  Along cuspidal edge singularities on a given surface in Euclidean 3-space,
which can be parametrized by a regular space curve, a unit normal vector field
$\nu$ is well-defined as a smooth vector field of the surface. A cuspidal edge
singular point is called generic if the osculating plane of the cuspidal edge
(as a regular space curve) is not orthogonal to $\nu$. This genericity is
equivalent to the condition that its limiting normal curvature $\kappa_\nu$
takes a non-zero value. In this paper, we show that a given generic (real
analytic) cuspidal edge can be isometrically deformed preserving $\kappa_\nu$
into a cuspidal edge whose singular set lies in a plane. Such a limiting
cuspidal edge is uniquely determined from the initial germ of the cuspidal
edge.
