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
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
})

// Calculate operating pressure angle
angles = map(rs, (r) => {
  return toDegrees(  acos(baseDiameter / 2 / r))
})

// Calculate the involute function
invas = map(angles, (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])
})

// Extrude the gear body
body = startSketchOn('XY')
  |> 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)
}

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({
       axis = [0, 0, 1],
       center = [0, 0, 0],
       instances = nTeeth,
       arcDegrees = 360,
       rotateDuplicates = true
     }, %)

// Define the constants of the keyway and the bore hole
keywayWidth = 0.250
keywayDepth = keywayWidth / 2
holeDiam = 2
holeRadius = 1
startAngle = asin(keywayWidth / 2 / holeRadius)

// Sketch the keyway and center hole and extrude
keyWay = startSketchOn(body, 'END')
  |> startProfileAt([
       holeRadius * cos(startAngle),
       holeRadius * sin(startAngle)
     ], %)
  |> xLine(keywayDepth, %)
  |> yLine(-keywayWidth, %)
  |> xLine(-keywayDepth, %)
  |> arc({
       angleEnd = 180,
       angleStart = -1 * 180 / pi() * startAngle + 360,
       radius = holeRadius
     }, %)
  |> arc({
       angleEnd = 180 / pi() * startAngle,
       angleStart = 180,
       radius = holeRadius
     }, %)
  |> close(%)
  |> extrude(-gearHeight, %)