In Reply To:
What your ideal MMF proposes is
a perpetual motion machine. At least I know I have one supporter on my side in this debate,
the US Patent office.
Simply show me a mechanism by which the energy of the different parts of the bicycle, when totaled up, remain constant while this bicycle is "coasting" along such that it would continue to coast forever. I will allow you to have frictionless bearings, joints, and chains. But, everything else must be real material with mass.
The difference between this problem and the "double pendulum" problem someone else presented is the double pendulum was simply converting potential energy into kinetic energy. In the MMF case there is a need to convert kinetic energy into kinetic energy through a fixed mechanism to keep the total energy constant. Good luck.
There are only two reasons why such a "perpetual motion cyclist" could not exist in reality are:
1) friction, and
2) the fact the ankle joint is flexible, not fixed.
You've already stated that you are willing to allow for a completely frictionless (i.e., lossless) environment - if you are willing to fix the ankle then badabing, badaboom! problem solved.