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Added rack2d() and various VNF generating functions to involute_gears.scad

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This commit is contained in:
Garth Minette 2020-10-19 22:53:56 -07:00
parent 8c2d06344f
commit fc7518b343
2 changed files with 411 additions and 169 deletions
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involute_gears.scad
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@ -77,12 +77,15 @@ function adendum(pitch=5) = module_value(pitch);
// Arguments:
// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
// clearance = If given, sets the clearance between meshing teeth.
function dedendum(pitch=5, clearance=undef) =
(clearance==undef)? (1.25 * module_value(pitch)) : (module_value(pitch) + clearance);
function dedendum(pitch=5, clearance) =
is_undef(clearance)? (1.25 * module_value(pitch)) :
(module_value(pitch) + clearance);
// Function: pitch_radius()
// Description: Calculates the pitch radius for the gear.
// 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.
// teeth = The number of teeth on the gear.
@ -98,7 +101,7 @@ function pitch_radius(pitch=5, teeth=11) =
// teeth = The number of teeth on the gear.
// clearance = If given, sets the clearance between meshing teeth.
// interior = If true, calculate for an interior gear.
function outer_radius(pitch=5, teeth=11, clearance=undef, interior=false) =
function outer_radius(pitch=5, teeth=11, clearance, interior=false) =
pitch_radius(pitch, teeth) +
(interior? dedendum(pitch, clearance) : adendum(pitch));
@ -111,22 +114,22 @@ function outer_radius(pitch=5, teeth=11, clearance=undef, interior=false) =
// teeth = The number of teeth on the gear.
// clearance = If given, sets the clearance between meshing teeth.
// interior = If true, calculate for an interior gear.
function root_radius(pitch=5, teeth=11, clearance=undef, interior=false) =
function root_radius(pitch=5, teeth=11, clearance, interior=false) =
pitch_radius(pitch, teeth) -
(interior? adendum(pitch) : dedendum(pitch, clearance));
// Function: base_radius()
// Description: Get the base circle for involute teeth.
// Description: Get the base circle for involute teeth, at the base of the teeth.
// Arguments:
// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
// teeth = The number of teeth on the gear.
// PA = Pressure angle in degrees. Controls how straight or bulged the tooth sides are.
function base_radius(pitch=5, teeth=11, PA=28) =
pitch_radius(pitch, teeth) * cos(PA);
// pressure_angle = Pressure angle in degrees. Controls how straight or bulged the tooth sides are.
function base_radius(pitch=5, teeth=11, pressure_angle=28) =
pitch_radius(pitch, teeth) * cos(pressure_angle);
// Function bevel_pitch_angle()
// Function: bevel_pitch_angle()
// Usage:
// x = bevel_pitch_angle(teeth, mate_teeth, [drive_angle]);
// Description:
@ -146,36 +149,36 @@ function _gear_q6(b,s,t,d) = _gear_polar(d,s*(_gear_iang(b,d)+t)); //
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
// Section: Modules
// Section: 2D Profiles
// Function&Module: gear_tooth_profile()
// Usage: As Module
// gear_tooth_profile(pitch, teeth, <PA>, <clearance>, <backlash>, <interior>, <valleys>);
// gear_tooth_profile(pitch, teeth, <pressure_angle>, <clearance>, <backlash>, <interior>, <valleys>);
// Usage: As Function
// path = gear_tooth_profile(pitch, teeth, <PA>, <clearance>, <backlash>, <interior>, <valleys>);
// path = gear_tooth_profile(pitch, teeth, <pressure_angle>, <clearance>, <backlash>, <interior>, <valleys>);
// 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.
// teeth = Total number of teeth along the rack
// PA = Pressure Angle. Controls how straight or bulged the tooth sides are. In degrees.
// 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
// interior = 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.
