noun
definition
The locus of a point on the circumference of a circle that rolls without slipping on the circumference of another circle.
Examples of epicycloids in a Sentence
Trundles and Pin-Wheels.If a wheel or trundle have cylindrical pins or staves for teeth, the faces of the teeth of a wheel suitable for driving it are described by first tracing external epicycloids, by rolling the pitch-circle of the pin-wheel or trundle on the pitch-circle of the driving-wheel, with the centre of a stave for a tracing-point, and then drawing curves parallel to, and within the epicycloids, at a distance from them equal to the radius of a stave.
Epicycloids are also examples of certain caustics.
In both cases the curves are epicycloids; in the first case the radii of the rolling and the fixed circles are a(2n - I) /4n and a/2n, and in the second, an/(2n+ I) and a/(2n4-I), where a is the radius of the mirror and n the number of reflections.