Singularity-invariant leg rearrangements in Stewart platforms

Abstract

The Stewart-Gough platform was first introduced by E. Gough in 1954 and, since then, it has been used for many applications thanks to its great stiffness, accuracy and robustness in comparison with serial manipulators. It has triggered the research on parallel manipulators and continues to be the center of many researches because, despite its simple geometry, its analysis translates into challenging mathematical problems. One of the most challenging ones is the geometric interpretation of its singularities, that is, those positions where the platform loses stiffness. A complete geometric characterization of these unstable poses is still an open problem. The present thesis provides new insight into this problem from a completely new approach: finding singularity-invariant leg rearrangements. Finding all the transformations that leave the solution of a problem invariant does not solve it, but it provides a lot of information that contribute to its resolution. In the Stewart-Gough platform context, this indirect approach consists in the characterization of all the leg rearrangements that leave the platform singularity locus invariant. Such singularity-invariant leg rearrangements are shown to be a powerful tool to obtain kinematically equivalent manipulators, to help to visualize at a glance the complexity of its kinematics and to provide a common and original framework for the study of both pose-dependent singularities and architectural singularities of Stewart-Gough platforms.