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Merge pull request #1291 from adrianVmariano/master

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bevel gear fixes & heigth field bugfix
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Revar Desmera 2023-10-18 21:55:21 -07:00 committed by GitHub
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4 changed files with 232 additions and 159 deletions
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1
drawing.scad
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@ -798,6 +798,7 @@ function arc(n, r, angle, d, cp, points, corner, width, thickness, start, wedge=
)
dir ? arcpts : reverse(arcpts)
) :
assert(is_def(points), "Arc not specified: must give points, angle, or width and thickness")
assert(is_path(points,[2,3]),"Point list is invalid")
// Arc is 3D, so transform points to 2D and make a recursive call, then remap back to 3D
len(points[0]) == 3? (

382
gears.scad
View file

@ -510,9 +510,10 @@ function _inherit_gear_thickness(thickness) =
// after switching off the drive
// Subsection: Bevel Gears
// Bevel gearing is another way of dealing with intersecting gear shafts. For bevel gears, the teeth centers lie on
// the surface of an imaginary cone, which is the pitch cone of the bevel gear. Two bevel gears mesh when their pitch cones
// touch along their length. The teeth of bevel gears narrow as they get closer to the center of the gear.
// Tooth dimensions and pitch diameter are referenced to the outer end of the teeth.
// the surface of an imaginary cone, which is the pitch cone of the bevel gear. Two bevel gears mesh when their pitch cone
// apexes coincide and the cones touch along their length. The teeth of bevel gears narrow as they get closer to the center of the gear.
// Tooth dimensions and pitch diameter (the base of the pitch cone) are referenced to the outer end of the teeth.
// Note that the pitch radius, computed the same was as for other gears, gives the radius of the pitch cone's base.
// Bevel gears can be made with straight teeth, analogous to spur gears, and with the
// same disadvantage of sudden full contact that is noisy. Spiral teeth are analogous to helical
// teeth on cylindrical gears: the teeth engage gradually and smoothly, transmitting motion more smoothly
@ -522,12 +523,12 @@ function _inherit_gear_thickness(thickness) =
// but with a zero angle. These share advantages of straight teeth and spiral teeth: they are quiet like
// straight teeth but they lack the axial thrust of spiral gears, and they can operate in both directions.
// They are also reportedly stronger than either spiral or bevel gears.
// Figure(3D,Med,VPT=[-5.10228,-3.09311,3.06426],VPR=[67.6,0,131.9],VPD=237.091,NoAxes): Straight tooth bevel gear with 45 degree angled teeth. To get a gear like this you must specify a spiral angle of zero and a cutter radius of zero.
// bevel_gear(mod=3,teeth=35,face_width=20,spiral_angle=0,cutter_radius=0);
// Figure(3D,Med,VPT=[-5.10228,-3.09311,3.06426],VPR=[67.6,0,131.9],VPD=237.091,NoAxes): Straight tooth bevel gear with 45 degree angled teeth. To get a gear like this you must specify a spiral angle of zero and a cutter radius of zero. This gear would mate with a copy of itself and would change direction of rotation without changing the rotation rate.
// bevel_gear(mod=3,teeth=35,mate_teeth=35,face_width=20,spiral=0,cutter_radius=0);
// Figure(3D,Med,VPT=[-5.10228,-3.09311,3.06426],VPR=[67.6,0,131.9],VPD=237.091,NoAxes): Straight tooth bevel gear with 45 degree angled teeth. A gear like this has a positive spiral angle, which determines how sloped the teeth are and a positive cutter radius, which determines how curved the teeth are.
// bevel_gear(mod=3,teeth=35,face_width=20);
// bevel_gear(mod=3,teeth=35,mate_teeth=35,face_width=20,slices=12);
// Figure(3D,Med,VPT=[-5.10228,-3.09311,3.06426],VPR=[67.6,0,131.9],VPD=237.091,NoAxes): Zerol tooth bevel gear with 45 degree angled teeth. A gear like this has a spiral angle of zero, but a positive cutter radius, which determines how curved the teeth are.
// bevel_gear(mod=3,teeth=35,face_width=20,spiral_angle=0);
// bevel_gear(mod=3,teeth=35,mate_teeth=35,face_width=20,spiral=0,slices=12);
// Continues:
// Bevel gears have demanding requirements for successful mating of two gears. Of course the tooth size
// and pressure angle must match. But beyond that, their pitch cones have to meet at their points.
@ -540,30 +541,37 @@ function _inherit_gear_thickness(thickness) =
// this is not required, and you can design pairs of bevel gears for any desired shaft angle.
// Note, however, that given a pair of teeth counts, a bevel gear pair is not possible at all angles.
// Figure(3D,Med,NoAxes,VPT=[-1.42254,-1.98925,13.5702],VPR=[76,0,145],VPD=263.435): Two zerol bevel gears mated with shafts at 90 degrees.
