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Merge remote-tracking branch 'upstream/master'

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This commit is contained in:
Adrian Mariano 2019-06-12 20:45:38 -04:00
commit 9557609b97
7 changed files with 759 additions and 409 deletions

94
arrays.scad
View file

@ -150,56 +150,42 @@ function list_range(n=undef, s=0, e=undef, step=1) =
function reverse(list) = [ for (i = [len(list)-1 : -1 : 0]) list[i] ];
// Function: list_set()
//
// list_set(indices, values, list, dftl, minlen)
// Takes the input list and returns a new list such that
// list[indices[i]] = values[i]
// for all of the (index,value) pairs supplied. If you supply indices
// that are beyond the length of the list then the list is extended
// and filled in with the dflt value.
//
// If you set minlen then the list is lengthed, if necessary, by padding
// with dflt to that length.
//
// The `indices` list can be in any order but run time will be (much) faster
// for long lists if it is already sorted. Reptitions are not allowed.
//
// Usage:
// list_set(indices, values, list, [dflt], [minlen])
// Description:
// Takes the input list and returns a new list such that `list[indices[i]] = values[i]` for all of
// the (index,value) pairs supplied. If you supply `indices` that are beyond the length of the list
// then the list is extended and filled in with the `dflt` value. If you set `minlen` then the list is
// lengthed, if necessary, by padding with `dflt` to that length. The `indices` list can be in any
// order but run time will be (much) faster for long lists if it is already sorted. Reptitions are
// not allowed.
// Arguments:
// indices = List of indices into `list` to set.
// values = List of values to set.
// list = List to set items in.
// dflt = Default value to store in sparse skipped indices.
// minlen = Minimum length to expand list to.
function list_set(indices,values,list=[],dflt=0,minlen=0) =
!is_list(indices) ? list_set(list,[indices],[values],dflt) :
assert(len(indices)==len(values),"Index list and value list must have the same length")
len(indices)==0 ? concat(list, replist(dflt, minlen-len(list))) :
let( sortind = list_increasing(indices) ? list_range(len(indices)) : sortidx(indices),
lastind = indices[select(sortind,-1)]
)
concat([for(j=[0:1:indices[sortind[0]]-1]) j>=len(list) ? dflt : list[j]], [values[sortind[0]]],
[for(i=[1:1:len(sortind)-1])
each
assert(indices[sortind[i]]!=indices[sortind[i-1]],"Repeated index")
concat(
[for(j=[1+indices[sortind[i-1]]:1:indices[sortind[i]]-1]) j>=len(list) ? dflt : list[j]],
[values[sortind[i]]]
)
],
slice(list,1+lastind, len(list)),
replist(dflt, minlen-lastind-1)
);
// Function: list_increasing()
// Usage:
// list_increasing(list)
// Description: returns true if the list is (non-strictly) increasing
function list_increasing(list,ind=0) = ind < len(list)-1 && list[ind]<=list[ind+1] ? list_increasing(list,ind+1) :
(ind>=len(list)-1 ? true : false);
// Function: list_decreasing()
// Usage:
// list_increasing(list)
// Description: returns true if the list is (non-strictly) decreasing
function list_decreasing(list,ind=0) = ind < len(list)-1 && list[ind]>=list[ind+1] ? list_increasing(list,ind+1) :
(ind>=len(list)-1 ? true : false);
!is_list(indices) ? list_set(list,[indices],[values],dflt) :
assert(len(indices)==len(values),"Index list and value list must have the same length")
let(
sortind = list_increasing(indices) ? list_range(len(indices)) : sortidx(indices),
lastind = indices[select(sortind,-1)]
)
concat(
[for(j=[0:1:indices[sortind[0]]-1]) j>=len(list) ? dflt : list[j]],
[values[sortind[0]]],
[for(i=[1:1:len(sortind)-1]) each
assert(indices[sortind[i]]!=indices[sortind[i-1]],"Repeated index")
concat(
[for(j=[1+indices[sortind[i-1]]:1:indices[sortind[i]]-1]) j>=len(list) ? dflt : list[j]],
[values[sortind[i]]]
)
],
slice(list,1+lastind, len(list)),
replist(dflt, minlen-lastind-1)
);
// Function: list_remove()
@ -210,7 +196,7 @@ function list_decreasing(list,ind=0) = ind < len(list)-1 && list[ind]>=list[ind+
// Arguments:
// list = The list to remove items from.
// elements = The list of indexes of items to remove.
function list_remove(list,elements) =
function list_remove(list, elements) =
!is_list(elements) ? list_remove(list,[elements]) :
let( sortind = list_increasing(elements) ? list_range(len(elements)) : sortidx(elements),
lastind = elements[select(sortind,-1)]
@ -235,6 +221,16 @@ function list_insert(list, pos, elements) =
);
// True if the list is (non-strictly) increasing
function list_increasing(list,ind=0) = ind < len(list)-1 && list[ind]<=list[ind+1] ? list_increasing(list,ind+1) :
(ind>=len(list)-1 ? true : false);
// True if the list is (non-strictly) decreasing
function list_decreasing(list,ind=0) = ind < len(list)-1 && list[ind]>=list[ind+1] ? list_increasing(list,ind+1) :
(ind>=len(list)-1 ? true : false);
// Function: list_shortest()
// Description:
// Returns the length of the shortest sublist in a list of lists.

23
coords.scad
View file

@ -91,18 +91,20 @@ function scale_points(pts, v=[0,0,0], cp=[0,0,0]) = [for (pt = pts) [for (i = [0
// Function: rotate_points2d()
// Usage:
// rotate_points2d(pts, ang, [cp]);
// rotate_points2d(pts, a, [cp]);
// Description:
// Rotates each 2D point in an array by a given amount, around an optional centerpoint.
// Arguments:
// pts = List of 3D points to rotate.
// ang = Angle to rotate by.
// a = Angle to rotate by.
// cp = 2D Centerpoint to rotate around. Default: `[0,0]`
function rotate_points2d(pts, ang, cp=[0,0]) =
approx(ang,0)? pts :
function rotate_points2d(pts, a, cp=[0,0]) =
approx(a,0)? pts :
let(
m = affine2d_zrot(ang)
) [for (pt = pts) m*point3d(pt-cp)+cp];
cp = point2d(cp),
pts = path2d(pts),
m = affine2d_zrot(a)
) [for (pt = pts) point2d(m*concat(pt-cp, [1])+cp)];
// Function: rotate_points3d()
@ -125,9 +127,11 @@ function rotate_points3d(pts, a=0, v=undef, cp=[0,0,0], from=undef, to=undef, re
(is_undef(from) && (a==0 || a==[0,0,0]))? pts :
let (
from = is_undef(from)? undef : (from / norm(from)),
to = is_undef(to)? undef : (to / norm(to))
to = is_undef(to)? undef : (to / norm(to)),
cp = point3d(cp),
pts2 = path3d(pts)
)
(!is_undef(from) && approx(from,to))? pts :
(!is_undef(from) && approx(from,to))? pts2 :
let (
mrot = reverse? (
!is_undef(from)? (
@ -151,7 +155,6 @@ function rotate_points3d(pts, a=0, v=undef, cp=[0,0,0], from=undef, to=undef, re
ang = vector_angle(from, to),
v = vector_axis(from, to)
)
echo("EEE",from=from,to=to,ang=ang,v=v,a=a)
affine3d_rot_by_axis(v, ang) * affine3d_rot_by_axis(from, a)
) : !is_undef(v)? (
affine3d_rot_by_axis(v, a)
@ -163,7 +166,7 @@ function rotate_points3d(pts, a=0, v=undef, cp=[0,0,0], from=undef, to=undef, re
),
m = affine3d_translate(cp) * mrot * affine3d_translate(-cp)
)
[for (pt = pts) point3d(m*concat(point3d(pt),[1]))];
[for (pt = pts2) point3d(m*concat(pt, fill=1))];

