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gears.scad
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//////////////////////////////////////////////////////////////////////////////////////////////
// LibFile: gears.scad
// Spur Gears, Bevel Gears, Racks, Worms and Worm Gears.
// Inspired by code by Leemon Baird, 2011, [email protected]
// Includes:
// include <BOSL2/std.scad>
// include <BOSL2/gears.scad>
// FileGroup: Parts
// FileSummary: Gears, racks, worms, and worm gears.
//////////////////////////////////////////////////////////////////////////////////////////////
_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
// circle (the "root circle") that touches the base of all the teeth, an
// outer circle that touches the tips of all the teeth, and the invisible
// pitch circle in between them. There is also a "base circle", which can
// be smaller than all three of the others, which controls the shape of
// the teeth. The side of each tooth lies on the path that the end of a
// string would follow if it were wrapped tightly around the base circle,
// then slowly unwound. That shape is an "involute", which gives this
// type of gear its name.
// Section: Gears
// Function&Module: spur_gear()
// Synopsis: Creates a spur gear, helical gear, or internal ring gear.
// SynTags: Geom, VNF
// Topics: Gears, Parts
// See Also: rack(), spur_gear(), spur_gear2d(), bevel_gear()
// Usage: As a Module
// 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(circ_pitch, teeth, thickness, [shaft_diam=], ...);
// vnf = spur_gear(mod=, teeth=, thickness=, [shaft_diam=], ...);
// Description:
// 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
// entire width, creating stress and noise. Helical gears have angled teeth and engage more gradually, so they
// 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 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 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 `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. 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:
// 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)
// ---
// hide = Number of teeth to delete to make this only a fraction of a circle
// pressure_angle = Controls how straight or bulged the tooth sides are. In degrees.
// clearance = Clearance gap at the bottom of the inter-tooth valleys.
// backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle
// helical = Teeth 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`.
// 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.
// 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(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(
// circ_pitch=5, teeth=20, thickness=10,
// shaft_diam=5, helical=-30, slices=12,
// $fa=1, $fs=1
// );
// Example: Herringbone Gear
// spur_gear(
// 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
// circ_pitch = 9; //all meshing gears need the same `circ_pitch` (and the same `pressure_angle`)
// thickness = 6;
// hole = 3;
// rack_base = 12;
// 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(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;
// circ_pitch = 5;
// n = 20;
// r = mesh_radius(circ_pitch,n);
// left(r) spur_gear(
// 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(
// circ_pitch=circ_pitch, teeth=n, thickness=10,
// shaft_diam=5, helical=ang2, slices=12,
// $fa=1, $fs=1
// );
// Example(Anim,Frames=36,VPT=[0,0,0],VPR=[55,0,25],VPD=375): Planetary Gear Assembly
// rteeth=56; pteeth=16; cteeth=24;
// circ_pitch=5; thick=10; pa=20;
// cr = mesh_radius(circ_pitch,cteeth);
// pr = mesh_radius(circ_pitch,pteeth);
// ring_gear(
// circ_pitch=circ_pitch,
// teeth=rteeth,
// thickness=thick,
// pressure_angle=pa);
// for (a=[0:3]) {
// zrot($t*90+a*90) back(cr+pr) {
// color("green")
// spur_gear(
// circ_pitch=circ_pitch,
// teeth=pteeth,
// thickness=thick,
// shaft_diam=5,
// pressure_angle=pa,
// spin=-$t*90*rteeth/pteeth);
// }
// }
// color("orange")
// zrot($t*90*rteeth/cteeth+$t*90+180/cteeth)
// spur_gear(
// circ_pitch=circ_pitch,
// teeth=cteeth,
// thickness=thick,
// shaft_diam=5,
// pressure_angle=pa);
function spur_gear(
circ_pitch,
teeth=11,
thickness,
shaft_diam = 0,
hide = 0,
pressure_angle,
clearance,
backlash = 0.0,
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("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]),
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 = PA,
hide = hide,
helical = helical,
clearance = clearance,
backlash = backlash,
internal = internal,
profile_shift = profile_shift,
hub_diam = shaft_diam
),
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(
circ_pitch,
teeth=11,
thickness,
shaft_diam = 0,
hide = 0,
pressure_angle,
clearance,
backlash = 0.0,
helical,
internal,
interior,
profile_shift,
slices,
herringbone=false,
pitch,
diam_pitch,
mod,
gear_spin = 0,
anchor = CENTER,
spin = 0,
orient = UP
) {
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]);
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(
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
);
}
} 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
);
}
}
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, Region
// Topics: Gears, Parts
// See Also: rack(), spur_gear(), spur_gear2d(), bevel_gear()
// Usage: As Module
// 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
// 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 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:
// 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.
// 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(circ_pitch=5, teeth=20);
// Example(2D): Metric Gear
// spur_gear2d(mod=2, teeth=20);
// Example(2D): Lower Pressure Angle
// spur_gear2d(circ_pitch=5, teeth=20, pressure_angle=20);
// Example(2D): Partial Gear
// 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;
// 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(cr+pr) {
// color("green")
// spur_gear2d(
// circ_pitch=circ_pitch,
// teeth=pteeth,
// pressure_angle=pa);
// }
// }
// color("orange")
// zrot(180/cteeth)
// spur_gear2d(
// circ_pitch=circ_pitch,
// teeth=cteeth,
// pressure_angle=pa);
// Example(2D): Called as a Function
// rgn = spur_gear2d(circ_pitch=8, teeth=16, hub_diam=5);
// region(rgn);
function spur_gear2d(
circ_pitch,
teeth = 11,
hide = 0,
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("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(
circ_pitch,
teeth = 11,
hide = 0,
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
) {
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));
rgn = spur_gear2d(
circ_pitch = circ_pitch,
teeth = teeth,
hide = hide,
pressure_angle = PA,
clearance = clearance,
helical = helical,
backlash = backlash,
profile_shift = profile_shift,
internal = internal,
hub_diam = hub_diam
);
pr = pitch_radius(circ_pitch, teeth, helical=helical);
attachable(anchor,spin, two_d=true, r=pr) {
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.
