Applying screw theory for summing sets of constraints in geometric tolerancing. (June 2017) - Arroyave-Tobón, Santiago; Teissandier, Denis; Delos, Vincent
Highlights: In tolerance analysis, sets of constraints can be modelled with polyhedra. These polyhedra are generally unbounded due to the degrees of freedom. Each polyhedron is decomposed into the sum of a polytope and some straight lines. The characterization of the straight lines is based on a kinematic analysis with screws. Accumulation of geometrical defects is calculated summing only the underlying poly-topes. Abstract: In tolerance analysis, approaches based on sets of constraints (also called convex hull techniques) are able to study simultaneously all the possible extreme configurations of a mechanism when simulating manufacturing defects in its components. The accumulation of these defects can be calculated by summing and intersecting 6-dimensional sets of constraints, i.e. polyhedra. These approaches tend to be time-consuming, however, because of the complexity resulting from manipulating sets in R 6 . In this paper, polyhedra are decomposed into a bounded set (a polytope) and an unbounded set (a set of straight lines). The unbounded part of the polyhedra is characterized by the degrees of freedom of the toleranced feature or the joint. Therefore, the decomposition can be performed based on a kinematic analysis of the studied assembly using screw systems. The proposed decomposition is presented for the most common features used in geometric tolerancing. The idea behind this strategy is, instead of summing polyhedra in R 6, to sum only their underlying polytopes by isolating the unbounded part of the operands. A slider-crank mechanism is used to show the gain in computational time of the proposed method in comparison with the strategy based on complete 6-dimensional sets of constraints.