Avoiding singularities in the workspace of a parallel robot is an important issue. The case of 3-RPR planar robots is an important subject of theoretical studies. We study the singularities of planar 3-RPR robots by using a new parameterization of the singular locus in a modified workspace. This approach enables us to give a simple alternative proof of a result recently proved by Husty: the complement of the singular locus in the workspace of a generic 3-RPR manipulator has two connected components (called aspects); we also give a procedure to design a singularity-free path connecting any two points in the same aspect. The parameterization introduced in this paper, due to its simple geometric properties, proves to be useful for the study of the singularities of 3-RPR robots.