Spherical Trochoid

radius of rolling circle as fractionof radius of fixed circle

2.5

distance of the generating pointfom the center of rolling circle

0.75

inclination of rolling circle plane

90°

roll the circle and trace the trochoid

5.

viewpoint

default

top

front

show sphere

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

is the angle between the planes of the base circle and the rolling circle.

For a spherical hypotrochoid,

ω<π/2

, and for a spherical epitrochoid,

ω>π/2

.

In the extreme cases,

ω=0

or

ω=π

, we get a planar hypotrochoid or epitrochoid, respectively.