// Example(2D):
// gear_tooth_profile(pitch=5, teeth=20, PA=20);
// gear_tooth_profile(pitch=5, teeth=20, pressure_angle=20);
// Example(2D):
// gear_tooth_profile(pitch=5, teeth=20, PA=20, valleys=false);
// gear_tooth_profile(pitch=5, teeth=20, pressure_angle=20, valleys=false);
// Example(2D): As a function
// stroke(gear_tooth_profile(pitch=5, teeth=20, PA=20, valleys=false));
// stroke(gear_tooth_profile(pitch=5, teeth=20, pressure_angle=20, valleys=false));
function gear_tooth_profile(
pitch = 3,
teeth = 11,
PA = 28,
pressure_angle = 28,
clearance = undef,
backlash = 0.0,
interior = false,
@ -185,7 +188,7 @@ function gear_tooth_profile(
p = pitch_radius(pitch, teeth),
c = outer_radius(pitch, teeth, clearance, interior),
r = root_radius(pitch, teeth, clearance, interior),
b = base_radius(pitch, teeth, PA),
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<b? k : -180/teeth,
@ -211,7 +214,7 @@ function gear_tooth_profile(
module gear_tooth_profile(
pitch = 3,
teeth = 11,
PA = 28,
pressure_angle = 28,
backlash = 0.0,
clearance = undef,
interior = false,
@ -224,7 +227,7 @@ module gear_tooth_profile(
points=gear_tooth_profile(
pitch = pitch,
teeth = teeth,
PA = PA,
pressure_angle = pressure_angle,
backlash = backlash,
clearance = clearance,
interior = interior,
@ -237,20 +240,20 @@ module gear_tooth_profile(
// Function&Module: gear2d()
// Usage: As Module
// gear2d(pitch, teeth, <hide>, <PA>, <clearance>, <backlash>, <interior>);
// gear2d(pitch, teeth, <hide>, <pressure_angle>, <clearance>, <backlash>, <interior>);
// Usage: As Function
// poly = gear2d(pitch, teeth, <hide>, <PA>, <clearance>, <backlash>, <interior>);
// poly = gear2d(pitch, teeth, <hide>, <pressure_angle>, <clearance>, <backlash>, <interior>);
// Description:
// When called as a module, creates a 2D involute spur gear. When called as a function, returns a
// 2D path for the perimeter of a 2D involute spur gear. Normally, you should just specify the
// first 2 parameters `pitch` and `teeth`, and let the rest be default values.
// Meshing gears must match in `pitch`, `PA`, and `helical`, and be separated by
// 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()`.
// Arguments:
// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
// teeth = Total number of teeth along the rack
// teeth = Total number of teeth around the spur gear.
// hide = Number of teeth to delete to make this only a fraction of a circle
// PA = Controls how straight or bulged the tooth sides are. In degrees.
// 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
// interior = If true, create a mask for difference()ing from something else.
@ -259,14 +262,17 @@ module gear_tooth_profile(
// Example(2D): Typical Gear Shape
// gear2d(pitch=5, teeth=20);
// Example(2D): Lower Pressure Angle
// gear2d(pitch=5, teeth=20, PA=20);
// gear2d(pitch=5, teeth=20, pressure_angle=20);
// Example(2D): Partial Gear
// gear2d(pitch=5, teeth=20, hide=15, PA=20);
// gear2d(pitch=5, teeth=20, hide=15, pressure_angle=20);
// Example(2D): Called as a Function
// path = gear2d(pitch=8, teeth=16);
// polygon(path);
function gear2d(
pitch = 3,
teeth = 11,
hide = 0,
PA = 28,
pressure_angle = 28,
clearance = undef,
backlash = 0.0,
interior = false,
@ -281,7 +287,7 @@ function gear2d(
p=gear_tooth_profile(
pitch = pitch,
teeth = teeth,
PA = PA,
pressure_angle = pressure_angle,
clearance = clearance,
backlash = backlash,
interior = interior,
@ -298,7 +304,7 @@ module gear2d(
pitch = 3,
teeth = 11,
hide = 0,
PA = 28,
pressure_angle = 28,
clearance = undef,
backlash = 0.0,
interior = false,
@ -309,7 +315,7 @@ module gear2d(
pitch = pitch,
teeth = teeth,
hide = hide,
PA = PA,
pressure_angle = pressure_angle,
clearance = clearance,
backlash = backlash,
interior = interior
@ -322,23 +328,135 @@ module gear2d(
}
// Module: gear()
// Usage:
// gear(pitch, teeth, thickness, <shaft_diam>, <hide>, <PA>, <clearance>, <backlash>, <helical>, <slices>, <interior>);
// Function&Module: rack2d()
// Usage: As a Function
// path = rack2d(pitch, teeth, base, <pressure_angle>, <backlash>);
// Usage: As a Module
// rack2d(pitch, teeth, base, <pressure_angle>, <backlash>);
// 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 circular pitch, or distance between teeth around the pitch circle, in mm.
