Unwin's Construction

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Unwin's Construction is a way to draw an approximation to an involute gear profile. It is suitable for either hand-drawn technical drawings or for CAD drawings.

Before you start Unwin's Construction, you need the following dimensions:

  • Addendum, a
  • Dedendum, b
  • Pitch Diameter, D
  • Tooth Thickness
  • Fillet Radius at base of tooth
  • Pressure Angle
Gear Circles.svg
  1. Draw the pitch circle, diameter D, about the centre of the gear, O. This is shown in red.
  2. Draw the outside diameter (green) by drawing a circle about O with a radius greater than the pitch circle by the value of the addendum.
  3. Draw the root diameter (light blue) by drawing a circle about O with a radius smaller than the pitch circle by the value of the dedendum.
Unwin's Construction 2.svg
  1. Draw a tangent to the pitch circle (pink).
  2. Draw a line (orange) through the intersection of the tangent with the pitch circle which makes an angle equal to the pressure angle, φ, with the tangent. This line is the line of action
  3. Draw a circle about O which is tangent to the line of action. This is the base circle and is shown in dark blue.
Unwin's Construction 3.svg
  1. Mark point A on the outside circle (green).
  2. On the line colinear with A and O, mark point B on the base circle (dark blue).
  3. Divide the distance AB into 3 equal parts. Mark point C on the line between A and B such that AC is one third of AB.
Unwin's Construction 4.svg
  1. Draw a line from C tangent with the base circle.
  2. Mark the point of tangency, D.
  3. Divide the distance DC in to 4 equal parts, and mark point E such that DE is one quarter of DC.
Unwin's Construction 5.svg
  1. Draw a circle about point E, passing through point C. This is part of the flank of the gear tooth and is shown in orange.
  2. About the point C draw a circle with the radius of the tooth thickness. Where it cuts the pitch circle, mark point F. This point is on the flank of the other side of the tooth.
Unwin's Construction 6.svg
  1. Draw a circle with the radius EC (called the profile radius) about point F. This arc is shown in dark green. Mark point G where it cuts the pitch circle.
  2. Draw in the fillet between the flank and the base circle. (more detail needed)
Unwin's Construction 7.svg
  1. Draw the profile radius, EC, from G. This is the other flank of the tooth.
  2. Add the fillet at the base of the tooth as before. (more detail needed)
Unwin's Construction 8.svg
  1. The tooth is now complete. The outside circle between the two flanks is the top of the tooth.
  2. This can be repeated for each tooth.