  The paper focuses on the stiffness analysis of multi-link serial planar
manipulators, which may demonstrate nonlinear stiffness behavior under the
compressive loading. Two important cases are considered, where the manipulator
has either a straight or non-straight initial configuration. It was proved that
in the first case the loading may cause the buckling if it exceeds some
critical value, and the manipulator suddenly changes its straight shape and
stiffness properties. For computing this critical force, a general
eigenvalue-based technique was proposed that can be applied to any multi-link
serial manipulator. For the second case dealing with non-straight initial
configurations, a universal energy-based technique was applied that allowed to
detect quasi-buckling phenomenon when it is observed very fast but not instant
change of the manipulator shape and its stiffness coefficient under the
loading. These results are illustrated by numerous examples of non-linear
stiffness behavior of three-and four-link manipulators that are subjected to
compressive force.
