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Gear profile fixes to eliminate self-intersection

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This commit is contained in:
Adrian Mariano
2025-04-26 20:47:27 -04:00
parent 682491aadf
commit ecce973f8e
1 changed files with 35 additions and 10 deletions
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45
gears.scad
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@@ -177,6 +177,15 @@ function _inherit_gear_thickness(thickness,dflt=10) =
// fwd(6.4) right(22) text("clearance", size=2.5);
// }
// Continues:
// If the clearance is too large it can lead to a self-intersecting gear profile. When this occurs, you
// will see a message indicating that the profile was clipped, and what the required clearance is to
// avoid the clipping. This can be a starting point for adjusting the clipping. Typical gear pressure angles,
// as noted above, are 14.5, 20, or sometimes 25 degrees, but in some cases, larger pressure angles
// may be useful. These large pressure angles can give rise to self-intersecting gear geometry even
// with a zero clearance. To get a valid model, such gears need a **negative** clearance value.
// Figure(2D,NoAxes): This gear has a 55 degree pressure angle. If you don't specify clearance, the message tells you it clipped at -2.2. Here we have used -2.3 to avoid a sharp corner in the valleys between teeth.
// spur_gear2d(mod=5, teeth=7, profile_shift=0, pressure_angle=55,clearance=-2.3);
// Continues:
// Another clearance requirement can present a serious problem when the number of teeth is low. As the gear rotates, the
// teeth may interfere with each other. This may require undercutting the gear teeth to create space, which weakens the teeth.
// Is is best to avoid gears with very small numbers of teeth when possible.
@@ -751,6 +760,7 @@ function _inherit_gear_thickness(thickness,dflt=10) =
// clearance = Clearance gap at the bottom of the inter-tooth valleys. Default: mod/4
// slices = Number of vertical layers to divide gear into. Useful for refining gears with `helical`.
// internal = If true, create a mask for difference()ing from something else.
// $gear_steps = Number of points to sample gear profile. Default: 16
// atype = Set to "root", "tip" or "pitch" to determine anchoring circle. Default: "pitch"
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#subsection-spin). Default: `0`
@@ -1126,6 +1136,7 @@ module spur_gear(
// gear_spin = Rotate gear and children around the gear center, regardless of how gear is anchored. Default: 0
// clearance = Gap between top of a tooth on one gear and bottom of valley on a meshing gear. Default: mod/4
// internal = If true, create a mask for difference()ing from something else.
// $gear_steps = Number of points to sample gear profile. Default: 16
// shaft_diam = If given, the diameter of the central shaft hole.
// atype = Set to "root", "tip" or "pitch" to determine anchoring circle. Default: "pitch"
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER`
@@ -1224,7 +1235,7 @@ function spur_gear2d(
assert(is_finite(shaft_diam) && shaft_diam>=0)
assert(is_integer(hide) && hide>=0 && hide<teeth)
assert(is_finite(PA) && PA>=0 && PA<90, "Bad pressure_angle value.")
assert(clearance==undef || (is_finite(clearance) && clearance>=0))
assert(clearance==undef || is_finite(clearance))
assert(is_finite(backlash) && backlash>=0)
assert(is_finite(helical) && abs(helical)<90)
assert(is_finite(gear_spin))
@@ -1292,7 +1303,7 @@ module spur_gear2d(
assert(is_finite(shaft_diam) && shaft_diam>=0)
assert(is_integer(hide) && hide>=0 && hide<teeth)
assert(is_finite(PA) && PA>=0 && PA<90, "Bad pressure_angle value.")
assert(clearance==undef || (is_finite(clearance) && clearance>=0))
assert(clearance==undef || is_finite(clearance))
assert(is_finite(backlash) && backlash>=0)
assert(is_finite(helical) && abs(helical)<90)
assert(is_finite(gear_spin));
@@ -1365,6 +1376,7 @@ module spur_gear2d(
// backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle
// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter.
// mod = The module of the gear (pitch diameter / teeth)
// $gear_steps = Number of points to sample gear profile. Default: 16
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#subsection-spin). Default: `0`
// orient = Vector to rotate top towards, after spin. See [orient](attachments.scad#subsection-orient). Default: `UP`
@@ -1512,6 +1524,7 @@ module ring_gear(
// backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle
// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter.
