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Involute

From DT Online


Description

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.


Constructions
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)

Involute.png
DT Online Buyers' Guide
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Helix Oxford Maths Set - Tin B43000 Linex Student Saver Bundle Helix Precision Plus Drawing Set A33002 Primary Shape Template Set Linex Circle Template with Tangential Squares Protractor and 45 1mm-36mm Circles 260x130mm Ref LXG1217T Helix National Curriculum Drawing Set Key Stage 3 & 4 Mathematics Geometry Helix 3 Piece Stencil Set / Letters Numbers and Symbols 10mm 20mm 30mm H90100 Linex Universal Architects Template with Room Furniture and Electrical Symbols Tinted Green Ref LXG1259S 3 French Curve Transparent Templates Stencils Helix T30000 Oxford 30-inch Acrylic Edged T-Square