On redundant flagged manipulators

Flagged in-parallel manipulators are attractive because their singularity loci admit a well-behaved decomposition, with a unique topology irrespective of the metrics of each particular design. In this paper, this topology is formally derived and all the cells, in the configuration space of the platform, of dimension 6 (non-singular) and dimension 5 (singular), together with their adjacencies, are worked out in detail. This characterization of the singularity loci is useful to come up with designs which admit control strategies free of singularities. In particular, it is shown that by adding an extra leg to any flagged manipulator, the resulting 7-leg structure admits a control strategy (by appropriately choosing which leg remains passive) that completely avoids singularities