or = outer_radius(circ_pitch=5, teeth=20); +// or = outer_radius(circ_pitch=5, teeth=20, helical=30); +// or = outer_radius(diam_pitch=10, teeth=17); // or = outer_radius(mod=2, teeth=16); // Example(2D): -// pr = outer_radius(pitch=5, teeth=11); -// #spur_gear2d(pitch=5, teeth=11); +// pr = outer_radius(circ_pitch=5, teeth=11); +// #spur_gear2d(circ_pitch=5, teeth=11); // color("black") // stroke(circle(r=pr),width=0.1,closed=true); -function outer_radius(pitch=5, teeth=11, clearance, internal=false, mod) = - let( pitch = is_undef(mod) ? pitch : pitch_value(mod) ) - pitch_radius(pitch, teeth) + - (internal? _dedendum(pitch, clearance) : _adendum(pitch)); + +function outer_radius(circ_pitch=5, teeth=11, clearance, internal=false, helical=0, profile_shift=0, mod, pitch, diam_pitch) = + let( circ_pitch = circular_pitch(pitch, mod, circ_pitch, diam_pitch) ) + pitch_radius(circ_pitch, teeth, helical) + ( + internal + ? _dedendum(circ_pitch, clearance, profile_shift=profile_shift) + : _adendum(circ_pitch, profile_shift=profile_shift) + ); /// Function: _root_radius() /// Usage: -/// rr = _root_radius(pitch|mod, teeth, [clearance], [internal]); +/// rr = _root_radius(circ_pitch, teeth, [helical], [clearance=], [internal=], [profile_shift=]); +/// rr = _root_radius(diam_pitch=, teeth=, [helical=], [clearance=], [internal=], [profile_shift=]); +/// rr = _root_radius(mod=, teeth=, [helical=], [clearance=], [internal=], [profile_shift=]); /// Topics: Gears /// Description: /// Calculates the root radius for the gear, at the base of the dedendum. /// Arguments: -/// 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. +/// --- /// clearance = If given, sets the clearance between meshing teeth. /// internal = If true, calculate for an internal gear. -/// mod = The metric module/modulus of the gear. +/// helical = The helical angle (from vertical) of the teeth on the gear. Default: 0 +/// profile_shift = Profile shift factor x. +/// 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. /// Example: -/// rr = _root_radius(pitch=5, teeth=11); +/// rr = _root_radius(circ_pitch=5, teeth=11); +/// rr = _root_radius(circ_pitch=5, teeth=16, helical=30); +/// rr = _root_radius(diam_pitch=10, teeth=11); /// rr = _root_radius(mod=2, teeth=16); /// Example(2D): -/// pr = _root_radius(pitch=5, teeth=11); +/// pr = _root_radius(circ_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, internal=false, mod) = - let( pitch = is_undef(mod) ? pitch : pitch_value(mod) ) - pitch_radius(pitch, teeth) - - (internal? _adendum(pitch) : _dedendum(pitch, clearance)); + +function _root_radius(circ_pitch, teeth, clearance, internal=false, helical=0, profile_shift=0, diam_pitch, mod, pitch) = + let( circ_pitch = circular_pitch(pitch, mod, circ_pitch, diam_pitch) ) + pitch_radius(circ_pitch, teeth, helical) - ( + internal + ? _adendum(circ_pitch, profile_shift=profile_shift) + : _dedendum(circ_pitch, clearance, profile_shift=profile_shift) + ); /// Function: _base_radius() /// Usage: -/// br = _base_radius(pitch|mod, teeth, [pressure_angle]); +/// br = _base_radius(circ_pitch, teeth, [pressure_angle], [helical]); +/// br = _base_radius(diam_pitch=, teeth=, [pressure_angle=], [helical=]); +/// br = _base_radius(mod=, teeth=, [pressure_angle=], [helical=]); /// Topics: Gears /// Description: /// Get the base circle for involute teeth, at the base of the teeth. @@ -1560,18 +2271,27 @@ function _root_radius(pitch=5, teeth=11, clearance, internal=false, mod) = /// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. /// teeth = The number of teeth on the gear. /// pressure_angle = Pressure angle in degrees. Controls how straight or bulged the tooth