  The paper presents a methodology to enhance the stiffness analysis of serial
and parallel manipulators with passive joints. It directly takes into account
the loading influence on the manipulator configuration and, consequently, on
its Jacobians and Hessians. The main contributions of this paper are the
introduction of a non-linear stiffness model for the manipulators with passive
joints, a relevant numerical technique for its linearization and computing of
the Cartesian stiffness matrix which allows rank-deficiency. Within the
developed technique, the manipulator elements are presented as pseudo-rigid
bodies separated by multidimensional virtual springs and perfect passive
joints. Simulation examples are presented that deal with parallel manipulators
of the Ortholide family and demonstrate the ability of the developed
methodology to describe non-linear behavior of the manipulator structure such
as a sudden change of the elastic instability properties (buckling).