// bevel_gear(mod=3,teeth=35,face_width=10,spiral_angle=0,mate_teeth=15);
// cyl(h=40,d=3,$fn=16,anchor=BOT);
// bevel_gear(mod=3,teeth=35,face_width=10,spiral=0,mate_teeth=15,backing=3);
// cyl(h=28,d=3,$fn=16,anchor=BOT);
// color("lightblue")left(pitch_radius(mod=3,teeth=35))up(pitch_radius(mod=3,teeth=15))
// yrot(90){zrot(360/15/2)bevel_gear(mod=3,teeth=15,face_width=10,spiral_angle=0,cutter_radius=-30,mate_teeth=35);
// cyl(h=60,d=3,$fn=16,anchor=BOT);}
// Figure(3D,Med,NoAxes,VPT=[1.55215,1.94725,16.4524],VPR=[76,0,181.4],VPD=263.435): Two zerol bevel gears mated with shafts at a 35 deg angle. Note that if the blue gear is tipped slightly more its shaft will intersect the shaft of the yellow gear underneath that gear; that indicates an impossible angle for this pair of teeth counts.
// function bevel_angles(z1,z2,shaft) =
// [atan(sin(shaft)/((z2/z1)+cos(shaft))),
// atan(sin(shaft)/((z1/z2)+cos(shaft)))];
// angles = bevel_angles(35,15,115);
// bevel_gear(mod=3,teeth=35,face_width=10,spiral_angle=0,pitch_angle=angles[0],cutter_radius=30);
// cyl(h=40,d=3,$fn=16,anchor=BOT);
// yrot(90){zrot(360/15/2)bevel_gear(mod=3,teeth=15,face_width=10,spiral=0,right_handed=true,mate_teeth=35);
// cyl(h=57,d=3,$fn=16,anchor=BOT);}
// Figure(3D,Med,NoAxes,VPT=[2.01253,-0.673328,8.98056],VPD=263.435,VPR=[79.5,0,68.6]): Two zerol bevel gears mated with shafts at a 115.38 deg angle. This is a planar bevel gear. The axes intersect on the pitch base of the yellow gear. If the blue gear is tipped slightly more its shaft will intersect the shaft of the yellow gear underneath that gear's pitch base, indicating an impossible angle for a normal bevel gear at this pair of teeth counts.
// ang=acos(-15/35);
// bevel_gear(mod=3,35,15,ang,spiral=0,backing=5,anchor="apex")
// cyl(h=25,d=3,$fn=16,anchor=BOT);
// color("lightblue")
// left(pitch_radius(mod=3,teeth=35))yrot(20)up(pitch_radius(mod=3,teeth=15))
// yrot(90)zrot(360/15/2){
// bevel_gear(mod=3,teeth=15,face_width=10,spiral_angle=0,cutter_radius=-30,pitch_angle=(angles[1]));
// cyl(h=60,d=3,$fn=16,anchor=BOT);
// }
// xrot(ang)
// bevel_gear(mod=3,15,35,ang,spiral=0,right_handed=true,anchor="apex")
// cyl(h=70,d=3,$fn=16,anchor=BOT);
// Continues:
// In the above figure you can see a gear that is very flat. A bevel gear that is perfectly flat is called a planar bevel gear or
// sometimes also a crown gear. The latter term may be confusing because it also refers to a similar looking
// but very different type of gear that is described below. A planar bevel gear can only mate with another
// compatible bevel gear. It has a degenerate cone with its apex on the gear itself, so the mating pinion gear cannot
// mate at a 90 degree angle because if it did, it's cone could not meet the center of the planar bevel gear.
// mate at a 90 degree angle because if it did, its cone could not meet the center of the planar bevel gear.
// If you request a larger shaft angle, the teeth of the bevel gear will tilt inward, producing an internal bevel gear.
// Gears with this design are rarely used. The mate of an interior gear is always an exterior gear.
// Figure(VPT=[-1.07698,0.67915,-2.25898],VPD=263.435,VPR=[69.7,0,49.3],NoAxes): Internal bevel gear (yellow) mated to an external bevel gear (blue) to achieve a 135 degree shaft angle.
// ang=135;
// bevel_gear(mod=3,35,15,ang,spiral=0,cone_backing=false);
// down(15)cyl(h=40,d=3,$fn=16,anchor=BOT);
// color("lightblue")
// back(pitch_radius(mod=3,teeth=35)+pitch_radius(mod=3,teeth=15))
// xrot(ang,cp=[0,-pitch_radius(mod=3,teeth=15),0]){
// bevel_gear(mod=3,15,35,ang,right_handed=true,spiral=0);
// cyl(h=40,d=3,$fn=16,anchor=BOT);
// }
// Subsection: Crown Gears (Face Gears)
// Crown gears, sometimes called Face Crown Gears or just Face Gears, are gears with teeth pointing straight up so
// the gear resembles a crown. This type of gear is not the same as a bevel gear with vertical teeth, which would mate
@ -1695,10 +1703,10 @@ module rack(
assert(is_finite(bottom) && bottom>d, "bottom is invalid or too small for teeth")
bottom
: is_def(width) ?
