The Quasi Parallel Curve of a Space Curve

Abstract

A parallel or offset curve is defined as a curve whose points are a fixed distance from a given curve. These curves are not parallel transport. Often, it has a more complex mathematical structure than the first curve. Offset curves are important in numerically controlled machining, for example, where a biaxial machine defines the shape of the cut made with a round cutting tool. In this study, the quasi parallel curve is defined with the help of the quasi frame of a given curve. According to all selections of the projection vector, the quasi frame equations of this curve are expressed in terms of the quasi elements of the given curve. The curvatures of the quasi parallel curve were obtained depending on the quasi curvatures of the main curve. The study was supported by examples. The examples confirm that the quasi parallel curve is not parallel transport.

Keywords

• Space curves
• parallel curves
• Frenet frame
• q-frame.

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