Genericity and Singularities of Robot Manipulators

The kinematic singularities of robot manipulators are studied from the point of view of the theory of singularities. The notion of a generic\u27\u27 kinematic map, whose singularities form smooth manifolds of prescribed dimension in the joint space of the manipulator, is examined. For three-joint robots, an equivalent algebraic condition for genericity using the Jacobian determinants is derived. This condition lends itself to symbolic computation and is sufficient for the study of decoupled manipulators. Orientation and translation singularities of manipulators are studied in detail. A complete characterization of orientation singularities of robots with any number of joints is given. The translation singularities of the eight possible topologies of three-joint robots are studied and the conditions on the link parameters for nongenericity are determined

Generic Singularities of Robot Manipulators

The singularities of the differential kinematic map, i.e. of the manipulator Jacobian, are considered. The authors first examine the notion of a generic kinematic map, whose singularities form smooth manifolds of prescribed dimension in the joint space of the manipulator. For three-joint robots, an equivalent condition for genericity using determinants is derived. The condition lends itself to symbolic computation and is sufficient for the study of decoupled manipulators, i.e. manipulators that an be separated into a three-joint translating part and a three-joint orienting part. The results are illustrated by analyzing the singularities of two classes of three-joint positioning robots

Superfluid-Insulator transition of ultracold atoms in an optical lattice in the presence of a synthetic magnetic field

We study the Mott insulator-superfluid transition of ultracold bosonic atoms in a two-dimensional square optical lattice in the presence of a synthetic magnetic field with p/q (p and q being co-prime integers) flux quanta passing through each lattice plaquette. We show that on approach to the transition from the Mott side, the momentum distribution of the bosons exhibits q precursor peaks within the first magnetic Brillouin zone. We also provide an effective theory for the transition and show that it involves q interacting boson fields. We construct, from a mean-field analysis of this effective theory, the superfluid ground states near the transition and compute, for q=2,3, both the gapped and the gapless collective modes of these states. We suggest experiments to test our theory.Comment: 4 pages, 4 figs; v

Density wave and supersolid phases of correlated bosons in an optical lattice

Motivated by the recent experiment on the Bose-Einstein condensation of $^{52}$Cr atoms with long-range dipolar interactions (Werner J. et al., Phys. Rev. Lett., 94 (2005) 183201), we consider a system of bosons with repulsive nearest and next-nearest neighbor interactions in an optical lattice. The ground state phase diagram, calculated using the Gutzwiller ansatz, shows, apart from the superfluid (SF) and the Mott insulator (MI), two modulated phases, \textit{i.e.}, the charge density wave (CDW) and the supersolid (SS). Excitation spectra are also calculated which show a gap in the insulators, gapless, phonon mode in the superfluid and the supersolid, and a mode softening of superfluid excitations in the vicinity of the modulated phases. We discuss the possibility of observing these phases in cold dipolar atoms and propose experiments to detect them

Beneficiation of Low Grade Wolframite Ore from Degana, Rajasthan

Woframite is one of the principal minerals containing tungsten and is considered as a strategic mineral because of its importance and short supply. It is a tungstate of iron and manganese. Low grade wolframite deposits occur in India at Agargaon, Nagpur, Kalimati, Singhbhum, Chennda-pathar, Bankura, jhirpalla, Ahmedabad, Kadavur and Urura-kanad, Tiruchinapalli and on Rawat hill, near Degana, Jodhpur

Benefication of low grade wolramite ore from Degana, Rajasthan

WOLFRAMITE is one of the principal minerals containing tungsten and is considered as a strategic mineral because of its importance and short supply. It is a tungstate of iron and manganese (Fe, Mn) WO4 and generally occurs in prismatic or tabular crystals having a hardness of about 5 and a specific gravity ranging between 7.2 and 7.5. It is usually black in colour and has a good cleavage which causes it to fracture readily into thin flakes It is fairly magnetic. It usually contains 60'6%,', W03, though theoretically it should contain 76.5% WO3

Singular value decomposition in parametrised tests of post-Newtonian theory

Various coefficients of the 3.5 post-Newtonian (PN) phasing formula of non-spinning compact binaries moving in circular orbits is fully characterized by the two component masses. If two of these coefficients are independently measured, the masses can be estimated. Future gravitational wave observations could measure many of the 8 independent PN coefficients calculated to date. These additional measurements can be used to test the PN predictions of the underlying theory of gravity. Since all of these parameters are functions of the two component masses, there is strong correlation between the parameters when treated independently. Using Singular Value Decomposition of the Fisher information matrix, we remove this correlations and obtain a new set of parameters which are linear combinations of the original phasing coefficients. We show that the new set of parameters can be estimated with significantly improved accuracies which has implications for the ongoing efforts to implement parametrised tests of PN theory in the data analysis pipelines.Comment: 17 pages, 6 figures, Accepted for publication in Classical and Quantum Gravity (Matches with the published version