Classification of 3-dimensional persistent screw systems: a numerical approach

In 1976, Hunt recovered screw theory by through geometric considerations and applied it to the analysis and synthesis of mechanisms. He has also discussed the special cases of various screw systems and proposed for them a classification based on a canonical bases of motion formed by principal screws. In addition to his classification, one of the most important result from Hunt's work, related to this thesis, is that some of the classified systems guarantee "full-cycle mobility" of mechanisms. They are known as Invariant screw systems (ISSs) and they are subalgebras of the Lie algebra se(3), which is the tangent space at the identity of the Lie group SE(3). This last one, constitutes a group of isometries of R^3, known as Special Euclidean Group. Recently a more general concept was presented: Persistent screw systems (PSSs) still exhibit relevant properties for "full-cycle motions". They represent the main topic of this thesis. Hence, a numerical method that allows us to find out what types of screw system that have dimension three are PSS, is proposed. Chapter 1 focuses on the main event regarding screw theory, tracing an historical line in order to introduce the state of art related to this work. Chapter 2 deals with some basic concepts related to screw theory. Chapter 3 introduces ISS ad PSS, with particular emphasis on their properties, which are important for guaranteeing "full-cycle motions" of mechanisms. It introduces also some basic procedures that allow the synthesis of many PSS generators. Chapter 4 formulates the problem on how find out PSSs of dimension three by presenting the characteristic equations associated to persistent systems and explains how validate them numerically with the aim to solve the equations properly. Further, the mathematical parametrizations are developed in order to establish what types of screw systems, according to Hunt's classification, are PSS. Chapter 5 summarizes the obtained results and discusses further developments.