A helical planetary gearset is a type of planetary gear system where the teeth of the sun gear, planet gears, and/or ring gear are helical rather than straight. This design allows for smoother, quieter operation, greater load-carrying capacity, and more flexible shaft alignment.

// Helical Planetary Gearset
// A helical planetary gearset is a type of planetary gear system where the teeth of the sun gear, planet gears, and/or ring gear are helical rather than straight. This design allows for smoother, quieter operation, greater load-carrying capacity, and more flexible shaft alignment.
// Categories: Automotive, Aerospace

// Set units
@settings(defaultLengthUnit = mm)

// Define a function to create a helical gear
fn helicalGear(nTeeth, module, pressureAngle, helixAngle, gearHeight) {
  // Calculate gear parameters
  pitchDiameter = module * nTeeth
  addendum = module
  deddendum = 1.25 * module
  baseDiameter = pitchDiameter * cos(pressureAngle)
  tipDiameter = pitchDiameter + 2 * module

  // Define the constants of the keyway and the bore hole
  keywayWidth = 1
  keywayDepth = keywayWidth / 2
  holeDiam = 7
  holeRadius = holeDiam / 2
  startAngle = asin(keywayWidth / 2 / holeRadius)

  // Sketch the keyway and center hole
  holeWithKeyway = startSketchOn(XY)
    |> startProfile(at = [
         holeRadius * cos(startAngle),
         holeRadius * sin(startAngle)
       ])
    |> xLine(length = keywayDepth)
    |> yLine(length = -keywayWidth)
    |> xLine(length = -keywayDepth)
    |> arc(angleStart = -1 * startAngle + 360deg, angleEnd = 180deg, radius = holeRadius)
    |> arc(angleStart = 180deg, angleEnd = startAngle, radius = holeRadius)
    |> close()

  // Define a function to create a rotated gear sketch on an offset plane
  fn helicalGearSketch(offsetHeight) {
    // Calculate the amount to rotate each planar sketch of the gear given the gear helix angle and total gear height
    helixCalc = acos(offsetHeight * tan(helixAngle) / (tipDiameter / 2))

    // Using the gear parameters, sketch an involute tooth spanning from the base diameter to the tip diameter
    helicalGearSketch = startSketchOn(offsetPlane(XY, offset = offsetHeight))
      |> startProfile(at = polar(angle = helixCalc, length = baseDiameter / 2))
      |> involuteCircular(
           startRadius = baseDiameter / 2,
           endRadius = tipDiameter / 2,
           angle = helixCalc,
           tag = $seg01,
         )
      |> line(endAbsolute = polar(angle = 160deg / nTeeth + helixCalc, length = tipDiameter / 2))
      |> involuteCircular(
           startRadius = baseDiameter / 2,
           endRadius = tipDiameter / 2,
           angle = -(4 * atan(segEndY(seg01) / segEndX(seg01)) - (3 * helixCalc)),
           reverse = true,
         )

      // Position the end line of the sketch at the start of the next tooth
      |> line(endAbsolute = polar(angle = 360deg / nTeeth + helixCalc, length = baseDiameter / 2))

      // Pattern the sketch about the center by the specified number of teeth, then close the sketch
      |> patternCircular2d(
           instances = nTeeth,
           center = [0, 0],
           arcDegrees = 360deg,
           rotateDuplicates = true,
         )
      |> close()
      |> subtract2d(tool = holeWithKeyway)
    return helicalGearSketch
  }

  // Draw a gear sketch on the base plane
  gearSketch001 = helicalGearSketch(offsetHeight = 0)

  // Draw a rotated gear sketch on a middle interstitial plane
  gearSketch002 = helicalGearSketch(offsetHeight = gearHeight / 2)

  // Draw a rotated gear sketch at the gear height offset plane
  gearSketch003 = helicalGearSketch(offsetHeight = gearHeight)

