Abstract: Flank line modifications on a form grinding machine include several traditional methods, such as additional radial motion, additional angular motion, and combined radial and angular motion, which inherently have a large flank twist. In contrast, the five-axis additional motion optimization iterative process is complex and exhibits poor stability. To address these issues, a simplified four-axis additional motion model is proposed to optimize the helical profile modification for typical crowning. The model supplements additional tangential motion (Y-axis) to form a four-axis linkage comprising X, Y, Z, and C, to control the twist errors of double flank form grinding. Meanwhile, third-order polynomials are used to describe the motion of each axis. The low-order polynomial model can significantly reduce the matrix solution calculation and improve iterative stability. The improved Levenberg-Marquardt (L-M) algorithm is introduced in the iterative optimization process to avoid singularity and the non-solution problem of the matrix, thereby stabilizing the additional motion solution calculation. Theoretical analysis and actual grinding experiments demonstrate that the proposed method effectively reduces tooth surface twist errors during the modification of helical gear tooth profiles and ensures the accuracy of the grinding modification.