An interactive design system has been developed for the design of automatic automotive transmission gear trains that can provide at least three forward and one reverse speed ratios. This user-friendly windowing system can access help files, display the functional representation of a mechanism, optimize the gear ratios and present the numerical results. The optimization procedure to find the optimum gear ratios and the corresponding number of gear teeth uses the Augmented Lagrangian Multiplier Method and can be applied to all epicyclic gear trains having two sets of three gears in which a ring gear is connected to a sun gear through a planetary gear. The Simpson and General Motors THM 440 gear trains are used to demonstrate the methodology. The gear teeth combinations are found such that they achieve the optimized gear ratios to within ±1% and satisfy the geometric constraints. PHIGS graphics functions are used in program routines to display the functional schematic of an epicyclic gear train on the computer screen. These routines are written in such a manner that other types of gear combinations can be displayed by simply adding additional modules to represent these new gear elements.