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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

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.

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

ω=π

, we get a planar hypotrochoid or epitrochoid, respectively.

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