  In this paper, tangent-, principal normal-, and binormal-wise associated
curves are defined such that each of these vectors of any given curve lies on
the osculating, normal, and rectifying plane of its mate, respectively. For
each associated curve, a new moving frame and the corresponding curvatures are
found, and in addition to this the possible solutions for distance functions
between the curve and its associated mate are discussed. In particular, it is
seen that the involute curves belong to the family of tangent associated
curves, the Bertrand and the Mannheim curves belong to the principal normal
associated curves. Finally, as an application, we present some examples and map
a given curve together with its mate and their frames.