29
geometry.scad
View file

@ -182,6 +182,35 @@ function line_segment_intersection(line,segment) =
) isect[2]<0-eps || isect[2]>1+eps ? undef : isect[0];
// Function: find_circle_2tangents()
// Usage:
// find_circle_2tangents(pt1, pt2, pt3, r|d);
// Description:
// Returns [centerpoint, normal] of a circle of known size that is between and tangent to two rays with the same starting point.
// Both rays start at `pt2`, and one passes through `pt1`, while the other passes through `pt3`.
// If the rays given are 180º apart, `undef` is returned. If the rays are 3D, the normal returned is the plane normal of the circle.
// Arguments:
// pt1 = A point that the first ray passes though.
// pt2 = The starting point of both rays.
// pt3 = A point that the second ray passes though.
// r = The radius of the circle to find.
// d = The diameter of the circle to find.
function find_circle_2tangents(pt1, pt2, pt3, r=undef, d=undef) =
let(
r = get_radius(r=r, d=d, dflt=undef),
v1 = normalize(pt1 - pt2),
v2 = normalize(pt3 - pt2)
) approx(norm(v1+v2))? undef :
assert(r!=undef, "Must specify either r or d.")
let(
a = vector_angle(v1,v2),
n = vector_axis(v1,v2),
v = normalize(mean([v1,v2])),
s = r/sin(a/2),
cp = pt2 + s*v/norm(v)
) [cp, n];
// Function: triangle_area2d()
// Usage:
// triangle_area2d(a,b,c);

