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The synthesis of mechanism the disc cam mechanism with oscillating follower has not been completed satisfactorily. The synthesis was solved completely by introducing a concept of auxiliary parallel line family based on the principle of analogous velocity chart. The left and right end points of intersection of the auxiliary parallel lines and the lines which limited the axis position of cam were solved. Through this method, the boundary points and lines of the axis position of cam were achieved in theory. Then the accurate analytical solution and the numerical discretization method for solving the points and lines were presented. According to this method, the minimum sizes of the base circle radius and the length of pendulum can be derived directly and the allowable selected area of the axis position of cam can be presented. The synthesis of the disc cam mechanism with oscillating follower is completed satisfactorily. The mechanism design example shows that this method is corrected and effective.