The linear interpolation of the machine tool motion axis will lead to the non-linear interpolation of tool position and tool axis vector, and the resulting nonlinear error is an important factor affecting the flank milling accuracy of the curved surface. In order to reduce the flank milling machining error caused by the nonlinear interpolation, the model of rotation-cutter axis deviation angle of turntable was established, and it was proved that the interpolation of the cutter axis vector must be nonlinear when the rotary axis of machine tool is linearly linked, and the linear interpolation conditions of the cutter axis vector were proposed.The spherical coordinate system was established in the machining coordinate system.The longitude and latitude differences of adjacent interpolation tool axis vectors in the spherical coordinate system were discussed and its influence on tool axis deviation angle were discussed. The calculation results show that the angle between the adjacent cutter axis vector and the maximum deviation angle between them is not monotonous. The optimization goal of minimizing the average latitude of the adjacent cutter orientation was proposed; by changing the workpiece clamping posture, the optimization conditions were satisfied. The flank milling of free-form surface parts was taken as an example to verify the constraint of the cutter orientation that satisfied the linear interpolation. By using the BC-axis configure machine tool and the average latitude of the cutter axis vector in the model of rotation-cutter axis deviation angle of turntable, the effectiveness of the proposed optimization method was verified.