assert(is_finite(width) && width>a+d, "Width is invalid or too small for teeth")
assert(is_finite(width) && width>a+d, "width is invalid or too small for teeth")
width - a
: is_def(backing) ?
assert(all_positive([backing]), "Backing must be a positive value")
assert(all_positive([backing]), "backing must be a positive value")
backing+d
: 2*d+a; // default case
l = teeth * trans_pitch;
@ -1796,10 +1804,10 @@ function rack(
assert(is_finite(bottom) && bottom>d, "bottom is invalid or too small for teeth")
bottom
: is_def(width) ?
assert(is_finite(width) && width>a+d, "Width is invalid or too small for teeth")
assert(is_finite(width) && width>a+d, "width is invalid or too small for teeth")
width - a
: is_def(backing) ?
assert(all_positive([backing]), "Backing must be a positive value")
assert(all_positive([backing]), "backing must be a positive value")
backing+d
: 2*d+a, // default case
l = teeth * trans_pitch,
@ -1930,10 +1938,10 @@ function rack2d(
assert(is_finite(bottom) && bottom>dedendum, "bottom is invalid or too small for teeth")
bottom
: is_def(width) ?
assert(is_finite(width) && width>adendum+dedendum, "Width is invalid or too small for teeth")
assert(is_finite(width) && width>adendum+dedendum, "width is invalid or too small for teeth")
width - adendum
: is_def(backing) ?
assert(all_positive([backing]), "Backing must be a positive value")
assert(all_positive([backing]), "backing must be a positive value")
backing+dedendum
: 2*dedendum+adendum // default case
)
@ -2029,10 +2037,10 @@ module rack2d(
assert(is_finite(bottom) && bottom>d, "bottom is invalid or too small for teeth")
bottom
: is_def(width) ?
assert(is_finite(width) && width>a+d, "Width is invalid or too small for teeth")
assert(is_finite(width) && width>a+d, "width is invalid or too small for teeth")
width - a
: is_def(backing) ?
assert(all_positive([backing]), "Backing must be a positive value")
assert(all_positive([backing]), "backing must be a positive value")
backing+d
: 2*d+a; // default case
l = teeth * trans_pitch;
@ -2091,7 +2099,7 @@ module rack2d(
// Arguments:
// circ_pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. Default: 5
// teeth = Total number of teeth around the entire perimeter. Default: 20
// backing = Distance from base of crown gear to roots of teeth (alternative to bottom and backing).
// backing = Distance from base of crown gear to roots of teeth (alternative to bottom and thickness).
// face_width = Width of the toothed surface in mm, from inside radius to outside. Default: 5
// ---
// bottom = Distance from crown's pitch plane (Z=0) to the bottom of the crown gear. (Alternative to backing or thickness)
@ -2157,10 +2165,10 @@ function crown_gear(
assert(is_finite(bottom) && bottom>d, "bottom is invalid or too small for teeth")
bottom
: is_def(thickness) ?
assert(is_finite(thickness) && thickness>a+d, "Width is invalid or too small for teeth")
assert(is_finite(thickness) && thickness>a+d, "thickness is invalid or too small for teeth")
thickness - a
: is_def(backing) ?
assert(all_positive([backing]), "Backing must be a positive value")
assert(all_positive([backing]), "backing must be a positive value")
backing+d
: 2*d+a, // default case
mod = module_value(circ_pitch=pitch),
@ -2245,10 +2253,10 @@ module crown_gear(
assert(is_finite(bottom) && bottom>d, "bottom is invalid or too small for teeth")
bottom
: is_def(thickness) ?
assert(is_finite(thickness) && thickness>a+d, "Width is invalid or too small for teeth")
assert(is_finite(thickness) && thickness>a+d, "thickness is invalid or too small for teeth")
thickness - a
: is_def(backing) ?
assert(all_positive([backing]), "Backing must be a positive value")
assert(all_positive([backing]), "backing must be a positive value")
backing+d
: 2*d+a; // default case
vnf = crown_gear(
@ -2271,88 +2279,90 @@ module crown_gear(
// Function&Module: bevel_gear()
// Synopsis: Creates a straight or spiral bevel gear.
// Synopsis: Creates a straight, zerol, or spiral bevel gear.
