Perpetual overbalanced wheel with mercury, Siddhānta Śiromani (1101/1200) by BhāskaraMuseo Galileo - Istituto e Museo di Storia della Scienza

Indian and Arab origins

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. 

Perpetual wheel with oscillating masses (1201/1300) by AnonymousMuseo Galileo - Istituto e Museo di Storia della Scienza

The earliest evidence from the Arab world dates from the same period: an anonymous 13th-century manuscript on waterwheels contains drawings and explanations of eight perpetual-motion wheels. The notion of a perpetual-motion machine began to spread in the West in the mid-13th century.

Rota perpetui motus (1301/1400) by Petrus PeregrinusMuseo Galileo - Istituto e Museo di Storia della Scienza

Perpetual motion in the Middle Ages

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.” 

Mechanical overbalanced wheel (1225/1235) by Villard de HonnecourtMuseo Galileo - Istituto e Museo di Storia della Scienza

Medieval evidence is generally scarce, because artisans and engineers did not communicate their knowledge in written form. However, we may reasonably assume that discussions of perpetual motion were common by the mid-14th century, as can be deduced from the works of these two authors, who refer to a debate between master-craftsmen and artisans that had been going on for some time.

Perpetual wheel with articulated arms (1420/1434) by Mariano di Iacopo known as TaccolaMuseo Galileo - Istituto e Museo di Storia della Scienza

The Sienese engineers

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

Perpetual overbalanced wheel (1419/1450) by Mariano di Jacopo known as TaccolaMuseo Galileo - Istituto e Museo di Storia della Scienza

In his De ingeneis, the Sienese Mariano di Jacopo, known as Taccola (1381-ca. 1458), describes the overbalanced wheel with articulated arms depicted by Honnecourt and in Arab manuscripts.

Recirculation mills (1478/1481) by Francesco di Giorgio MartiniMuseo Galileo - Istituto e Museo di Storia della Scienza

He also provides diagrams of overbalanced wheels and of what appears to be a wheel with moving arms and buckets for excavation. Another Sienese engineer, Francesco di Giorgio (1439-1501), explores the topic of a recirculation mill.

Recirculation mill (1465/1470) by Francesco di Giorgio MartiniMuseo Galileo - Istituto e Museo di Storia della Scienza

He draws a hydraulic motor connected to a piston pump or an Archimedes’ screw that was supposed to be powered by the force of the falling water raised by the motor itself.

Perpetual overbalanced wheel (1480) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

Studies by the young Leonardo

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.

Perpetual motion pump (1480/1482) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

Eventually, he imagined full-fledged hydraulic power plants composed of several wheels powered by the millpond fed by the basin into which the water would be conveyed by Archimedes’ screws or pumps driven by the motors themselves.

Study of a self-powered water-lifting machine (1480 circa) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

Leonardo seems to have realized the difficulty of achieving perpetual motion, for he increased the complexity of these machines in an attempt to find the solution that would keep the entire system in motion.

Study of a perpetual wheel with a variable set up (1487/1490) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

Studies on perpetual wheels

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.

Self-propelling perpetual motion hydraulic system (1487/1490) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

Studies of perpetual engines based on the Archimedean screw (1487/1490) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

Studies of perpetual overbalanced wheels (1487/1490) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

Studies for the design of a perpetual wheel (1490) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

Perpetual motion pumping system (1490/1495) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

Studies for the design of a perpetual wheel (1493/1495) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

Folio 1062 recto of Codex Atlanticus and the perpetual wheels in Codex Forster II

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. 

Reflection on the impossibility of perpetual motion (1487/1490) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

He concludes his study by proposing a new perpetual-wheel system, set in motion by balls rolling from one end to the other of two straight channels interconnected to form a continuous course. These models are also reproduced and explained in the Forster II.

Studies of perpetual engines based on the Archimedean screw (1487/1490) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

Further studies on perpetual wheels

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.