639
involute_gears.scad
View file

@ -47,194 +47,255 @@
// Function: circular_pitch()
// Description: Get tooth density expressed as "circular pitch".
// Arguments:
// mm_per_tooth = Distance between teeth around the pitch circle, in mm.
function circular_pitch(mm_per_tooth=5) = mm_per_tooth;
// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
function circular_pitch(pitch=5) = pitch;
// Function: diametral_pitch()
// Description: Get tooth density expressed as "diametral pitch".
// Arguments:
// mm_per_tooth = Distance between teeth around the pitch circle, in mm.
function diametral_pitch(mm_per_tooth=5) = PI / mm_per_tooth;
// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
function diametral_pitch(pitch=5) = PI / pitch;
// Function: module_value()
// Description: Get tooth density expressed as "module" or "modulus" in millimeters
// Arguments:
// mm_per_tooth = Distance between teeth around the pitch circle, in mm.
function module_value(mm_per_tooth=5) = mm_per_tooth / PI;
// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
function module_value(pitch=5) = pitch / PI;
// Function: adendum()
// Description: The height of the gear tooth above the pitch radius.
// Arguments:
// mm_per_tooth = Distance between teeth around the pitch circle, in mm.
function adendum(mm_per_tooth=5) = module_value(mm_per_tooth);
// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
function adendum(pitch=5) = module_value(pitch);
// Function: dedendum()
// Description: The depth of the gear tooth valley, below the pitch radius.
// Arguments:
// mm_per_tooth = Distance between teeth around the pitch circle, in mm.
// 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(mm_per_tooth=5, clearance=undef) =
(clearance==undef)? (1.25 * module_value(mm_per_tooth)) : (module_value(mm_per_tooth) + clearance);
function dedendum(pitch=5, clearance=undef) =
(clearance==undef)? (1.25 * module_value(pitch)) : (module_value(pitch) + clearance);
// Function: pitch_radius()
// Description: Calculates the pitch radius for the gear.
// Arguments:
// mm_per_tooth = Distance between teeth around the pitch circle, in mm.
// number of teeth = The number of teeth on the gear.
function pitch_radius(mm_per_tooth=5, number_of_teeth=11) =
mm_per_tooth * number_of_teeth / PI / 2;
// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
// teeth = The number of teeth on the gear.
function pitch_radius(pitch=5, teeth=11) =
pitch * teeth / PI / 2;
// Function: outer_radius()
// Description:
// Calculates the outer radius for the gear. The gear fits entirely within a cylinder of this radius.
// Arguments:
// mm_per_tooth = Distance between teeth around the pitch circle, in mm.
// number of teeth = The number of teeth on the gear.
// 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.
// interior = If true, calculate for an interior gear.
function outer_radius(mm_per_tooth=5, number_of_teeth=11, clearance=undef, interior=false) =
pitch_radius(mm_per_tooth, number_of_teeth) +
(interior? dedendum(mm_per_tooth, clearance) : adendum(mm_per_tooth));
function outer_radius(pitch=5, teeth=11, clearance=undef, interior=false) =
pitch_radius(pitch, teeth) +
(interior? dedendum(pitch, clearance) : adendum(pitch));
// Function: root_radius()
// Description:
// Calculates the root radius for the gear, at the base of the dedendum.
// Arguments:
// mm_per_tooth = Distance between teeth around the pitch circle, in mm.
// number of teeth = The number of teeth on the gear.
// 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.
// interior = If true, calculate for an interior gear.
function root_radius(mm_per_tooth=5, number_of_teeth=11, clearance=undef, interior=false)
= pitch_radius(mm_per_tooth, number_of_teeth) -
(interior? adendum(mm_per_tooth) : dedendum(mm_per_tooth, clearance));
function root_radius(pitch=5, teeth=11, clearance=undef, interior=false) =
pitch_radius(pitch, teeth) -
(interior? adendum(pitch) : dedendum(pitch, clearance));
// Function: base_radius()
// Description: Get the base circle for involute teeth.
// Arguments:
// mm_per_tooth = Distance between teeth around the pitch circle, in mm.
// number_of_teeth = The number of teeth on the gear.
// pressure_angle = Pressure angle in degrees. Controls how straight or bulged the tooth sides are.
function base_radius(mm_per_tooth=5, number_of_teeth=11, pressure_angle=28)
= pitch_radius(mm_per_tooth, number_of_teeth) * cos(pressure_angle);
// 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);
// Function bevel_pitch_angle()
// Usage:
// bevel_pitch_angle(teeth, mate_teeth, [drive_angle]);
// Description:
// Returns the correct pitch angle (bevelang) for a bevel gear with a given number of tooth, that is
// matched to another bevel gear with a (possibly different) number of teeth.
// Arguments:
// teeth = Number of teeth that this gear has.
// mate_teeth = Number of teeth that the matching gear has.
// drive_angle = Angle between the drive shafts of each gear. Usually 90º.
function bevel_pitch_angle(teeth, mate_teeth, drive_angle=90) =
atan(sin(drive_angle)/((mate_teeth/teeth)+cos(drive_angle)));
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
// Section: Modules
// Module: gear_tooth_profile()
// Function&Module: gear_tooth_profile()
// Description:
// Creates the 2D profile for an individual gear tooth.
// 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:
// mm_per_tooth = This is the "circular pitch", the circumference of the pitch circle divided by the number of teeth
// number_of_teeth = Total number of teeth along the rack
// pressure_angle = Controls how straight or bulged the tooth sides are. In degrees.
// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
// teeth = Total number of teeth along the rack
// PA = 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
// bevelang = Angle of beveled gear face.
// clearance = Gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters)
// 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.
// Example(2D):
// gear_tooth_profile(mm_per_tooth=5, number_of_teeth=20, pressure_angle=20);
module gear_tooth_profile(
mm_per_tooth = 3,
number_of_teeth = 11,
pressure_angle = 28,
backlash = 0.0,
bevelang = 0.0,
clearance = undef,
interior = false
) {
function polar(r,theta) = r*[sin(theta), cos(theta)]; //convert polar to cartesian coordinates
function 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 q7(f,r,b,r2,t,s) = q6(b,s,t,(1-f)*max(b,r)+f*r2); //radius a fraction f up the curved side of the tooth
function q6(b,s,t,d) = polar(d,s*(iang(b,d)+t)); //point at radius d on the involute curve
// gear_tooth_profile(pitch=5, teeth=20, PA=20);
// Example(2D):
// gear_tooth_profile(pitch=5, teeth=20, PA=20, valleys=true);
function gear_tooth_profile(
pitch = 3,
teeth = 11,
PA = 28,
backlash = 0.0,
clearance = undef,
interior = false,
valleys = true
) = let(
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),
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,
isteps = 5,
pts = concat(
valleys? [
_gear_polar(r-1, -180.1/teeth),
_gear_polar(r, -180.1/teeth),
] : [
],
[_gear_polar(r, kk)],
[for (i=[0: 1:isteps]) _gear_q7(i/isteps,r,b,c,k, 1)],
[for (i=[isteps:-1:0]) _gear_q7(i/isteps,r,b,c,k,-1)],
[_gear_polar(r, -kk)],
valleys? [
_gear_polar(r, 180.1/teeth),
_gear_polar(r-1, 180.1/teeth),
] : [
]
)
) reverse(pts);
p = pitch_radius(mm_per_tooth, number_of_teeth);
c = outer_radius(mm_per_tooth, number_of_teeth, clearance, interior);
r = root_radius(mm_per_tooth, number_of_teeth, clearance, interior);
b = base_radius(mm_per_tooth, number_of_teeth, pressure_angle);
t = mm_per_tooth/2-backlash/2; //tooth thickness at pitch circle
k = -iang(b, p) - t/2/p/PI*180; //angle to where involute meets base circle on each side of tooth
scale([1, 1/cos(bevelang), 1])
module gear_tooth_profile(
pitch = 3,
teeth = 11,
PA = 28,
backlash = 0.0,
clearance = undef,
interior = false,
valleys = true
) {
r = root_radius(pitch, teeth, clearance, interior);
translate([0,-r,0])
polygon(
points=[
polar(r-1, -181/number_of_teeth),
polar(r, -181/number_of_teeth),
polar(r, r<b ? k : -180/number_of_teeth),
q7(0/5,r,b,c,k, 1),q7(1/5,r,b,c,k, 1),q7(2/5,r,b,c,k, 1),q7(3/5,r,b,c,k, 1),q7(4/5,r,b,c,k, 1),q7(5/5,r,b,c,k, 1),
q7(5/5,r,b,c,k,-1),q7(4/5,r,b,c,k,-1),q7(3/5,r,b,c,k,-1),q7(2/5,r,b,c,k,-1),q7(1/5,r,b,c,k,-1),q7(0/5,r,b,c,k,-1),
polar(r, r<b ? -k : 180/number_of_teeth),
polar(r, 181/number_of_teeth),
polar(r-1, 181/number_of_teeth),
