A counter gear transmits the rotation angle, so the angular velocity ratio of the gear does not necessarily need to be constant in the meshing process. As a pinion has a small number of teeth when combined with an internal gear for counters, tooth interference can occur with the use of an involute curve. This paper introduces circular arcs that represent a tooth profile and fillet for the profile design of a pinion through the combination of arcs with lines. The straight line of a rack tooth represents the profile of a mating internal gear. Thus, the circular arc and line maintain contact during the rotation of the counter gear. This paper presents an analysis of the meshing of the circular arc tooth and rack tooth along with the properties of the counter gear, such as the change in rotational velocity and amount of backlash. The contact ratio of the counter gear is 1 because the tooth contact occurs between circular arcs and line. The initial position of tooth contact, which denotes the simultaneous contact of two teeth, is found. As the rotation of the pinion, only one tooth keeps the contact situation. This meshing property is analyzed by the geometrical constraints of the tooth profile in contact and the results are presented as graphical diagrams in which tooth-arc movements are superimposed.