// SynTags: Geom, VNF
// Topics: Gears, Parts
// See Also: rack(), rack2d(), spur_gear(), spur_gear2d(), bevel_pitch_angle(), bevel_gear()
// Usage: As a Module
// bevel_gear(circ_pitch, teeth, face_width, [pitch_angle=]|[mate_teeth=], [shaft_diam=], [hide=], [pressure_angle=], [clearance=], [backlash=], [cutter_radius=], [spiral_angle=], [left_handed=], [slices=], [internal=]);
// bevel_gear(mod=, teeth=, face_width=, [pitch_angle=]|[mate_teeth=], [shaft_diam=], [hide=], [pressure_angle=], [clearance=], [backlash=], [cutter_radius=], [spiral_angle=], [left_handed=], [slices=], [internal=]);
// gear_dist(mod=|diam_pitch=|circ_pitch=, teeth, mate_teeth, [shaft_angle], [shaft_diam], [face_width=], [hide=], [spiral=], [cutter_radius=], [right_handed=], [pressure_angle=], [backing=|thickness=|bottom=], [cone_backing=], [backlash=], [slices=], [internal=], [gear_spin=], ...) [ATTACHMENTS];
// Usage: As a Function
// vnf = bevel_gear(circ_pitch, teeth, face_width, [pitch_angle=]|[mate_teeth=], [hide=], [pressure_angle=], [clearance=], [backlash=], [cutter_radius=], [spiral_angle=], [left_handed=], [slices=], [internal=]);
// vnf = bevel_gear(mod=, teeth=, face_width=, [pitch_angle=]|[mate_teeth=], [hide=], [pressure_angle=], [clearance=], [backlash=], [cutter_radius=], [spiral_angle=], [left_handed=], [slices=], [internal=]);
// vnf = gear_dist(mod=|diam_pitch=|circ_pitch=, teeth, mate_teeth, [shaft_angle], [face_width=], [hide=], [spiral=], [cutter_radius=], [right_handed=], [pressure_angle=], , [backing=|thickness=|bottom=], [cone_backing=], [backlash=], [slices=], [internal=], [gear_spin=], ...);
// 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
// parameters, and let the rest be default values. In straight bevel gear sets, when each tooth
// Creates a spiral, zerol, or straight bevel gear. In straight bevel gear sets, when each tooth
// engages it inpacts the corresponding tooth. The abrupt tooth engagement causes impact stress
// which makes them more prone to breakage. Spiral bevel gears have teeth formed along spirals so
// they engage more gradually, resulting in a less abrupt transfer of force, so they are quieter
// in operation and less likely to break.
// .
// The module `bevel_gear()` gives a gear in the XY plane, centered on the origin, with one tooth
// centered on the positive Y axis. The various functions below it take the same parameters, and
// return various measurements for the gear. The most important function is `mesh_radius()`, which tells
// how far apart to space gears that are meshing, and `outer_radius()`, which gives the size of the
// region filled by the gear. A gear has a "pitch circle", which is an invisible circle that cuts
// through the middle of each tooth (though not the exact center). In order for two gears to mesh,
// their pitch circles should just touch, if no profile shifting is done). So the distance between
// their centers should be `mesh_radius()` for one, plus `mesh_radius()` for the other, which gives
// the radii of their pitch circles and profile shifts. In order for two gears to mesh, they must
// have the same `circ_pitch` and `pressure_angle` parameters. `circ_pitch` gives the number of millimeters
// of arc around the pitch circle covered by one tooth and one space between teeth. The `pressure_angle`
// controls how flat or bulged the sides of the teeth are. Common values include 14.5 degrees and 20
// degrees, and occasionally 25. The default here is 20 degrees. Larger numbers bulge out more,
// giving stronger teeth. The ratio of `teeth` for two meshing gears gives how many times one will make a full
// Bevel gears must be created in mated pairs to work together at a chosen shaft angle. You therefore
// must specify both the number of teeth on the gear and the number of teeth on its mating gear.
// Additional requirements for bevel gears to mesh are that they share the same
// tooth size and the same pressure angle and they must be of opposite handedness.
// The pressure angle controls how much the teeth bulge at their
// sides and is almost always 20 degrees for standard bevel gears. 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.
// every tooth on the other, for more even wear. So relatively prime numbers of teeth are good.
// .
// The gear appears centered on the origin, with one tooth
// centered on the positive Y axis. The base of the pitch cone (the "pitchbase") will lie in the XY plane. This is
// the natural position: in order to mesh the mating gear must be positioned so their pitch bases are tangent.
// The apexes of the pitch cones must coincide.
// .
// By default backing will be added to ensure
// that the center of the gear (where there are no teeth) is at least half the face width in thickness.
// You can change this using the `backing`, `thickness` or `bottom` parameters. The backing appears with
// a conical shape, extended the sloped edges of the teeth. You can set `cone_backing=false` if your application
// requires cylindrical backing.
// Arguments:
// circ_pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. Default: 5
// teeth = Total number of teeth around the entire perimeter. Default: 20
// face_width = Width of the toothed surface in mm, from inside to outside. Default: 10
// ---
// pitch_angle = Angle of beveled gear face. Default: 45
// mate_teeth = The number of teeth in the gear that this gear will mate with. Overrides `pitch_angle` if given.
// shaft_diam = Diameter of the hole in the center, in mm. Module use only. Default: 0 (no shaft hole)
// teeth = Number of teeth on the gear
// mate_teeth = Number of teeth on the gear that will mate to this gear
// shaft_angle = Angle between the shafts of the two gears. Default: 90
// --
// mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth.
// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter.
// circ_pitch = distance between teeth around the pitch circle.
