The goal of this research is to improve our ability to do automatic flexible assembly. There are three objectives to this end: First, develop the science of part mating, with application to flexible assembly system design. Second, develop a quantification of dexterity which can be applied to model the assembly process, analyze assembly devices and synthesize assembly systems. Finally, demonstrate the usefulness of dexterity as a common measure of assembly tasks and assembly devices. The methods to be employed in this research will include the analysis of the physics of assembly primitives and the mechanics of assembly devices using screw algebra, and the development of dexterity models using parts entropy measures and an index of difficulty for position and force. Applications of dexterity research in engineering will initially take the form of a handbook of assembly system applications. This should in turn stimulate design simplification of piece parts resulting in products which require the least amount of dexterity needed. Expected results include new robotic assembly devices, automatic path planning algorithms which include complete descriptions of the assembly process, and optimal assembly task location within the workspace.