// teeth = Total number of teeth along the rack
// base = Height of rack in mm, from tooth top 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
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
// 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.
// "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.
// Example(2D):
// rack2d(pitch=5, teeth=10, base=5, pressure_angle=20);
// Example(2D): Called as a Function
// path = rack2d(pitch=8, teeth=8, base=5, pressure_angle=28);
// polygon(path);
function rack2d(
pitch = 5,
teeth = 20,
base = 10,
pressure_angle = 28,
backlash = 0.0,
clearance = undef,
anchor = CENTER,
spin = 0
) =
let(
a = adendum(pitch),
d = dedendum(pitch, clearance),
xa = a * sin(pressure_angle),
xd = d * sin(pressure_angle),
l = teeth * pitch,
anchors = [
anchorpt("adendum", [0,a,0], BACK),
anchorpt("adendum-left", [-l/2,a,0], LEFT),
anchorpt("adendum-right", [l/2,a,0], RIGHT),
anchorpt("dedendum", [0,-d,0], BACK),
anchorpt("dedendum-left", [-l/2,-d,0], LEFT),
anchorpt("dedendum-right", [l/2,-d,0], RIGHT),
],
path = [
[-(teeth-1)/2 * pitch + -1/2 * pitch, a-base],
[-(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-base],
]
) reorient(anchor,spin, two_d=true, size=[l,2*abs(a-base)], anchors=anchors, p=path);
module rack2d(
pitch = 5,
teeth = 20,
base = 10,
pressure_angle = 28,
backlash = 0.0,
clearance = undef,
anchor = CENTER,
spin = 0
) {
a = adendum(pitch);
d = dedendum(pitch, clearance);
l = teeth * pitch;
anchors = [
anchorpt("adendum", [0,a,0], BACK),
anchorpt("adendum-left", [-l/2,a,0], LEFT),
anchorpt("adendum-right", [l/2,a,0], RIGHT),
anchorpt("dedendum", [0,-d,0], BACK),
anchorpt("dedendum-left", [-l/2,-d,0], LEFT),
anchorpt("dedendum-right", [l/2,-d,0], RIGHT),
];
path = rack2d(
pitch = pitch,
teeth = teeth,
base = base,
pressure_angle = pressure_angle,
backlash = backlash,
clearance = clearance
);
attachable(anchor,spin, two_d=true, size=[l, 2*abs(a-base)], anchors=anchors) {
polygon(path);
children();
}
}
// Section: 3D Gears and Racks
// Function&Module: gear()
// Usage: As a Module
// gear(pitch, teeth, thickness, <shaft_diam>, <hide>, <pressure_angle>, <clearance>, <backlash>, <helical>, <slices>, <interior>);
// Usage: As a Function
// vnf = gear(pitch, teeth, thickness, <shaft_diam>, <hide>, <pressure_angle>, <clearance>, <backlash>, <helical>, <slices>, <interior>);
// Description:
// Creates a (potentially helical) involute spur gear. The module `gear()` gives an involute spur
// gear, with reasonable defaults for all the parameters. Normally, you should just choose the
// first 4 parameters, and let the rest be default values. The module `gear()` gives a gear in the
// XY plane, centered on the origin, with one tooth centered on the positive Y axis. The various
// functions below it take the same parameters, and return various measurements for the gear. The
// XY plane, centered on the origin, with one tooth centered on the positive Y axis. The
// most important is `pitch_radius()`, which tells how far apart to space gears that are meshing,
// and `outer_radius()`, which gives the size of the region filled by the gear. A gear has a "pitch
// circle", which is an invisible circle that cuts through the middle of each tooth (though not the
// exact center). In order for two gears to mesh, their pitch circles should just touch. So the
// distance between their centers should be `pitch_radius()` for one, plus `pitch_radius()` for the
// other, which gives the radii of their pitch circles. In order for two gears to mesh, they must
// have the same `pitch` and `PA` parameters. `pitch` gives the number of millimeters of arc around
// the pitch circle covered by one tooth and one space between teeth. The `PA` controls how flat or
// 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
@ -352,7 +470,7 @@ module gear2d(
// thickness = Thickness of gear in mm
// shaft_diam = Diameter of the hole in the center, in mm
// hide = Number of teeth to delete to make this only a fraction of a circle
// PA = Controls how straight or bulged the tooth sides are. In degrees.