// SynTags: Geom, VNF
// Topics: Gears, Parts
// See Also: rack2d(), spur_gear(), spur_gear2d(), bevel_gear()
// Usage: As a Module
// rack(pitch, teeth, thickness, height, [pressure_angle=], [backlash=], [clearance=], [helical=]) [ATTACHMENTS];
// rack(mod=, teeth=, thickness=, height=, [pressure_angle=], [backlash]=, [clearance=], [helical=]) [ATTACHMENTS];
// Usage: As a Function
// vnf = rack(pitch, teeth, thickness, height, [pressure_angle=], [backlash=], [clearance=], [helical=]);
// vnf = rack(mod=, teeth=, thickness=, height=, [pressure_angle=], [backlash=], [clearance=], [helical=]);
// Description:
// This is used to create a 3D rack, which is a linear bar with teeth that a gear can roll along.
// A rack can mesh with any gear that has the same `pitch` and `pressure_angle`.
// 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 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: 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
// 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`
// Extra Anchors:
// "adendum" = At the tips of the teeth, at the center of rack.
// "adendum-left" = At the tips of the teeth, at the left end of the rack.
// "adendum-right" = At the tips of the teeth, at the right end of the rack.
// "adendum-back" = At the tips of the teeth, at the back of the rack.
// "adendum-front" = At the tips of the teeth, at the front of the rack.
// "dedendum" = At the base of the teeth, at the center of rack.
// "dedendum-left" = At the base of the teeth, at the left end of the rack.
// "dedendum-right" = At the base of the teeth, at the right end of the rack.
// "dedendum-back" = At the base of the teeth, at the back of the rack.
// "dedendum-front" = At the base of the teeth, at the front of the rack.
// Example(VPR=[60,0,325],VPD=130):
// rack(pitch=5, teeth=10, thickness=5, height=5, pressure_angle=20);
// Example: Rack for Helical Gear
// rack(pitch=5, teeth=10, thickness=5, height=5, pressure_angle=20, helical=30);
// Example: Alternate Helical Gear
// rack(pitch=5, teeth=10, thickness=5, height=5, pressure_angle=20, helical=-30);
// Example: Metric Rack
// rack(mod=2, teeth=10, thickness=5, height=5, pressure_angle=20);
// Example(Anim,VPT=[0,0,12],VPD=100,Frames=6): Rack and Pinion
// teeth1 = 16; teeth2 = 16;
// pitch = 5; thick = 5; helical = 30;
// pr = pitch_radius(pitch, 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, teeth2, thickness=thick, helical=helical, shaft_diam=5, orient=BACK);
module rack(
pitch,
teeth = 20,
thickness,
height = 10,
pressure_angle,
backlash = 0.0,
clearance,
helical,
profile_shift = 0,
gear_travel=0,
circ_pitch,
diam_pitch,
mod,
anchor = CENTER,
spin = 0,
orient = UP
) {
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),
named_anchor("adendum-right", [ l/2,0,a], RIGHT),
named_anchor("adendum-front", [0,-thickness/2,a], DOWN),
named_anchor("adendum-back", [0, thickness/2,a], UP),
named_anchor("dedendum", [0,0,-d], BACK),
named_anchor("dedendum-left", [-l/2,0,-d], LEFT),
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),
];
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 = PA,
backlash = backlash,
clearance = clearance,
helical = helical,
profile_shift = profile_shift
);
}
}
children();
}
}
function rack(
pitch,
teeth = 20,
thickness,
height = 10,
pressure_angle,
backlash = 0.0,
clearance,
helical,
profile_shift = 0,
circ_pitch,
diam_pitch,
mod,
gear_travel=0,
anchor = CENTER,
spin = 0,
orient = UP
) =
let(
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),
named_anchor("adendum-right", [ l/2,0,a], RIGHT),
named_anchor("adendum-front", [0,-thickness/2,a], DOWN),
named_anchor("adendum-back", [0, thickness/2,a], UP),
named_anchor("dedendum", [0,0,-d], BACK),
named_anchor("dedendum-left", [-l/2,0,-d], LEFT),
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),
]
) reorient(anchor,spin,orient, size=size, anchors=anchors, p=out);
// Function&Module: rack2d()
// Synopsis: Creates a 2D gear rack.
// SynTags: Geom, Path
// Topics: Gears, Parts
// See Also: rack(), spur_gear(), spur_gear2d(), bevel_gear()
// Usage: As a Module
// rack2d(pitch, teeth, height, [pressure_angle=], [backlash=], [clearance=]) [ATTACHMENTS];
// rack2d(mod=, teeth=, height=, [pressure_angle=], [backlash=], [clearance=]) [ATTACHMENTS];
// Usage: As a Function
// path = rack2d(pitch, teeth, height, [pressure_angle=], [backlash=], [clearance=]);
// path = rack2d(mod=, teeth=, height=, [pressure_angle=], [backlash=], [clearance=]);
// Description:
// This is used to create a 2D rack, which is a linear bar with teeth that a gear can roll along.
// A rack can mesh with any gear that has the same `pitch` and `pressure_angle`.
// 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 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 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
// 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.