The paper presents the method for the optimal synthesis of four-link mechanism generating open/closed paths with time prescription. Although the method is suitable for both closed and open paths, it enables decreasing the number of design parameters describing dimensions, orientation and position of a path generator. Compared to the methods presented in the references, this is a one-phase synthesis method; although the number of design parameters is reduced, the method does not require affine transformations to be performed on the synthesised mechanism. The effectiveness of the method is discussed based on examples of three paths, with two taken from the literature.