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In this paper, we introduce a new class of curves \alpha called af-rectifying curves, which its f-position vector defined by{\alpha}_{f}(s)=\int f(s)T(s)ds always lie in the rectifying plane of \alpha,where f is an integrable function and T is the speed curve of {\alpha}. Inparticular case, when the function f=0 or constant, the class of f-rectifyingcurves are helix or rectifying curves, respectively. The classification and thecharacterization of such curves in terms of their curvature and the torsionfunctions are given with a physical interpretation. We close this study withsome examples.

A new class of curves generalizing helix and rectifying curves