private void CalculatePoints()
{
// Unrotated tooth tip is on the X axis
ToothTip = Involutes.CreatePt(PitchCircleDiameter / 2, 0);
// Navigate down the slope of the tooth face
FaceEnd = Involutes.CreatePt(
PitchCircleDiameter / 2 - ToothFaceLength * Math.Cos(UndercutAngle),
-ToothFaceLength * Math.Sin(UndercutAngle));
// Now find the centre of the undercut circle
UnderCutCentre = Involutes.CreatePt
(FaceEnd.X - CutDiameter * Math.Sin(UndercutAngle) / 2,
FaceEnd.Y + CutDiameter * Math.Cos(UndercutAngle) / 2);
// Find the coordinates of the back tip corner of
// the next tooth in an anticlockwise direction
BackTip = Involutes.CreatePt(ToothTip.X * Math.Cos(GapAngle),
ToothTip.X * Math.Sin(GapAngle));
// Find the coordinates of the tangent to the
// undercut circle of a line drawn from the
// back of the tooth tip
double tipToEndAngle =
Math.Asin(CutDiameter / (2 * Involutes.DistanceBetween(BackTip, UnderCutCentre)));
double tiptoCtrAngle =
Math.Atan2(BackTip.Y - UnderCutCentre.Y, BackTip.X - UnderCutCentre.X);
BackAngle =
tiptoCtrAngle + Math.PI / 2 - tipToEndAngle;
OneToothProfile = ComputeOnePitch();
}
private void CalculatePoints()
{
List <PointF> points = new List <PointF>();
double innerRadius = InnerDiameter / 2;
double cutterRadius = CutDiameter / 2;
// Calculate the cutter centre for the tooth
// of the ratchet gear at the innermost end
double m = -ToothDepth / (innerRadius * ToothAngle);
double xs = Math.Sqrt(cutterRadius * cutterRadius / (1 + m * m));
double ys = m * xs;
PointF cutterCentre = Involutes.CreatePt(innerRadius + xs, ys);
// Find the start angle and the end angle for the curve. The curve starts
// at the X axis and heads towards negative Y. The end angle is where the
// curve becomes tangential to a radial from the centre of the ratchet.
// If the cutter centre lies outside the pitch circle, then the ratchet
// will not be able to have a tooth at right angles to the direction
// of rotation, and the ratchet is able to skip teeth under high torque.
// Nonetheless, we calculate the tooth shape and return a warning.
double radiusOfCutterCentre = Involutes.DistanceBetween(PointF.Empty, cutterCentre);
double cutterCentreAngle = Math.Asin(-ys / radiusOfCutterCentre);
double tangentAngle = cutterCentreAngle
+ Math.Asin(cutterRadius / radiusOfCutterCentre);
double endAngle = Math.PI - Math.Atan2(-ys, xs);
double startAngle = 3 * Math.PI / 2 - tangentAngle;
points.Add(Involutes.RotateAboutOrigin
(-ToothAngle, PointAtAngle(ToothAngle - tangentAngle)));
// Add the points for the cutter curve
points.AddRange(Involutes.CirclePoints
(endAngle, startAngle, Involutes.AngleStep, cutterRadius, cutterCentre)
.Reverse());
// Check that the radius of the cutter was not too great to
// provide a latch at right angles to the radial from the centre
// of the ratchet.
double actualInnerRadius = Involutes.DistanceBetween(PointF.Empty, cutterCentre) - cutterRadius;
double actualOuterRadius = Involutes.DistanceBetween(PointF.Empty, points[0]);
if (Involutes.DistanceBetween(PointF.Empty, points[1]) > actualOuterRadius)
{
Information += "Cutter diameter too great for locking ratchet. Setting it to zero.\r\n";
CutDiameter = 0;
CalculatePoints();
return;
}
// Now add the slope
for (double angle = 0; angle < ToothAngle - tangentAngle; angle += Involutes.AngleStep)
{
points.Add(PointAtAngle(angle));
}
OneToothProfile = Involutes.LinearReduction(points, (float)MaxError);
Information += $"Actual inner diameter: {2 * actualInnerRadius:N2}, "
+ $"actual outer diameter: {2 * actualOuterRadius:N2}\r\n";
}
