This paper applied the contact principle of deferential geometry in to the 5-axis NC machining, researched the best contact condition of tool and the surfaces, analysis the contact degree of the intersection line of the cutter and the surfaces。Compared with other references , the theory of this paper is more restrict , going deep into the parameter of third order instead of the second order, suitable to the primary analytical geometry and the simulation surface of the numerical geometry, with definite procedure of calculation , and easy to solve the function, comparing to UG Programming, the efficiency is more than 30 times .
keywords: surface contact NC machining