  Lattice materials are interesting mechanical metamaterials, and their
mechanical properties are often related to the presence of mechanisms. The
existence of periodic mechanisms can be indicated by the presence of
Guest-Hutchinson (GH) modes, since GH modes are sometimes infinitesimal
versions of periodic mechanisms. However, not every GH mode comes from a
periodic mechanism. This paper focuses on: (1) clarifying the relationship
between GH modes and periodic mechanisms; and (2) answering the question: which
GH modes come from periodic mechanisms? We focus primarily on a special lattice
system, the Kagome lattice. Our results include explicit formulas for all
two-periodic mechanisms of the Kagome lattice, and a necessary condition for a
GH mode to come from a periodic mechanism in general. We apply our necessary
condition to the two-periodic GH modes, and also to some special GH modes found
by Fleck and Hutchinson using Bloch-type boundary conditions on the unit cell
of the Kagome lattice.
