This animation showcases the shape diversity of trochoids and cycloids, specifically epicycloids, pericycloids, and hypocycloids.

Animation and Variation of a cycloid or a trochoid with interactive sliders

Epitrochoid (or rather with cusps Epicycloid)
A moveable (yellow) wheel runs around a fixed (gray) wheel

Hypotrochoid (or rather with cusps Hypocycloid)

Peritrochoid (or rather with cusps Pericycloid)

Angle of the connecting line between the centers of the revolving and of the stationary wheel as well as the horizontal axis
φ (Phi): 330
Radius of the fixed wheel
rR 4
Radius of the revolving wheel
rG 1
Distance of the point which generates the trochoid to the center of the revolving wheel
a: 1.5
Show zoom and save dialog
Explanation of the table: the first 3 rows shows curtate trochoids
Quantity of
self-intersecting points
Quantity of
inflection points
Special cases
presented graphically

x 0  
x 0 x genäherte Geradführungen
00 x X
x 0 x Spitzen
x 0  
x 0 Mehrfach-Selbstschnittpunkt;
x 0  
Starting angle of the revolving wheel
γ0 (Gamma0): 150
Show zoom and save dialog

Double generation of trochoids

All trochoids can be generated by another alternative pair of wheels:
    This epitrochoid with the transmission ratio i= and the distance a= is identical to the
peritrochoid with the transmission ratio i= and the distance a=