Mechanisms such as those used in space applications, robotics, micro-electromechanical systems or watchmaking must meet strict environmental specifications related to thermal exchanges, electromagnetic exchanges, radiation resistance, vacuum compatibility, vibrations and shock tolerance, gravity, and forces and moments exchanges, etc. Within this broad list, this thesis focuses on the reaction forces and moments exported by mechanisms onto their supporting structures, as well as on the effects of the fictitious forces arising when they are embarked on non-inertial (accelerating) reference frames. Fictitious forces (also known as inertial or pseudo forces) are generally categorized as centrifugal forces, Coriolis forces, Euler forces, and translational inertial forces. This thesis addresses mechanism balancing, which is the design approach intended to reduce the forces exported by mechanisms onto their environment and to reduce the effect of the fictitious forces onto the mechanisms.

After a broad introduction to the topic of mechanism balancing and various fields of applications with a particular focus on horology, a state-of-the-art review presents historical and modern techniques for mitigating the effects of external perturbations on mechanical oscillators and the methods for adjusting their stiffness and inertial properties to tune their eigenfrequencies and balancing defects. Most of the existing literature focuses on balance-spring oscillators, leaving a significant gap in the application of frequency tuning and balancing principles to other types of oscillators. This motivates the need for new methods tailored to new oscillator designs.

Three conceptual chapters written as standalone scientific articles introduce a novel exhaustive taxonomy of mechanism balancing types. This classification is composed of four primary balancing types and their combinations, resulting in a total of 15 balancing types. The taxonomy rigorously states the definitions, conditions, and properties of each main balancing type and illustrates each category with a representative elementary 1-DOF mechanism. This taxonomy is consolidated by a theoretical demonstration using a Lagrangian approach studying inertial couplings of a generic n-DOF mechanism mounted on a 6-DOF platform. The proposed theoretical framework is applied to practical applications in horology by analyzing a selection of existing clock and watch oscillators.

Two technical chapters use the proposed framework for the design of new 1- and 2-DOF dynamically balanced flexure-based horological oscillators, respectively named Wattone and Wattwins. The study of these two mechanisms covers their ideal kinematics as well as their flexure implementation and uses a pseudo-rigid-body model (PRBM) along with the Lagrangian formalism to derive its equations of motion describing the oscillator's behavior (especially sag and eigenfrequencies) under gravity and angular perturbations. The analytical and numerical predictions are validated via experimental measurements made on two centimeter-scale titanium prototypes. Key contributions include new protocols for measuring force and dynamic balancing defects and new tuning methods for eigenfrequency adjustment and balancing.

Through its conceptual contributions and their practical use for the design of novel balanced oscillators, this thesis aims at setting a comprehensive reference in the field of mechanism balancing.