A general form of non-linear differential motion equations for the elastic mechanism is presented. Based on the analysis of the structure property of the equations, a numerical solution method which combines the State Space Method with Iterative Method is put forward. The solution efficiency and precision are improved greatly through analyzing the solution method of the matrix exponent function and the equations with belt shape and side block coefficient matrices. Finally, as an example, the dynamic properties of a mold oscillation mechanism with 4-eccentric axes for continuous casting machine are analyzed. The results illustrate the correctness and feasibility of the method.

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