EPICYCLOID
Compute, Plot, and Tabulate an Epicycloid Curve

EPICYCLOID is a MATLAB library which computes, plots and tabulates an epicycloid curve.

An epicycloid is the curve traced by a point on the perimeter of a circle of radius r1 which is rolling around the perimeter of a a circle of radius r2. Normally, r1 is smaller than r2.

The equations for the (x,y) coordinates of the point are:

        x(t) = (r1+r2) * cos(t) - r1 * cos ( (r1+r2)*t/r1 )
        y(t) = (r1+r2) * sin(t) - r1 * sin ( (r1+r2)*t/r2 )

It is usual to write k = r2/r1. If k is an integer, then the curve is closed, and has k cusps. If k is rational, and in lowest terms is p/q, then it has p cusps. Otherwise, if k is irrational, then mathematically the curve is not closed, and fills the annulus of radiuses r2 and r2+r1.

To use the programs, you specify:

k, the ratio r2/r1,
s, the number of times the small circle should roll around the big one
n, the number of points to compute.

Licensing:

The computer code and data files made available on this web page are distributed under the GNU LGPL license.

Languages:

EPICYCLOID is available in a MATLAB version.

Related Data and Programs:

epicycloid_test

Source Code:

epicycloid_plot.m, plots points along an epicycloid.
epicycloid_rt.m, computes (r,t) points along an epicycloid.
epicycloid_xy.m, computes XY points along an epicycloid.
r8vec2_print_some.m, prints "some" of an R8VEC2.
r8vec2_write.m, writes an R8VEC2 file.
timestamp.m, prints the current YMDHMS date as a time stamp.

Last modified on 09 January 2019.

EPICYCLOID Compute, Plot, and Tabulate an Epicycloid Curve

Licensing:

Languages:

Related Data and Programs:

Source Code:

EPICYCLOID
Compute, Plot, and Tabulate an Epicycloid Curve