sides are. -/// mod = The metric module/modulus of the gear. +/// helical = The helical angle (from vertical) of the teeth on the gear. Default: 0 +/// --- +/// 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. /// Example: -/// br = _base_radius(pitch=5, teeth=20, pressure_angle=20); +/// br = _base_radius(circ_pitch=5, teeth=20, pressure_angle=20); +/// br = _base_radius(circ_pitch=5, teeth=20, pressure_angle=20, helical=30); +/// br = _base_radius(diam_pitch=10, 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); +/// pr = _base_radius(circ_pitch=5, teeth=11); +/// #spur_gear2d(circ_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); + +function _base_radius(circ_pitch, teeth, pressure_angle=20, helical=0, diam_pitch, mod, pitch) = + let( + circ_pitch = circular_pitch(pitch, mod, circ_pitch, diam_pitch), + trans_pa = atan(tan(pressure_angle)/cos(helical)) + ) + pitch_radius(circ_pitch, teeth, helical) * cos(trans_pa); // Function: bevel_pitch_angle() @@ -1602,6 +2322,7 @@ function _base_radius(pitch=5, teeth=11, pressure_angle=28, mod) = // 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))); @@ -1616,22 +2337,24 @@ function bevel_pitch_angle(teeth, mate_teeth, drive_angle=90) = // Description: // Calculate the thickness of the worm gear. // Arguments: -// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. Default: 5 +// circ_pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. Default: 5 // teeth = Total number of teeth along the rack. Default: 30 // worm_diam = The pitch diameter of the worm gear to match to. Default: 30 +// --- // worm_arc = The arc of the worm to mate with, in degrees. Default: 60 degrees // crowning = The amount to oversize the virtual hobbing cutter used to make the teeth, to add a slight crowning to the teeth to make them fit the work easier. Default: 1 // clearance = Clearance gap at the bottom of the inter-tooth valleys. -// mod = The metric module/modulus of the gear. +// 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. // Example: -// thick = worm_gear_thickness(pitch=5, teeth=36, worm_diam=30); +// thick = worm_gear_thickness(circ_pitch=5, teeth=36, worm_diam=30); // thick = worm_gear_thickness(mod=2, teeth=28, worm_diam=25); // Example(2D): -// pitch = 5; teeth=17; +// circ_pitch = 5; teeth=17; // worm_diam = 30; starts=2; -// y = worm_gear_thickness(pitch=pitch, teeth=teeth, worm_diam=worm_diam); +// y = worm_gear_thickness(circ_pitch=circ_pitch, teeth=teeth, worm_diam=worm_diam); // #worm_gear( -// pitch=pitch, teeth=teeth, +// circ_pitch=circ_pitch, teeth=teeth, // worm_diam=worm_diam, // worm_starts=starts, // orient=BACK @@ -1640,22 +2363,104 @@ function bevel_pitch_angle(teeth, mate_teeth, drive_angle=90) = // 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) = + +function worm_gear_thickness(circ_pitch, teeth, worm_diam, worm_arc=60, crowning=1, clearance, diam_pitch, mod, pitch) = let( - pitch = is_undef(mod) ? pitch : pitch_value(mod), + circ_pitch = circular_pitch(pitch, mod, circ_pitch, diam_pitch), r = worm_diam/2 + crowning, pitch_thick = r * sin(worm_arc/2) * 2, - pr = pitch_radius(pitch, teeth), - rr = _root_radius(pitch, teeth, clearance, false), + pr = pitch_radius(circ_pitch, teeth), + rr = _root_radius(circ_pitch, teeth, clearance, false), pitchoff = (pr-rr) * sin(worm_arc/2), thickness = pitch_thick + 2*pitchoff ) thickness; -function _gear_polar(r,t) = r*[sin(t),cos(t)]; -function _gear_iang(r1,r2) = sqrt((r2/r1)*(r2/r1) - 1)/PI*180 - acos(r1/r2); //unwind a string this many degrees to go from radius r1 to radius r2 -function _gear_q6(b,s,t,d) = _gear_polar(d,s*(_gear_iang(b,d)+t)); //point at radius d on the involute