// backing = Distance from bottom of bevel gear to bottom corner of teeth (Alternative to bottom or thickness). Default: 0 if the gear is thick enough (see above)
// bottom = Distance from bevel gear's pitch base to the bottom of the bevel gear. (Alternative to backing or thickness)
// thickness = Thickness of bevel gear at the center, where there are no teeth. (Alternative to backing or bottom).
// cone_backing = If true backing extends conical shape of the gear; otherwise backing is an attached cylinder. Default: true
// face_width = Width of teeth. Default: 10
// shaft_diam = Diameter of the hole in the center, or zero for no hole. (Module only.) Default: 0
// hide = Number of teeth to delete to make this only a fraction of a circle. Default: 0
// pressure_angle = Controls how straight or bulged the tooth sides are. In degrees. Default: 20
// clearance = Clearance gap at the bottom of the inter-tooth valleys. Default: module/4
// backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle. Default: 0
// spiral = The base angle for spiral teeth. If zero the teeth will be zerol or straight. Default: 30
// cutter_radius = Radius of spiral arc for teeth. If 0, then gear will have straight teeth. Default: 30
// spiral_angle = The base angle for spiral teeth. If zero the teeth will be zerol or straight. Default: 30
// left_handed = If true, the gear returned will have a left-handed spiral. Default: false
// right_handed = If true, the gear returned will have a right-handed teeth. Default: false
// slices = Number of vertical layers to divide gear into. Useful for refining gears with `spiral`. Default: 1
// internal = If true, create a mask for difference()ing from something else.
// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter.
// mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth.
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER`
// gear_spin = Rotate gear and children around the gear center, regardless of how gear is anchored. Default: 0
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: "pitchbase"
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#subsection-spin). Default: `0`
// orient = Vector to rotate top towards, after spin. See [orient](attachments.scad#subsection-orient). Default: `UP`
// Extra Anchors:
// "pitchbase" = With the base of the pitch cone in the XY plane, centered at the origin. This is the natural height for the gear, and the default anchor.
// "apex" = At the pitch cone apex for the bevel gear.
// "pitchbase" = At the natural height of the pitch radius of the beveled gear.
// "flattop" = At the top of the flat top of the bevel gear.
// Side Effects:
// If internal is true then the default tag is "remove"
// Example: Beveled Gear
// Example(NoAxes): Bevel Gear with zerol teeth
// bevel_gear(
// circ_pitch=5, teeth=36, face_width=10, shaft_diam=5,
// pitch_angle=45, spiral_angle=0
// circ_pitch=5, teeth=36, mate_teeth=36,
// shaft_diam=5, spiral=0
// );
// Example: Spiral Beveled Gear and Pinion
// Example(NoAxes): Spiral Beveled Gear and Pinion. Note conical backing added to the yellow gear to prevent it from being thin.
// t1 = 16; t2 = 28;
// bevel_gear(
// color("lightblue")bevel_gear(
// circ_pitch=5, teeth=t1, mate_teeth=t2,
// slices=12, anchor="apex", orient=FWD
// );
// bevel_gear(
// circ_pitch=5, teeth=t2, mate_teeth=t1, left_handed=true,
// slices=12, anchor="apex", spin=180/t2
// circ_pitch=5, teeth=t2, mate_teeth=t1, right_handed=true,
// slices=12, anchor="apex", backing=3, spin=180/t2
// );
// Example(Anim,Frames=4,VPD=175): Manual Spacing of Pinion and Gear
// Example(Anim,Frames=4,VPD=175,NoAxes): Manual Spacing of Pinion and Gear. Here conical backing has been turned off.
// t1 = 14; t2 = 28; circ_pitch=5;
// back(pitch_radius(circ_pitch, t2)) {
// color("lightblue")back(pitch_radius(circ_pitch, t2)) {
// yrot($t*360/t1)
// bevel_gear(
// circ_pitch=circ_pitch, teeth=t1, mate_teeth=t2, shaft_diam=5,
@ -2362,50 +2372,70 @@ module crown_gear(
// down(pitch_radius(circ_pitch, t1)) {
// zrot($t*360/t2)
// bevel_gear(
// circ_pitch=circ_pitch, teeth=t2, mate_teeth=t1, left_handed=true,
// shaft_diam=5, slices=12, spin=180/t2
// circ_pitch=circ_pitch, teeth=t2, mate_teeth=t1, right_handed=true,
// shaft_diam=5, slices=12, backing=3, spin=180/t2, cone_backing=false
// );
// }
// Example(NoAxes,VPT=[24.4306,-9.20912,-29.3331],VPD=292.705,VPR=[71.8,0,62.5]): Bevel gears at a non right angle, positioned by aligning the pitch cone apexes.
// ang=65;
// bevel_gear(mod=3,35,15,ang,spiral=0,backing=5,anchor="apex")
// cyl(h=48,d=3,$fn=16,anchor=BOT);
// color("lightblue")
// xrot(ang)
// bevel_gear(mod=3,15,35,ang,spiral=0,right_handed=true,anchor="apex")
// cyl(h=65,d=3,$fn=16,anchor=BOT);
// Example(VPT=[6.39483,26.2195,8.93229],VPD=192.044,VPR=[76.7,0,63.3],NoAxes): At this extreme 135 degree angle the yellow gear has internal teeth. This is a rare configuration.
