Kinematic Structures for Processing of Surfaces with a Circle Directrix and a Straight Line Generatrix (Part IV)

Abstract

A body with a given geometry can be obtained by various manufacturing procedures, entailing, however, different surface quality, dimensional precision and (most importantly) productivity. Each body is characterised by one or more surfaces, simple or complex, as the case may be. It is known that a surface is characterised by a directrix and a generatrix, as well as by the modality of its physical achievement by means of the machines and tools uses for manufacturing. The directrix is obtained as a result of a primary motion and possibly one or more secondary motions. The generatrix is obtained as a result of one secondary motion, rarely more. If the generatrix is materialized on a tool, then a secondary motion is not necessary. In addition one or more auxiliary motions are needed. Other generation modalities not excluded, from the theory of surface generation on machine-tools it is known that the directrix, as well as the generatrix can be: materialized; generated by copying; kinematically generated as the trajectory of a point; kinematically generated as the envelope of a family of curves; generated by rolling; or programmed. Typically in literature generation “by copying” and “programmed generation” of the directrix and generatrix are not addressed distinctively, both being assumed as of the same nature. The recent evolution of industrial electronics and implicitly of machine-tools has determined a clear differentiation between the kinematics and construction of machine-tools (still) using generation by copying from a master and the kinematics of NC machine-tools. The paper is one of kinematic synthesis, oriented towards innovation-invention, and presents by means of examples, not necessarily known or typical, all six cases of generation of surfaces characterised by a straight line generatrix and a circle directrix obtained kinematically as the envelope of a family of curves.