  // Loft each rotated gear sketch together to form a helical gear
  helicalGear = loft([
    gearSketch001,
    gearSketch002,
    gearSketch003
  ])

  return helicalGear
}

// Define a function to create a ring gear
fn ringGear(nTeeth, module, pressureAngle, helixAngle, gearHeight) {
  // Calculate gear parameters
  pitchDiameter = module * nTeeth
  addendum = module
  deddendum = 1.25 * module
  baseDiameter = pitchDiameter * cos(pressureAngle)
  tipDiameter = pitchDiameter + 2 * module

  // Define a function to create a rotated gear sketch on an offset plane
  fn ringGearSketch(offsetHeight) {
    // Calculate the amount to rotate each planar sketch of the gear given the gear helix angle and total gear height
    helixCalc = acos(offsetHeight * tan(helixAngle) / (tipDiameter / 2))

    // Using the gear parameters, sketch an involute tooth spanning from the base diameter to the tip diameter
    ringTeeth = startSketchOn(offsetPlane(XY, offset = offsetHeight))
      |> startProfile(at = polar(angle = helixCalc, length = baseDiameter / 2))
      |> involuteCircular(
           startRadius = baseDiameter / 2,
           endRadius = tipDiameter / 2,
           angle = helixCalc,
           tag = $seg01,
         )
      |> line(endAbsolute = polar(angle = 200deg / nTeeth + helixCalc, length = tipDiameter / 2))
      |> involuteCircular(
           startRadius = baseDiameter / 2,
           endRadius = tipDiameter / 2,
           angle = -(4 * atan(segEndY(seg01) / segEndX(seg01)) - (3 * helixCalc)),
           reverse = true,
         )

      // Position the end line of the sketch at the start of the next tooth
      |> line(endAbsolute = polar(angle = 360 / nTeeth + helixCalc, length = baseDiameter / 2))

      // Pattern the sketch about the center by the specified number of teeth, then close the sketch
      |> patternCircular2d(
           instances = nTeeth,
           center = [0, 0],
           arcDegrees = 360deg,
           rotateDuplicates = true,
         )
      |> close()

    // Create a circular body that is larger than the tip diameter of the gear, then subtract the gear profile from the body
    ringGearSketch = startSketchOn(offsetPlane(XY, offset = offsetHeight))
      |> circle(center = [0, 0], radius = tipDiameter / 1.85)
      |> subtract2d(tool = ringTeeth)
    return ringGearSketch
  }

  // Draw a gear sketch on the base plane
  gearSketch001 = ringGearSketch(offsetHeight = 0)

  // Draw a rotated gear sketch on a middle interstitial plane
  gearSketch002 = ringGearSketch(offsetHeight = gearHeight / 2)

  // Draw a rotated gear sketch at the gear height offset plane
  gearSketch003 = ringGearSketch(offsetHeight = gearHeight)

  // Loft each rotated gear sketch together to form a ring gear
  ringGear = loft([
    gearSketch001,
    gearSketch002,
    gearSketch003
  ])

  return ringGear
}

// Create the outer ring gear for the planetary gearset
ringGear(
  nTeeth = 42,
  module = 1.5,
  pressureAngle = 14deg,
  helixAngle = -25deg,
  gearHeight = 5,
)

// Create a central sun gear using a small helical gear
helicalGear(
  nTeeth = 12,
  module = 1.5,
  pressureAngle = 14deg,
  helixAngle = 25deg,
  gearHeight = 5,
)

// Create the helical planet gears
numPlanetGears = 3
helicalGear(
       nTeeth = 12,
       module = 1.5,
       pressureAngle = 14deg,
       helixAngle = -25deg,
       gearHeight = 5,
     )
  |> translate(y = (12 + 12) / 2 * 1.5 + 2.7)
  |> patternCircular3d(
       instances = numPlanetGears,
       axis = [0, 0, 1],
       center = [0, 0, 0],
       arcDegrees = 360deg,
       rotateDuplicates = false,
     )


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