A Mechanical Paradox

"Make four wheels, one wheel as thick as the other three. Cut teeth in all the wheels. Put the thin wheels in one axis. Set the thick wheel to them so that its teeth may take into those of the three thin ones. Turn the thick wheel. One of the thin wheels turns one way, one the other and the third no way at all."

How can this be possible?

This "paradox" was invented by James Ferguson, and apparently used in a disagreement with an atheist clockmaker to prove the existence of God!

If he (Ferguson) could make a device to meet the criteria, then the clockmaker would believe that God existed. At least that's the story. I came across it for the first time while browsing in the BHI library, and made a working copy of the machine when I returned home.

Work it out for yourself!

or Click here for the solution.

Ferguson used the principle to make an orrery, which I have copied. Click here for pictures.