// pressure_angle = Controls how straight or bulged the tooth sides are. In degrees.
// clearance = Clearance gap at the bottom of the inter-tooth valleys.
// backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle
// helical = Teeth rotate this many degrees from bottom of gear to top. 360 makes the gear a screw with each thread going around once.
@ -366,16 +484,16 @@ module gear2d(
// gear(pitch=5, teeth=20, thickness=8, shaft_diam=5);
// Example: Helical Gear
// gear(pitch=5, teeth=20, thickness=10, shaft_diam=5, helical=-30, slices=12, $fa=1, $fs=1);
// Example: Assembly of Gears
// Example(2D): Assembly of Gears
// n1 = 11; //red gear number of teeth
// n2 = 20; //green gear
// n3 = 5; //blue gear
// n4 = 20; //orange gear
// n5 = 8; //gray rack
// pitch = 9; //all meshing gears need the same `pitch` (and the same `PA`)
// pitch = 9; //all meshing gears need the same `pitch` (and the same `pressure_angle`)
// thickness = 6;
// hole = 3;
// height = 12;
// rack_base = 12;
// d1 =pitch_radius(pitch,n1);
// d12=pitch_radius(pitch,n1) + pitch_radius(pitch,n2);
// d13=pitch_radius(pitch,n1) + pitch_radius(pitch,n3);
@ -385,14 +503,51 @@ module gear2d(
// translate([ d13, 0, 0]) rotate([0,0,-($t-n3/4+n1/4+1/2)*360/n3]) color([0.75,0.75,1.00]) gear(pitch,n3,thickness,hole);
// translate([ d13, 0, 0]) rotate([0,0,-($t-n3/4+n1/4+1/2)*360/n3]) color([0.75,0.75,1.00]) gear(pitch,n3,thickness,hole);
// translate([-d14, 0, 0]) rotate([0,0,-($t-n4/4-n1/4+1/2-floor(n4/4)-3)*360/n4]) color([1.00,0.75,0.50]) gear(pitch,n4,thickness,hole,hide=n4-3);
// translate([(-floor(n5/2)-floor(n1/2)+$t+n1/2)*9, -d1+0.0, 0]) color([0.75,0.75,0.75]) rack(pitch=pitch,teeth=n5,thickness=thickness,height=height,anchor=CENTER);
// translate([(-floor(n5/2)-floor(n1/2)+$t+n1/2)*9, -d1+0.0, 0]) color([0.75,0.75,0.75]) rack(pitch=pitch,teeth=n5,thickness=thickness,base=rack_base,anchor=CENTER,orient=BACK);
function gear(
pitch = 3,
teeth = 11,
thickness = 6,
shaft_diam = 3,
hide = 0,
pressure_angle = 28,
clearance = undef,
backlash = 0.0,
helical = 0,
slices = 2,
interior = false,
anchor = CENTER,
spin = 0,
orient = UP
) =
let(
p = pitch_radius(pitch, teeth),
c = outer_radius(pitch, teeth, clearance, interior),
r = root_radius(pitch, teeth, clearance, interior),
twist = atan2(thickness*tan(helical),p),
rgn = [
gear2d(
pitch = pitch,
teeth = teeth,
pressure_angle = pressure_angle,
hide = hide,
clearance = clearance,
backlash = backlash,
interior = interior
),
if (shaft_diam > 0) circle(d=shaft_diam, $fn=max(12,segs(shaft_diam/2)))
],
vnf = linear_sweep(rgn, height=thickness, center=true)
) reorient(anchor,spin,orient, h=thickness, r=p, p=vnf);
module gear(
pitch = 3,
teeth = 11,
thickness = 6,
shaft_diam = 3,
hide = 0,
PA = 28,
pressure_angle = 28,
clearance = undef,
backlash = 0.0,
helical = 0,
@ -412,7 +567,7 @@ module gear(
gear2d(
pitch = pitch,
teeth = teeth,
PA = PA,
pressure_angle = pressure_angle,
hide = hide,
clearance = clearance,
backlash = backlash,
@ -429,9 +584,11 @@ module gear(
