AN EXTENSION OF SCREW THEORY AND ITS APPLICATION TO THE AUTOMATION OF INDUSTRIAL ASSEMBLIES

Interest in mathematical models that adequately predict what happens in the process of assembling industrial parts has heightened in recent times. This is a result of the desire to automate the assembly process. Up to this point there has not been much success in deriving adequate mathematical models of the assembly process.;Basic to the theory of assembly is the classical theory of screws which, however, required substantial extensions for this application. The thesis begins with a review of basic screw theory, including line geometry and reciprocal screw systems, and new and more general derivations of some of these screw systems. We then extend the screw theory by introducing such concepts as "repelling" and "contrary" screw pairs, and "total freedom.".;Finally, we give a method of characterizing assemblies of industrial parts. Using the extended screw theory, we then analyze the "general peg-in-hole assembly" and subsequently give a mathematical description of this particular assembly.;This thesis is an attempt to develop mathematical models of parts assembly. Assembly involves motion of bodies which generally contact each other during the process. Hence, we study the kinematics of the relative motion of contacting bodies.