Geometric analysis of parallel mechanisms

The primary objective of this dissertation is to demonstrate the incontestable effectiveness of geometric methods to the design and analysis of parallel mechanisms. To this end, it is shown how geometry brings deep insight into the principles of motion, much better than algebraic or numerical methods. Furthermore, this thesis is expected to prove that geometry develops creativity and intuition, abilities much needed for the proper synthesis and study of complex mechanisms. The extensive use of basic geometry in this thesis uncovers the unseen properties of well-known parallel mechanisms. In addition, common misconceptions are examined and refuted. Through detailed comparisons and explanations, it is attempted to foster the reliance on the geometric approach. Finally, two promising research directions are identified and recommended. This thesis is divided into three main parts. While the progress through these parts goes from the plane to three and then six degrees of freedom in space, the complexity does not follow the same advance. On the other hand, the focus goes from the general survey of all 3-DOF planar parallel mechanisms, to the analysis of a class of 3-DOF spatial parallel mechanisms, to the study of a single architecture of a 6-DOF parallel mechanism. Firstly, the singularities of all 3-DOF planar parallel mechanisms are fully analysed. The velocity equations are derived by using both screw theory and differentiation with respect to time. For this purpose, a considerable attention is paid to explaining the not-so-well-known use of screw theory in the plane. Once these velocity equations are set up, an exhaustive study on the various types of singularities of these mechanisms