// Module: bevel_gear()
// Usage:
// bevel_gear(pitch, teeth, face_width, pitch_angle, <shaft_diam>, <hide>, <PA>, <clearance>, <backlash>, <cutter_radius>, <spiral_angle>, <slices>, <interior>);
// Function&Module: bevel_gear()
// Usage: As a Module
// bevel_gear(pitch, teeth, face_width, pitch_angle, <shaft_diam>, <hide>, <pressure_angle>, <clearance>, <backlash>, <cutter_radius>, <spiral_angle>, <slices>, <interior>);
// Usage: As a Function
// vnf = bevel_gear(pitch, teeth, face_width, pitch_angle, <hide>, <pressure_angle>, <clearance>, <backlash>, <cutter_radius>, <spiral_angle>, <slices>, <interior>);
// Description:
// Creates a (potentially spiral) bevel gear. The module `bevel_gear()` gives a bevel gear, with
// reasonable defaults for all the parameters. Normally, you should just choose the first 4
@ -444,8 +601,8 @@ module gear(
// 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 `PA` parameters. `pitch` gives the number of millimeters of arc around
// the pitch circle covered by one tooth and one space between teeth. The `PA` controls how flat or
// 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
@ -459,7 +616,7 @@ module gear(
// face_width = Width of the toothed surface in mm, from inside to outside.
// shaft_diam = Diameter of the hole in the center, in mm
// hide = Number of teeth to delete to make this only a fraction of a circle
// PA = Controls how straight or bulged the tooth sides are. In degrees.
// 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
// pitch_angle = Angle of beveled gear face.
@ -480,6 +637,106 @@ module gear(
// t1 = 16; t2 = 28;
// bevel_gear(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, slices=12, anchor="apex", spin=180/t2);
function bevel_gear(
pitch = 3,
teeth = 11,
face_width = 10,
pitch_angle = 45,
mate_teeth = undef,
hide = 0,
pressure_angle = 20,
clearance = undef,
backlash = 0.0,
cutter_radius = 30,
spiral_angle = 35,
left_handed = false,
slices = 1,
interior = false,
anchor = "pitchbase",
spin = 0,
orient = UP
) =
let(
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, interior),
pitchoff = (pr-rr) * cos(pitch_angle),
ocone_rad = opp_ang_to_hyp(pr, pitch_angle),
icone_rad = ocone_rad - face_width,
cutter_radius = cutter_radius==0? 1000 : cutter_radius,
midpr = (icone_rad + ocone_rad) / 2,
radcp = [0, midpr] + polar_to_xy(cutter_radius, 180+spiral_angle),
angC1 = law_of_cosines(a=cutter_radius, b=norm(radcp), c=ocone_rad),
angC2 = law_of_cosines(a=cutter_radius, b=norm(radcp), c=icone_rad),
radcpang = vang(radcp),
sang = radcpang - (180-angC1),
eang = radcpang - (180-angC2),
slice_us = [for (i=[0:1:slices]) i/slices],
apts = [for (u=slice_us) radcp + polar_to_xy(cutter_radius, lerp(sang,eang,u))],
polars = [for (p=apts) [vang(p)-90, norm(p)]],
profile = gear_tooth_profile(
pitch = pitch,
teeth = teeth,
pressure_angle = pressure_angle,
clearance = clearance,
backlash = backlash,
interior = interior,
valleys = false,
center = true
),
verts1 = [
for (polar=polars) [
let(
u = polar.y / ocone_rad,
