To simplify the complexity of designing interference free tooth profile pairs for gear pumps，a new method is proposed to directly obtain complex interference free driven tooth profile designs from the interference free active tooth profile.A general coordinate equation for the internal conjugate tooth profile was established with conjugate distance and transmission angle as design parameters.By analyzing the interference of the tooth profile and the coordinate variation relationship at the interference point，innovative methods for zero coordinate derivative and minimum meshing angle are proposed.The application verification is carried out through involute and linear tooth profile design.The results indicate that the conjugate distance and transmission angle are functions of contact ratio，locking angle，and the number of teeth on the driving gear； the zero coordinate derivative method is equivalent to the zero curvature radius method，and the minimum locking angle is solely a function of contact ratio and the number of teeth on the driving gear，for example，when the driving and driven teeth‑number is 6 and 9，the coincidence‑degree is 1.04，the standard pressure angle （20°） and the standard addendum coefficient （1.0），the minimum engagement-angle without interference is 28.57º for involute tooth‑profile； when the driving and driven teeth‑number is 9 and 12，The zero coordinate derivative method is straightforward，and the locking angle design theory is correct and reliable，making it applicable to interference‑free designs of any internal meshing tooth‑profile pairs.

internal meshing tooth‑profile pairs  /  tooth‑profile design without interference  /  zero coordinate derivative  /  minimum locking angle  /  zero curvature radius  /  involute gear  /  straight‑line gear