A spring is an elastic object, generally made of steel, used and optimized to store mechanical energy.

In classical mechanics, the ideal spring is adopted for the study of the harmonic oscillator.

The springs appear around the fifteenth century in padlocks and watches. By replacing the weight system that normally operated the clocks with a spring-loaded mechanism, watchmakers were able to make wearable and reliable instruments. In 1559 Taqi al-Din created a spring-loaded astronomical clock.

In 1676 the English physicist Robert Hooke discovered a functional relationship suitable to schematize the action of the spring, ie that the force exerted is proportional to its extension: "Ut tensio, sic vis" which means "as the extension, so the strength" . This relationship goes under the name of Hooke's Law.

Drawing of a spring device in the Madrid Code

In the Madrid I Codex of Leonardo da Vinci, dating back to the end of the fifteenth century, a spring is used as an elastic element. In the Madrid Code, Leonardo designs and studies many mechanisms to obtain different types of motion, often without a specific purpose and only to explore the possibilities of mechanical science. They are studies of simple machines, evolutions or different ways to obtain the development and transmission of motion. Some of these mechanisms are:

  • Molla con trasmissione elicoidale e motore a molla con ingranaggio elicoidale - Codice Madrid I, f. 4r
  • Molla autobloccante - Codice Madrid I, f. 13v
  • Carica a molla progressiva - Codice Madrid I, f. 14r
  • Motore a molla sfasato - Codice Madrid I, f. 16r
  • Motore a molla elicoidale - Codice Madrid I, f. 45r

On the fourth page of the manuscript we find the first system with a motor that uses springs: a spring motor with helical transmission. This mechanism starts from the assumption that a charged spring yields maximum force at the beginning and while it is discharged becomes weaker and weaker. This force is defined by the value of stiffness R, expressed as force / space. The final aim is therefore to make this energy transfer linear and constant.

The particular type of spring designed by Leonardo for this application, is still widely used (for example in shutters, handles and column drills) and is still called "spiral spring of Archimedes", as based on the concept of Archimedes .


The microscopic physical motif for which the spring accumulates potential energy is the stretching of the intermolecular bonds, while its macroscopic behavior is defined for many materials by Hooke's law, which states that the elongation of an elastic body is directly proportional to the force of applied traction. In the same way the contraction is proportional to the compression force.

This applies within the limit of elastic deformation, defined as the maximum force limit applied within which the released elastic body returns to its dimensions preceding the application of force; beyond this limit the atomic bonds break and rearrange, and the spring is permanently deformed. In several materials this limit is not precisely defined and there are deformation phenomena with repeated use (aging): in these cases Hooke's law is not respected.