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Epitrochoids and Hypotrochoids

by mattmoses, published

Epitrochoids and Hypotrochoids by mattmoses Apr 26, 2011

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License

Public Domain
Epitrochoids and Hypotrochoids by mattmoses is licensed under the Public Domain license.

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Summary

This is a Public Domain OpenSCAD file with epitrochoids and hypotrochoids.

These shapes are useful for making mechanisms like
Roots Blowers http://www.thingiverse.com/thing:8068
Wankel Engines http://www.thingiverse.com/thing:8069
and Moineau Pumps http://www.thingiverse.com/thing:7958

An EPITROCHOID is a curve traced by a point
fixed at a distance "d"
to the center of a circle of radius "r"
as the circle rolls
outside another circle of radius "R".

An HYPOTROCHOID is a curve traced by a point
fixed at a distance "d"
to the center of a circle of radius "r"
as the circle rolls
inside another circle of radius "R".

An EPICYCLOID is an epitrochoid with d = r.

An HYPOCYCLOID is an hypotrochoid with d = r.

See http://en.wikipedia.org/wiki/Epitrochoid
and http://en.wikipedia.org/wiki/Hypotrochoid

Instructions

Download, open with OpenSCAD, and have fun!

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I just realized something. This is exactly what we need to create cycloidal gears... which would be a much better tooth profile for the Printable Clock project than involute!

http://en.wikipedia.org/wiki/Cycloid_gearhttp://en.wikipedia.org/wiki/C...

This could solve a lot of our current friction issues!

I was just looking at gear generation code. Way useful!

Yes, they're good for Moineau pumps too, though since I didn't have this, I went with a hypocycloid that degenerated into a straight line.

here is an animation of a rolling disk generating a hypotrochoid, using the openscad script:

Awesome, this is exactly the kind of foundational work that comes in really handy.

Thank you!

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