Boundary formed by trochoids of different parameters.

Mathematica Notebook for This Page.



Trochoid describe a family of curves. (See: Curve Family Index) Trochoid is defined as the trace of a point fixed on a circle that rolls along a line. Sometimes the name trochoid is used to mean hypotrochoid and epitrochoid. (curve traced by rolling circle on another circle) More generally, trochoid is any curve that is the locus of a point fixed to a curve A, while A rolls on another curve B without slipping.

trochoid trochoidGen
Trochoid Tracing. r:=1, h:={.5, 1, 2.5}.


Let the radius of the rolling circle be r and the distance from the tracing point Q to the center of the circle be h.


Special Cases

Cyloid (blue), extended cycloid (green), contracted cycloid (red).
trochoid trochoidRadialVar
This animation shows the trochoid with parameters r:=1 and h increase from 0 to 3. The radial of the curve is also ploted as black dots. When r==h, it is a cycloid and its radial is a circle.

Related Web Sites

See: Websites on Plane Curves, Printed References On Plane Curves.

Robert Yates: Curves and Their Properties.

Graphing Calculator