The paper focuses on the enhanced stiffness modeling of robotic manipulators
by taking into account influence of the external force/torque acting upon the
end point. It implements the virtual joint technique that describes the
compliance of manipulator elements by a set of localized six-dimensional
springs separated by rigid links and perfect joints. In contrast to the
conventional formulation, which is valid for the unloaded mode and small
displacements, the proposed approach implicitly assumes that the loading leads
to the non-negligible changes of the manipulator posture and corresponding
amendment of the Jacobian. The developed numerical technique allows computing
the static equilibrium and relevant force/torque reaction of the manipulator
for any given displacement of the end-effector. This enables designer detecting
essentially nonlinear effects in elastic behavior of manipulator, similar to
the buckling of beam elements. It is also proposed the linearization procedure
that is based on the inversion of the dedicated matrix composed of the
stiffness parameters of the virtual springs and the Jacobians/Hessians of the
active and passive joints. The developed technique is illustrated by an
application example that deals with the stiffness analysis of a parallel
manipulator of the Orthoglide family.Comment: ISSN 2070-372