OLD DOMINION UNIVERSITY COLLEGE OF SCIENCES DEPARTMENT OF MATHEMATICS AND STATISTICS

TROCHOIDS

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A trochoid is obtained by following a point on the spoke of a wheel as the wheel rolls in a straight line without slipping .

Consider a circle of radius R as it rolls in a straight line. Tracing the point A , which is a distance less than R along the spoke, produces a curtate cycloid.

Tracing the point B, which is exactly a distance R along the spoke, produces a cycloid.

Tracing the point C, which is a distance greater than R along the spoke, produces a prolate cycloid.

HYPOCYCLOIDS

Following the motion of a point P on a spoke of a circle of radius b, as it rolls without slipping on the inside of a second circle of radius a>b, produces a curve which is called a hypocycloid.

EPICYCLOIDS

Following the motion of a point P on a spoke of a circle of radius b, as it rolls without slipping on the outside of a second circle of radius a>b, produces a curve which is called a epicycloid.

Gear teeth are frequently made to conform to the cycloid shape so that there is more of a rolling rather than sliding contact when the gears mesh.

Polyhedra

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