Abstract: Based on the mathematical definition of orientation tolerance in ANSI Y14.5.1M-1994, the notation of hint datum is pointed out and orientation tolerance zone of national standard is defined strictly with point-set vector equation. Kinematics theory in measurement geometry and mathematic definition theory is combined. And then develop a strict mathematical definition method, which is adapted to be expressed, processed and data transfer with computers.

Key words: Hint datum, Orientation tolerance, Tolerance zone