]
points=gear_tooth_profile(
pitch = pitch,
teeth = teeth,
PA = PA,
backlash = backlash,
clearance = clearance,
interior = interior,
valleys = valleys
)
);
}
// Module: gear2d()
// Function&Module: gear2d()
// Description:
// Creates a 2D involute spur gear, with reasonable defaults for all the parameters.
// Normally, you should just specify the first 2 parameters, and let the rest be default values.
// Meshing gears must match in mm_per_tooth, pressure_angle, and twist,
// 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 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
// the sum of their pitch radii, which can be found with `pitch_radius()`.
// Arguments:
// mm_per_tooth = This is the "circular pitch", the circumference of the pitch circle divided by the number of teeth
// number_of_teeth = Total number of teeth along the rack
// teeth_to_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.
// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
// teeth = Total number of teeth along the rack
// 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.
// 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
// bevelang = Angle of beveled gear face.
// interior = If true, create a mask for difference()ing from something else.
// Example(2D): Typical Gear Shape
// gear2d(mm_per_tooth=5, number_of_teeth=20);
// gear2d(pitch=5, teeth=20);
// Example(2D): Lower Pressure Angle
// gear2d(mm_per_tooth=5, number_of_teeth=20, pressure_angle=20);
// gear2d(pitch=5, teeth=20, PA=20);
// Example(2D): Partial Gear
// gear2d(mm_per_tooth=5, number_of_teeth=20, teeth_to_hide=15, pressure_angle=20);
// gear2d(pitch=5, teeth=20, hide=15, PA=20);
function gear2d(
pitch = 3,
teeth = 11,
hide = 0,
PA = 28,
clearance = undef,
backlash = 0.0,
interior = false
) = let(
pts = concat(
[for (tooth = [0:1:teeth-hide-1])
each rot(tooth*360/teeth,
planar=true,
p=gear_tooth_profile(
pitch = pitch,
teeth = teeth,
PA = PA,
clearance = clearance,
backlash = backlash,
interior = interior,
valleys = false
)
)
],
hide>0? [[0,0]] : []
)
) pts;
module gear2d(
mm_per_tooth = 3,
number_of_teeth = 11,
teeth_to_hide = 0,
pressure_angle = 28,
clearance = undef,
backlash = 0.0,
bevelang = 0.0,
interior = false
pitch = 3,
teeth = 11,
hide = 0,
PA = 28,
clearance = undef,
backlash = 0.0,
interior = false
) {
r = root_radius(mm_per_tooth, number_of_teeth, clearance, interior);
ang = 360/number_of_teeth/2;
union() {
for (i = [0:1:number_of_teeth-teeth_to_hide-1] ) {
rotate(i*360/number_of_teeth) {
translate([0,r,0]) {
gear_tooth_profile(
mm_per_tooth = mm_per_tooth,
number_of_teeth = number_of_teeth,
pressure_angle = pressure_angle,
clearance = clearance,
backlash = backlash,
bevelang = bevelang,
interior = interior
);
}
polygon([
[-r*sin(ang), r*cos(ang)],
[0,0],
[r*sin(ang), r*cos(ang)]
]);
}
}
}
polygon(
gear2d(
pitch = pitch,
teeth = teeth,
hide = hide,
PA = PA,
clearance = clearance,
backlash = backlash,
interior = interior
)
);
}
@ -256,85 +317,253 @@ module gear2d(
// 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 `mm_per_tooth`
// and `pressure_angle` parameters. `mm_per_tooth` gives the number
// 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 `pressure_angle` controls how flat or
// and one space between teeth. The `PA` 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 `number_of_teeth` for two meshing gears gives how many
// 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:
// mm_per_tooth = This is the "circular pitch", the circumference of the pitch circle divided by the number of teeth
// number_of_teeth = Total number of teeth around the entire perimeter
// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
// teeth = Total number of teeth around the entire perimeter
// thickness = Thickness of gear in mm
// hole_diameter = Diameter of the hole in the center, in mm
// teeth_to_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.
// 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.
// 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
// bevelang = Angle of beveled gear face.
// twist = Teeth rotate this many degrees from bottom of gear to top. 360 makes the gear a screw with each thread going around once.
// slices = Number of vertical layers to divide gear into. Useful for refining gears with `twist`.
// helical = Teeth rotate this many degrees from bottom of gear to top. 360 makes the gear a screw with each thread going around once.
// slices = Number of vertical layers to divide gear into. Useful for refining gears with `helical`.
// scale = Scale of top of gear compared to bottom. Useful for making crown gears.
// interior = If true, create a mask for difference()ing from something else.
// 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`
// orient = Vector to rotate top towards, after spin. See [orient](attachments.scad#orient). Default: `UP`
// Example: Spur Gear
// gear(mm_per_tooth=5, number_of_teeth=20, thickness=8, hole_diameter=5);
// gear(pitch=5, teeth=20, thickness=8, shaft_diam=5);
// Example: Beveled Gear
// gear(mm_per_tooth=5, number_of_teeth=20, thickness=10*cos(45), hole_diameter=5, twist=-30, bevelang=45, slices=12, $fa=1, $fs=1);
// gear(pitch=5, teeth=20, thickness=10, shaft_diam=5, helical=-30, slices=12, $fa=1, $fs=1);
module gear(
mm_per_tooth = 3,
number_of_teeth = 11,
thickness = 6,
hole_diameter = 3,
teeth_to_hide = 0,
pressure_angle = 28,
clearance = undef,
backlash = 0.0,
bevelang = 0.0,
twist = undef,
slices = undef,
interior = false,
anchor = CENTER,
spin = 0,
orient = UP
pitch = 3,
teeth = 11,
PA = 28,
thickness = 6,
hide = 0,
shaft_diam = 3,
clearance = undef,
backlash = 0.0,
helical = 0,
slices = 2,
interior = false,
anchor = CENTER,
spin = 0,
orient = UP
) {
p = pitch_radius(mm_per_tooth, number_of_teeth);
c = outer_radius(mm_per_tooth, number_of_teeth, clearance, interior);
r = root_radius(mm_per_tooth, number_of_teeth, clearance, interior);
p2 = p - (thickness*tan(bevelang));
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);
orient_and_anchor([p, p, thickness], orient, anchor, spin=spin, geometry="cylinder", chain=true) {
difference() {
linear_extrude(height=thickness, center=true, convexity=10, twist=twist, scale=p2/p, slices=slices) {
linear_extrude(height=thickness, center=true, convexity=10, twist=twist) {
gear2d(
mm_per_tooth = mm_per_tooth,
number_of_teeth = number_of_teeth,
teeth_to_hide = teeth_to_hide,
pressure_angle = pressure_angle,
clearance = clearance,
backlash = backlash,
bevelang = bevelang,
interior = interior
pitch = pitch,
teeth = teeth,
PA = PA,
hide = hide,
clearance = clearance,
backlash = backlash,
interior = interior
);
}
if (hole_diameter > 0) {
cylinder(h=2*thickness+1, r=hole_diameter/2, center=true);
if (shaft_diam > 0) {
cylinder(h=2*thickness+1, r=shaft_diam/2, center=true);
}
if (bevelang != 0) {
h = (c-r)*sin(bevelang);
translate([0,0,-thickness/2]) {
difference() {
cube([2*c/cos(bevelang),2*c/cos(bevelang),2*h], center=true);
cylinder(h=h, r1=r, r2=c, center=false);
}
children();
}
}
// Module: bevel_gear()
// Description:
// Creates a (potentially spiral) bevel gear.
// The module `bevel_gear()` gives an bevel 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 `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 `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
// bulged the sides of the teeth are. Common values include 14.5
// degrees and 20 degrees, and occasionally 25. Though I've seen 28
// recommended for plastic gears. Larger numbers bulge out more, giving
// stronger teeth, so 28 degrees is the default here.
// The ratio of `teeth` for two meshing gears gives how many
// times one will make a full revolution when the the other makes one
// full revolution. If the two numbers are coprime (i.e. are not
// both divisible by the same number greater than 1), then every tooth
// on one gear will meet every tooth on the other, for more even wear.
// So coprime numbers of teeth are good.
// Arguments:
// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
// teeth = Total number of teeth around the entire perimeter
// 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.
// 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
// bevelang = Angle of beveled gear face.
// spiral_rad = Radius of spiral arc for teeth. If 0, then gear will not be spiral. Default: 0
// spiral_ang = The base angle for spiral teeth. Default: 0
