Departing somewhat from the classical techniques of mechanism synthesis, a design process is developed whereby the speed of the digital computer is a primary design criterion. By efficient use of basic input-output kinematic relationships and the computer’s random number generator, it is possible to obtain four or six-link mechanisms in a few minutes of computer time without any knowledge of synthesis techniques. Although the random approach is applied in this paper to the design of four-link and six-link function generators, it is an approach applicable to coupler-curve, multi-degree of freedom, and three-dimensional synthesis problems.