Escapement-Based Movements as Positioning Mechanisms: Design and Modelling

This work has been triggered by an industrial project targeting the design of a mechatronic injector for the medical field. Injections are usually performed using a syringe, a quite clumsy tool that transforms the injection task in a positioning one. The quality of injections can be enhanced by using devices that help control the injected dose, or the injection rate, but usually at the cost of a slower operation, a reduced manoeuvrability, or a short battery life for electrically-powered devices. The idea was therefore to provide a cordless miniaturised injector capable of managing the dosage as well as injection rate according to the user's desires, with the constraint that it should have a long battery life. This is why escapementbased movements are investigated in this work. Such stepper movements, where a regulator controls the speed at which a stock of mechanical energy is emptied, have been used for centuries in clockwork. Purely mechanical devices, the regulators are designed to work at a given frequency, with the stability of said frequency as the main objective. For the discussed application, the use of an electronic regulator permits variable injection rates and simplifies dosage control. Beingmostly used in clockwork, escapement-based movements are hardly mentioned, let alone studied, outside this field in the literature. This research is aimed at filling this void to provide engineers with the basics for the design of escapement-based movements, using Pahl & Beitz's design methodology. First of all, a general structure of suchmovements is proposed. Using functional analysis, a canvas for the requirements specification of a movement is given. To ensure an efficient and fast evaluation of the quality of a solution at any stage of the development, modelling and design tools are suggested. The industrial project is then used as a case study that exemplifies the concepts introduced. The requirements, a selected functioning principle, and the main technical solutions are described. The application of the modelling tools is done in two parts, representing two subsystems designed concurrently but separately: the purely mechanical part of the movement that includes the escapement, and the mechatronic regulator. The dynamic and energetic performances of both subsystems are modelled, using relevant techniques. Analytical models characterise the mechanical part of the system, using advantageously the stepper nature of the system. Because they are analytical, the models require very limited computational resources and are thus extremely convenient design tools. They also permit a stochastic study of the influence of manufacturing tolerances on said performance. Regulators, in particular electronically-controlled ones, are then discussed. An optimisation strategy for highly constrained problems is proposed. It consists in first optimising a set of input parameters towards acceptable values for the constraints. Once one or more sets of parameters re