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Dimensional synthesis of mechanisms to trace given paths is an important problem with no exact solution. In this paper, the problem is divided into representation of curve shape and learning the relation between curve shape and mechanism dimensions. Curve shape is represented by Fourier descriptors of cumulative angular deviation of the curve, which do not depend on the position or scale of the curve. An artificial neural network (ANN) is trained to learn the (unknown) relation between the Fourier descriptors of a planar curve and the dimensions of the mechanism tracing that curve. Presented with any simple, closed, planar curve, the ANN suggests the dimensions of a four-bar whose coupler curve is similar in shape. A local optimization procedure further refines the results. Examples presented indicate the method is successful as long as the curve shape is such that the mechanism is able to trace it.