  We propose a framework to realize helical edge states in phononic systems
using two identical lattices with interlayer couplings between them. A
methodology is presented to systematically transform a quantum mechanical
lattice which exhibits edge states to a phononic lattice, thereby developing a
family of lattices with edge states. Parameter spaces with topological phase
boundaries in the vicinity of the transformed system are illustrated to
demonstrate the robustness to mechanical imperfections. A potential realization
in terms of fundamental mechanical building blocks is presented for the
hexagonal and Lieb lattices. The lattices are composed of passive components
and the building blocks are a set of disks and linear springs. Furthermore, by
varying the spring stiffness, topological phase transitions are observed,
illustrating the potential for tunability of our lattices.
