Spherical Cycloid

radius of rolling circle as fractionof radius of fixed circle

2.5

inclination of rolling circle plane

1.57

roll the circle and trace the cycloid

5.

viewpoint

default

top

front

show base sphere

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

ω

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

ω<π/2

creates a spherical hypocycloid and

ω>π/2

gives a spherical epicycloid.

In the extreme cases of

ω=0

or

ω=π

, we get a planar hypocycloid and epicycloid, respectively.