General mechanical engineering - General kinematics

The need for a science specifically concerned with the study of movements, independently of the causes that produce them, was keenly felt in the early 18th century. The aim was to explain the movement of increasingly complex machines by breaking them down into sub-assemblies, in other words, to create a theory of mechanisms. The creation of the École Polytechnique in 1794 marked the birth of this new discipline. In 1808, Lanz and Bétancourt published Essai sur la composition des machines and, in 1813, Lazare Carnot La géométrie du mouvement. But the decisive impetus came from Ampère, who, after an in-depth critique, published the manifesto of the new science:

"It is to this science, in which movements are considered in themselves as we observe them in the bodies that surround us and especially in the devices called machines, that I have given the name kinematics (from $\mathrm{\chi \tau }\nu ϵ\mathrm{\mu \alpha }$ , movement)" (Essay on the Philosophy of Science, 1830).

It wasn't long before the mathematical foundations were laid. In fact, some results were already available. Here are a few of the most important:

• Descartes (1596-1650): instantaneous center of rotation (CIR) in plane motion ;

• Euler (1707-1783): motion around a fixed point, plane motion, Euler-Sarary construction;

• D'Alembert (1717-1783): motion around a fixed point (infinitesimal displacement);

• Jean Bernoulli (1667-1748): instantaneous center of rotation (CIR) for plane motion ;

• Cauchy (1789-1857): rolling curve in plane motion (Descartes had found that the CIR was the point of contact);

• Chasles (1793-1880): the most general motion is helical;

• Poinsot (1777-1859): representation of motion around a fixed point;

• Ampère (1775-1836): creation of the word kinematics ;

• Coriolis (1792-1843): composition of accelerations.

Since then, kinematics has been divided into pure kinematics and applied kinematics. Today, pure kinematics, or simply kinematics, is the study of motion independently of material supports. While there have been important contributions since the last century, the main body of theory was already established.

Following in the footsteps of other authors (in particular R. Bricard, M. Cazin, J.L. Destouches), we wanted to give a highly structured formulation that would allow a great economy of thought,...