A satellite flexographic printing machine includes a central printing roller. A plurality of root rollers are installed around the central printing roller. The central printing roller coaxially rigidly connects large gears. Each roller corresponds to a roller gear, and the large gears are Each type of roller gear meshing transmission is characterized in that a differential transmission device is arranged between each plate roller and the corresponding plate roller gear, and each differential transmission device includes a first sun gear, a second sun gear and a worm gear and worm gear. In the structure, the first sun gear and the corresponding plate roller gear are coaxially and rigidly connected, and the rotation shaft of the second sun gear passes through the first sun gear and is coaxially and rigidly connected with the corresponding plate roller, and the first sun gear, the second sun gear, The rotary centers of the three worm gears are on the same straight line. The first sun gear and the second sun gear are provided with planetary gears. The two planet gears are coaxially and rigidly connected. The rotation shafts of the two planetary gears are supported on the worm wheel and the bearing plate. The disk is fixedly attached to the worm gear.