Study for the design of an overbalanced wheel (1495 circa) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

Studies for the design of a perpetual wheel with articulated arms (1493/1495) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

Studies for the design of a mechanical perpetual wheel (1497) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

Studies for the design of a mechanical perpetual wheel (1499/1500) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

Model of an hydromechanical perpetual wheel (2019) by After Leonardo da Vinci, Codex Atlanticus, f. 1062v, Concept: Andrea Bernardoni and Alexander Neuwahl, and Construction: Artes Mechanicae, FlorenceMuseo Galileo - Istituto e Museo di Storia della Scienza

A perpetual motor with pistons

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).

Study for the design of an overbalanced wheel (1499/1500) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

A new idea

In the early 1500s, Leonardo’s studies of perpetual motion found a fresh impetus thanks to his experiments on the water element. He saw hydrostatic pressure as an antagonist to gravitational force and thus considered using it to assist the upward movement of the overbalanced wheels, which were immersed in a basin up to their rotation axis.

Analysis of Domenico Balestrieri’s perpetual wheel (1508/1510) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

Studies for the design of a mechanical perpetual wheel (1515) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

Perpetual hydraulic wheel (1513/1514) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

Studies for an Archimedean screw (1513/1514) by Leonardo da VinciMuseo Galileo - Istituto e Museo di Storia della Scienza

Frontespiece of "Dialogo" written by Galileo Galilei (1632) by Galilei, Galileo 1564-1642Museo Galileo - Istituto e Museo di Storia della Scienza

Galileo and perpetual motion

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.

Mechanism for a bell tower clock with verge escapement and foliot (1451/1500) by Unknown, Northern ItalyMuseo Galileo - Istituto e Museo di Storia della Scienza

Between uncertainty and fraud

In the 18th century, views on the feasibility of perpetual motion remained confused. Within the context of the physics developed by Isaac Newton, however, the conviction emerged that—in the real world—the value of a dynamic effect could never be exactly equal to or even greater than its own cause. In other words, a part, however small, of the momentum of a mechanical system is always lost in resistance and attrition. This belief did not stop theorists, who conjectured the possible existence of natural forces of a different type from the three then known: gravitation, electrical force, and magnetic force. Nor did it deter inventors, ever in search of that “tiny something” capable of making their mechanical dreams come true. Most of all, it did not dissuade fraudsters, who, amid the general uncertainty, often established their credibility and obtained subsidies.

“Perpetual motion” clock (1660/1680) by Giuseppe Campani (attr.)Museo Galileo - Istituto e Museo di Storia della Scienza

Perpetual overbalanced wheel with spheres (1724) by Jacob LeupoldMuseo Galileo - Istituto e Museo di Storia della Scienza

Mechanical paradox (1801/1820) by Italian makeMuseo Galileo - Istituto e Museo di Storia della Scienza

Zamboni’s “Perpetual electromotor” and its parts (1851/1900) by Italian makeMuseo Galileo - Istituto e Museo di Storia della Scienza

"Descrizione ed uso dell’elettromotore perpetuo" (1814) by Giuseppe ZamboniMuseo Galileo - Istituto e Museo di Storia della Scienza

New method of impelling machinery without the aid of steam, water, wind, air, or fire (1822) by George LintonMuseo Galileo - Istituto e Museo di Storia della Scienza

On the dynamical theory of heat... (1853) by William ThompsonMuseo Galileo - Istituto e Museo di Storia della Scienza

The end of perpetual motion?

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.

Réflexions sur la puissance motrice du feu... (1824) by Nicolas Léonard Sadi CarnotMuseo Galileo - Istituto e Museo di Storia della Scienza

Vorlesungen über Thermodynamik (1897) by Max PlanckMuseo Galileo - Istituto e Museo di Storia della Scienza

Feynman Physics / The Feynman Lectures on Physics (1975) by Richard P. Feynman, Robert B. Leighton, and Matthew SandsMuseo Galileo - Istituto e Museo di Storia della Scienza

6 versus 9 (2019) by Alberto Fabiani, Artes MechanicaeMuseo Galileo - Istituto e Museo di Storia della Scienza

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