A geometric approach of form tolerance formulation and evaluation

We first present a unified geometric formulation of form tolerances using an extended least-squares (E-LSQ) approach. Then, using properties of configuration 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 efficiency of the least-squares approach, but also possesses of computational accuracy of min-max algorithms. The outstanding properties of the geometric formulation include: 1) coordinate-free representation; 2) in conformance to the tolerance standard; and 3) easy implementation.