There are many studies on regular rectifying curves in classical differential geometry, and important results have been obtained. However, these studies are limited for a smooth curve with singular points. To examine such curves and surfaces, the concept of framed curve, which is the general form of regular and Legendre curves, is used. Framed curves are defined as curves that have a moving frame with singular points in Euclidean space. We investigate framed rectifying curves via the dilation of framed curves on S 2 in R 3 . Moreover, the result of dilation of framed curves is the framed rectifying curve or not. We give some classifications for the dilation of framed curves. Finally, we give some related examples with their figures.

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Investigations are very important for non-regular curves in differential geometry. Framed curves have been used recently to study singular curves, and they have many contributions to singularity theory. In this study, framed Tzitzeica curves are introduced with the help of framed curves. In addition, some framed special curves that satisfy the Tzitzeica condition are given. New results have been obtained among the framed curves of these curves.

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