Transmission principle is the basis of design theory. This work proposed new oscillating gear transmission of cosine shockwave push rod with arbitrary tooth difference. Tooth profile curve of the shockwave gear is cosine curve or its equidistant curve; profiles at both ends of push-rod oscillating tooth are cylindrical curves; internal tooth profile is the envelope curve in cylindrical profile group: shockwave cam keeps fixed ratio of transmission with oscillating tooth carrier, and oscillating tooth moves along the radial hole of oscillating tooth carrier with circumferential movement. The basic structure and transmission principle are described to prove that the transmission has fixed ratio. Besides, different ways of installation and roller numbers are utilized to obtain twelve transmission ratios, thus establishing theoretical, actual equation of tooth profile for design of such transmission.