Modèle du solide indéformable

Le modèle du solide indéformable est un modèle de solide fréquemment utilisé en mécanique des systèmes de points matériels. Il s'agit d'une idéalisation de la notion usuelle de corps (à l'état) solide, considéré comme absolument rigide, et négligeant toute déformation. Première approche Le solide indéformable est un modèle utilisé en mécanique pour décrire le comportement d'un corps (objet, pièce). Comme son nom l'indique, on considère qu'au cours du temps la distance entre deux points donnés ne varie pas. Cela signifie que l'on néglige les phénomènes de déformation élastique et a fortiori plastique, et que le solide ne présente pas de rupture. Ce modèle est très utilisé en cinématique et en dynamique, où il constitue la base de l'étude des mouvements du solide. Par rapport au modèle du point matériel, il permet de prendre en compte la rotation propre de l'objet par rapport au référentiel. Principe d'équiprojectivité des vitesses Une des principales conséque

Stability of Equilibria for the so(4) Free Rigid Body

Tudor Ratiu, Murat Turhan

The stability for all generic equilibria of the Lie-Poisson dynamics of the so(4) rigid body dynamics is completely determined. It is shown that for the generalized rigid body certain Cartan subalgebras (called of coordinate type) of so(n) are equilibrium points for the rigid body dynamics. In the case of so(4) there are three coordinate type Cartan subalgebras whose intersection with a regular adjoint orbit gives three Weyl group orbits of equilibria. These coordinate type Cartan subalgebras are the analogues of the three axes of equilibria for the classical rigid body in so(3). In addition to these coordinate type Cartan equilibria there are others that come in curves.

2012

Design, analysis, testing and applications of two-body and three-body kinematic mounts

Johannes Richard Cornelis Geerit Kruis

Kinematic couplings are used when two rigid bodies need to be repeatedly and accurately positioned with respect to each other. They allow for sub-micron positioning repeatability by suppressing play and reducing strains in the bodies. Typical applications are lens mounts, work piece mounts and docking interfaces for astrophysics, semiconductor and metrology applications. This thesis generalizes the well-known concept of two-body kinematic couplings to three-body kinematic mounts. The goal of the thesis is: To pave the way for high precision assembly using kinematic mounts by providing an exhaustive catalogue of all twobody and three-body kinematic mounts and to test key configurations experimentally. The main contributions of this thesis are: - State of the art survey of essential knowledge in the field of kinematic couplings. - Rigorous problem statement for the design of two-body and three-body kinematic mounts. - Rigorous limitation of the scope of research to three-body kinematic mounts whose contact points lie exclusively on three convergent orthogonal lines and whose constraint lines are parallel to these lines. - An exhaustive catalogue of three-body kinematic mounts consisting of seven configurations in 3D and nine configurations in 2D. - An exhaustive set of four conditions satisfied by three-body 3-dimensional kinematic mounts. - An exhaustive set of seven conditions satisfied by three-body 2-dimensional kinematic mounts. - Realization of a two-body kinematic mount and a three-body kinematic mount in metal, and precise measurement of their positioning accuracy on a 3D coordinate measurement machine at the Swiss Federal Institute of Metrology. Positioning error of 0.2 microns and 5 microradian achieved with two-body kinematic mounts. Positioning error of 1 micron and 50 microradian achieved with three-body kinematic mounts. - Realization of three-body kinematic mounts in Silicon by Deep Reactive Ion Etching processes (DRIE) and experimental measurement of their positioning error. - Physical implementation of nesting forces and assembly methods allowing for the physical construction of kinematic mounts. - Physical realizations in robotics, optics and aerospace using our new kinematic mounts.

EPFL2016

Etude des propriétés morphologiques et catalytiques d'agrégats d'or triés en taille et déposés sur le TiO2(110)

Raphaël Vallotton

This thesis aims to find, for the first time, a direct relation between the size and morphology of small metallic nanostructures (gold in this case) supported on a metal-oxide surface to their catalytic activity. In this perspective, three main topics have been treated during this thesis. The first part concerns the design and realization of a Scanning Tunneling Microscope (STM) supposed to work over a wide temperature range (4K < T ≤ 300K). This new device replaces an existing solution. The coarse approach of the scanning tip towards the sample is realized by an axial motor based on a sapphire prism gliding on shear piezos in the stick&slip mode. The new STM is very rigid moving the resonance frequencies to higher values with respect to the existing solution. Operation of the motor down to T = 8K has been proven, however topographic imaging has been performed only in the temperature range 77K < T ≤ 300K. The second part of this work focuses on a study of the evolution of the morphology of gold nanoparticles on a TiO2(110) surface. Size-selected clusters Aun+ (n = 5, 7) are deposited at a well defined kinetic energy on the surface held at room temperature. Subsequent annealing of the sample has been performed stepwise. After each temperature increase, the morphology has been determined by STM. The evolution as a function of surface temperature has been studied for two different surface reconstructions, TiO2(110)-(1×1) and TiO2(110)-(2×1). The deposition process leads only to small fragmentation and the morphology is stable up to T = 400K. Further increase of the surface temperature leads to sintering of the particles by Ostwald ripening as shown by an exponential decrease of the island density with temperature. The main topic of this thesis, the correlation between morphology and catalytic activity, is described in the last part of this manuscript. For the first time we are able to relate the onset of CO2 production from CO and O2 to a clear change in the morphology. The catalytic activity of the particles strongly depends on their size and dimensionality. The relative activity per particle has been determined and we find a clear maximum for clusters containing 60 atoms and are 3 to 4 monolayers high. These results are discussed in contrast of literature data on the same but also on different metal-oxide surfaces.

EPFL2009