Based on the transmission principle of the positive-drive cam mechanism,the tooth profile theory of a new type of liner-movable-gear-drive-mechanism with arbitrary tooth difference is proposed.The tooth profile equation of the shock wave and the center wheel is proposed,and the geometrical proof of the indirect conjugation of the tooth profile and the center tooth profile is carried out. The relationship among the number of movable teeth,the number of teeth of the shock wave and the number of teeth of the center wheel is deduced,and the feature that movable teeth should distribute uniformly is proved. The transmission ratio of the new movable gear extension is deduced in term of the relative angular velocity method. The design examples are provided to show the adoptability of the two kinds of tooth profile given,symmetrical tooth profile and asymmetric tooth profile.