// slices = Number of vertical layers to divide gear into. Useful for refining gears with `spiral`.
// scale = Scale of top of gear compared to bottom. Useful for making crown gears.
// interior = If true, create a mask for difference()ing from something else.
// 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`
// orient = Vector to rotate top towards, after spin. See [orient](attachments.scad#orient). Default: `UP`
// Example: Beveled Gear
// bevel_gear(pitch=5, teeth=36, face_width=10, shaft_diam=5, spiral_rad=-20, spiral_ang=35, bevelang=45, slices=12, $fa=1, $fs=1);
module bevel_gear(
pitch = 3,
teeth = 11,
PA = 20,
face_width = 6,
bevelang = 45,
hide = 0,
shaft_diam = 3,
clearance = undef,
backlash = 0.0,
spiral_rad = 0,
spiral_ang = 0,
slices = 2,
interior = false,
anchor = CENTER,
spin = 0,
orient = UP
) {
thickness = face_width * cos(bevelang);
slices = spiral_rad==0? 1 : slices;
spiral_rad = spiral_rad==0? 10000 : spiral_rad;
p1 = pitch_radius(pitch, teeth);
r1 = root_radius(pitch, teeth, clearance, interior);
c1 = outer_radius(pitch, teeth, clearance, interior);
dx = thickness * tan(bevelang);
dy = (p1-r1) * sin(bevelang);
scl = (p1-dx)/p1;
p2 = pitch_radius(pitch*scl, teeth);
r2 = root_radius(pitch*scl, teeth, clearance, interior);
c2 = outer_radius(pitch*scl, teeth, clearance, interior);
slice_u = 1/slices;
Rm = (p1+p2)/2;
H = spiral_rad * cos(spiral_ang);
V = Rm - abs(spiral_rad) * sin(spiral_ang);
spiral_cp = [H,V,0];
S = norm(spiral_cp);
theta_r = acos((S*S+spiral_rad*spiral_rad-p1*p1)/(2*S*spiral_rad)) - acos((S*S+spiral_rad*spiral_rad-p2*p2)/(2*S*spiral_rad));
theta_ro = acos((S*S+spiral_rad*spiral_rad-p1*p1)/(2*S*spiral_rad)) - acos((S*S+spiral_rad*spiral_rad-Rm*Rm)/(2*S*spiral_rad));
theta_ri = theta_r - theta_ro;
extent_u = 2*(p2-r2)*tan(bevelang) / thickness;
slice_us = concat(
[for (u = [0:slice_u:1+extent_u]) u]
);
lsus = len(slice_us);
vertices = concat(
[
for (u=slice_us, tooth=[0:1:teeth-1]) let(
p = lerp(p1,p2,u),
r = lerp(r1,r2,u),
theta = lerp(-theta_ro, theta_ri, u),
profile = gear_tooth_profile(
pitch = pitch*(p/p1),
teeth = teeth,
PA = PA,
clearance = clearance,
backlash = backlash,
interior = interior,
valleys = false
),
pp = rot(theta, cp=spiral_cp, p=[0,Rm,0]),
ang = atan2(pp.y,pp.x)-90,
pts = affine3d_apply(pts=profile, affines=[
move([0,-p,0]),
rot([0,ang,0]),
rot([bevelang,0,0]),
move(pp),
rot(tooth*360/teeth),
move([0,0,thickness*u])
])
) each pts
], [
[0,0,-dy], [0,0,thickness]
]
);
lcnt = (len(vertices)-2)/lsus/teeth;
function _gv(layer,tooth,i) = ((layer*teeth)+(tooth%teeth))*lcnt+(i%lcnt);
function _lv(layer,i) = layer*teeth*lcnt+(i%(teeth*lcnt));
faces = concat(
[
for (sl=[0:1:lsus-2], i=[0:1:lcnt*teeth-1]) each [
[_lv(sl,i), _lv(sl+1,i), _lv(sl,i+1)],
[_lv(sl+1,i), _lv(sl+1,i+1), _lv(sl,i+1)]
]
], [
for (tooth=[0:1:teeth-1], i=[0:1:lcnt/2-1]) each [
[_gv(0,tooth,i), _gv(0,tooth,i+1), _gv(0,tooth,lcnt-1-(i+1))],
[_gv(0,tooth,i), _gv(0,tooth,lcnt-1-(i+1)), _gv(0,tooth,lcnt-1-i)],
[_gv(lsus-1,tooth,i), _gv(lsus-1,tooth,lcnt-1-(i+1)), _gv(lsus-1,tooth,i+1)],
[_gv(lsus-1,tooth,i), _gv(lsus-1,tooth,lcnt-1-i), _gv(lsus-1,tooth,lcnt-1-(i+1))],
]
], [
for (tooth=[0:1:teeth-1]) each [
[len(vertices)-2, _gv(0,tooth,0), _gv(0,tooth,lcnt-1)],
[len(vertices)-2, _gv(0,tooth,lcnt-1), _gv(0,tooth+1,0)],
[len(vertices)-1, _gv(lsus-1,tooth,lcnt-1), _gv(lsus-1,tooth,0)],
[len(vertices)-1, _gv(lsus-1,tooth+1,0), _gv(lsus-1,tooth,lcnt-1)],
]
]
);
orient_and_anchor([p1, p1, thickness], orient, anchor, spin=spin, size2=[p2,p2], geometry="cylinder", chain=true) {
union() {
difference() {
down(thickness/2) {
polyhedron(points=vertices, faces=faces, convexity=floor(teeth/2));
}
if (shaft_diam > 0) {
cylinder(h=2*thickness+1, r=shaft_diam/2, center=true);
}
if (bevelang != 0) {
h = (c1-r1)/tan(45);
down(thickness/2+dy) {
difference() {
cube([2*c1/cos(45),2*c1/cos(45),2*h], center=true);
cylinder(h=h, r1=r1-0.5, r2=c1-0.5, center=false, $fn=teeth*4);
}
}
up(thickness/2-0.01) {
cylinder(h=(c2-r2)/tan(45)*5, r1=r2-0.5, r2=lerp(r2-0.5,c2-0.5,5), center=false, $fn=teeth*4);
}
}
}
@ -347,14 +576,14 @@ module gear(
// Module: rack()
// Description:
// The module `rack()` gives a rack, which is a bar with teeth. A
// rack can mesh with any gear that has the same `mm_per_tooth` and
// `pressure_angle`.
// rack can mesh with any gear that has the same `pitch` and
// `PA`.
// Arguments:
// mm_per_tooth = This is the "circular pitch", the circumference of the pitch circle divided by the number of teeth
// number_of_teeth = Total number of teeth along the rack
// 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.
// pressure_angle = Controls how straight or bulged the tooth sides are. In degrees.
// PA = 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`
@ -371,24 +600,24 @@ module gear(
// "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.
// Example:
// rack(mm_per_tooth=5, number_of_teeth=10, thickness=5, height=5, pressure_angle=20);
// rack(pitch=5, teeth=10, thickness=5, height=5, PA=20);
module rack(
mm_per_tooth = 5,
number_of_teeth = 20,
thickness = 5,
height = 10,
pressure_angle = 28,
backlash = 0.0,
clearance = undef,
anchor = CENTER,
spin = 0,
orient = UP
pitch = 5,
teeth = 20,
thickness = 5,
height = 10,
PA = 28,
backlash = 0.0,
clearance = undef,
anchor = CENTER,
spin = 0,
orient = UP
) {
a = adendum(mm_per_tooth);
d = dedendum(mm_per_tooth, clearance);
xa = a * sin(pressure_angle);
xd = d * sin(pressure_angle);
l = number_of_teeth * mm_per_tooth;
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),
@ -402,20 +631,20 @@ module rack(
anchorpt("dedendum-bottom", [0,-d,-thickness/2], DOWN),
];
orient_and_anchor([l, 2*abs(a-height), thickness], orient, anchor, spin=spin, anchors=anchors, chain=true) {
left((number_of_teeth-1)*mm_per_tooth/2) {
left((teeth-1)*pitch/2) {
linear_extrude(height = thickness, center = true, convexity = 10) {
for (i = [0:1:number_of_teeth-1] ) {
translate([i*mm_per_tooth,0,0]) {
for (i = [0:1:teeth-1] ) {
translate([i*pitch,0,0]) {
polygon(
points=[
[-1/2 * mm_per_tooth - 0.01, a-height],
[-1/2 * mm_per_tooth, -d],
[-1/4 * mm_per_tooth + backlash - xd, -d],
[-1/4 * mm_per_tooth + backlash + xa, a],
[ 1/4 * mm_per_tooth - backlash - xa, a],
[ 1/4 * mm_per_tooth - backlash + xd, -d],
[ 1/2 * mm_per_tooth, -d],
[ 1/2 * mm_per_tooth + 0.01, a-height],
[-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],
]
);
}
@ -438,22 +667,22 @@ n2 = 20; //green gear
n3 = 5; //blue gear
n4 = 20; //orange gear
n5 = 8; //gray rack
mm_per_tooth = 9; //all meshing gears need the same mm_per_tooth (and the same pressure_angle)
pitch = 9; //all meshing gears need the same `pitch` (and the same `PA`)
thickness = 6;
hole = 3;
height = 12;
d1 =pitch_radius(mm_per_tooth,n1);
d12=pitch_radius(mm_per_tooth,n1) + pitch_radius(mm_per_tooth,n2);
d13=pitch_radius(mm_per_tooth,n1) + pitch_radius(mm_per_tooth,n3);
d14=pitch_radius(mm_per_tooth,n1) + pitch_radius(mm_per_tooth,n4);
d1 =pitch_radius(pitch,n1);
d12=pitch_radius(pitch,n1) + pitch_radius(pitch,n2);
d13=pitch_radius(pitch,n1) + pitch_radius(pitch,n3);
d14=pitch_radius(pitch,n1) + pitch_radius(pitch,n4);
translate([ 0, 0, 0]) rotate([0,0, $t*360/n1]) color([1.00,0.75,0.75]) gear(mm_per_tooth,n1,thickness,hole);
translate([ 0, d12, 0]) rotate([0,0,-($t+n2/2-0*n1+1/2)*360/n2]) color([0.75,1.00,0.75]) gear(mm_per_tooth,n2,thickness,hole);
translate([ d13, 0, 0]) rotate([0,0,-($t-n3/4+n1/4+1/2)*360/n3]) color([0.75,0.75,1.00]) gear(mm_per_tooth,n3,thickness,hole);
translate([ d13, 0, 0]) rotate([0,0,-($t-n3/4+n1/4+1/2)*360/n3]) color([0.75,0.75,1.00]) gear(mm_per_tooth,n3,thickness,hole);
translate([-d14, 0, 0]) rotate([0,0,-($t-n4/4-n1/4+1/2-floor(n4/4)-3)*360/n4]) color([1.00,0.75,0.50]) gear(mm_per_tooth,n4,thickness,hole,teeth_to_hide=n4-3);
translate([(-floor(n5/2)-floor(n1/2)+$t+n1/2-1/2)*9, -d1+0.0, 0]) rotate([0,0,0]) color([0.75,0.75,0.75]) rack(mm_per_tooth,n5,thickness,height);
translate([ 0, 0, 0]) rotate([0,0, $t*360/n1]) color([1.00,0.75,0.75]) gear(pitch,n1,thickness,hole);
translate([ 0, d12, 0]) rotate([0,0,-($t+n2/2-0*n1+1/2)*360/n2]) color([0.75,1.00,0.75]) gear(pitch,n2,thickness,hole);
translate([ d13, 0, 0]) rotate([0,0,-($t-n3/4+n1/4+1/2)*360/n3]) color([0.75,0.75,1.00]) gear(pitch,n3,thickness,hole);
translate([ d13, 0, 0]) rotate([0,0,-($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+n1/2-1/2)*9, -d1+0.0, 0]) rotate([0,0,0]) color([0.75,0.75,0.75]) rack(pitch,n5,thickness,height);
*/

