Generalization and evaluation of vectorial tolerances

In recent years, vectorial tolerancing has emerged as a new alternative for representing workpiece tolerances. In contrast to conventional geometric tolerances which originated from hard gauging practices, vectorial tolerancing follows the working principle of coordinate measuring machines and CAD/ CAM systems. Moreover it provides feedback from measurement directly to manufacturing process control. Many believe it is a better tolerancing method to tie design, manufacuturing, and measurement together. However, the current proposal of vectorial tolerancing has some limitations. First, the currently adopted orientation vector is not sufficient for representing true 3D orientations. As a result, the orientation of a free form surface cannot be properly established. Second, there is lacking a unified and consistent method for the evaluation of vectorial tolerances. This paper proposes a new orientation vector which provides a more general mathematical basis for representing vectorial tolerances. It enables tr...