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This paper introduces a new method for workspace boundary determination on general structure manipulators. The method uses a branch-and-prune technique to isolate a set of output singularities and then classifies the points on such a set according to whether they correspond to motion impediments in the workspace. A detailed map of the workspace is obtained as a result, where all interior and exterior regions, together with the singularity and barrier sets that separate them, get clearly identified. The method can deal with open- or closed-chain manipulators, whether planar or spatial, and is able to take joint limits into account. Advantages over previous general methods based on continuation include the ability to converge to all boundary points, even in higher dimensional cases, and the fact that manual guidance with a priori knowledge of the workspace is not required. Examples are included that show the performance of the method on benchmark problems documented in the literature, as well as on new ones unsolved so far.