m = up((1-u) * pr / tan(pitch_angle)) *
up(pitchoff) *
zrot(polar.x/sin(pitch_angle)) *
back(u * pr) *
xrot(pitch_angle) *
scale(u)
)
for (tooth=[0:1:teeth-1])
each apply(xflip() * zrot(360*tooth/teeth) * m, path3d(profile))
]
],
thickness = abs(verts1[0][0].z - select(verts1,-1)[0].z),
vertices = [for (x=verts1) down(thickness/2, p=reverse(x))],
sides_vnf = vnf_vertex_array(vertices, caps=false, col_wrap=true, reverse=true),
top_verts = select(vertices,-1),
bot_verts = select(vertices,0),
gear_pts = len(top_verts),
face_pts = gear_pts / teeth,
top_faces =[
for (i=[0:1:teeth-1], j=[0:1:(face_pts/2)-1]) each [
[i*face_pts+j, (i+1)*face_pts-j-1, (i+1)*face_pts-j-2],
[i*face_pts+j, (i+1)*face_pts-j-2, i*face_pts+j+1]
],
for (i=[0:1:teeth-1]) each [
[gear_pts, (i+1)*face_pts-1, i*face_pts],
[gear_pts, ((i+1)%teeth)*face_pts, (i+1)*face_pts-1]
]
],
vnf1 = vnf_merge([
[
[each top_verts, [0,0,top_verts[0].z]],
top_faces
],
[
[each bot_verts, [0,0,bot_verts[0].z]],
[for (x=top_faces) reverse(x)]
],
sides_vnf
]),
vnf = left_handed? vnf1 : xflip(p=vnf1),
anchors = [
anchorpt("pitchbase", [0,0,pitchoff-thickness/2]),
anchorpt("flattop", [0,0,thickness/2]),
anchorpt("apex", [0,0,hyp_ang_to_opp(ocone_rad,90-pitch_angle)+pitchoff-thickness/2])
]
) reorient(anchor,spin,orient, vnf=vnf, extent=true, anchors=anchors, p=vnf);
module bevel_gear(
pitch = 3,
teeth = 11,
@ -488,7 +745,7 @@ module bevel_gear(
mate_teeth = undef,
shaft_diam = 3,
hide = 0,
PA = 20,
pressure_angle = 20,
clearance = undef,
backlash = 0.0,
cutter_radius = 30,
@ -503,81 +760,32 @@ module bevel_gear(
slices = cutter_radius==0? 1 : slices;
pitch_angle = is_undef(mate_teeth)? pitch_angle : atan(teeth/mate_teeth);
pr = pitch_radius(pitch, teeth);
ipr = pr - face_width*sin(pitch_angle);
rr = root_radius(pitch, teeth, clearance, interior);
pitchoff = (pr-rr) * cos(pitch_angle);
ocone_rad = opp_ang_to_hyp(pr, pitch_angle);
icone_rad = ocone_rad - face_width;
cutter_radius = cutter_radius==0? 1000 : cutter_radius;
midpr = (icone_rad + ocone_rad) / 2;
radcp = [0, midpr] + polar_to_xy(cutter_radius, 180+spiral_angle);
angC1 = law_of_cosines(a=cutter_radius, b=norm(radcp), c=ocone_rad);
angC2 = law_of_cosines(a=cutter_radius, b=norm(radcp), c=icone_rad);
radcpang = vang(radcp);
sang = radcpang - (180-angC1);
eang = radcpang - (180-angC2);
slice_us = [for (i=[0:1:slices]) i/slices];
apts = [for (u=slice_us) radcp + polar_to_xy(cutter_radius, lerp(sang,eang,u))];
polars = [for (p=apts) [vang(p)-90, norm(p)]];
profile = gear_tooth_profile(
pitch = pitch,
teeth = teeth,
PA = PA,
clearance = clearance,
backlash = backlash,
interior = interior,
valleys = false,
center = true
thickness = face_width * cos(pitch_angle);
vnf = bevel_gear(
pitch = pitch,
teeth = teeth,
face_width = face_width,
pitch_angle = pitch_angle,
hide = hide,
pressure_angle = pressure_angle,
clearance = clearance,
backlash = backlash,
cutter_radius = cutter_radius,
spiral_angle = spiral_angle,
left_handed = left_handed,
slices = slices,
