Bessler found the answer where everyone was looking.

Third clue.

Bessler said in Apologia Poetica, "These foolish ravings of my enemies will be held up to total ridicule by all intelligent people, who, with true understanding, have sought the Mobile in a place no different from that in which I eventually found it."

To paraphrase the above, Bessler said intelligent people had already looked for the solution where he found it.

In hindsight this clue reveals something so astoundingly obvious that I find it hard to believe that no one has independently thought of it - I certainly didn't.  The history of overbalancing wheels shows that the same designs are repeatedly 'discovered' by each person who comes fresh to this subject.

JC

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

A wheel is a circular component that is intended to rotate on an axle. (thanks to wikipedia)

I've moved my half-built mechanisms onto a slightly larger MDF disc as they were protruding from the edge at one point and catching on the supporting frame. I have continued to use the same disc for some time and really it's a bit too small for my design. I find that getting relative sizes right can be a problem.  I have the design on paper but there are often compromises to be made when the actual build begins.  Sometimes parts that ideally work within certain parameters don't always obey my requirements!  Just kidding, actually I did not anticipate just how much range of movement a certain part would be capable of until I built the mechanism, off the supporting structure.  The result is that I need a bigger supporting structure, which is not a problem as I had one prepared for an earlier version.

Despite my fear of my wheels being judged as of inferior quality, I shall post pictures of both failed and/or successful current and future models, should I build any more.

I'm going to post some comments about my theory and perhaps some hints on the design.  I know that as these appear some critics will dismiss them out of hand and others will argue logically against them, but I would like to suggest that until the complete picture or at least more of it becomes available, it might be thought better to refrain from at least completely dismissing them, because I have one or two surprises to post later on which might just convince otherwise.

JC

My last wheel build?

I've been actively persuing the solution to Bessler's wheel for many years but I haven't felt it necessary to publish pictures of the many, many failed models I've made over a number of years.  

To be honest I would be ashamed to put them on public display given the professional-looking models I see other people post.  Mine are made out of pieces of MDF, used and reused over and over again until they are so full of holes I fear that they will fall apart; pieces of mild steel amd aluminium; stiff-nuts so used and reused that they are no longer capable of holding fast; some bolts cross-threaded so I have to clamp them in a pair of pliers and force the nuts round to get them past the crossed threads; weights of various materials, mostly pieces sawn from a mild steel bar, or bunches of steel or lead washers; levers of mild steel only a quarter of an inch wide or thicker pieces of aluminium and also so full of holes that they too are fast approaching their demise. 

The axle is a length of screwed thread with two nuts on it clamping the MDF sheet.  This rests in a couple of plastic fixings meant to hold copper plumbing pipes to the wall, which are screwed onto two upright wooden pillars which in turn are screwed to a base board - it works, don't knock it!

So, do I buy more new material and set to work again building and rebuilding new designs?  Or do I just share what I know and hope that someone else finds something useful in my work and goes on to achieve the success I looked for?

In a way this is an 'aha' moment a small revelation, because if I do share what I know, instead of having to continue to build I can just keep posting my ideas here and let someone else do the work!  No contest!  But I'll just finish this last model.

JC