Geometric formulation of orientation tolerances

The rapid proliferation of coordinate measuring machines (CMM) triggered the need for precise and rigorous formulations of each tolerance concept. In this paper, we employ the concept of configuration space of symmetric features to define each type of datum features and orientation tolerances. The establishment of datum features and orientation tolerances are formulated in an linear programming approach. Using properties of Lie groups and Lie algebra, a simple, unified and coordinate free algorithm for datum establishment and orientation tolerance is developed. The results of the algorithm comply to the definitions stipulated in the standard ANSI Y14.5M