5
primitives.scad
View file

@ -176,11 +176,12 @@ module cylinder(r=undef, d=undef, r1=undef, r2=undef, d1=undef, d2=undef, h=unde
r1 = get_radius(r1=r1, r=r, d1=d1, d=d, dflt=1);
r2 = get_radius(r1=r2, r=r, d1=d2, d=d, dflt=1);
l = first_defined([h, l]);
hh = h/2;
sides = segs(max(r1,r2));
size = [r1*2, r1*2, l];
orient_and_anchor(size, orient, anchor, center, spin=spin, size2=[r2*2,r2*2], noncentered=BOTTOM, geometry="cylinder", chain=true) {
linear_extrude(height=l, scale=r2/r1, convexity=2, center=true) {
circle(r=r1, $fn=sides);
rotate_extrude(convexity=2, $fn=sides) {
polygon([[0,hh],[r2,hh],[r1,-hh],[0,-hh]]);
}
children();
}

307
shapes.scad
View file

@ -15,6 +15,8 @@
//
// Description:
// Creates a cube or cuboid object, with optional chamfering or rounding.
// Negative chamfers and roundings can be applied to create external masks,
// but only apply to edges around the top or bottom faces.
//
// Arguments:
// size = The size of the cube.
@ -34,20 +36,28 @@
// cuboid(20, p1=[10,0,0]);
// Example: Rectangular cube, with given X, Y, and Z sizes.
// cuboid([20,40,50]);
// Example: Rectangular cube defined by opposing cornerpoints.
// Example: Cube by Opposing Corners.
// cuboid(p1=[0,10,0], p2=[20,30,30]);
// Example: Rectangular cube with chamferred edges and corners.
// Example: Chamferred Edges and Corners.
// cuboid([30,40,50], chamfer=5);
// Example: Rectangular cube with chamferred edges, without trimmed corners.
// Example: Chamferred Edges, Untrimmed Corners.
// cuboid([30,40,50], chamfer=5, trimcorners=false);
// Example: Rectangular cube with rounded edges and corners.
// Example: Rounded Edges and Corners
// cuboid([30,40,50], rounding=10);
// Example: Rectangular cube with rounded edges, without trimmed corners.
// Example: Rounded Edges, Untrimmed Corners
// cuboid([30,40,50], rounding=10, trimcorners=false);
// Example: Rectangular cube with only some edges chamferred.
// Example: Chamferring Selected Edges
// cuboid([30,40,50], chamfer=5, edges=edges([TOP+FRONT,TOP+RIGHT,FRONT+RIGHT]), $fn=24);
// Example: Rectangular cube with only some edges rounded.
// Example: Rounding Selected Edges
// cuboid([30,40,50], rounding=5, edges=edges([TOP+FRONT,TOP+RIGHT,FRONT+RIGHT]), $fn=24);
// Example: Negative Chamferring
// cuboid([30,40,50], chamfer=-5, edges=edges([TOP,BOT], RIGHT), $fn=24);
// Example: Negative Chamferring, Untrimmed Corners
// cuboid([30,40,50], chamfer=-5, edges=edges([TOP,BOT], RIGHT), trimcorners=false, $fn=24);
// Example: Negative Rounding
// cuboid([30,40,50], rounding=-5, edges=edges([TOP,BOT], RIGHT), $fn=24);
// Example: Negative Rounding, Untrimmed Corners
// cuboid([30,40,50], rounding=-5, edges=edges([TOP,BOT], RIGHT), trimcorners=false, $fn=24);
// Example: Standard Connectors
// cuboid(40) show_anchors();
module cuboid(
@ -78,12 +88,61 @@ module cuboid(
majrots = [[0,90,0], [90,0,0], [0,0,0]];
orient_and_anchor(size, orient, anchor, spin=spin, chain=true) {
if (chamfer != undef) {
isize = [for (v = size) max(0.001, v-2*chamfer)];
if (edges == EDGES_ALL && trimcorners) {
hull() {
cube([size.x, isize.y, isize.z], center=true);
cube([isize.x, size.y, isize.z], center=true);
cube([isize.x, isize.y, size.z], center=true);
if (chamfer<0) {
cube(size, center=true) {
attach(TOP) prismoid([size.x,size.y], [size.x-2*chamfer,size.y-2*chamfer], h=-chamfer, anchor=TOP);
attach(BOT) prismoid([size.x,size.y], [size.x-2*chamfer,size.y-2*chamfer], h=-chamfer, anchor=TOP);
}
} else {
isize = [for (v = size) max(0.001, v-2*chamfer)];
hull() {
cube([size.x, isize.y, isize.z], center=true);
cube([isize.x, size.y, isize.z], center=true);
cube([isize.x, isize.y, size.z], center=true);
}
}
} else if (chamfer<0) {
ach = abs(chamfer);
cube(size, center=true);
// External-Chamfer mask edges
difference() {
union() {
for (i = [0:3], axis=[0:1]) {
if (edges[axis][i]>0) {
vec = EDGE_OFFSETS[axis][i];
translate(vmul(vec/2, size+[ach,ach,-ach])) {
rotate(majrots[axis]) {
cube([ach, ach, size[axis]], center=true);
}
}
}
}
// Add multi-edge corners.
if (trimcorners) {
for (za=[-1,1], ya=[-1,1], xa=[-1,1]) {
if (corner_edge_count(edges, [xa,ya,za]) > 1) {
translate(vmul([xa,ya,za]/2, size+[ach-0.01,ach-0.01,-ach])) {
cube([ach+0.01,ach+0.01,ach], center=true);
}
}
}
}
}
// Remove bevels from overhangs.
for (i = [0:3], axis=[0:1]) {
if (edges[axis][i]>0) {
vec = EDGE_OFFSETS[axis][i];
translate(vmul(vec/2, size+[2*ach,2*ach,-2*ach])) {
rotate(majrots[axis]) {
zrot(45) cube([ach*sqrt(2), ach*sqrt(2), size[axis]+2.1*ach], center=true);
}
}
}
}
}
} else {
difference() {
@ -117,17 +176,74 @@ module cuboid(
} else if (rounding != undef) {
sides = quantup(segs(rounding),4);
sc = 1/cos(180/sides);
isize = [for (v = size) max(0.001, v-2*rounding)];
if (edges == EDGES_ALL) {
minkowski() {
cube(isize, center=true);
if (trimcorners) {
sphere(r=rounding*sc, $fn=sides);
} else {
intersection() {
zrot(180/sides) cylinder(r=rounding*sc, h=rounding*2, center=true, $fn=sides);
rotate([90,0,0]) zrot(180/sides) cylinder(r=rounding*sc, h=rounding*2, center=true, $fn=sides);
rotate([0,90,0]) zrot(180/sides) cylinder(r=rounding*sc, h=rounding*2, center=true, $fn=sides);
if(rounding<0) {
cube(size, center=true);
zflip_copy() {
up(size.z/2) {
difference() {
down(-rounding/2) cube([size.x-2*rounding, size.y-2*rounding, -rounding], center=true);
down(-rounding) {
yspread(size.y-2*rounding) xcyl(l=size.x-3*rounding, r=-rounding);
xspread(size.x-2*rounding) ycyl(l=size.y-3*rounding, r=-rounding);
}
}
}
}
} else {
isize = [for (v = size) max(0.001, v-2*rounding)];
minkowski() {
cube(isize, center=true);
if (trimcorners) {
sphere(r=rounding*sc, $fn=sides);
} else {
intersection() {
zrot(180/sides) cylinder(r=rounding*sc, h=rounding*2, center=true, $fn=sides);
rotate([90,0,0]) zrot(180/sides) cylinder(r=rounding*sc, h=rounding*2, center=true, $fn=sides);
rotate([0,90,0]) zrot(180/sides) cylinder(r=rounding*sc, h=rounding*2, center=true, $fn=sides);
}
}
}
}
} else if (rounding<0) {
ard = abs(rounding);
cube(size, center=true);
// External-Chamfer mask edges
difference() {
union() {
for (i = [0:3], axis=[0:1]) {
if (edges[axis][i]>0) {
vec = EDGE_OFFSETS[axis][i];
translate(vmul(vec/2, size+[ard,ard,-ard])) {
rotate(majrots[axis]) {
cube([ard, ard, size[axis]], center=true);
}
}
}
}
// Add multi-edge corners.
if (trimcorners) {
for (za=[-1,1], ya=[-1,1], xa=[-1,1]) {
if (corner_edge_count(edges, [xa,ya,za]) > 1) {
translate(vmul([xa,ya,za]/2, size+[ard-0.01,ard-0.01,-ard])) {
