Architecture singularities in flagged parallel manipulators

Flagged manipulators are of interest because they are the only Stewart-Gough platforms for which a cell decomposition of their singularity loci is available. Here we show that the known family of such manipulators can be enlarged if one allows robot designs that, for some particular parameter values, become architecturally singular. Along this line, the most general 6-6 flagged manipulator is derived by applying a singularity-preserving transformation that leaves the relative position between two lines invariant. This transformation opens up the possibility of an "equal cross ratios" architectural singularity, which is shown to appear clearly in the factorization of the Jacobian determinant. From the 6-6 flagged manipulator, all the extended family of (possibly architecturally-singular) flagged manipulators is derived.