A differential-geometric analysis of singularities of point trajectories of serial and parallel manipulators

In this paper, we present a differential-geometric approach to analyze the singularities of task space point trajectories of two and three-degree-of-freedom serial and parallel manipulators. At non-singular configurations, the first-order, local properties are characterized by metric coefficients, and, geometrically, by the shape and size of a velocity ellipse or an ellipsoid. At singular configurations, the determinant of the matrix of metric coefficients is zero and the velocity ellipsoid degenerates to an ellipse, a line or a point, and the area or the volume of the velocity ellipse or ellipsoid becomes zero. The degeneracies of the velocity ellipsoid or ellipse gives a simple geometric picture of the possible task space velocities at a singular configuration. To study the second-order properties at a singularity, we use the derivatives of the metric coefficients and the rate of change of area or volume. The derivatives are shown to be related to the possible task space accelerations at a singular configuration. In the case of parallel manipulators, singularities may lead to either loss or gain of one or more degrees-of-freedom. For loss of one or more degrees-of-freedom, ther possible velocities and accelerations are again obtained from a modified metric and derivatives of the metric coefficients. In the case of a gain of one or more degrees-of-freedom, the possible task space velocities can be pictured as growth to lines, ellipses, and ellipsoids. The theoretical results are illustrated with the help of a general spatial 2R manipulator and a three-degree-of-freedom RPSSPR-SPR parallel manipulator.

Symmetry-breaking transitions in equilibrium shapes of coherent precipitates: Effect of elastic anisotropy and inhomogeneity

We examine the symmetry-breaking transitions in equilibrium shapes of coherent precipitates in two-dimensional (2-D) systems under a plane-strain condition with the principal misfit strain components epsilon(xx)*. and epsilon(yy)*. For systems with cubic elastic moduli, we first show all the shape transitions associated with different values of t = epsilon(yy)*/epsilon(xx)*. We also characterize each of these transitions, by studying its dependence on elastic anisotropy and inhomogeneity. For systems with dilatational misfit (t = 1) and those with pure shear misfit (t = -1), the transition is from an equiaxed shape to an elongated shape, resulting in a break in rotational symmetry. For systems with nondilatational misfit (-1 < t < 1; t not equal 0), the transition involves a break in mirror symmetries normal to the x- and y-axes. The transition is continuous in all cases, except when 0 < t < 1. For systems which allow an invariant line (-1 less than or equal to t < 0), the critical size increases with an increase in the particle stiffness. However, for systems which do not allow an invariant line (0 < t less than or equal to 1), the critical size first decreases, reaches a minimum, and then starts increasing with increasing particle stiffness; moreover, the transition is also forbidden when the particle stiffness is greater than a critical value.

Effect of lattice orientation on crack tip constraint in ductile single crystals

In this work, the effect of lattice orientation on the fields prevailing near a notch tip is investigated pertaining to various constraint levels in FCC single crystals. A modified boundary layer formulation is employed and numerical solutions under mode I, plane strain conditions are generated by assuming an elastic-perfectly plastic FCC single crystal. The analysis is carried out corresponding to different lattice orientations with respect to the notch line. It is found that the near-tip deformation field, especially the development of kink or slip shear bands is sensitive to the constraint level. The stress distribution and the size and shape of the plastic zone near the notch tip are also strongly influenced by the level of T-stress. The present results clearly establish that ductile single crystal fracture geometries would progressively lose crack tip constraint as the T-stress becomes more negative irrespective of lattice orientation. Also, the near-tip field for a range of constraint levels can be characterized by two-parameters such as K-T or J-Q as in isotropic plastic solids.

Mapping of large scale 158 mu m [CII] line emission: Orion A

We present the first results of an observational programme undertaken to map the fine structure line emission of singly ionized carbon ([ CII] 157 : 7409 mum) over extended regions using a Fabry Perot spectrometer newly installed at the focal plane of a 100 cm balloon- borne far- infrared telescope. This new combination of instruments has a velocity resolution of similar to 200 km s(-1) and an angular resolution of 1.'5. During the first flight, an area of 30' x 15' in Orion A was mapped. These observations extend over a larger area than previous observations, the map is fully sampled and the spectral scanning method used enables reliable estimation of the continuum emission at frequencies adjacent to the [ CII] line. The total [ CII] line luminosity, calculated by considering up to 20% of the maximum line intensity is 0.04% of the luminosity of the far- infrared continuum. We have compared the [ CII] intensity distribution with the velocity- integrated intensity distributions of (CO)-C-13(1- 0), CI(1- 0) and CO( 3- 2) from the literature. Comparison of the [ CII], [ CI] and the radio continuum intensity distributions indicates that the largescale [ CII] emission originates mainly from the neutral gas, except at the position of M 43, where no [ CI] emission corresponding to the [ CII] emission is seen. Substantial part of the [ CII] emission from here originates from the ionized gas. The observed line intensities and ratios have been analyzed using the PDR models by Kaufman et al. ( 1999) to derive the incident UV flux and volume density at a few selected positions. The models reproduce the observations reasonably well at most positions excepting the [ CII] peak ( which coincides with the position of theta(1) Ori C). Possible reason for the failure could be the simplifying assumption of a homogeneous plane parallel slab in place of a more complicated geometry.

