# Spherical Trochoid

Spherical Trochoid

This Demonstration simulates the generation of a spherical trochoid by a point attached to a circle rolling without sliding along the edge of another circle (the base circle) on the same sphere (the base sphere).

A spherical cycloid is traced by a point on the rolling circle's edge; a spherical trochoid is drawn by a point attached to the circle at a distance greater than or less than its radius. A spherical trochoid becomes a spherical cycloid if the distance of the generating point to the rolling circle's center is equal to its radius.

ω

For a spherical hypotrochoid, , and for a spherical epitrochoid, .

ω<π/2

ω>π/2

In the extreme cases, or , we get a planar hypotrochoid or epitrochoid, respectively.

ω=0

ω=π