  We show that if the joints of a bar and joint framework $(G,p)$ are
positioned as `generically' as possible subject to given symmetry constraints
and $(G,p)$ possesses a `fully-symmetric' infinitesimal flex (i.e., the
velocity vectors of the infinitesimal flex remain unaltered under all symmetry
operations of $(G,p)$), then $(G,p)$ also possesses a finite flex which
preserves the symmetry of $(G,p)$ throughout the path. This and other related
results are obtained by symmetrizing techniques described by L. Asimov and B.
Roth in their paper `The Rigidity Of Graphs' from 1978 and by using the fact
that the rigidity matrix of a symmetric framework can be transformed into a
block-diagonalized form by means of group representation theory. The finite
flexes that can be detected with these symmetry-based methods can in general
not be found with the analogous non-symmetric methods.
