Cycloidal Bicycle Gear

CAD..

http://www.gearsolutions.com/article/detail/5674/animated-cad-solutions-for-gear-mechanism-design

Cool software....

http://www.camnetics.com/gearteq/index.htm

Here is a design calculator...

http://www.csparks.com/watchmaking/CycloidalGears/CycloidCalculator.html

Cool video...

http://www.youtube.com/watch?v=U6LSrtudfMA

???

On the bicycles I have seen, the pedal sprockets are all larger than the wheel sprockets. This is a speed increase, rather than decrease.

I was wondering about efficiency of cycloidal gearing, which remind me of a chain & sprocket that slips, without the benefit of the simple roller bearing, contained in a chain

here's an interesting little comparison between involute & cycloidal gearing

I know in practice that it's very hard to beat the efficiency of a chain & sprocket

any kind of gears require the added weight of a housing & the additional friction of seals to keep the lubrication in & the dirt out

it will be very difficult to beat a planetary set up for overall performance & price

Also, there are multi speed hubs coming out of Taiwan, the old British company of Sturmey-archer has moved there, look here:-

http://www.sheldonbrown.com/sturmey-archer.html

Or here:-

http://en.wikipedia.org/wiki/Hub_gear

There is a lot of competion around!!!

May I suggest you buy some and take them apart, thats not illegal.....