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Abstract
This thesis presents the geometrical synthesis of spherical parallel manipulators of 3-RRR topology using real-coded genetic algorithms. The intended use of this kind of robot is an hybrid numerically-controlled machine tool with six degrees of freedom composed of two parallel manipulators: one for the orientation degrees of freedom and one for the translation degrees of freedom. The presented work consists exclusively in the orientation part. The initially established specifications of the machine tool are used in the choice of optimization criteria.
The first goal of this work is to describe the entire class of spherical 3-RRR manipulators using a minimal set of geometrical parameters. Twelve independent parameters have been identified. Using this parameterization, the kinematics is studied and the inverse kinematics problem is addressed.
In order to optimize the set of geometrical parameters for the intended use, workspaces computation of studied manipulators must be done. This task is handled numerically by discretizing space using 2k-trees which are a generalization of bintrees, quadtrees and octrees. A generic C++ library has been developed to tackle all kinds of cases.
The possible collisions between manipulator legs are not taken into account when workspaces computation rely exclusively on inverse kinematics. It is shown in this work that collision detection must be implemented in order to obtain results of sufficient precision. Two techniques are presented and integrated to the workspace computation: one based on a polyhedral model and one using a wireframe model to represent manipulator links. (Abstract shortened by UMI.)
