Leonardo da Vinci and Perpetual Motion

The oldest description of a perpetual-motion machine dates from 7th-century India. The mathematician Brahmagupta, who wanted to represent the cyclical and eternal motion of the heavens, designed an overbalanced wheel whose rotation was powered by the flow of mercury inside its hollow spokes. In the 12th century, another Indian mathematician, Bhāskara, altered the wheel design by giving the hollow spokes a curved shape, producing an asymmetrical course in constant imbalance. 

The oldest European reference to a perpetual-motion machine is a drawing of an overbalanced wheel—clearly influenced by Arab models—in the notebook of Villard de Honnecourt, a 13th-century architect from Picardy. Another document shares the same geographic provenance: in his study on the lodestone, the 13th-century scientist Pierre de Maricourt presents a curious perpetual wheel powered by “magnetic induction.” 

The manuscripts by 15th-century Italian engineers show their attempts to apply the concept of perpetual motion to operating machines. 

The young Leonardo was fascinated by the drawings of recirculation mills that he discovered in manuscripts by other engineers, and he studied the subject thoroughly. He imagined basins that would be filled with water by automatic means.

In the first half of the 1490s, Leonardo abandoned the notion of recirculation mills and began to study wheels overbalanced by mechanical means (with moving or oscillating spheres) or hydraulic means (systems using Archimedes’ screws to raise and lower water). He designed several versions and probably also built models. However, he concluded his studies by rejecting the possibility of perpetual motion. Identifying gravity and attrition as the forces that made it impossible, he compared perpetual motion to the alchemists’ quest for the transmutation of metals.

In folio 1062 recto (ca. 1497-1500) of the Codex Atlanticus, Leonardo presents the various mechanical wheels that he had studied thus far, featuring oscillating arms and running balls. 

By the mid-1490s, Leonardo concluded that perpetual motion was impossible, but he continued to explore the possibility of building rotating systems capable of remaining in motion. Of particular interest are his studies on Archimedes’ screws. He designed and modified them in an attempt to harness the flow of water to create the imbalance needed to keep the screws turning. This would allow their use as motors to power operating machines.

On the verso of folio 1062 of the Codex Atlanticus, Leonardo describes a model that differs from his other studies in his attention to materials. It is an overbalanced motor with two cylinders, and two pistons connected by a hydraulic circuit moving between them. In the drawing, the wheel is fitted with a pair of these systems mounted at right angles to each other. However, Leonardo envisaged fitting four on the same axle, so as to have a cylinder—and thus a motive force—every 30 degrees. Moving downward, the piston pushes the water contained in the system into the other cylinder. This increases the imbalance and so facilitates rotation. The wheel movement is regulated by a verge escapement (foliot).

Apart from passing references in the Dialogue on the Two Major Systems of the World, Galileo did not leave us a systematic examination of perpetual motion, probably because he recognized its impossibility. In his view, only a circular, uniform motion such as that of the planets could be perpetual—and surely not a rectilinear motion, constantly accelerated or slowed. To be in perpetual motion, the object itself would need to be incorruptible and eternal. Both conditions are necessary, but are never concomitant in nature. Galileo’s replies to a few letters describing perpetual-motion machines are lost, but we may assume that he urged his correspondents to search for the real causes of the motion produced by the machines, as he believed no human artifice could violate nature’s laws.

In the early 19th century, the dissemination of steam engines promoted the development of thermodynamics. This new branch of physics did not prove the non-existence of perpetual motion, but posited it as an axiom to deduce that an engine’s efficiency could never reach 100%. Some of the energy powering a thermo-mechanical system is inevitably dissipated. Later, as the atomic processes underlying motion and heat were understood, and with the statistical definition of the concept of irreversibility of natural phenomena, the question of perpetual motion was finally answered. While perpetual motion is not impossible in theory, it is extremely improbable. In fact, it is more likely that a monkey typing at random on a keyboard will write War and Peace than that someone will achieve perpetual motion.