// ang=135;
// bevel_gear(mod=3,35,15,ang);
// color("lightblue")
// back(pitch_radius(mod=3,teeth=35)+pitch_radius(mod=3,teeth=15))
// xrot(ang,cp=[0,-pitch_radius(mod=3,teeth=15),0])
// bevel_gear(mod=3,15,35,ang,right_handed=true);
function bevel_gear(
circ_pitch,
teeth,
face_width = 10,
pitch_angle = 45,
mate_teeth,
shaft_angle=90,
backing,thickness,bottom,
face_width = 10,
hide = 0,
pressure_angle = 20,
clearance,
backlash = 0.0,
cutter_radius = 30,
spiral_angle = 35,
left_handed = false,
spiral = 35,
right_handed = false,
slices = 5,
internal,
interior,
cone_backing = true,
pitch,
circ_pitch,
diam_pitch,
mod,
anchor = "pitchbase",
spin = 0,
orient = UP
) = let(
dummy = !is_undef(interior) ? echo("In bevel_gear(), the argument 'interior=' has been deprecated, and may be removed in the future. Please use 'internal=' instead."):0,
internal = first_defined([internal,interior,false]),
gear_spin = 0,
orient = UP,
_return_anchors = false
) = assert(all_integer([teeth,mate_teeth]) && teeth>=3 && mate_teeth>=3, "Must give teeth and mate_teeth, integers greater than or equal to 3")
assert(all_nonnegative([spiral]), "spiral must be nonnegative")
assert(all_nonnegative([cutter_radius]), "cutter_radius must be nonnegative")
let(
circ_pitch = _inherit_gear_pitch("bevel_gear()",pitch, circ_pitch, diam_pitch, mod),
PA = _inherit_gear_pa(pressure_angle),
spiral_angle = _inherit_gear_helical(spiral_angle, invert=!internal),
spiral = _inherit_gear_helical(spiral),
face_width = _inherit_gear_thickness(face_width),
slices = cutter_radius==0? 1 : slices,
pitch_angle = is_undef(mate_teeth)? pitch_angle : atan(teeth/mate_teeth),
max_ang = acos(-min(mate_teeth/teeth, teeth/mate_teeth)),
dummy2 = assert(is_finite(shaft_angle) && shaft_angle>0 && shaft_angle<180,"shaft_angle must be strictly between 0 and 180"),
pitch_angle = posmod(atan(sin(shaft_angle)/((mate_teeth/teeth)+cos(shaft_angle))),180),
pr = pitch_radius(circ_pitch, teeth),
rr = _root_radius(circ_pitch, teeth, clearance, internal),
rr = _root_radius(circ_pitch, teeth, clearance),
pitchoff = (pr-rr) * sin(pitch_angle),
ocone_rad = opp_ang_to_hyp(pr, pitch_angle),
ocone_rad = pitch_angle<90 ? opp_ang_to_hyp(pr, pitch_angle)
: opp_ang_to_hyp(pitch_radius(circ_pitch,mate_teeth), shaft_angle-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),
radcp = [0, midpr] + polar_to_xy(cutter_radius, 180+spiral),
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 = v_theta(radcp),
@ -2417,7 +2447,6 @@ function bevel_gear(
pressure_angle = PA,
clearance = clearance,
backlash = backlash,
internal = internal,
center = true
)),
verts1 = [
@ -2439,114 +2468,155 @@ function bevel_gear(
each apply(xflip() * zrot(360*tooth/teeth) * m, path3d(profile))
]
],
botz = verts1[0][0].z,
topz = last(verts1)[0].z,
thickness = abs(topz - botz),
cpz = (topz + botz) / 2,
botz = verts1[0][0].z, // bottom of center
topz = last(verts1)[0].z, // top of center
ctr_thickness = topz - botz,
vertices = [for (x=verts1) reverse(x)],
sides_vnf = vnf_vertex_array(vertices, caps=false, col_wrap=true, reverse=true),
top_verts = last(vertices),
bot_verts = vertices[0],
gear_pts = len(top_verts),
face_pts = gear_pts / teeth,
top_faces =[
minbacking = -min(0,ctr_thickness),
backing = is_def(backing) ?
assert(all_nonnegative([backing]), "backing must be a non-negative value")
assert(ctr_thickness>0 || backing>0, "internal gears require backing>0")
backing-min(0,ctr_thickness)
: is_def(thickness) ?
let(thick_OK=is_finite(thickness) && (thickness>abs(ctr_thickness) || (thickness==ctr_thickness && ctr_thickness>0)))
assert(thick_OK, str("thickness is invalid or too small for teeth; thickness must be larger than ",abs(ctr_thickness)))
thickness-ctr_thickness
: is_def(bottom)?
