Involute

An Involute is the path traced, or Locus, of the end of a piece of string as it is kept tight and unwrapped from a circle. It produces a curve similar to an Archimedean Spiral but not exactly the same.

The involute is an important curve for the design of gears. Teeth shaped as an involute exhibit ‘true rolling motion’ (i.e. motion without slipping or scrubbing) as the gear teeth engage, which makes for a smooth transition of speed and force between one gear and the next in the gear train.

Drawing an Involute

Draw a generating circle and divide it into a number of sectors (say 12 in this example). Regard the radial dividers as Normals and, from each one, draw Tangents to the circle at right angles to them as shown. Note: These tangents to the circle will become normals to the eventual involute. Along each tangent in turn measure lengths equal to the arc lengths of the sectors uncovered as shown. Sketch a fair curve through the points (or use French Curves or a flexible strip for example)

File:InvoluteCurve.jpg