interior = interior,
anchor=CENTER
);
verts1 = [
for (polar=polars) [
let(
u = polar.y / ocone_rad,
m = up((1-u) * pr / tan(pitch_angle)) *
up(pitchoff) *
zrot(polar.x/sin(pitch_angle)) *
back(u * pr) *
xrot(pitch_angle) *
scale(u)
)
for (tooth=[0:1:teeth-1])
each apply(xflip() * zrot(360*tooth/teeth) * m, path3d(profile))
]
];
thickness = abs(verts1[0][0].z - select(verts1,-1)[0].z);
vertices = [for (x=verts1) down(thickness/2, p=reverse(x))];
sides_vnf = vnf_vertex_array(vertices, caps=false, col_wrap=true, reverse=true);
top_verts = select(vertices,-1);
bot_verts = select(vertices,0);
gear_pts = len(top_verts);
face_pts = gear_pts / teeth;
top_faces =[
for (i=[0:1:teeth-1], j=[0:1:(face_pts/2)-1]) each [
[i*face_pts+j, (i+1)*face_pts-j-1, (i+1)*face_pts-j-2],
[i*face_pts+j, (i+1)*face_pts-j-2, i*face_pts+j+1]
],
for (i=[0:1:teeth-1]) each [
[gear_pts, (i+1)*face_pts-1, i*face_pts],
[gear_pts, ((i+1)%teeth)*face_pts, (i+1)*face_pts-1]
]
];
vnf1 = vnf_merge([
[
[each top_verts, [0,0,top_verts[0].z]],
top_faces
],
[
[each bot_verts, [0,0,bot_verts[0].z]],
[for (x=top_faces) reverse(x)]
],
sides_vnf
]);
vnf = left_handed? vnf1 : xflip(p=vnf1);
anchors = [
anchorpt("pitchbase", [0,0,pitchoff-thickness/2]),
anchorpt("flattop", [0,0,thickness/2]),
anchorpt("apex", [0,0,hyp_ang_to_opp(ocone_rad,90-pitch_angle)+pitchoff-thickness/2])
anchorpt("apex", [0,0,adj_ang_to_opp(pr,90-pitch_angle)+pitchoff-thickness/2])
];
attachable(anchor,spin,orient, vnf=vnf, extent=true, anchors=anchors) {
attachable(anchor,spin,orient, r1=pr, r2=ipr, h=thickness, anchors=anchors) {
difference() {
vnf_polyhedron(vnf, convexity=teeth);
if (shaft_diam > 0) {
@ -589,19 +797,22 @@ module bevel_gear(
}
// Module: rack()
// Usage:
// rack(pitch, teeth, thickness, height, <PA>, <backlash>);
// Function&Module: rack()
// Usage: As a Module
// rack(pitch, teeth, thickness, base, <pressure_angle>, <backlash>);
// Usage: As a Function
// vnf = rack(pitch, teeth, thickness, base, <pressure_angle>, <backlash>);
// Description:
// The module `rack()` gives a rack, which is a bar with teeth. A
// rack can mesh with any gear that has the same `pitch` and
// `PA`.
// 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 circular pitch, or distance between teeth around the pitch circle, in mm.
// teeth = Total number of teeth along the rack
// thickness = Thickness of rack in mm (affects each tooth)
// height = Height of rack in mm, from tooth top to back of rack.
// PA = Controls how straight or bulged the tooth sides are. In degrees.
// base = Height of rack in mm, from tooth top 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
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
@ -610,21 +821,21 @@ module bevel_gear(
// "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-top" = At the tips of the teeth, at the top of the rack.
// "adendum-bottom" = At the tips of the teeth, at the bottom 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-top" = At the base of the teeth, at the top of the rack.
