The Generalization of Rectifying Helices

Abstract

This work establishes connections between different classes of arbitrary speed rectifying helices. We further analyze how the involute of a space curve can exhibit spherical helicity and how the evolute can inherit rectifying properties, thereby providing an alternative characterization of these helices. These relationships, along with their interplay with involutes and evolutes, are supported by illustrative examples that offer deeper insights into their geometric properties.