// mod = The module of the gear (pitch diameter / teeth)
// $gear_steps = Number of points to sample gear profile. Default: 16
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#subsection-spin). Default: `0`
// Anchor Types:
@@ -2455,7 +2468,6 @@ module crown_gear(
// xrot(ang,cp=[0,-pitch_radius(mod=3,teeth=15),0])
// bevel_gear(mod=3,15,35,ang,right_handed=true);
echo(VPT=$vpt,VPR=$vpr,VPD=$vpd);
@@ -3333,7 +3345,7 @@ function _gear_tooth_profile(
_involute = function(base_r,a)
let(b=a*PI/180) base_r * [cos(a)+b*sin(a), sin(a)-b*cos(a)],
steps = 16,
steps = !is_undef($gear_steps) ? $gear_steps : 16,
circ_pitch = circular_pitch(pitch=pitch, circ_pitch=circ_pitch, diam_pitch=diam_pitch, mod=mod),
mod = module_value(circ_pitch=circ_pitch),
clear = default(clearance, 0.25 * mod),
@@ -3342,7 +3354,7 @@ function _gear_tooth_profile(
arad = outer_radius(circ_pitch, teeth, helical=helical, profile_shift=profile_shift, internal=internal, shorten=shorten),
prad = pitch_radius(circ_pitch, teeth, helical=helical),
brad = _base_radius(circ_pitch, teeth, pressure_angle, helical=helical),
rrad = _root_radius(circ_pitch, teeth, clearance, helical=helical, profile_shift=profile_shift, internal=internal),
rrad = _root_radius(circ_pitch, teeth, clear, helical=helical, profile_shift=profile_shift, internal=internal),
srad = max(rrad,brad),
tthick = circ_pitch/PI / cos(helical) * (PI/2 + 2*profile_shift * tan(pressure_angle)) + (internal?backlash:-backlash),
tang = tthick / prad / 2 * 180 / PI,
@@ -3426,7 +3438,6 @@ function _gear_tooth_profile(
// Round out the clearance valley
rcircum = 2 * PI * (internal? ma_rad : rrad),
rpart = (180/teeth-tang)/360,
round_r = min(clear, rcircum*rpart),
line1 = internal
? select(tooth_half_raw,-2,-1)
: select(tooth_half_raw,0,1),
@@ -3437,6 +3448,8 @@ function _gear_tooth_profile(
rcorner = internal
? [last(line1), isect_pt, line2[0]]
: [line2[0], isect_pt, line1[0]],
maxr = norm(rcorner[0]-rcorner[1])*tan(vector_angle(rcorner)/2), // Max radius that will actually fit on the corner
round_r = min(maxr, clear, rcircum*rpart),
rounded_tooth_half = deduplicate([
if (!internal && round_r>0) each arc(n=8, r=round_r, corner=rcorner),
if (!internal && round_r<=0) isect_pt,
@@ -3464,17 +3477,29 @@ function _gear_tooth_profile(
tooth_half = !undercut_max? rounded_tooth_half :
strip_left(rounded_tooth_half, 0),
// look for self-intersections in the gear profile. If found, clip them off
invalid = [for(i=idx(tooth_half)) if (atan2(tooth_half[i].y,tooth_half[i].x)>90+180/teeth) i],
clipped = invalid==[] ? tooth_half
: let(
ind = last(invalid),
ipt = line_intersection([[0,0],polar_to_xy(1,90+180/teeth)], select(tooth_half,ind,ind+1)),
c = prad - mod*(1-profile_shift) - norm(ipt)
)
echo(str(teeth, " tooth gear profile clipped at clearance = ",c))
[
ipt,
each slice(tooth_half, ind+1,-1)
],
// Mirror the tooth to complete it.
full_tooth = deduplicate([
each tooth_half,
each reverse(xflip(tooth_half)),
each clipped,
each reverse(xflip(clipped)),
]),
// Reduce number of vertices.
tooth = path_merge_collinear(
resample_path(full_tooth, n=ceil(2*steps), keep_corners=30, closed=false)
),
out = center? fwd(prad, p=tooth) : tooth
) out;