assert(is_finite(bottom) && bottom-pitchoff>minbacking,
str("bottom is invalid or too small for teeth, must exceed ",minbacking+pitchoff))
bottom-pitchoff
: ctr_thickness>face_width/2 ? 0
: -ctr_thickness+face_width/2,
cpz = (topz + botz - backing) / 2,
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]
],
]
],
flat_top_faces = [
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]
]
],
backing_vert = backing==0? []
: !cone_backing ? down(backing,[for(i=[0:1:teeth-1]) each( [bot_verts[i*face_pts], bot_verts[(i+1)*face_pts-1]])])
: let(
factor = tan(pitch_angle-90)*backing
)
[for(i=[0:1:teeth-1]) let(
A = bot_verts[i*face_pts],
B = bot_verts[(i+1)*face_pts-1],
adjA = point3d(factor*unit(point2d(A)),-backing),
adjB = point3d(factor*unit(point2d(B)),-backing)
)
each [ A+adjA, B+adjB]],
shift = len(bot_verts),
backing_bot_faces = backing==0? flat_top_faces
:[for (i=idx(backing_vert))
[shift+len(backing_vert), shift+(i+1)%len(backing_vert),shift+i]
],
backing_side_faces = backing==0 ? []
: [
for (i=[0:1:teeth-1])
each [
[shift+2*i,shift+(2*i+1),(i+1)*face_pts-1],
[shift+2*i+1,shift+2*((i+1)%teeth), ((i+1)%teeth)*face_pts],
[(i+1)*face_pts-1, i*face_pts, shift+2*i],
[((i+1)%teeth)*face_pts, (i+1)*face_pts-1, shift+2*i+1]
]
],
vnf1 = vnf_join([
[
[each top_verts, [0,0,top_verts[0].z]],
top_faces
concat(teeth_top_faces, flat_top_faces)
],
[
[each bot_verts, [0,0,bot_verts[0].z]],
[for (x=top_faces) reverse(x)]
[each bot_verts,each backing_vert, [0,0,bot_verts[0].z-backing] ],
[for (x=concat(teeth_top_faces,backing_bot_faces,backing_side_faces)) reverse(x)]
],
sides_vnf
]),
lvnf = left_handed? vnf1 : xflip(p=vnf1),
vnf = down(cpz, p=lvnf),
lvnf = right_handed? vnf1 : xflip(p=vnf1),
vnf = zrot(gear_spin,down(cpz, p=lvnf)),
anchors = [
named_anchor("pitchbase", [0,0,pitchoff-thickness/2]),
named_anchor("flattop", [0,0,thickness/2]),
named_anchor("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);
named_anchor("pitchbase", [0,0,pitchoff-ctr_thickness/2+backing/2]),
named_anchor("flattop", [0,0,ctr_thickness/2+backing/2]),
named_anchor("apex", [0,0,hyp_ang_to_opp(pitch_angle<90?ocone_rad:icone_rad,90-pitch_angle)+pitchoff-ctr_thickness/2+backing/2])
],
final_vnf = reorient(anchor,spin,orient, vnf=vnf, extent=true, anchors=anchors, p=vnf)
)
_return_anchors==false ? final_vnf
: [final_vnf, anchors, ctr_thickness+backing];
module bevel_gear(
circ_pitch,
teeth,
face_width = 10,
pitch_angle = 45,
mate_teeth,
shaft_angle=90,
bottom,backing,thickness,cone_backing=true,
face_width = 10,
shaft_diam = 0,
pressure_angle = 20,
clearance = undef,
backlash = 0.0,
cutter_radius = 30,
spiral_angle = 35,
left_handed = false,
spiral = 35,
right_handed = false,
slices = 5,
internal,
interior,
pitch,
diam_pitch,
circ_pitch,
mod,
anchor = "pitchbase",
spin = 0,
gear_spin=0,
orient = UP
) {
dummy = !is_undef(interior) ? echo("In bevel_gear(), the argument 'interior=' has been deprecated, and may be removed in the future. Please use 'internal=' instead."):0;
internal = first_defined([internal,interior,false]);
circ_pitch = _inherit_gear_pitch("bevel_gear()",pitch, circ_pitch, diam_pitch, mod);
PA = _inherit_gear_pa(pressure_angle);
spiral_angle = _inherit_gear_helical(spiral_angle, invert=!internal);
spiral = _inherit_gear_helical(spiral);
face_width = _inherit_gear_thickness(face_width);
slices = cutter_radius==0? 1 : slices;
pitch_angle = is_undef(mate_teeth)? pitch_angle : atan(teeth/mate_teeth);
pitch_angle = atan(sin(shaft_angle)/((mate_teeth/teeth)+cos(shaft_angle)));
pr = pitch_radius(circ_pitch, teeth);
ipr = pr - face_width*sin(pitch_angle);
rr = _root_radius(circ_pitch, teeth, clearance, internal);
rr = _root_radius(circ_pitch, teeth, clearance);
pitchoff = (pr-rr) * sin(pitch_angle);
vnf = bevel_gear(
vnf_anchors = bevel_gear(
circ_pitch = circ_pitch,
teeth = teeth,
mate_teeth = mate_teeth,
shaft_angle=shaft_angle,
bottom=bottom,thickness=thickness,backing=backing,cone_backing=cone_backing,
