Architecture singularities in flagged parallel manipulators
ABSTRACT 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.
Article: On -Transforms[show abstract] [hide abstract]
ABSTRACT: Any set of two legs in a Gough-Stewart platform sharing an attachment is defined as a Delta component. This component links a point in the platform (base) to a line in the base (platform). Thus, if the two legs, which are involved in a Delta component, are rearranged without altering the location of the line and the point in their base and platform local reference frames, the singularity locus of the Gough-Stewart platform remains the same, provided that no architectural singularities are introduced. Such leg rearrangements are defined as Delta-transforms, and they can be applied sequentially and simultaneously. Although it may seem counterintuitive at first glance, the rearrangement of legs using simultaneous Delta-transforms does not necessarily lead to leg configurations containing a Delta component. As a consequence, the application of Delta-transforms reveals itself as a simple, yet powerful, technique for the kinematic analysis of large families of Gough-Stewart platforms. It is also shown that these transforms shed new light on the characterization of architectural singularities and their associated self-motions.IEEE Transactions on Robotics 01/2010; · 2.54 Impact Factor
Article: On Delta -Transforms.IEEE Transactions on Robotics. 01/2009; 25:1225-1236.
[show abstract] [hide abstract]
ABSTRACT: In this paper we derive stratifications of the Euclidean motion group, which provide a complete description of the singular locus in the configuration space of a family of parallel manipulators, and we study the adjacency between the strata. We prove that classically known cell decompositions of the flag manifold restricted to the open subset parameterizing the affine real flags are still stratifications, and we introduce a refinement of the classical Ehresmann-Bruhat order that characterizes the adjacency between all the different strata. Then we show how, via a four-fold covering morphism, the stratifications of the Euclidean motion group are induced.Geometriae Dedicata 04/2012; 141(1):19-32. · 0.36 Impact Factor