// "dedendum-bottom" = At the base of the teeth, at the bottom 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:
// rack(pitch=5, teeth=10, thickness=5, height=5, PA=20);
// rack(pitch=5, teeth=10, thickness=5, base=5, pressure_angle=20);
module rack(
pitch = 5,
teeth = 20,
thickness = 5,
height = 10,
PA = 28,
base = 10,
pressure_angle = 28,
backlash = 0.0,
clearance = undef,
anchor = CENTER,
@ -633,40 +844,30 @@ module rack(
) {
a = adendum(pitch);
d = dedendum(pitch, clearance);
xa = a * sin(PA);
xd = d * sin(PA);
l = teeth * pitch;
anchors = [
anchorpt("adendum", [0,a,0], BACK),
anchorpt("adendum-left", [-l/2,a,0], LEFT),
anchorpt("adendum-right", [l/2,a,0], RIGHT),
anchorpt("adendum-top", [0,a,thickness/2], UP),
anchorpt("adendum-bottom", [0,a,-thickness/2], DOWN),
anchorpt("dedendum", [0,-d,0], BACK),
anchorpt("dedendum-left", [-l/2,-d,0], LEFT),
anchorpt("dedendum-right", [l/2,-d,0], RIGHT),
anchorpt("dedendum-top", [0,-d,thickness/2], UP),
anchorpt("dedendum-bottom", [0,-d,-thickness/2], DOWN),
anchorpt("adendum", [0,0,a], BACK),
anchorpt("adendum-left", [-l/2,0,a], LEFT),
anchorpt("adendum-right", [ l/2,0,a], RIGHT),
anchorpt("adendum-front", [0,-thickness/2,a], DOWN),
anchorpt("adendum-back", [0, thickness/2,a], UP),
anchorpt("dedendum", [0,0,-d], BACK),
anchorpt("dedendum-left", [-l/2,0,-d], LEFT),
anchorpt("dedendum-right", [ l/2,0,-d], RIGHT),
anchorpt("dedendum-front", [0,-thickness/2,-d], DOWN),
anchorpt("dedendum-back", [0, thickness/2,-d], UP),
];
attachable(anchor,spin,orient, size=[l, 2*abs(a-height), thickness], anchors=anchors) {
left((teeth-1)*pitch/2) {
linear_extrude(height = thickness, center = true, convexity = 10) {
for (i = [0:1:teeth-1] ) {
translate([i*pitch,0,0]) {
polygon(
points=[
[-1/2 * pitch - 0.01, a-height],
[-1/2 * pitch, -d],
[-1/4 * pitch + backlash - xd, -d],
[-1/4 * pitch + backlash + xa, a],
[ 1/4 * pitch - backlash - xa, a],
[ 1/4 * pitch - backlash + xd, -d],
[ 1/2 * pitch, -d],
[ 1/2 * pitch + 0.01, a-height],
]
);
}
}
attachable(anchor,spin,orient, size=[l, thickness, 2*abs(a-base)], anchors=anchors) {
xrot(90) {
linear_extrude(height=thickness, center=true, convexity=teeth*2) {
rack2d(
pitch = pitch,
teeth = teeth,
base = base,
pressure_angle = pressure_angle,
backlash = backlash,
clearance = clearance
);
}
}
children();
@ -674,6 +875,47 @@ module rack(
}
function rack(
pitch = 5,
teeth = 20,
thickness = 5,
base = 10,
pressure_angle = 28,
backlash = 0.0,
clearance = undef,
anchor = CENTER,
spin = 0,
orient = UP
) =
let(
a = adendum(pitch),
d = dedendum(pitch, clearance),
l = teeth * pitch,
anchors = [
anchorpt("adendum", [0,0,a], BACK),
anchorpt("adendum-left", [-l/2,0,a], LEFT),
anchorpt("adendum-right", [ l/2,0,a], RIGHT),
anchorpt("adendum-front", [0,-thickness/2,a], DOWN),
anchorpt("adendum-back", [0, thickness/2,a], UP),
anchorpt("dedendum", [0,0,-d], BACK),
anchorpt("dedendum-left", [-l/2,0,-d], LEFT),
anchorpt("dedendum-right", [ l/2,0,-d], RIGHT),
anchorpt("dedendum-front", [0,-thickness/2,-d], DOWN),
anchorpt("dedendum-back", [0, thickness/2,-d], UP),
],
path = rack2d(
pitch = pitch,
teeth = teeth,
base = base,
pressure_angle = pressure_angle,
backlash = backlash,
clearance = clearance
),
vnf = linear_sweep(path, height=thickness, anchor="origin", orient=FWD)
) reorient(anchor,spin,orient, size=[l, thickness, 2*abs(a-base)], anchors=anchors, p=vnf);
// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap

2
version.scad
View file

@ -8,7 +8,7 @@
//////////////////////////////////////////////////////////////////////
BOSL_VERSION = [2,0,452];
BOSL_VERSION = [2,0,453];
// Section: BOSL Library Version Functions