Ph.D Student | Shvalb Nir |
---|---|

Subject | The Configuration Spaces of Parallel Mechanisms |

Department | Department of Mechanical Engineering |

Supervisor | Professor Emeritus Moshe Shoham |

Full Thesis text |

We study the configuration space of some parallel mechanisms that are in use, that is, mechanisms such that their underlying graph structure contains loops. Starting with the configuration spaces of arachnoid mechanisms which consist of k branches each has an arbitrary number of links and a fixed initial point, while all branches end at one common end-point. We show that generically, the configuration spaces of such mechanisms are manifolds, and determine the conditions for the exceptional cases. The configuration space of planar arachnoid mechanisms having k branches, each with two links is fully characterized for both the non-singular and the singular cases.

Applying these results we study the motion planning problem for such planar manipulators. A topological analysis is used to understand the global structure of the configuration space so that motion planning problem can be solved exactly.

The worst-case complexity of
our algorithm is O(k^{3}N^{3}), where N is the maximum number of
links in a leg. Examples illustrating our method are given.

Next we study the configuration space of a parallel polygonal mechanism, having a moving polygonal platform, and k branches each has an arbitrary number of links and a fixed initial point, We give necessary conditions for the existence of topological singularities; and show that generically the configuration space is a smooth manifold.

we analyze these cases and give simple geometrical conditions for those to arise. In the planar case, we construct an explicit Morse function on the configuration space, and show how geometric information about the mechanism can be used to identify the critical points. Finally we describe how topological singularities give rise to instantaneous kinematic singularities and explicit example is provided.