  Twisted gravitational waves (TGWs) are nonplanar unidirectional Ricci-flat
solutions of general relativity. Thus far only TGWs of Petrov type \emph{II}
are implicitly known that depend on a solution of a partial differential
equation and have wave fronts with negative Gaussian curvature. A special
Petrov type \emph{D} class of such solutions that depends on an arbitrary
function is explicitly studied in this paper and its Killing vectors are worked
out. Moreover, we concentrate on two solutions of this class, namely, the
Harrison solution and a simpler solution we call the $w$-metric and determine
their Penrose plane-wave limits. The corresponding transition from a nonplanar
TGW to a plane gravitational wave is elucidated.
