Fixed failed rendering of gear.

involute_gears.scad

@@ -26,6 +26,7 @@
 
 
 use <transforms.scad>
+use <math.scad>
 include <constants.scad>
 
 
@@ -147,40 +148,56 @@ function base_radius(mm_per_tooth=5, number_of_teeth=11, pressure_angle=28)
 // interior = If true, create a mask for difference()ing from something else.
 // Example(2D):
 // gear_tooth_profile(mm_per_tooth=5, number_of_teeth=20, pressure_angle=20);
-module gear_tooth_profile(
+function _gear_polar(r,theta) = r*[sin(theta), cos(theta)]; //convert polar to cartesian coordinates
+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_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
+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_tooth_profile(
  mm_per_tooth = 3, //this is the "circular pitch", the circumference of the pitch circle divided by the number of teeth
  number_of_teeth = 11, //total number of teeth around the entire perimeter
  pressure_angle = 28, //Controls how straight or bulged the tooth sides are. In degrees.
  backlash = 0.0, //gap between two meshing teeth, in the direction along the circumference of the pitch circle
  bevelang = 0.0, //Gear face angle for bevelled gears.
  clearance = undef, //gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters)
  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
-
- 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])
- translate([0,-r,0])
- polygon(
+) = let(
+ 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 = -_gear_iang(b, p) - t/2/p/PI*180, //angle to where involute meets base circle on each side of tooth
+ mat = matrix3_scale([1,1/cos(bevelang), 1]) * matrix3_translate([0,-r,0]),
  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),
+ _gear_polar(r, -181/number_of_teeth),
+ _gear_polar(r, r<b ? k : -180/number_of_teeth),
+ _gear_q7(0/5,r,b,c,k, 1), _gear_q7(1/5,r,b,c,k, 1), _gear_q7(2/5,r,b,c,k, 1), _gear_q7(3/5,r,b,c,k, 1), _gear_q7(4/5,r,b,c,k, 1), _gear_q7(5/5,r,b,c,k, 1),
+ _gear_q7(5/5,r,b,c,k,-1), _gear_q7(4/5,r,b,c,k,-1), _gear_q7(3/5,r,b,c,k,-1), _gear_q7(2/5,r,b,c,k,-1), _gear_q7(1/5,r,b,c,k,-1), _gear_q7(0/5,r,b,c,k,-1),
+ _gear_polar(r, r<b ? -k : 180/number_of_teeth),
+ _gear_polar(r, 181/number_of_teeth),
  ]
+ ) matrix3_apply(points, [mat]);
+
+
+module gear_tooth_profile(
+ mm_per_tooth = 3, //this is the "circular pitch", the circumference of the pitch circle divided by the number of teeth
+ number_of_teeth = 11, //total number of teeth around the entire perimeter
+ pressure_angle = 28, //Controls how straight or bulged the tooth sides are. In degrees.
+ backlash = 0.0, //gap between two meshing teeth, in the direction along the circumference of the pitch circle
+ bevelang = 0.0, //Gear face angle for bevelled gears.
+ clearance = undef, //gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters)
+ interior = false
+) {
+ path = gear_tooth_profile(
+ mm_per_tooth = mm_per_tooth,
+ number_of_teeth = number_of_teeth,
+ pressure_angle = pressure_angle,
+ backlash = backlash,
+ bevelang = bevelang,
+ clearance = clearance,
+ interior = interior
  );
+ polygon(path);
 }
 
 
@@ -205,6 +222,37 @@ module gear_tooth_profile(
 // gear2d(mm_per_tooth=5, number_of_teeth=20, pressure_angle=20);
 // Example(2D): Partial Gear
 // gear2d(mm_per_tooth=5, number_of_teeth=20, teeth_to_hide=15, pressure_angle=20);
+function gear2d(
+ mm_per_tooth = 3, //this is the "circular pitch", the circumference of the pitch circle divided by the number of teeth
+ number_of_teeth = 11, //total number of teeth around the entire perimeter
+ teeth_to_hide = 0, //number of teeth to delete to make this only a fraction of a circle
+ pressure_angle = 28, //Controls how straight or bulged the tooth sides are. In degrees.
+ clearance = undef, //gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters)
+ backlash = 0.0, //gap between two meshing teeth, in the direction along the circumference of the pitch circle
+ bevelang = 0.0,
+ interior = false
+) = let(
+ r = root_radius(mm_per_tooth, number_of_teeth, clearance, interior),
+ ang = 360/number_of_teeth/2,
+ pts = [
+ for (i = [0:1:number_of_teeth-teeth_to_hide-1] ) let(
+ mat = matrix3_zrot(-i*360/number_of_teeth) * matrix3_translate([0,r,0])
+ ) each matrix3_apply(
+ 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
+ ), [mat]
+ ),
+ if (teeth_to_hide>0) [0,0]
+ ]
+ ) pts;
+
+
 module gear2d(
  mm_per_tooth = 3, //this is the "circular pitch", the circumference of the pitch circle divided by the number of teeth
  number_of_teeth = 11, //total number of teeth around the entire perimeter
@@ -215,30 +263,17 @@ module gear2d(
  bevelang = 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: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)]
- ]);
- }
- }
- }
+ path = 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
+ );
+ polygon(path);
 }