cube([ard+0.01,ard+0.01,ard], center=true);
}
}
}
}
}
// Remove roundings from overhangs.
for (i = [0:3], axis=[0:1]) {
if (edges[axis][i]>0) {
vec = EDGE_OFFSETS[axis][i];
translate(vmul(vec/2, size+[2*ard,2*ard,-2*ard])) {
rotate(majrots[axis]) {
cyl(l=size[axis]+2.1*ard, r=ard);
}
}
}
}
}
@ -438,6 +554,12 @@ module right_triangle(size=[1, 1, 1], anchor=ALLNEG, spin=0, orient=UP, center=u
// Example: Putting it all together
// cyl(l=40, d1=25, d2=15, chamfer1=10, chamfang1=30, from_end=true, rounding2=5);
//
// Example: External Chamfers
// cyl(l=50, r=30, chamfer=-5, chamfang=30, $fa=1, $fs=1);
//
// Example: External Roundings
// cyl(l=50, r=30, rounding1=-5, rounding2=5, $fa=1, $fs=1);
//
// Example: Standard Connectors
// xdistribute(40) {
// cyl(l=30, d=25) show_anchors();
@ -461,7 +583,7 @@ module cyl(
size2 = [r2*2,r2*2,l];
sides = segs(max(r1,r2));
sc = circum? 1/cos(180/sides) : 1;
phi = atan2(l, r1-r2);
phi = atan2(l, r2-r1);
orient_and_anchor(size1, orient, anchor, spin=spin, center=center, size2=size2, geometry="cylinder", chain=true) {
zrot(realign? 180/sides : 0) {
if (!any_defined([chamfer, chamfer1, chamfer2, rounding, rounding1, rounding2])) {
@ -477,110 +599,66 @@ module cyl(
if (chamfer != undef) {
assert(chamfer <= r1, "chamfer is larger than the r1 radius of the cylinder.");
assert(chamfer <= r2, "chamfer is larger than the r2 radius of the cylinder.");
assert(chamfer <= l/2, "chamfer is larger than half the length of the cylinder.");
}
if (cham1 != undef) {
assert(cham1 <= r1, "chamfer1 is larger than the r1 radius of the cylinder.");
assert(cham1 <= l/2, "chamfer1 is larger than half the length of the cylinder.");
}
if (cham2 != undef) {
assert(cham2 <= r2, "chamfer2 is larger than the r2 radius of the cylinder.");
assert(cham2 <= l/2, "chamfer2 is larger than half the length of the cylinder.");
}
if (rounding != undef) {
assert(rounding <= r1, "rounding is larger than the r1 radius of the cylinder.");
assert(rounding <= r2, "rounding is larger than the r2 radius of the cylinder.");
assert(rounding <= l/2, "rounding is larger than half the length of the cylinder.");
}
if (fil1 != undef) {
assert(fil1 <= r1, "rounding1 is larger than the r1 radius of the cylinder.");
assert(fil1 <= l/2, "rounding1 is larger than half the length of the cylinder.");
}
if (fil2 != undef) {
assert(fil2 <= r2, "rounding2 is larger than the r1 radius of the cylinder.");
assert(fil2 <= l/2, "rounding2 is larger than half the length of the cylinder.");
}
dy1 = abs(first_defined([cham1, fil1, 0]));
dy2 = abs(first_defined([cham2, fil2, 0]));
assert(dy1+dy2 <= l, "Sum of fillets and chamfer sizes must be less than the length of the cylinder.");
dy1 = first_defined([cham1, fil1, 0]);
dy2 = first_defined([cham2, fil2, 0]);
maxd = max(r1,r2,l);
path = concat(
[[0,l/2]],
!is_undef(cham2)? (
let(
p1 = [r2-cham2/tan(chang2),l/2],
p2 = lerp([r2,l/2],[r1,-l/2],abs(cham2)/l)
) [p1,p2]
) : !is_undef(fil2)? (
let(
cn = find_circle_2tangents([r2-fil2,l/2], [r2,l/2], [r1,-l/2], r=abs(fil2)),
ang = fil2<0? phi : phi-180,
steps = ceil(abs(ang)/360*segs(abs(fil2))),
step = ang/steps,
pts = [for (i=[0:1:steps]) let(a=90+i*step) cn[0]+abs(fil2)*[cos(a),sin(a)]]
) pts
) : [[r2,l/2]],
!is_undef(cham1)? (
let(
p1 = lerp([r1,-l/2],[r2,l/2],abs(cham1)/l),
p2 = [r1-cham1/tan(chang1),-l/2]
) [p1,p2]
) : !is_undef(fil1)? (
let(
cn = find_circle_2tangents([r1-fil1,-l/2], [r1,-l/2], [r2,l/2], r=abs(fil1)),
ang = fil1<0? 180-phi : -phi,
steps = ceil(abs(ang)/360*segs(abs(fil1))),
step = ang/steps,
pts = [for (i=[0:1:steps]) let(a=(fil1<0?180:0)+(phi-90)+i*step) cn[0]+abs(fil1)*[cos(a),sin(a)]]
) pts
) : [[r1,-l/2]],
[[0,-l/2]]
);
rotate_extrude(convexity=2) {
hull() {
difference() {
union() {
difference() {
back(l/2) {
if (cham2!=undef && cham2>0) {
rr2 = sc * (r2 + (r1-r2)*dy2/l);
chlen2 = min(rr2, cham2/sin(chang2));
translate([rr2,-cham2]) {
rotate(-chang2) {
translate([-chlen2,-chlen2]) {
square(chlen2, center=false);
}
}
}
} else if (fil2!=undef && fil2>0) {
translate([r2-fil2*tan(vang),-fil2]) {
circle(r=fil2);
}
} else {
translate([r2-0.005,-0.005]) {
square(0.01, center=true);
}
}
}
// Make sure the corner fiddly bits never cross the X axis.
fwd(maxd) square(maxd, center=false);
}
difference() {
fwd(l/2) {
if (cham1!=undef && cham1>0) {
rr1 = sc * (r1 + (r2-r1)*dy1/l);
chlen1 = min(rr1, cham1/sin(chang1));
translate([rr1,cham1]) {
rotate(chang1) {
left(chlen1) {
square(chlen1, center=false);
}
}
}
} else if (fil1!=undef && fil1>0) {
right(r1) {
translate([-fil1/tan(vang),fil1]) {
fsegs1 = quantup(segs(fil1),4);
circle(r=fil1,$fn=fsegs1);
}
}
} else {
right(r1-0.01) {
square(0.01, center=false);
}
}
}
// Make sure the corner fiddly bits never cross the X axis.
square(maxd, center=false);
}
// Force the hull to extend to the axis
right(0.01/2) square([0.01, l], center=true);
}
// Clear anything left of the Y axis.
left(maxd/2) square(maxd, center=true);
// Clear anything right of face
right((r1+r2)/2) {
rotate(90-vang*2) {
fwd(maxd/2) square(maxd, center=false);
}
}
}
}
polygon(path);
}
//!place_copies(path) sphere(d=1);
}
}
children();
@ -621,7 +699,11 @@ module cyl(
// }
module xcyl(l=undef, r=undef, d=undef, r1=undef, r2=undef, d1=undef, d2=undef, h=undef, anchor=CENTER)
{
cyl(l=l, h=h, r=r, r1=r1, r2=r2, d=d, d1=d1, d2=d2, orient=RIGHT, anchor=anchor) children();
anchor = rot(from=RIGHT, to=UP, p=anchor);
cyl(l=l, h=h, r=r, r1=r1, r2=r2, d=d, d1=d1, d2=d2, orient=RIGHT, anchor=anchor) {
for (i=[0:1:$children-2]) children(i);
if ($children>0) children(0);
}
}
@ -658,7 +740,11 @@ module xcyl(l=undef, r=undef, d=undef, r1=undef, r2=undef, d1=undef, d2=undef, h
// }
module ycyl(l=undef, r=undef, d=undef, r1=undef, r2=undef, d1=undef, d2=undef, h=undef, anchor=CENTER)
{
cyl(l=l, h=h, r=r, r1=r1, r2=r2, d=d, d1=d1, d2=d2, orient=BACK, anchor=anchor) children();
anchor = rot(from=BACK, to=UP, p=anchor);
cyl(l=l, h=h, r=r, r1=r1, r2=r2, d=d, d1=d1, d2=d2, orient=BACK, anchor=anchor) {
for (i=[0:1:$children-2]) children(i);
if ($children>0) children(0);
}
}
@ -695,7 +781,10 @@ module ycyl(l=undef, r=undef, d=undef, r1=undef, r2=undef, d1=undef, d2=undef, h
// }
module zcyl(l=undef, r=undef, d=undef, r1=undef, r2=undef, d1=undef, d2=undef, h=undef, anchor=CENTER)
{
cyl(l=l, h=h, r=r, r1=r1, r2=r2, d=d, d1=d1, d2=d2, orient=UP, anchor=anchor) children();
cyl(l=l, h=h, r=r, r1=r1, r2=r2, d=d, d1=d1, d2=d2, orient=UP, anchor=anchor) {
for (i=[0:1:$children-2]) children(i);
if ($children>0) children(0);
}
}