curve -function _gear_q7(f,r,b,r2,t,s) = _gear_q6(b,s,t,(1-f)*max(b,r)+f*r2); //radius a fraction f up the curved side of the tooth +// Function: mesh_radius() +// Synopsis: Returns the distance between two gear centers. +// Topics: Gears, Parts +// See Also: worm(), worm_gear(), pitch_radius(), outer_radius() +// Usage: +// dist = mesh_radius(pitch, teeth, [helical=], [profile_shift=], [pressure_angle=]); +// dist = mesh_radius(mod=, teeth=, [helical=], [profile_shift=], [pressure_angle=]); +// Description: +// Calculate the distance between the centers of two gears. +// Arguments: +// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. Default: 5 +// teeth = Total number of teeth in the first gear. If given 0, we assume this is a rack or worm. +// --- +// helical = The helical angle (from vertical) of the teeth on the first gear. Default: 0 +// profile_shift = Profile shift factor x for the first gear. Default: 0 +// pressure_angle = The pressure angle of the gear. +// 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. +// Example(2D): +// pitch=5; teeth1=7; teeth2=24; +// mr1 = mesh_radius(pitch, teeth1); +// mr2 = mesh_radius(pitch, teeth2); +// left(mr1) spur_gear2d(pitch, teeth1, gear_spin=-90); +// right(mr2) spur_gear2d(pitch, teeth2, gear_spin=90-180/teeth2); +// Example: Non-parallel Helical Gears +// pitch=5; teeth1=15; teeth2=24; ha1=45; ha2=30; thick=10; +// mr1 = mesh_radius(pitch, teeth1, helical=ha1); +// mr2 = mesh_radius(pitch, teeth2, helical=ha2); +// left(mr1) spur_gear(pitch, teeth1, helical=ha1, thickness=thick, gear_spin=-90); +// right(mr2) xrot(ha1+ha2) spur_gear(pitch, teeth2, helical=ha2, thickness=thick, gear_spin=90-180/teeth2); +// Example(2D): Disable Auto Profile Shifting on the Small Gear +// pitch=5; teeth1=7; teeth2=24; +// mr1 = mesh_radius(pitch, teeth1, profile_shift=0); +// mr2 = mesh_radius(pitch, teeth2); +// left(mr1) spur_gear2d(pitch, teeth1, profile_shift=0, gear_spin=-90); +// right(mr2) spur_gear2d(pitch, teeth2, gear_spin=90-180/teeth2); +// Example(2D): Manual Profile Shifting +// pitch=5; teeth1=7; teeth2=24; ps1 = 0.5; ps2 = -0.2; +// mr1 = mesh_radius(pitch, teeth1, profile_shift=ps1); +// mr2 = mesh_radius(pitch, teeth2, profile_shift=ps2); +// left(mr1) spur_gear2d(pitch, teeth1, profile_shift=ps1, gear_spin=-90); +// right(mr2) spur_gear2d(pitch, teeth2, profile_shift=ps2, gear_spin=90-180/teeth2); + +function mesh_radius( + circ_pitch, + teeth, + helical=0, + profile_shift, + pressure_angle=20, + diam_pitch, + mod, + pitch +) = + let( + circ_pitch = circular_pitch(pitch, mod, circ_pitch, diam_pitch), + profile_shift = default(profile_shift, teeth>0? auto_profile_shift(teeth,pressure_angle) : 0), + mod = circ_pitch / PI, + pr = teeth>0? pitch_radius(circ_pitch, teeth, helical) : 0, + r = pr + profile_shift * mod + ) r; + + +// Function: auto_profile_shift() +// Synopsis: Returns the recommended profile shift for a gear. +// Topics: Gears, Parts +// See Also: worm(), worm_gear(), pitch_radius(), outer_radius() +// Usage: +// x = auto_profile_shift(teeth, pressure_angle); +// x = auto_profile_shift(teeth, min_teeth=); +// Description: +// Calculates the recommended profile shift to avoid gear tooth undercutting. +// Arguments: +// teeth = Total number of teeth in the gear. +// pressure_angle = The pressure angle of the gear. +// --- +// min_teeth = If given, the minimum number of teeth on a gear that has acceptable undercut. + +function auto_profile_shift(teeth, pressure_angle=20, min_teeth) = + let( + min_teeth = is_undef(min_teeth) + ? 2 / pow(sin(pressure_angle),2) + : min_teeth + ) + teeth > floor(min_teeth)? 0 : + 1 - (teeth / min_teeth);