  A framework is a graph and a map from its vertices to R^d. A framework is
called universally rigid if there is no other framework with the same graph and
edge lengths in R^d' for any d'. A framework attachment is a framework
constructed by joining two frameworks on a subset of vertices. We consider an
attachment of two universally rigid frameworks that are in general position in
R^d. We show that the number of vertices in the overlap between the two
frameworks must be sufficiently large in order for the attachment to remain
universally rigid. Furthermore, it is shown that universal rigidity of such
frameworks is preserved even after removing certain edges. Given positive
semidefinite stress matrices for each of the two initial frameworks, we
analytically derive the PSD stress matrices for the combined and edge-reduced
frameworks. One of the benefits of the results is that they provide a general
method for generating new universally rigid frameworks.
