Studies of perpetual overbalanced wheels

In folio 473r of the Codex Atlanticus, also dating back to 1490, one can see how Leonardo was progressively moving the study of perpetual motion to an increasingly abstract level: hydraulic motors and operating machines disappeared from the illustrations to be replaced by geometric schemes or plans of articulated wheels.11 Leonardo appears to focus more and more on the search for kinematics that allow to unbalance the wheel: the moving masses are only imagined and on paper only the structure of the wheel is illustrated, together with a limited number of specific configurations of the device, as if they were visual aids for the system’s conception. In this sheet, Leonardo takes into consideration for the first time the idea of replacing the articulated arms with spherical masses that, due to gravity, move along asymmetrical paths designed to unbalance the system. He develops two types of wheel intended to create either a “radial unbalance” or a “peripheral unbalance,” depending on the path taken by the sphere: from the centre towards the periphery or along the circumference. In these studies Leonardo retrieved a model of a wheel with asymmetrical spokes, derived from the Indo-Islamic tradition and based on the displacement of mercury in cavities in the spokes. Leonardo replaces the mercury with a sphere which, thanks to the rotation of the system, while descending falls towards the circumference only to be pushed towards the centre while ascending. The continued rotation was thought possible because the convex path of the sphere in the descending phase caused it to fall towards the circular edge, hitting it.
These projects represent an attempt to find a synthesis between the two traditional systems of imbalance, respectively with oscillating masses and displacement of mercury, which can be linked to the Arab tradition and even to the earlier Indian tradition, in the work of the 12th-century astronomer Bhāskara.