Bulletin of the institute of mathematics Academia Sinica vol:33 issue:2 pages:77-90
Rectifying curves are introduced in  as space curves whose position vector always lies in its rectifying plane. In this article, we establish a surprising simple relationship between rectifying curves and the notion of centrodes in mechanics. Furthermore, we show that rectifying curves are indeed the extremal curves which satisfy the equality case of a general inequality. Further geometric properties of rectifying curves are also presented.