In order to reveal the nonlinear dynamics behavior of the transmission mechanism of the roller movable tooth. A translational-pure torsional coupled dynamics model is established with considering the number of movable tooth,the gap between the teeth and the dynamic loads. The relative displacement between the various parts of the meshing line is derived. The system nonlinear dynamics differential equations and coordinate transformation of differential equations are worked,and the non-dimensional treatment is carried out. The dimensionless differential equations is solved by the numerical analysis software,the phase diagram and Poincare diagram are obtained. The influence of parameter variation on the nonlinear characteristics of the system is analyzed by change the parameter of eccentric distance and meshing damping. The results show that the movement of system is different by the changing of the eccentric distance. With the reducing of the eccentric distance,the system enters the periodic movement through the chaotic motion,and then enters the chaotic motion through the quasi-periodic. If the eccentric distance is not choose bigger and smaller,the vibration response amplitude of the mechanism is reduced,the stability of the system can be improved.