  Supergravity brane solutions allow for a generalised type of Kaluza-Klein
reduction onto brane worldvolumes. The known replacement of a flat worldvolume
metric by a Ricci-flat metric constitutes a consistent Kaluza-Klein truncation
of the starting higher-dimensional supergravity theory down to a
lower-dimensional pure gravity theory.
  This paper shows how to extend such a brane-worldvolume pure-gravity
consistent truncation to that for a full nonlinear supergravity theory for the
Type IIB D3-brane and the M-theory/Type IIA M5-brane. The extension of
worldvolume supersymmetry is given by the unbroken supersymmetry of the
original flat "skeleton" brane. Compatibility with further worldvolume diagonal
and transverse vertical dimensional reductions is also shown, providing the
brane-worldvolume supergravity embeddings of all descendants of the skeleton
D3- and M5-branes. Examples are given of brane-worldvolume supergravity
solutions embedded into the corresponding higher-dimensional supergravities.
