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How do I calculate the curve generated by a point on the rim of a rolling wheel, with...

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How do I calculate the curve generated by a point on the rim of a rolling wheel, with radius r? What are three examples of cycloids and inverted cycloids in life around you?

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The curve generated by a point on the rim of a rolling wheel is called a cycloid. The equation of a cycloid generated by a wheel of radius r is determined by two points:

`x=r(theta-sintheta)`

`y=r(1-costheta)`     

Where `theta` is the angle in radians through which the rolling circle is rotated.

Cycloids are used to form the outlines of teeth of certain gears used in machine design. It has also been used for architectural arches.

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