# Model of an hydromechanical perpetual wheel

The wheel described by Leonardo works thanks to the action of two identical elements rotated at 90 degrees to one another, each consisting of two pistons mounted on opposed cylinders joined together by an S-shaped channel to form a pneumatic circuit filled with water. During the rotation of the system the weight of the pistons makes them move, thus pumping water from one cylinder to the other through long bellows. Leonardo thought that the displacement of the liquid would create a favourable moment for the rotation thanks to the sum of the weight of the piston (placed so as to maximize the moment) with that of the liquid, pumped from the same side. This causes a break in the equilibrium compared to the other side, where there is only the weight of the piston which is also positioned in such a way as to minimize the moment. To prevent the bellows from rotting, Leonardo recommends using wine instead of water. The illustration shows two of these hydromechanical devices arranged perpendicularly to each other, but in the note on the side Leonardo specifies that the wheel can also be made with eight of these modules (sixteen “branches”), which would be at 22.5 degrees. To regulate the rotary motion of the system Leonardo inserts a verge escapement with foliot. A perpetual wheel of the same type appears on folio 74r of Codex Madrid I, where it is classified as “sophistic motion”, i.e. a device that cannot function.
The realization of the model required substantial adaptations with respect to Leonardo’s original design, which presents features not compatible with public display. A first problem concerns the speed with which the machine moves. This model is equipped with a motion regulation system consisting of a verge escapement with foliot, a device requiring low rotation speed in order to work. Consequently, the pneumatic wheel, which transmits motion to the escapement through a pair of gears with a reduction ratio of 1:35, would have a speed in the order of one revolution per hour, a motion virtually imperceptible to visitors. The original scheme was then modified by decoupling the pneumatic wheel from the escapement, so that each of the two systems could operate at the most appropriate speed. Another problem concerns the bellows which, due to their small diameter and the considerable lengthening required by the stroke of the pistons, cannot be made of leather, as is customary. It is therefore necessary to use a thinner elastic membrane, such as an animal gut (latex in the model), supported on the inside by wire wound in a spiral. Again due to display concerns, it was decided not to use fluids: the ducts that, according to Leonardo’s indications, should have contained water are represented by transparent plexiglas elements.