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)

Geeignete Browser sind

  • Internet Explorer 10 and higher
  • Mozilla Firefox 3.6 and higher
  • Apple Safari 3.2 and higher
  • Google Chrome 14 and higher
  • Opera 11.0 and higher
  • iOS Safari 3.2 and higher
  • Opera Mobile 10.0 and higher
  • Android Browser 2.2 and higher

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
Quantity of
self-intersecting points
Quantity of
points of inflection
Special case

x 0  
x 0 x genäherte Geradführungen
00 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=

User interface explained

Summary of all links of this page:

Additional links:


© Volker Jaekel, May 7th 2018

email address to request bug fixing: