The watchmaking crisis of the nineteen-seventies in effect marked an interruption of scientific research into the working of mechanical watches. For the past few years, a revival of interest in these timepieces has given industrialists the financial resources needed to improve the performance of existing systems and create new mechanisms. The escapement is the only subsystem of a watch movement which combines an energy transfer function with a direct mechanical action on the oscillating weight : its role here is therefore fundamental. This thesis describes a design approach leading up to the development of an escapement mechanism which satisfies the requirements of the movement suppliers as effectively as possible ; this procedure is based on four phases : formulation, synthesis, analysis and evaluation. Analysis is divided into a quantitative part and a qualitative part. While the state of the art essentially centres on calculation of the performance of a particular escapement, this thesis highlights on the one hand a synthesis-based method which systematically presents the different solutions that may be adopted to make a free escapement ; and on the other, the development of qualitative analysis tools enabling a choice of interesting solutions to be made among the numerous variants which emerge from the synthesis. With regard to the state of the art, the main contributions of this thesis are: an in-depth study of the different sources of interference with the precision of a mechanical watch movement, as well as the potential for improvement of the escapement, the definition of a functional specification for free escapements, the notion of the geometrical function condition and a clear demonstration of the importance of analysis of tolerances, a method of quantitative energy analysis for free escapements, a qualitative analysis of energy transfer in an escapement, the latter being demonstrated by two interacting masses moving on an axis ; the relationship between the efficiency of an escapement and its inertia as well as the quality factor of the oscillator is established, a synthesis approach based on the breakdown of functions, enabling original escapements to be proposed, the systematic search for new escapements with tangential pulses, a nomenclature of free escapements, energy and chronometric study of alternative methods for the transfer of energy to the oscillator.