  In this paper, we present a novel integrated method for designing nonlinear
stiffness systems based on a general spring-boundary model (GSBM) to study the
number of mechanical configurations for nonlinear stiffness systems designed by
the combination of a linear spring with a nonlinear boundary. GSBM consists of
a lumped mass, a special-shaped track, a roller rolling in the track and GLSM
with either positive or negative stiffness. The integrated method considers
pre-tensioned, pre-compressed and original length conditions of GLSM to design
roller trajectories to customize nonlinear stiffness systems. It is proved that
the mechanical configurations of nonlinear stiffness systems designed by the
combination of a linear spring with a nonlinear boundary are not limited to
one, but six or eight forms: for systems with nonnegative or nonpositive
potential energy, there are six independent mechanical configurations, and for
other systems, there are eight independent mechanical configurations.
