M.Sc Student | Keren Yuval |
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Subject | Conversion of Variational Geometry Problems to Parametric Geometry |

Department | Department of Mechanical Engineering |

Supervisor | Professor Emeritus Moshe Shpitalni |

Product development entails numerous changes until the mechanical design matches product requirements. Often a new part is based on the design of its predecessor with small changes, such as changes in the geometry dimensions and/or quantitative features, such as center of gravity or moment of inertia. A typical case is of a family of parts that consists of bodies with similar topology that are differentiated by their dimensions only. In order to avoid redefining and drafting each part again every time a dimension is changed, as was required by former CAD systems, we need a tool that allows for efficient changing of dimensions. Even though many of the constraints in producing a part are not purely geometric (for example, strength), they can be translated into geometric constraints. Note that a variational geometry solution is needed not only in CAD but in other fields as well, including robot and mechanism kinematics, motion planning and mathematical proofs.

This research suggested an
approach for converting **variational geometry** into **parametric geometry**,
by means of creating auxiliary constraints and automatically finding a
sequential construction, using a graph representation of the problem, and
various graph algorithms. The solution strategy is based on decomposing the
problem into a sequential process consisting of pre-programmed
elementary-cases, and on construction of auxiliary geometry by geometric
elements and constraints transformations, which yield new paths in the graph
representation of the problem. Use of auxiliary geometry and constraints can
thus decompose strongly connected components in the original graph, and assist
traditional constraints solution techniques.