  A bar-joint framework $(G,p)$ is the combination of a finite simple graph
$G=(V,E)$ and a placement $p:V\rightarrow \mathbb{R}^d$. The framework is rigid
if the only edge-length preserving continuous motions of the vertices arise
from isometries of the space. Motivated by applications where boundary
conditions play a significant role, one may generalise and consider linearly
constrained frameworks where some vertices are constrained to move on fixed
affine subspaces. Streinu and Theran characterised exactly which linearly
constrained frameworks are generically rigid in 2-dimensional space. In this
article we extend their characterisation to symmetric frameworks. In particular
necessary combinatorial conditions are given for a symmetric linearly
constrained framework in the plane to be isostatic (i.e. minimally
infinitesimally rigid) under any finite point group symmetry. In the case of
rotation symmetry groups whose order is either 2 or odd, these conditions are
then shown to be sufficient under suitable genericity assumptions, giving
precise combinatorial descriptions of symmetric isostatic graphs in these
contexts.
