Why my friends wheel system won't reinforce itself

[AK1984]

I had a friend share an idea with me, and i said it was wrong, but he wouldn't believe me, mostly because I'm a layman and couldn't give more evidence than 'if it was that easy someone would've thought of it', or 'it's too close to perpetual motion which is impossible'.

The idea is you have a wheel system, (two wheels, one big one small, connected by a chain running around the outside, similar to a bicycle gear system) For simplicity say 1 turn of the big wheel causes 2 turns of the smaller wheel. That's fine, correct? Now he says suppose the smaller wheel has a rod connecting it's center to the center of another big wheel positioned right beside it. That big wheel is in turn connected by chain to another small wheel, which is positioned back next to the original wheel, also having a rod connecting its center to the original big wheel, creating a loop. My friend says since 1 turn of the first wheel causes 2 turns of the second, which should turn the big wheel its connected to by a rod through their centers 2 turns as well. Now 2 turns of this big wheel would turn the second small wheel 4 turns. That's all fine, right? But he says that last wheel will turn the original wheel 4 times as well, causing the next wheel to turn 8 times, and so forth etc. He says it just keeps turning on itself, in some sort of positive feedback system.

I tell him that's too close to perpetual motion, but he wants an actual answer why it wouldn't work, which i couldn't really give on my own.

 

[rcgldr]

The wheels won't turn. To make this simpler, imagine the first two wheels each have a sprocket and the sprockets are connected by a chain. Unless the smaller wheel's sprocket size is 1/2 the larger wheels sprocket size, the inner and outer chains interfere with each other and prevent any movement.

 

[schroder]

It can’t work. Suppose the original big wheel is turning at 1 rpm, then the small wheel it is geared to will be turning at 2 rpm. The second big wheel is on the same shaft as the small wheel, so it is also turning at 2 rpm. Now that second big wheel is geared to drive the last small wheel at 4 rpm. But your friend thinks that last small wheel can be on the same shaft as the original wheel that is turning at only one rpm! There cannot be two different angular velocities on the same shaft so nothing will turn; it will be locked up. It is sort of like having hinges on both sides of a door and trying to open it.

But your friend should not feel bad as there are still some people on this forum, including “physics mentors” who believe a wind-powered cart can go directly down wind faster than the wind that is powering it, based upon the same type of “logic” and “gearing”!