Extending the algebraic method to identify dimensional chains for angular tolerance charting

Tolerance charting, as a practical tool to determine nominal working dimensions and their tolerances for the process operations of a product, has been used in manufacturing industry for many decades. In the past years, many researchers have made great efforts on the tolerance charts for products with square-shouldered features (that is, 1D tolerance charting) and a few researchers have discussed tolerance charts for products with angular features, which are more complicated than the former. A few researchers have even presented an approach to identifying dimensional chains for angular tolerance charting. This paper proposes an algebraic method to establish dimensional chains for angular tolerance charting, which is the extension of the previous algebraic approach for 1D tolerance charting. The problems and characteristics of angular tolerance charting and the new algebraic approach are discussed. Both the forward and the reverse dimensional chains can be obtained from the algebraic method, so the nominal values of tolerances of the working dimensions can be determined. An example is presented to illustrate the method.