  When moving from one arbitrary location at another, a parallel manipulator
may change its assembly-mode without crossing a singularity. Because the
non-singular change of assembly-mode cannot be simply detected, the actual
assembly-mode during motion is difficult to track. This paper proposes a global
explanatory approach to help better understand non-singular assembly-mode
changing motions for 3-RPR planar parallel manipulators. The approach consists
in fixing one of the actuated joints and analyzing the configuration-space as a
surface in a 3-dimensional space. Such a global description makes it possible
to display all possible non-singular assembly-mode changing trajectories.
