Analyse, synthèse et création d'échappements horlogers par la théorie des engrenages

In principle, knowledge of watch and clock escapements is acquired through the study of the geometry and operation of numerous realizations, studied patiently one after the other. Knowing the classics, one can hope to construct a new realizations by borrowing components from one or geometry from another. Currently, there is no formal model or systematic approach which permits any other method of learning escapements and creating new ones. The purpose of this thesis is fill this gap by describing a formal model which will provide a systematic approach to escapements. We will not limit ourselves to the study of the geometry and operation of fundamental escapements but will add a formalism which has only been partially used in the past, outlining gear tooth profiles. The operation of proposed escapements will thus be characterized by an abstract geometric shape called the primitive outline. As opposed to visible escapement geometry, primitive outlines differ very little from one escapement to the other, making them an excellent basis for escapement unification. After going from existing geometries to primitive outlines we will reverse course. The method of outlining gear tooth profiles will allow us, based on existing primitive outlines, to construct new escapements. We will push this method to create a new primitive outline which, according to traditional criteria, appears to have unprecedented efficiency.