Singularity Analysis of Zero-Torsion Parallel Mechanisms

International audienceThis paper presents the singularity analysis of four 3-DOF symmetric zero-torsion parallel mechanisms. These mechanisms are composed of three identical legs ending with a spherical joint that is constrained to move in one of three equally spaced plane intersecting at one line. The computation of the singularity loci is based on the degeneracy of the system of screws applied on the platform by the legs. The whole study is based on the use of a special orientation representation, previously introduced under the name of Tilt-and-Torsion angles. This representation is briefly introduced. Then the interdependence between the Cartesian coordinates of the general class of parallel mechanisms is derived. Finally, the singularity loci are derived and the size of the workspace taking into account all singular configurations is shown

Synthesis and singularity analysis of N-UU parallel wrists: A symmetric space approach

We report some recent advances in kinematics and singularity analysis of the mirrorsymmetric N-UU parallel wrists using symmetric space theory. We show that both the finite displacement and infinitesimal singularity kinematics of a N-UU wrist are governed by the mirror symmetry property and half-angle property of the underlying motion manifold, which is a symmetric submanifold of the special Euclidean group SE(3). Our result is stronger than and may be considered a closure of Hunt's argument for instantaneous mirror symmetry in his pioneering exposition of constant velocity shaft couplings. Moreover, we show that the wrist can, to some extent, be treated as a spherical mechanism, even though dependent translation exists, and the singularity-free workspace of a N-UU wrist may be analytically derived. This leads to a straightforward optimal design for maximal singularity-free workspace

The cosmological BCS mechanism and the Big Bang Singularity

We provide a novel mechanism that resolves the Big Bang Singularity present in FRW space-times without the need for ghost fields. Building on the fact that a four-fermion interaction arises in General Relativity when fermions are covariantly coupled, we show that at early times the decrease in scale factor enhances the correlation between pairs of fermions. This enhancement leads to a BCS-like condensation of the fermions and opens a gap dynamically driving the Hubble parameter $H$ to zero and results in a non-singular bounce, at least in some special cases.Comment: replaced to match the journal versio

Cosmology in Palatini theories of gravity

We discuss recent results on the cosmology of extended theories of gravity formulated in the Palatini approach, i.e., assuming that metric and connection are independent fields. In particular, we focus on the attempts to explain the cosmic speedup with f(R) theories and on models that avoid the big bang singularity. The field equations for gravity Lagrangians of the form f(g_{\mu\nu},{R^\alpha}_{\beta\mu\nu}) (including torsion) are explicitly derived and discussed.Comment: 16 pages, no figures. Contribution to the Proceedings of Spanish Relativity Meeting ERE2011, Madrid 29 August - 2 September 2011 . Plenary tal