A Geometric Approach of Form Tolerance Formulation and Evaluation

Rigorous and precise formulation of tolerancing and dimensioning plays an important role in tolerance evaluation using CMMs. In this paper, we rst present a uniied geometric formulation of form tolerances using an extended least-squares E-LSQ approach. Then, using properties of connguration space of symmetric features an iterative algorithm is developed to solve the E-LSQ problem. Simulation results show that the algorithm not only keeps computational eeciency of least-squares approach, but also possesses of computational accuracy of min-max algorithms. The outstanding properties of the geometric formulation are: 1 coordinate-free representation of connguration space of symmetric features; 2 in conformance to the tolerance standard; 3 easily implementation of tolerance evaluation.