Flagged Parallel Manipulators

The conditions for a parallel manipulator to be flagged can be simply expressed in terms of linear dependencies between the coordinates of its leg attachments, both on the base and on the platform. These dependencies permit to describe the manipulator singularities in terms of incidences between two flags (hence, the name ldquoflaggedrdquo). Although these linear dependencies might look, at first glance, too restrictive, in this paper, the family of flagged manipulators is shown to contain large subfamilies of six-legged and three-legged manipulators. The main interest of flagged parallel manipulators is that 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 (nonsingular) and dimension 5 (singular), together with their adjacencies, are worked out in detail.