Involutes An involute is the locus of a point on a line as the line rolls along a shape It can also be thought of as the locus of the end of a piece of string as the string is wound/unwound around the circumference of a plane figure

Applications of Involutes Involutes are used to determine the length of belts used in pulleys and other machines Involutes are also used to calculate the amount of material required to create tyres and wheels

Involute of a Square

C B A B A C B D A A

Involute of a Triangle

B A B C A A

Involute of a Hexagon

A A B B C C D D A B C D E C E B F B A A A

Involute of a Circle

9 8 8 10 7 7 9 6 6 8 7 5 6 5 7 5 4 4 4 6 11 3 3 2 3 5 2 10 4 1 9 6 5 3 2 1 4 1 2 8 1 3 7 1 2 6 2 3 5 1 4 4 1 5 2 3 1 2 3 1 2 1 1 2 3 4 5 6 7 8 9 10 11 12 4 1 2 3

Making Involute models http://www.math.nmsu.edu/~breakingaway/Lessons/involute1/involute.html

Tangents to Involutes

Tangents to Involutes Normal Tangent Involutes are curves, and as with all curves a tangent can be drawn to the involute

Tangent to an involute at point P

Normal Tangent

Tangent to an involute at point P

Normal Tangent