As the high order polynomial curve has no rigid and flexible impact, a new model of five polynomial curves is provided to achieve any tooth-difference pure rolling movable tooth transmission. Tooth profile equations of central gear are derived based on speed conversion and envelope principle, and the design conditions of avoiding interference of tooth profile are formulated. Variation of the central gear curvature radius and influence of the movable tooth axis radius on the properties of tooth profile are analyzed. Meshing characteristics is indicated by the pressure angle based on the meshing principle of movable tooth drive, and the characterization parameters which affect the minimum pressure angle and force transmission tooth profile region are analyzed, it provides design basis for the selection of geometrical parameters of any tooth-difference pure rolling movable tooth transmission. Design examples are given to verify the validity of theoretical analysis results. The simulation example shows that this new tooth transmission design has good force effect and smooth transmission. The design method is simple and it is easy to form the modular design and series design, so it has broad application prospects.