Update gear.kcl

gear/gear.kcl

@@ -1,65 +1,82 @@
-// Gear
+// Spur Gear
 // A rotating machine part having cut teeth or, in the case of a cogwheel, inserted teeth (called cogs), which mesh with another toothed part to transmit torque. Geared devices can change the speed, torque, and direction of a power source. The two elements that define a gear are its circular shape and the teeth that are integrated into its outer edge, which are designed to fit into the teeth of another gear.
 
 
 // Define constants
-gearRadius = 2 
-nTeeth = 8
-width = 2 
+nTeeth = 21
+module = 0.5
+pitchDiameter = module * nTeeth
+pressureAngle = 20
+addendum = module
+deddendum = 1.25 * module
+baseDiameter = pitchDiameter * cos(toRadians(pressureAngle))
+tipDiameter = pitchDiameter + 2 * module
+gearHeight = 3
 
+// Interpolate points along the involute curve
+cmo = int(101)
+rs = map([0..cmo], (i) => {
+  return baseDiameter / 2 + i / cmo * (tipDiameter - baseDiameter) / 2
+})
 
-// Create a function for sketch of a single tooth
-fn tooth = () => {
-  toothSketch = startSketchOn('XY')
-    |> startProfileAt([0, gearRadius], %)
-    |> arc({
-         angleStart: 90,
-         angleEnd: 90 - (180 / pi() * asin(0.7376425 / gearRadius)),
-         radius: gearRadius
-       }, %, $base)
-    |> angledLine({
-         angle: 180 - (180 / pi() * asin(0.7376425 / gearRadius)),
-         length: 0.0001
-       }, %)
-    |> tangentialArc({
-         offset: -70 + 180 / pi() * asin(0.7376425 / gearRadius),
-         radius: 0.389854023
-       }, %, $philly)
-    |> line([-0.329118, 0.904244], %)
-    |> tangentialArcTo([
-         lastSegX(%) - 0.157636,
-         lastSegY(%) + 0.110378
-       ], %, $corner)
-    |> xLineTo(0, %)
-    |> xLineTo(-1 * segEndX(corner), %)
-    |> tangentialArcTo([
-         lastSegX(%) - 0.157636,
-         lastSegY(%) - 0.110378
-       ], %)
-    |> lineTo([-1 * segEndX(philly), segEndY(philly)], %, $tag2)
-    |> tangentialArcTo([-1 * segEndX(base), segEndY(base)], %)
-    |> arc({
-         angleEnd: 90,
-         angleStart: 90 + 180 / pi() * asin(0.7376425 / gearRadius),
-         radius: gearRadius
-       }, %)
-    |> close(%)
-    |> extrude(width, %)
-  return [toothSketch]
-}
+// Calculate operating pressure angle
+as = map(rs, (r) => {
+  return toDegrees(acos(baseDiameter / 2 / r))
+})
+
+// Calculate the involute function
+invas = map(as, (a) => {
+  return tan(toRadians(a)) - toRadians(a)
+})
+
+// Map the involute curve
+xs = map([0..cmo], (i) => {
+  return rs[i] * cos(invas[i])
+})
+
+ys = map([0..cmo], (i) => {
+  return rs[i] * sin(invas[i])
+})
 
-// Create  the body
+// Extrude the gear body
 body = startSketchOn('XY')
-  |> circle({ center: [0, 0], radius: gearRadius }, %)
-  |> extrude(width, %)
+  |> circle({
+       center: [0, 0],
+       radius: baseDiameter / 2
+     }, %)
+  |> extrude(gearHeight, %)
+
+toothAngle = 360 / nTeeth / 1.5
+
+// Plot the involute curve
+fn leftInvolute = (i, sg) => {
+  j = int(100 - i) // iterate backwards
+  return lineTo([xs[j], ys[j]], sg)
+}
 
-// Pattern the teeth around the body
-teeth = tooth()
+fn rightInvolute = (i, sg) => {
+  x = rs[i] * cos(toRadians(-toothAngle + toDegrees(atan(ys[i] / xs[i]))))
+  y = -rs[i] * sin(toRadians(-toothAngle + toDegrees(atan(ys[i] / xs[i]))))
+  return lineTo([x, y], sg)
+}
+
+// Draw gear teeth
+start = startSketchOn('XY')
+  |> startProfileAt([xs[101], ys[101]], %)
+teeth = reduce([0..100], start, leftInvolute)
+  |> arc({
+       angleStart: 0,
+       angleEnd: toothAngle,
+       radius: baseDiameter / 2
+     }, %)
+  |> reduce([1..101], %, rightInvolute)
+  |> close(%)
+  |> extrude(gearHeight, %)
   |> patternCircular3d({
-       arcDegrees: 360,
        axis: [0, 0, 1],
        center: [0, 0, 0],
        instances: nTeeth,
+       arcDegrees: 360,
        rotateDuplicates: true
      }, %)
 
@@ -70,8 +87,8 @@ holeDiam = 2
 holeRadius = 1
 startAngle = asin(keywayWidth / 2 / holeRadius)
 
-// sketch the keyway and center hole and extrude
-sketch001 = startSketchOn(body, 'END')
+// Sketch the keyway and center hole and extrude
+keyWay = startSketchOn(body, 'END')
   |> startProfileAt([
        holeRadius * cos(startAngle),
        holeRadius * sin(startAngle)
@@ -90,4 +107,4 @@ sketch001 = startSketchOn(body, 'END')
        radius: holeRadius
      }, %)
   |> close(%)
-  |> extrude(-width, %)
+  |> extrude(-gearHeight, %)