Abstract: Concerning the peripheral docking system of Russian Soyuz spacecraft in ASTP,the paper first studies the structure and basic motion relations of the differential damping mechanism and builds a simplified motion model.Then,by using Kinematics Influence Coefficients(KIC) method,the first and second order of Kinematics Influence Coefficients matrix which can describe each part motion are given.On the basis of kinematics modeling,it discusses the kinetic energy of transmission parts in the differential mechanism,the potential energy of springs connecting with screw rods or gear differential units,and the Rayleigh dissipative function of electromagnetical dampers and friction damper while the dissipative force is considered as being linear with velocity.By means of the Second Lagrange Equation,the mechanism movement differential equations are given and gets the mechanism dynamics modeling is got.Finally the expression of system stiffness coefficient and system damping coefficient in arbitrary docking mode are reached.