Transmission principle is the basis of studying design theory. This work proposed new oscillating gear transmission of hypocycloidal shockwave push rod with arbitrary tooth difference. Tooth profile curve of the shockwave gear is hypocycloidal 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 teeth move along the radial hole of oscillating tooth carrier with circumferential movement. After describing the basic structure, tooth profile equations for shockwave device and center gear are derived based on speed conversion and envelope principle. Then we propose a design condition that tooth interfere does not occur in center gear, laying the foundation for design of such transmission.