In order to simplify root profile processing of common Roots rotor with outer arc, the construction of inner arc rotor was proposed. Based on the unified construction equation under the given inner conjugate profile, by using the Euler-Savary equation for conjugate relation of rotor pairs and the limit feature that the curvature radius on outer conjugate profile is 0 at a certain point, the general limit criterion for known inner conjugate profile was derived. According to the general limit criterion, the limit features of inner arc profile was deduced. Finally, the maximum shape factor and maximum volume utilization factor of inner arc rotor were compared with the outer arc rotor. The results show that when the curvature radius of inner conjugate profile at middle point is perpendicular to the central axis, rotor profile is in the limit state; the root profile of inner arc rotor can be finished by standard hole machining method at one time, which is the simplest; compared with the outer arc rotor, the maximum shape factor decreases by 5.0% for 2 lobes, 3.7% for 3 lobes and 2.6% for 4 lobes, and the maximum volume utilization factor decreases by 12.5%, 7.2% and 0.1%.