  The aim of this paper is to characterize the uniqueness domains in the
workspace of parallel manipulators, as well as their image in the joint space.
The notion of aspect introduced for serial manipulators in [Borrel 86] is
redefined for such parallel manipulators. Then, it is shown that it is possible
to link several solutions to the direct kinematic problem without meeting a
singularity, thus meaning that the aspects are not uniqueness domains.
Additional surfaces are characterized in the workspace which yield new
uniqueness domains. An octree model of spaces is used to compute the joint
space, the workspace and all other newly defined sets. This study is
illustrated all along the paper with a 3-RPR planar parallel manipulator.
