Cycloids and Trochoids

This page is a sub-page of our page on Plane Curves.

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Related KMR-pages:

The Brachistochrone (= The curve of quickest descent)
The Tautochrone (= The curve of equal descent)

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Other relevant sources of information:

Cycloids at Wikipedia
Trochoids at Wikipedia
Trochoids at Wolfram MathWorld
Epicycloids at Wikipedia
Epitrochoids at Wikipedia
Hypocycloids at Wikipedia
Hypotrochoids at Wikipedia
History of the Cycloid at Wikipedia
• The mathematics of the Epicycloid – A historical journey with a modern perspective
Cycloidal curves
Trochoidal Wave
Deferents and epicycles at Wikipedia

Joe Freedman’s Amazing Cycloid Drawing Machine

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The interactive simulations on this page can be navigated with the Free Viewer
of the Graphing Calculator.

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Cycloids and Trochoids

Cycloid and Trochoid – orbits:

The interactive simulation that generated this movie.
Drag the blue point at the bottom horizontally to change the Trochoid.

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Cycloid-Evolute:

The interactive simulation that created this movie.

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CycloidEvolute – Involutes:

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The interactive simulation that will create this movie.

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Epicycloids and Hypocycloids

An interactive simulation of Epicycloids and Hypocycloids.
Drag the blue point horizontally to change between epicycloid (= the blue point to the left of the green point) and hypocycloid (= the blue point to the right of the green point).
The horizontal position of the green point controls the radius of the moving circle.

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Epicycloid:

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The interactive simulation that created this movie.

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Hypocycloid:

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The interactive simulation that will create this movie.

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Epitrochoid Flash Animation (Sergio Flores Morales on YouTube):

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Luxor hypotrochoids alternative take (C ormullion on YouTube):

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