face_width = face_width,
pitch_angle = pitch_angle,
pressure_angle = PA,
clearance = clearance,
backlash = backlash,
cutter_radius = cutter_radius,
spiral_angle = spiral_angle,
left_handed = left_handed,
spiral = spiral,
right_handed = right_handed,
slices = slices,
internal = internal,
anchor=CENTER
anchor=CENTER,
gear_spin=gear_spin,
_return_anchors=true
);
axis_zs = [for (p=vnf[0]) if(norm(point2d(p)) < EPSILON) p.z];
thickness = max(axis_zs) - min(axis_zs);
anchors = [
named_anchor("pitchbase", [0,0,pitchoff-thickness/2]),
named_anchor("flattop", [0,0,thickness/2]),
named_anchor("apex", [0,0,adj_ang_to_opp(pr,90-pitch_angle)+pitchoff-thickness/2])
];
default_tag("remove",internal) {
attachable(anchor,spin,orient, r1=pr, r2=ipr, h=thickness, anchors=anchors) {
difference() {
vnf_polyhedron(vnf, convexity=teeth/2);
if (shaft_diam > 0) {
cylinder(h=2*thickness+1, r=shaft_diam/2, center=true, $fn=max(12,segs(shaft_diam/2)));
}
}
children();
vnf=vnf_anchors[0];
anchors=vnf_anchors[1];
thickness = vnf_anchors[2];
attachable(anchor,spin,orient, vnf=vnf, extent=true, anchors=anchors) {
difference() {
vnf_polyhedron(vnf, convexity=teeth/2);
if (shaft_diam > 0)
cylinder(h=2*thickness, r=shaft_diam/2, center=true, $fn=max(12,segs(shaft_diam/2)));
}
children();
}
}
@ -3742,7 +3812,7 @@ function _base_radius(circ_pitch, teeth, pressure_angle=20, helical=0, diam_pitc
// }
// #bevel_gear(
// pitch=5, teeth=t1, mate_teeth=t2,
// spiral_angle=0, cutter_radius=1000,
// spiral=0, cutter_radius=1000,
// slices=12, anchor="apex", orient=BACK
// );

4
rounding.scad
View file

@ -851,6 +851,7 @@ function _path_join(paths,joint,k=0.5,i=0,result=[],relocate=true,closed=false)
d_next = is_vector(joint[i]) ? joint[i][1] : joint[i]
)
assert(d_first>=0 && d_next>=0, str("Joint value negative when adding path ",i+1))
assert(d_first<path_length(revresult),str("Path ",i," is too short for specified cut distance ",d_first))
assert(d_next<path_length(nextpath), str("Path ",i+1," is too short for specified cut distance ",d_next))
let(
@ -861,7 +862,8 @@ function _path_join(paths,joint,k=0.5,i=0,result=[],relocate=true,closed=false)
let(
first_dir=firstcut[2],
next_dir=nextcut[2],
corner = line_intersection([firstcut[0], firstcut[0]-first_dir], [nextcut[0], nextcut[0]-next_dir],RAY,RAY)
corner = approx(firstcut[0],nextcut[0]) ? firstcut[0]
: line_intersection([firstcut[0], firstcut[0]-first_dir], [nextcut[0], nextcut[0]-next_dir],RAY,RAY)
)
assert(is_def(corner), str("Curve directions at cut points don't intersect in a corner when ",
loop?"closing the path":str("adding path ",i+1)))

4
shapes3d.scad
View file

@ -3352,7 +3352,7 @@ module fillet(l=1.0, r, ang=90, overlap=0.01, d, length, h, height, anchor=CENTE
// data = This is either the 2D rectangular array of heights, or a function literal that takes X and Y arguments.
// size = The [X,Y] size of the surface to create. If given as a scalar, use it for both X and Y sizes. Default: `[100,100]`
// bottom = The Z coordinate for the bottom of the heightfield object to create. Any heights lower than this will be truncated to very slightly above this height. Default: -20
// maxz = The maximum height to model. Truncates anything taller to this height. Default: 99
// maxz = The maximum height to model. Truncates anything taller to this height. Set to INF for no truncation. Default: 100
// xrange = A range of values to iterate X over when calculating a surface from a function literal. Default: [-1 : 0.01 : 1]
// yrange = A range of values to iterate Y over when calculating a surface from a function literal. Default: [-1 : 0.01 : 1]
// style = The style of subdividing the quads into faces. Valid options are "default", "alt", and "quincunx". Default: "default"
@ -3420,7 +3420,7 @@ function heightfield(data, size=[100,100], bottom=-20, maxz=100, xrange=[-1:0.04
for (x = [0:1:xcnt-1]) [
size.x * (x/(xcnt-1)-0.5),
size.y * (y/(ycnt-1)-0.5),
data[y][x]
min(data[y][x],maxz)
]
]
] : [