The "Overbalanced Wheel". It was thought that the metal balls on the right side would turn the wheel because of the longer lever arm, but since the left side had more balls than the right side, the torque was balanced and the perpetual movement could not be achieved.
Perpetual motion wheels are invariably cyclic, that is, all motions of the wheel and its parts are repeated exactly during each complete revolution. So if a weight moves to a larger radius once per cycle, it must also be pulled back to the original radius later during the cycle. The work done in changing the radius by a certain amount from large to small is equal and opposite to the work done in changing the radius by the same amount from small to large. We gain no net energy per cycle.