Success in synthesis of mechanisms for path generation usually depends on providing a good starting point to the optimizer. This paper presents a completely automatic method that performs a global search from a random starting point. A two-step synthesis process involves searching for a coupler curve of optimal shape followed by optimization of size, orientation, and position of the solution mechanism. For the first step, an objective function evaluating shape difference between two curves, irrespective of the differences in their sizes, orientation, and position, is defined based on Fourier descriptors of the curves. This function is minimized using a stochastic global search method derived from simulated annealing, followed by Powell’s method for fast convergence. In the second stage, using properties of Fourier descriptors, a set of points is located on the solution curve that is analogous to points specified on the desired curve. The size, orientation, and position of the solution mechanism is then determined by minimizing the distance between analogous points.