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In tolerancing analysis, geometrical or contact specifications can berepresented by polytopes. Due to the degrees of invariance of surfaces and thatof freedom of joints, these operand polytopes are originally unbounded in mostof the cases (i.e. polyhedra). Homri et al. proposed the introduction ofvirtual boundaries (called cap half-spaces) over the unbounded displacements ofeach polyhedron to turn them into 6-polytopes. This decision was motivated bythe complexity that operating on polyhedra in R6 supposes. However, thatstrategy has to face the multiplication of the number of cap half-spaces duringthe computation of Minkowski sums. In general, the time for computing capfacets is greater than for computing facets representing real limits of boundeddisplacements. In order to deal with that, this paper proposes the use of thetheory of screws to determine the set of displacements that defines thepositioning of one surface in relation to another. This set of displacementsdefines the subspace of R6 in which the polytopes of the respective surfaceshave to be projected and operated to avoid calculating facets and verticesalong the directions of unbounded displacements. With this new strategy it ispossible to decrease the complexity of the Minkowski sums by reducing thedimension of the operands and consequently reducing the computation time. Anexample illustrates the method and shows the time reduction during thecomputations.

Adapting polytopes dimension for managing degrees of freedom in tolerancing analysis