Cycloid animation: Shape diversity of Trochoids and Cycloids

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

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

Hypotrochoid (or with cusps Hypocycloid)

Peritrochoid (or 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
Qunatity of
self-intersecting points
Qunatity of
points of inflection
Special case

x
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
 
 

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=