The main problem with "overbalanced" wheel designs in general is "keeling." That is the tendency of an allegedly overbalanced wheel to become "bottom heavy," or to "keel" like a ship in the sea. Once any wheel has keeled, it requires a net input of energy to keep it going.
you can use keeling at your advantage and provide a mechanism that will remove a weight at an offset of the wheel natural balance (Bottom heavy). That will cause the wheel to keel again. You would repeat the process until you have no weights to remove. The problem now, would be to put back the weight on the opposite side of where you removed it.
When faced with a new or interesting wheel idea, it is often advantageous to perform a quick torque analysis. To do so, first draw a vertical line down the middle of the design through the wheel's axle. Then measure the distance from each weight horizontally to the center line. Finally, compare the sum of the distances of weights on the right side of the center line to the sum of the distances of the weights on the left side of the center line. Often, you will find that the proposed design is actually turning the wrong way, which means that the idea was probably pushed just past the point of keeling by its author's imagination.
A trade in speed will then become the problem, suppose you have a greater amount of weight on one side of the wheel (the side where the weights are nearer to the axle); you want that side to lift, but the density of weight on that side is equal to the other side. Ingenious mechanism must be provided to change the speed of those lifting weights to overcome the equal density or balance of the wheel. You are left with the same problem as before, no turning wheel.
However, inventors normally put too much moving parts in those wheel ideas, too much weights. A working wheel, must be or may be able to work with only two weights, one near the axle and one farther on the other side. The way it would work, would be to combine keeling and weight distance from the axle to provide lifting advantage. The speed of those weights will change relative to their distance from the axle, you need to lift the weight again on top of the wheel at 12, so overbalance alone will not work.
(Courtesy of Jim_Mich)
One way to calculate leverage on a lever that has forces in different directions is to envision the lever as two pulleys rotating around the fulcum point. Extend the force lines until they are at right angles to the fulcrum point. Then calculate the distance from each force line to the fulcrum point. Knowledge of trigonometry helps. These distances represent the imaginary pulley diameters. The ratio between the two diameters is the ratio of the two forces on the lever.
Summary of Bucket Wheels : Observations & Conclusions about OOB Wheels
(Courtesy of Fletcher)
A Class One 'Out Of Balance' [OOB] wheel shifts weights around the wheel with the use of levers, springs etc. It also incorporates methods of shifting weights radially around the circumference in preference to in or out movement.
Class One wheels start in a naturally balanced position [symmetrical weight division left & right of the vertical line down thru the axle] & by shifting a weight closer to the axle or further from it, it is intended to create an OOB condition which will cause keeling [torque production], forcing the wheel to rotate to find its balanced position & hopefully back to an unbalanced position again. This is the most common type of wheel design.
Class One wheels 'trade width for height' & in the process of repositioning weights & resultant keeling, the wheels CoG is lowered & moved sideways. While this causes initial rotation it is not self sustaining because of normal & well known system energy losses.
N.B. The CoG always finds its lowest position or position of least potential energy [least PE] which is the natural order of things.
Class Two OOB wheels attempt to have weights repositioned within the wheel without the CoG being lowered in the process. The Bucket & Float mech is an example of a Class Two Wheel.
Weights are also repositioned but the special counter weight mech has a compensatory effect so that the CoG always remains at the same level. It does not drop & does not reach its position of least potential [it's already there & stays there]. The water bucket acts like a vertical spring & is not affected by back torque usually associated with 'hard' repositioning systems. The internal self contained mech is no better in reality than a free standing separate cam wheel or journal & could be replaced by one.
While this looks to be an improvement on Class One wheels, normal system losses stop it from self sustaining also, so, even a CoG that does not drop as it cycles is still of no practical advantage or importance.
Class Three OOB wheels, in order to self sustain, must lift the CoG to above the axle, at least temporarily for part of the cycle. This must come about from the dynamics of motion to temporarily make the wheel top heavy so that in its new unbalanced state it wants to keel. As it moves to find its keel position its CoG is again lifted above the axle, unbalancing the wheel in a continuous alternating fashion.
Many would describe this action as "Boot Strapping" i.e. the ability to lift oneself by hauling on your own boot laces, & accordingly it is generally dismissed outright as a physical impossibility. While that premis may be true for static conditions it may not hold true for all dynamic conditions. For example, a mechanism within a wheel swinging or rotating [under movement relative to the wheel] & using the objects inertia to create Centripetal / Centrifugal Forces [CF], as a childs top lifting its own CoG while spinning shows. Another well known dynamic force that requires velocity to generate is the non conservative force of Aerodynamic Lift.