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Abstract
This thesis presents the different ways to resolve the direct kinematic of the 3-PRIIR and the Star-like topology. The principal goal of this work is to demonstrate that the 3-PRIIR can't have more than two solutions of the DK problem, and also to demonstrate that the Star can have more than two assembly modes. The first chapter of this thesis presents the basic definitions and the general notions of robotic necessary to the understanding of the following chapters. Thereafter, a kinematic study on the 3-PRIIR manipulators is presented. This study includes (1) the solution of the inverse kinematic problem; (2) the determination of the jacobian matrices; (3) the numerical resolution of the DK problem based on the jacobian matrices; (4) the algebraic solution of the DK; (5) and finally, some numerical examples.
The third chapter contains a kinematic study for all the Star-like topology. It includes the first, second, third and fifth points of the chapter 2. Moreover, it contains an algebraic formulation which describes the mathematical equations of the direct kinematic problem of the Star-like topology. The chapter 4 presents a graphical method to resolve the direct kinematic for all the Star-like topology based on the CAD system CATIAV5R8. We will also resolve some numerical examples from Star manipulators. This method allows us to find all of the solutions and then all of the Star assembly modes.
