The Parallel Trajectory Ruled Surfaces

Abstract

The parallel curves are especially used in numerically controlled machining where a biaxial machine defines the shape of the cut made with a round cutting tool. In this study, trajectory ruled surfaces are investigated whose base curve is the parallel curve of a prescribed curve. Some results related with their developability and minimality are obtained. In addition, the conditions are investigated for the base curve to be a special curve. Parallel trajectory ruled surfaces are illustrated with examples.