Hyper-activation of the TCP4 transcription factor in Arabidopsis thaliana accelerates multiple aspects of plant maturation

Plant organs are initiated as primordial outgrowths, and require controlled cell division and differentiation to achieve their final size and shape. Superimposed on this is another developmental program that orchestrates the switch from vegetative to reproductive to senescence stages in the life cycle. These require sequential function of heterochronic regulators. Little is known regarding the coordination between organ and organismal growth in plants. The TCP gene family encodes transcription factors that control diverse developmental traits, and a subgroup of class II TCP genes regulate leaf morphogenesis. Absence of these genes results in large, crinkly leaves due to excess division, mainly at margins. It has been suggested that these class II TCPs modulate the spatio-temporal control of differentiation in a growing leaf, rather than regulating cell proliferation per se. However, the link between class II TCP action and cell growth has not been established. As loss-of-function mutants of individual TCP genes in Arabidopsis are not very informative due to gene redundancy, we generated a transgenic line that expressed a hyper-activated form of TCP4 in its endogenous expression domain. This resulted in premature onset of maturation and decreased cell proliferation, leading to much smaller leaves, with cup-shaped lamina in extreme cases. Further, the transgenic line initiated leaves faster than wild-type and underwent precocious reproductive maturation due to a shortened adult vegetative phase. Early senescence and severe fertility defects were also observed. Thus, hyper-activation of TCP4 revealed its role in determining the timing of crucial developmental events, both at the organ and organism level.

Boxicity of Line Graphs

The boxicity of a graph H, denoted by View the MathML source, is the minimum integer k such that H is an intersection graph of axis-parallel k-dimensional boxes in View the MathML source. In this paper we show that for a line graph G of a multigraph, View the MathML source, where Δ(G) denotes the maximum degree of G. Since G is a line graph, Δ(G)≤2(χ(G)−1), where χ(G) denotes the chromatic number of G, and therefore, View the MathML source. For the d-dimensional hypercube Qd, we prove that View the MathML source. The question of finding a nontrivial lower bound for View the MathML source was left open by Chandran and Sivadasan in [L. Sunil Chandran, Naveen Sivadasan, The cubicity of Hypercube Graphs. Discrete Mathematics 308 (23) (2008) 5795–5800]. The above results are consequences of bounds that we obtain for the boxicity of a fully subdivided graph (a graph that can be obtained by subdividing every edge of a graph exactly once).

Potential and Electric Field Profiles for Transmission line Insulators

Transmission of bulk power at high voltages over very long distances has become very imperative. At present, throughout the globe, this task has been mostly performed by overhead transmission lines. The dual task of mechanically supporting and electrically isolating the live phase conductors from the support tower is performed by string insulators. Whether in clean condition or under polluted conditions, the electrical stress distribution along the insulators governs the possible flashover, which is quite detrimental to the system. However, a reliable data on stress distribution in commonly employed string insulators are rather scarce. Considering this, the present work has made an attempt to study accurately, the field distribution in 220 kV strings for six different types of porcelain/ceramic insulators (Normal and Antifog discs) used for high voltage transmission. The surface charge simulation method is employed for the required field computation. Voltage and electric stress distribution is deduced and compared across different types of discs. A comparison on normalised surface resistance, which is an indicator for the stress concentration under polluted condition, is also attempted.

Micro stepping of Shape Memory Alloy based Poly Phase motor

In literature we find broadly two types of shape memory alloy based motors namely limited rotation motor and unlimited rotation motor. The unlimited rotation type SMA based motor reported in literature uses SMA springs for actuation. An attempt has been made in this paper to develop an unlimited rotation type balanced poly phase motor based on SMA wire in series with a spring in each phase. By isolating SMA actuation and spring action we are able achieve a constant force by the SMA wire through out its range of operation. The Poly phase motor can be used in stepping mode for generating incremental motion and servo mode for generating continuous motion. A method of achieving servo motion by micro stepping is presented. Micro stepping consists of controlling single-phase temperature with a position feedback. The motor has been modeled with a new approach to the SMA wire Hysterysis model. Motor is simulated for different responses and the results are compared with the experimental data.

Shape memory alloy based motor

Design and characterization of a new shape memory alloy wire based Poly Phase Motor has been reported in this paper. The motor can be used either in stepping mode or in servo mode of operation. Each phase of the motor consists of an SMA wire with a spring in series. The principle of operation of the poly phase motor is presented. The motor resembles a stepper motor in its functioning though the actuation principles are different and hence has been characterized similar to a stepper motor. The motor can be actuated in either direction with different phase sequencing methods, which are presented in this work. The motor is modelled and simulated and the results of simulations and experiments are presented. The experimental model of the motor is of dimension 150mm square, 20mm thick and uses SMA wire of 0·4mm diameter and 125mm of length in each phase.