Analyse Cinétostatique des Machine Parallèles à Translations

摘要

The aim of this thesis is to propose new tools for the design and analysis of translational Parallel Kinematic Machines (PKM), which are translational parallel robotic manipulators aimed at manufacturing. First, an exhaustive state-of-the-art on PKM design is presented, and focuses on structural and geometrical synthesis of translational PKM. A new concept is then proposed: the Regular Dextrous Workspace (RDW). It is a part of the workspace whose shape is regular (cube, cylinder) and the kinetostatic performances (transmission factor, conditioning index) are bounded inside the RDW. Two methods are proposed to determine the RDW : one is based on interval analysis and is numerically reliable, while the other is based on Cartesian workspace discretization, is faster and more intuitive but does not prove the result numerically. The two methods are complementary. Interesting PKM features regarding manufacturing constraints are evaluated thanks to the RDW volume and to the ratio between this volume and the workspace. New performance indices tting translational PKM constraints are then proposed and can help optimising PKM geometry or compare several translational PKM. For instance, we compare several Linear Delta PKM, a 3-UPU based PKM. Few papers deal with PKM comparison, which is one interest of this contribution. Our second major contribution is a method to improve translational PKM stiffness from influence analysis of geometrical parameters that are not related to RDW volume. We use an existing stiffness method that model links flexibility with virtual elastic joints. A major advantage of this method is its genericity: it can be easily adapted to any PKM. We implement this method with MAPLE, i.e. it is a symbolic implementation, which is new. The stiffness matrix of a translational PKM prototype, the Orthoglide (built at IRCCyN), is then computed as a function of the geometrical parameters and the Cartesian coordinates, and one can easily observe each parameter influence. If we had used a Finite Elements Method, it would have taken time to mesh the structure for each Cartesian position. Analysing each parameter influence allows to display the critical links regarding the machine stiffness. Symbolic expressions of stiffness matrix elements can not be visualized as their size can vary up to ten worksheets, therefore a cascade decomposition is proposed to make this vizualisation easier. Then, the Orthoglide stiffness analysis is simultaneously conducted with dynamic analysis in order to study the relationship between dynamic performances and static stiffness performances.