71
transforms.scad
View file

@ -284,9 +284,9 @@ function rot(a=0, v=undef, cp=undef, from=undef, to=undef, reverse=false, p=unde
rot(a=a, v=v, cp=cp, from=from, to=to, reverse=reverse, p=[p], planar=planar)[0]
) : (
planar? (
is_undef(from)? rotate_points2d(p, a=ang*rev, cp=cp) : (
is_undef(from)? rotate_points2d(p, a=a*rev, cp=cp) : (
approx(from,to)? p :
rotate_points2d(p, ang=vector_angle(from,to)*sign(vector_axis(from,to)[2])*rev, cp=cp)
rotate_points2d(p, a=vector_angle(from,to)*sign(vector_axis(from,to)[2])*rev, cp=cp)
)
) : (
rotate_points3d(p, a=a, v=v, cp=(is_undef(cp)? [0,0,0] : cp), from=from, to=to, reverse=reverse)
@ -386,9 +386,10 @@ module zrot(a=0, cp=undef)
// Function&Module: scale()
// Usage: As Module
// scale(SCALAR) ...
// scale([X,Y,Z]) ...
// Usage: Scale Points
// pts = scale(a, pts);
// pts = scale(a, p);
// Usage: Get Scaling Matrix
// mat = scale(a);
// Description:
@ -397,14 +398,16 @@ module zrot(a=0, cp=undef)
// scaling factors in `a`. When called as a function with a list of points in the `p` argument,
// returns the list of points, with each one scaled by the [X,Y,Z] scaling factors in `a`.
// Arguments:
// a = The [X,Y,Z] scaling factors.
// a = The [X,Y,Z] scaling factors, or a scalar value for uniform scaling across all axes. Default: 1
// p = If called as a function, the point or list of points to scale.
// Example(NORENDER):
// pt1 = scale([2,3,4], p=[3,1,4]); // Returns: [6,3,16]
// pt1 = scale(3, p=[3,1,4]); // Returns: [9,3,12]
// pt2 = scale([2,3,4], p=[3,1,4]); // Returns: [6,3,16]
// pt3 = scale([2,3,4], p=[[1,2,3],[4,5,6]]); // Returns: [[2,6,12], [8,15,24]]
// mat2d = scale([2,3]); // Returns: [[2,0,0],[0,3,0],[0,0,1]]
// mat3d = scale([2,3,4]); // Returns: [[2,0,0,0],[0,3,0,0],[0,0,4,0],[0,0,0,1]]
function scale(a=[1,1,1], p=undef) =
function scale(a=1, p=undef) =
let(a = is_num(a)? [a,a,a] : a)
is_undef(p)? (
len(a)==2? affine2d_scale(a) : affine3d_scale(point3d(a))
) : (
@ -466,10 +469,10 @@ module zscale(z) scale([1,1,z]) children();
// Mirrors the children along the X axis, like `mirror([1,0,0])` or `xscale(-1)`
//
// Usage:
// xflip([cp]) ...
// xflip([x]) ...
//
// Arguments:
// cp = A point that lies on the plane of reflection.
// x = The X coordinate of the plane of reflection. Default: 0
//
// Example:
// xflip() yrot(90) cylinder(d1=10, d2=0, h=20);
@ -477,10 +480,10 @@ module zscale(z) scale([1,1,z]) children();
// color("red", 0.333) yrot(90) cylinder(d1=10, d2=0, h=20);
//
// Example:
// xflip(cp=[-5,0,0]) yrot(90) cylinder(d1=10, d2=0, h=20);
// xflip(x=-5) yrot(90) cylinder(d1=10, d2=0, h=20);
// color("blue", 0.25) left(5) cube([0.01,15,15], center=true);
// color("red", 0.333) yrot(90) cylinder(d1=10, d2=0, h=20);
module xflip(cp=[0,0,0]) translate(cp) mirror([1,0,0]) translate(-cp) children();
module xflip(x=0) translate([x,0,0]) mirror([1,0,0]) translate([-x,0,0]) children();
// Module: yflip()
@ -489,10 +492,10 @@ module xflip(cp=[0,0,0]) translate(cp) mirror([1,0,0]) translate(-cp) children()
// Mirrors the children along the Y axis, like `mirror([0,1,0])` or `yscale(-1)`
//
// Usage:
// yflip([cp]) ...
// yflip([y]) ...
//
// Arguments:
// cp = A point that lies on the plane of reflection.
// y = The Y coordinate of the plane of reflection. Default: 0
//
// Example:
// yflip() xrot(90) cylinder(d1=10, d2=0, h=20);
@ -500,10 +503,10 @@ module xflip(cp=[0,0,0]) translate(cp) mirror([1,0,0]) translate(-cp) children()
// color("red", 0.333) xrot(90) cylinder(d1=10, d2=0, h=20);
//
// Example:
// yflip(cp=[0,5,0]) xrot(90) cylinder(d1=10, d2=0, h=20);
// yflip(y=5) xrot(90) cylinder(d1=10, d2=0, h=20);
// color("blue", 0.25) back(5) cube([15,0.01,15], center=true);
// color("red", 0.333) xrot(90) cylinder(d1=10, d2=0, h=20);
module yflip(cp=[0,0,0]) translate(cp) mirror([0,1,0]) translate(-cp) children();
module yflip(y=0) translate([0,y,0]) mirror([0,1,0]) translate([0,-y,0]) children();
// Module: zflip()
@ -512,10 +515,10 @@ module yflip(cp=[0,0,0]) translate(cp) mirror([0,1,0]) translate(-cp) children()
// Mirrors the children along the Z axis, like `mirror([0,0,1])` or `zscale(-1)`
//
// Usage:
// zflip([cp]) ...
// zflip([z]) ...
//
// Arguments:
// cp = A point that lies on the plane of reflection.
// z = The Z coordinate of the plane of reflection. Default: 0
//
// Example:
// zflip() cylinder(d1=10, d2=0, h=20);
@ -523,10 +526,10 @@ module yflip(cp=[0,0,0]) translate(cp) mirror([0,1,0]) translate(-cp) children()
// color("red", 0.333) cylinder(d1=10, d2=0, h=20);
//
// Example:
// zflip(cp=[0,0,-5]) cylinder(d1=10, d2=0, h=20);
// zflip(z=-5) cylinder(d1=10, d2=0, h=20);
// color("blue", 0.25) down(5) cube([15,15,0.01], center=true);
// color("red", 0.333) cylinder(d1=10, d2=0, h=20);
module zflip(cp=[0,0,0]) translate(cp) mirror([0,0,1]) translate(-cp) children();
module zflip(z=0) translate([0,0,z]) mirror([0,0,1]) translate([0,0,-z]) children();
@ -1661,11 +1664,11 @@ module mirror_copy(v=[0,0,1], offset=0, cp=[0,0,0])
// Makes a copy of the children, mirrored across the X axis.
//
// Usage:
// xflip_copy([cp], [offset]) ...
// xflip_copy([x], [offset]) ...
//
// Arguments:
// offset = Distance to offset children right, before copying.
// cp = A point that lies on the mirroring plane.
// x = The X coordinate of the mirroring plane. Default: 0
//
// Side Effects:
// `$orig` is true for the original instance of children. False for the copy.
@ -1680,11 +1683,11 @@ module mirror_copy(v=[0,0,1], offset=0, cp=[0,0,0])
// color("blue",0.25) cube([0.01,15,15], center=true);
//
// Example:
// xflip_copy(cp=[-5,0,0]) yrot(90) cylinder(h=20, r1=4, r2=0);
// xflip_copy(x=-5) yrot(90) cylinder(h=20, r1=4, r2=0);
// color("blue",0.25) left(5) cube([0.01,15,15], center=true);
module xflip_copy(offset=0, cp=[0,0,0])
module xflip_copy(offset=0, x=0)
{
mirror_copy(v=[1,0,0], offset=offset, cp=cp) children();
mirror_copy(v=[1,0,0], offset=offset, cp=[x,0,0]) children();
}
@ -1694,11 +1697,11 @@ module xflip_copy(offset=0, cp=[0,0,0])
// Makes a copy of the children, mirrored across the Y axis.
//
// Usage:
// yflip_copy([cp], [offset]) ...
// yflip_copy([y], [offset]) ...
//
// Arguments:
// offset = Distance to offset children back, before copying.
// cp = A point that lies on the mirroring plane.
// y = The Y coordinate of the mirroring plane. Default: 0
//
// Side Effects:
// `$orig` is true for the original instance of children. False for the copy.
@ -1713,11 +1716,11 @@ module xflip_copy(offset=0, cp=[0,0,0])
// color("blue",0.25) cube([15,0.01,15], center=true);
//
// Example:
// yflip_copy(cp=[0,-5,0]) xrot(-90) cylinder(h=20, r1=4, r2=0);
// yflip_copy(y=-5) xrot(-90) cylinder(h=20, r1=4, r2=0);
// color("blue",0.25) fwd(5) cube([15,0.01,15], center=true);
module yflip_copy(offset=0, cp=[0,0,0])
module yflip_copy(offset=0, y=0)
{
mirror_copy(v=[0,1,0], offset=offset, cp=cp) children();
mirror_copy(v=[0,1,0], offset=offset, cp=[0,y,0]) children();
}
@ -1727,15 +1730,15 @@ module yflip_copy(offset=0, cp=[0,0,0])
// Makes a copy of the children, mirrored across the Z axis.
//
// Usage:
// zflip_copy([cp], [offset]) ...
// `$idx` is set to the index value of each copy.
// zflip_copy([z], [offset]) ...
//
// Arguments:
// offset = Distance to offset children up, before copying.
// cp = A point that lies on the mirroring plane.
// z = The Z coordinate of the mirroring plane. Default: 0
//
// Side Effects:
// `$orig` is true for the original instance of children. False for the copy.
// `$idx` is set to the index value of each copy.
//
// Example:
// zflip_copy() cylinder(h=20, r1=4, r2=0);
@ -1746,11 +1749,11 @@ module yflip_copy(offset=0, cp=[0,0,0])
// color("blue",0.25) cube([15,15,0.01], center=true);
//
// Example:
// zflip_copy(cp=[0,0,-5]) cylinder(h=20, r1=4, r2=0);
// zflip_copy(z=-5) cylinder(h=20, r1=4, r2=0);
// color("blue",0.25) down(5) cube([15,15,0.01], center=true);
module zflip_copy(offset=0, cp=[0,0,0])
module zflip_copy(offset=0, z=0)
{
mirror_copy(v=[0,0,1], offset=offset, cp=cp) children();
mirror_copy(v=[0,0,1], offset=offset, cp=[0,0,z]) children();
}