  The paper presents a methodology to enhance the stiffness analysis of
parallel manipulators with parallelogram-based linkage. It directly takes into
account the influence of the external loading and allows computing both the
non-linear ``load-deflection" relation and relevant rank-deficient stiffness
matrix. An equivalent bar-type pseudo-rigid model is also proposed to describe
the parallelogram stiffness by means of five mutually coupled virtual springs.
The contributions of this paper are highlighted with a parallelogram-type
linkage used in a manipulator from the Orthoglide family.
