Written by u.hornstein
Program to draw animated graphs of cycloids, epicycloids and hypocycloids.
Programm zum animierten Zeichnen von Zykloiden, Epizykloiden und Hypozykloiden.
General info on cycloids can easily be found in Wikipedia:
This program was originally quickly written for my nephew
Joel Krause. We studied the mechanism of high and low tides of the
oceans. One of the factors is the centrifugal force of the earth
while rotating around an axis which is not going through the earth's
center. This program can be used to show the movement of the center of the earth
(or moon) when looking at the earth-moon system.
"Cycloids.opo" can calculate and display these routes, and many more, but not to scale, and only one at a time.
This picture, taken from the German Wikipedia, shows the meaning
of the variable lambda as used in Cycloids.opo:
Some sample epicycloid outputs, computed and animated by Cycloids.opo:
The dots are equi-distant in time, i. e. closely set dots mean slow speed.
The above mentioned path of the center of the earth looks about like this (bumps
grossly enlarged compared to the reality, sun in the center):
The looks of hypocycloids are left for you to discover.
The program is published including source code. Just put the
Cycloids.opo file in any folder of your choice and run it (mark
it and press enter).
Thanks to U.
Krinzner for his free workshop on Sprite programming. The use
of sprites was a nice exercise for me: I could not only draw the
cycloids, but also the motion of the moving circle.
Be sure to know the Disclaimer, valid for all of my software.
Executable on Psion machines (ER5) like Psion 5, 5mx, 5mxPro, Ericsson MC218, Netbook. Tested on MC218 only.Download Cycloids.zip (Version 1.01 with source code) Downloads: 825 (since 19.4.2008)
relevant terms: epicycle, cycloid, epicycloid, hypocycloid, epitrochoid, cardioid, spirograph, Zykloid, Epizykloid, Hypozykloid, Psion.