Abstract An original method referred to as Galerkin's method in mathematics has been proposed for determining the dimensions of a mechanism which is to approximate a given continuous function. The application of this method has been shown on a four-bar for 3- and 5-parameter cases. Here synthesis has been realized by solving the system of equations derived from the conditions whereby the four-bar displacement function is orthogonal to a set of selected weighting functions, which are equal, in number, to the number of existing parameters and are continuous within domain interest. Its effectiveness has been demonstrated on several examples.