Parametric oscillation holds the key to working Bessler's wheel.

Second clue.

A swing has its centre of gravity below the pivot, unlike a perfectly balanced wheel whose centre of gravity lies at its axle or pivot.

With a child standing on the swing's seat,  the centre of gravity is lower and is closer the seat.  If the child bends his legs he lowers the centre of gravity even more and if he straightens them he raises it again.  If he rocks the swing a little he can make it move back and forth a greater distance by timing the straightening and bending of his legs

But the swing moves to and fro whereas we seek a solution in which the swing moves only in one direction, around and around the pivot. There is a sport known as ‘Kiiking’ in the native language of Estonia where it is practised as a national sport.  In kiiking the ropes are rigid steel bars, enabling the swinger to build up his swings until he passes over the top of the pivot - his feet are of course attached to the seat.

Yes, I know, another elementary clue, and yet a vital ingredient in making Bessler's wheel work.

JC

No wheels exist in nature.

Throughout history, most inventions were inspired by the natural world. The idea for the pitchfork and table fork came from forked sticks; the aeroplane from gliding birds. But the wheel is a one hundred percent homo sapien innovation. As Michael LaBarbera—a professor of biology and anatomy at the University of Chicago—wrote in a 1983 issue of  "The American Naturalist", 'only bacterial flagella, dung beetles and tumbleweeds come close. And even they are “wheeled organisms” in the loosest use of the term, since they use rolling as a form of locomotion'.

Thanks to the Smithsonian, there's a lot more there. -

http://www.smithsonianmag.com/science-nature/A-Salute-to-the-Wheel.html

The Ouroboros is an ancient symbol depicting a serpent or dragon eating its own tail.  There is an ongoing hoax about the hoop snake which is supposed to exhibit similar propensities.  It is reputed to be able form itself into a hoop and roll after its prey at speeds up to 60 miles an hour! They can alter their shapes as they go, and even roll up hill.  This reminds me of Fletcher's post on the besslerwheel forum about suggesting to Bessler that he tried out that idea with his own wheel to see if it would roll uphill.

JC

To enable a gravity-wheel to rotate.

First clue.

To make the gravity-wheel react to gravity you need to create an overbalanced situation.

You can do that on a clockwise rotating wheel, by placing each weight further outwards at some point between twelve o'clock and six o'clock, and closer in, between six o'clock and twelve o'clock.

To make the wheel continue to overbalance you need to bring the weight which is further out, back in again, at or close to six o'clock.  Then you have to make it move out again, between twelve o'clock and six 'clock. Elementary my dear Watson.

JC

Bessler's wheels, out-of-balance and set to spin spontaneously.

There's been some talk about whether Bessler's wheel was out of balance and if it was balanced when stationary.  It seems obvious to me that because the first two one-way wheels began to spin spontaneously as soon as the brake was released it must have been out of balance while stationary and it was only the brake or lock or ties which held it motionless. 

I ignore suggestions that the wheel was stopped at an opportune moment so that at that point it was out-of-balance.  It would be too difficult to arrange for those who tested it to stop it at that particular spot - if there was one.  And anyway many people commented on the evenness of its rotation and any unevenness would indicate flat spots and high spots which would be suitable for stopping in an unbalanced position.

If you suspend an object from any point, let go of it and allow it to come to rest, the centre of gravity will lie along a vertical line that passes through the point of suspension. The centre of gravity will generally lie below the suspension point.

So if we wish to make the overbalanced wheel continue to turn, then we have to find a way of raising that point which generally lies below the suspension point. 

JC