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Involutes

Involutes. An involute is the locus of a point on a line as the line rolls along a shape It can also be though t 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.

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Involutes

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  1. 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

  2. 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

  3. Involute of a Square

  4. A B C C B D B A A A

  5. Involute of aTriangle

  6. B B C A A A

  7. Involute of a Hexagon

  8. A A B B C C D D A C B D E C E B F B A A A

  9. Involute of a Circle

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

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

  12. Tangents to Involutes

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

  14. Tangent to an involute at point P P

  15. Normal Tangent

  16. Tangent to an involute at point P P

  17. Normal Tangent

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