Cycloidal Speed Reducer in OpenSCAD

By request of Syvwlch ( http://www.thingiverse.com/syvwlch ) and WilliamAAdams ( http://www.thingiverse.com/WilliamAAdams ), here is a stand-alone public-domain OpenSCAD cycloidal speed reducer. As with the Wankel Engine and Roots Blower I recently posted, this is intended more as an example of an interesting mechanism than as a practical device. If you want a practical printable speed reducer, you might consider one of the other alternatives like

the worm drives on this Tank http://www.thingiverse.com/thing:8080 or
differential planetary gears http://www.thingiverse.com/thing:7390 or
cascaded spur gears http://www.thingiverse.com/thing:7379 or
this planetary gear reducer http://www.thingiverse.com/thing:8460

There are several cycloidal-type mechanisms already on Thingiverse, such as
http://www.thingiverse.com/thing:3617 and http://www.thingiverse.com/thing:3736

There are also several interesting external sites like:
http://www.zincland.com/hypocycloid/
http://fabricationsofthemind.com/2010/07/09/extruder-design-1-printable-1001-hypocycloidal-gearbox/
https://github.com/triffid/Differential_Hypocycloid
http://reprap.org/wiki/Differential_Hypocycloid
http://en.wikipedia.org/wiki/Gerotor
http://en.wikipedia.org/wiki/Gear_pump

and many many interesting youtube videos such as
http://www.youtube.com/watch?v=bRn1K2XeWVE
http://www.youtube.com/watch?v=3WvPF6uGCq4
http://www.youtube.com/watch?v=CG2sPuqEXBg
http://www.youtube.com/watch?v=AMtyFwMDL7w
http://www.youtube.com/watch?v=h236SP86nnQ

This present script is based on a design by M.F. Hill described in his 1928 patent "Internal Rotor", number 1,682,563:

http://www.google.com/patents/about?id=mdF5AAAAEBAJ&dq=1682563

Note that this design is based on an offset hypocycloid, similar to Figure I in Hill's patent. Most of the contemporary designs appear to be based on an offset epicycloid, more closely resembling Figure V in the patent.

The motivated student can modify the code so it generates epicycloidal-based profiles. Hint: start by making a module ``epitrochoidBandFast(n, r, thickness, r_off)". The motivated student could also probably clean up my train-wreck of code and/or figure out how to do arrays in OpenSCAD.

Note also that these rotors can be used for pumps - see the gifs in the comments for an example.