Here are the videos:

With a still camera trike1

With a moving camera trike2

If you have trouble playing the videos, you might
try downloading the free VLC Media Player.

And here is their explanation:

Summary and Simplified Explanation for the Trike Demo

The only factor that matters in the direction of the 
initial movement is the sign (±) of the initial 
acceleration.  The amount of force used (as long as it 
is in the positive direction, for the purposes of our 
demo, forward) and the amount of frictional force from 
the ground have no consequence for our demo.  The only 
factors that matter are the magnitude of the radius of 
the wheel and the magnitude of the radius of the pedal. 
We find this out from the equation four from the site 

http://www.amherst.edu/~physicsqanda/Trikeans.htm 

which reads as follows:

 a = FR(R - r)/(I + mRČ )   

where F stands for the force being applied to the 
pedal, R is the radius of the wheel, I is the moment 
of inertia for the wheel, which is a constant, and r 
is the radius of the pedal.  Since the radius for 
neither the wheel nor the pedal can ever be negative, 
and neither can the mass or inertia, the only governing 
factor of whether or not the trike will move forward is 
if the radius of the wheel is larger than the radius of 
the pedals.  Since the radius of the pedals can never 
be larger than the radius of the wheel on a working 
trike/bike, it will always move forward.  You can try 
this demo with any bicycle or tricycle, and all you 
have to do is make sure that it will not turn, and 
follow the steps shown in the video clips.



Comment added by GBA:  I would say that what 
matters is whether or not the frictional force
is larger than the pushing force.  The analysis
at the Amherst site shows that, as long as the
pedal radius is shorter than the wheel radius,
the frictional force will always be less than
the pushing force, hence the sum of the 
horizontal forces will be forward.  (The
surprising fact is that, if the pedal radius is
larger than the wheel radius, the frictional
force will be larger than the pushing force.)
So, as Jim and Sterling wrote, the pedal radius 
is the controlling factor, but from my 
perspective what it controls is the size of the 
frictional force at the ground.