Ph.D Student | Ben-Horin Patricia |
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Subject | Geometrical Analysis of Parallel Robots |

Department | Department of Mechanical Engineering |

Supervisor | Professor Moshe Shoham |

Full Thesis text |

Singularities of parallel robots have attracted many researchers in the last three decades. Undoubtedly, the need to foretell the unstable configuration spaces that these robots possess is crucial since a notable part of their workspace lies on a region of this nature. Much research was done in this area, mainly using screw theory, line geometry and inspecting the Jacobian determinant. Since these approaches do not provide a complete understanding of the geometrical nature of the singular regions, it calls for search of innovate tools able to increase the geometrical understanding of these incidences. This is the purpose of the present research.

Grassmann-Cayley algebra is a self-evident tool for analyzing geometric
conditions between elements since it enables to formulate intersection and
union of points, lines and planes in a compact and invariant manner. The main
advantage of this algebra is its ability to write the geometric entities
without explicitly involving their coordinates. The intersection and union
operations create some determinants called *brackets*, which are very
useful in the analysis of the Jacobian matrix determinant.

In this work this algebra was used to analyze the singularities of parallel robots and was applied to interpret the geometrical meaning of their nature. Starting from the well-known Gough-Stewart platforms and applying it also to other spatial robot architectures, the robots were classified by the geometric nature of their singularities.