Synthese topologique et geometrique des manipulateurs paralleles en translation

This thesis presents a contribution to the topological and geometric synthesis of parallel manipulators (PMs). Focus was put on 3-degree-of-freedom (DOF) PMs, and especially on translational PMs (TPMs).; The topology of a manipulator is, in general, the description of the structure of its kinematic chain, i.e. the type of its kinematic pairs and their general arrangement, while its geometry is a set of dimensional and geometric constraints on the relative position and orientation of its kinematic pairs.; This work is aimed at developing topological and geometric synthesis tools in order that TPMs of all topologies and geometries can be generated and evaluated systematically.; The first objective of this thesis is to propose a general topological and geometric synthesis approach allowing of the determination of the topology of a PM according to its manipulator's DOF and its end-effector's (EE) DOF. The second objective is to derive topologies of PMs which generate only translational displacement. The third objective is to develop a reasonable number of kinematic models which can apply to TPMs of all topologies and geometries.; First of all, a literature review was carried out in order to pinpoint key issues concerning the topological and kinematic synthesis of PMs and base our research on the most recent achievements in the related fields. After that, the synthesis problem was studied.; The first problem addressed in this thesis is to identify the particular aspects of spatial manipulator topologies and geometries. To this end, analysis of known spatial manipulator architectures was performed and the terms topology and geometry were redefined in order to take into consideration the structure characteristics proper to spatial manipulators. The analysis also leads to a topological representation with which kinematic chain structure and the mobility can be better characterized. The representation has a graph structure and can be easily adapted for matrix form numerical representation, making it possible for topologies to be generated systematically.; The second problem is to formulate relations between the topology of a. PM and its manipulator's DOF and EE's DOF. To better characterize a manipulator as a mechanism and its EE as a rigid body, appropriate definitions were made on the manipulator's degree of freedom (DOF), the end-effector's degree of mobility (DOM), and the nature of the end-effector's mobility (NOM). In order to establish relations between topology and DOF and DOM, the concept of initial configuration was introduced which lead to an integrated topology and geometry representation. From the analysis of a set of linear equations established in displacement tangent space at the initial configuration, topology and geometry conditions were then derived for a PM to have a given DOF and DOM in the tangent space. According to the group theory, the PM will have the given DOF and DOM within a neighborhood of the initial configuration. However, tangent space analysis does not ensure that the NOM will not change once the PM leaves the initial configuration.; Analysis in displacement space was then performed and a new topological synthesis approach was proposed. With this approach, the resulting PMs will only generate translational displacement within an entire neighborhood of the initial configuration. The analyses in tangent space and in displacement space together lead to a new topological and geometric synthesis approach of TPMs.; In order to achieve automatic synthesis, a kinematic model was proposed which takes both topology and geometry as design variables and can therefore apply to TMs of all topologies and geometries. This was done by performing a special frame assignment, which enables prismatic joints and revolute joints to be treated in a unified way. Then for the first time, the forward and inverse kinematic problems of TPMs were systematically studied.; The work presented in this thesis makes it possible to creat...