The invention discloses an output-gap-free movable tooth transmission device. The device is composed of a shock device, a movable-tooth gear and a fixed-tooth gear, wherein the shock device of the movable tooth transmission device is designed to be composed of an elastic flexible ring and a driver, the elastic flexible ring is tightened and installed on the inner sides of movable teeth of the movable tooth gear by a certain degree of tightness, and tightly presses all the movable teeth on the tooth profile of the fixed tooth gear through expansion force generated by deformation of the elasticflexible ring, so that the movable teeth are meshed with the tooth profile of the fixed tooth gear in a gapless mode; and meanwhile, the elastic flexible ring is used for pressing tightly working movable teeth meshed with the fixed tooth gear on a working side contact surface of a movable tooth groove on a movable tooth frame through a pin shaft, and pressing tightly non-working teeth separated and returned on a non-working contact surface of the movable tooth groove on the movable tooth frame through a pin shaft, so that tight pressing is conducted both in the forward and reverse directions simultaneously in a gapless mode, and both forward rotation and reverse rotation are conducted in a gapless mode.