When parts are machined, especially on heavy machine tools, an accurate description of the rotations around the geometric axes is required. The work adds the concept of rotation around the machine and the workpiece axes. Both types of rotation in mechanics are related to internal and external rotations, which we describe in detail. We show how both types convert to each other and how conversion formulas are derived. The resulting conversions are formalized as functions in the C and MATLAB programming languages. The result of this mathematical description will be transferred to a new transformation cycle that can be used on machines as a standard.
Science Journal 