This work presents an approach for the synthesis of four-bar planar mechanisms for function, path, and motion generation based upon the use of invariant descriptors and local database generation and search methods;Transformation and descriptor methods are used to characterize the motion of four-bar planar mechanisms (function, path and motion generation) and to store the invariant characteristic information in a database. Spatial transforms, one-dimensional Fourier transforms, two-dimensional Fourier transforms, and invariant moments are used to generate invariant characteristic descriptors. The resulting characteristic information for each curve is invariant regardless of the rotation, translation or scaling of the curves. A description of each method and the relative performance of file development and search methods are developed. Over 8,000 function, path and motion solutions are generated for global search solutions for each transform and descriptor method. The function, path and motion solutions are based on the solutions developed by Hrones and Nelson and based on the implementation of a random search of a local design space. Solution comparison and matching techniques are discussed, and implemented, to evaluate the deviation of a candidate curve to curves stored in a database;A methodology is developed to allow the designer to investigate a local design space by generating a database of candidate solutions based on the random development of four-bar mechanisms. The designer may then define a desired solution and search the generated candidate solution files. This technique supports the evaluation of a local solution space through the generation, characterization, and identification of candidate mechanisms that may be practical to implement. After the identification of candidate mechanisms, local optimization techniques may be used with candidate mechanisms.