This paper presents design imaginary skew rack cutters having teeth of two parabolic coefficients to generate spur and helical gears. First, a mathematical model of the imaginary rack cutter having teeth of two parabolic coefficients is derived using geometric relations and coordinate transformation. After the relationship between the coordinate system of the imaginary rack cutter and that of the helical gear pair is set up, a family of imaginary rack cutter surfaces is obtained using the homogeneous coordinate transformation matrix to transfer the coordinate system of the rack cutters to that of the helical gear. Based on the gear theory, the equations of meshing between the rack cutter and the helical gear are determined. Substituting the equations of meshing into the family of imaginary rack cutter surfaces, a pinion and a gear are generated and their geometries are plotted using an in-house software package. Based on the assembly errors, tooth contact analysis is performed to determine the influences of kinematic assembly errors and the parabolic coefficients. Results show that maximum parabolic coefficient value of the imaginary skew rack cutter exists in order to avoid undercutting and it can be determined.