Nonrigid geometric metrology using generalized numerical inspection fixtures

Freeform surfaces have become an integral part of the automobile and aerospace industries. The parts with a very thin wall in proportion to their size are referred to as nonrigid (or flexible) parts. Generally, for the geometric inspection of such flexible parts, special inspection fixtures, in combination with coordinate measuring systems (CMM), are used because these parts may have different shapes in a free state from the design model due to dimensional and geometric variations, gravity loads and residual strains. A general procedure to eliminate the use of inspection fixtures will be developed. Presented methodology is based on the fact that the interpoint geodesic distance between any two points of a shape remains unchangeable during isometric deformation. This study elaborates on the theory and general methods for the metrology of nonrigid parts. We will merge existing technologies in metric and computational geometry, statistics, and finite element method to develop a general approach to the geometrical inspection of nonrigid parts.