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In order to increase the efficiency in the machining of the sculptured surfaces, the contact principle of differential geometry is applied to the 5-axis NC machining; The best contact condition between tool and the surfaces is researched. Through analysis the contact degree of the intersection line of the cutter and the surfaces is known. In comparison to previous studies, the theory is more restricted and accurate by going beyond the second-order parameters into the third-order, suiting both the primary surfaces of analytical geometry and the computer-generated surfaces of the computation geometry. It has definite procedure of calculation, and the equations are easy to solve. The thought process is very clear: First, suppose that there is a surface of third-order, the coefficients of which are arbitrary; Then find out the best posture of the circle in order that the circle and the surface will most closely contact with each other at the origin position; Finally, develop the surface into a third-order surface at every point of machining and employ the results mentioned above to find the best cutter posture at every point of machining. As a result, the equations are easy to solve, and the concept is clear.
In order to increase the efficiency in the machining of the sculptured surfaces, the contact principle of differential geometry is applied to the 5-axis NC machining; The best contact condition between tool and the surfaces is researched. Through analysis the contact degree of the intersection line of the cutter and the surfaces are known. In comparison with previous studies, the theory is more restricted and accurate by going beyond the second-order parameters into the third-order, suiting both the primary surfaces of analytical geometry and the computer-generated surfaces of the computation geometry. It has definite procedure of calculation, and the equations are easy to solve. The thought process is very clear: First, suppose that there is a surface of third-order, the coefficients of which are arbitrary; Then find out the best posture of the circle in order that the circle and the surface will most closely contact with each other at the origin position; Finally, develop the surface in to a third-order surface at every point of machining and employ the results mentioned above to find the best cutter posture at every point of machining. As a result, the equations are easy to solve, and the concept is clear.