Classical screw theory: A fresh look using dual eigenvalue approach

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general screw systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. The formulation is illustrated with examples of practical manipulators.

A near-singular, flexure jointed, moment sensitive Stewart platform based fore-torque sensor

A force-torque sensor capable of accurate measurement of the three components of externally applied forces and moments is required for force control in robotic applications involving assembly operations. The goal in this paper is to design a Stewart platform based force torque sensor at a near-singular configuration sensitive to externally applied moments. In such a configuration, we show an enhanced mechanical amplification of leg forces and thereby higher sensitivity for the applied external moments. In other directions, the sensitivity will be that of a normal load sensor determined by the sensitivity of the sensing element and the associated electronic amplification, and all the six components of the force and torque can be sensed. In a sensor application, the friction, backlash and other non-linearities at the passive spherical joints of the Stewart platform will affect the measurements in unpredictable ways. In this sensor, we use flexural hinges at the leg interfaces of the base and platform of the sensor. The design dimensions of the flexure joints in the sensor have been arrived at using FEA. The sensor has been fabricated, assembled and instrumented. It has been calibrated for low level loads and is found to show linearity and marked sensitivity to moments about the three orthogonal X, Y and Z axes. This sensor is compatible for usage as a wrist sensor for a robot under development at ISRO Satellite Centre.

An Empirical Study of Synthesis of Multiple State Devices by Engineering Designers

Automated synthesis of mechanical designs is an important step towards the development of an intelligent CAD system. Research into methods for supporting conceptual design using automated synthesis has attracted much attention in the past decades. The research work presented here is based on an empirical study of the process of synthesis of multiple state mechanical devices. As a background to the work, the paper explores concepts of what mechanical device, state, single state and multiple state are, and in the context of the above observational studies, attempts to identify the outstanding issues for supporting multiple state synthesis of mechanical devices.

GEMS of SAPPhIRE: A Framework for Designing?

This paper proposes a framework of designing for conceptual and early embodiment design that uses physical laws and effects explicitly as a central aspect for designing. This is especially important in domains that make explicit use of physical laws and effects in their design, such as novel sensors. The objectives of the paper are: (a) Develop a model, (b) Empirically evaluate the model and (c) Propose a framework. The model is developed by integrating the activity- and outcome-based elements. The model is validated empirically by analyzing protocols of design sessions to find instances of activities and outcomes. Based on the findings, a framework is proposed on how designing should be done. Elements of GEMS (Generate-Evaluate-Modify-Select) and SAPPhIRE (State change-Action-Part-Phenomenon-Input-oRgan-Effect) are used for developing the model.Empirical evaluation confirms that designing can be modeled with the activity and outcome elements. The paper concludes with the identification of areas that require support and future work.

Effect of Electromagnetic Stirring on Macrosegregation during Solidification of a Binary Alloy

The effect of electromagnetic stirring of melt on the final macrosegregation in the continuous casting of an aluminium alloy billet is studied numerically. A continuum mixture model for solidification in presence of electromagnetic stirring is presented. As a case study, simulations are performed for direct chill (DC) casting of an Al-Cu alloy and the effect of electromagnetic stirring on macrosegregation is analysed. The model predicts the temperature, velocity, and species distribution in the mold. As a special case, we have also studied the case in which dendritic particles are fragmented at the interface due to vigorous electromagnetic stirring. For this case, an additional conservation equation for the transport of solid fraction is solved. For modeling the resistance offered by moving solid crystals, a switching function in the momentum equations is used for variation of viscosity. The fragmentation and transport of dendritic particles has a profound effect on the final macrosegregation and microstructure of the solidified billet. It is found that the application of electromagnetic stirring in continuous casting of billets results in better temperature uniformity and macrosegregation pattern.

Thermodynamic study of oxygen in liquid lead tin alloys

The activity coefficients of oxygen in liquid lead-tin alloys have been measured between 550 and 1100°C by use of solid oxide galvanic cells Pt, Ni-NiO I Zr02 Solid electrolyte I 0 (Pb + Sn), Cermet, Pt Pt, Fe-FeO I Zr02 Solid electrolyte I O(Pb + Sn), Cermet, Pt Alcock and Richardson's quasi-chemical equation, with the coordination number of atoms set to 2, is found to predict successfully the activity coefficients of oxygen in these alloys.The relative partial molar enthalpy and entropy of oxygen ?t 1 atom per cent in the alloys have been calculated from ttva variation of the activity coefficient with temperature. The addition of tin to an unsaturated solution of oxygen in lead is shown to decrease significantly both the partial molar enthalpy and entropy of oxygen. As the measurements were restricted to a narrow range between 750-1100'C in lead-rich alloys, however, the pronounced variation of the partial molar enthalpy of oxygen with temperature at constant alloy composition predicted by the quasi-chemical model could not be verified.

Solubility and activity of oxygen in liquid gallium and gallium copper alloys

The solubility of oxygen in liquid gallium in the temperature range 775 –1125 °C and in liquid gallium-copper alloys at 1100 °C, in equilibrium with β-Ga2O3, has been measured by an isopiestic equilibrium technique. The solubility of oxygen in pure gallium is given by the equation log (at.% O) = −7380/T + 4.264 (±0.03) Using recently measured values for the standard free energy of formation of β-Ga2O3 and assuming that oxygen obeys Sievert's law up to the saturation limit, the standard free energy of solution of oxygen in liquid gallium may be calculated : View the MathML sourceΔ°298 = −52 680 + 6.53T (±200) cal where the standard state for dissolved oxygen is an infinitely dilute solution in which the activity is equal to atomic per cent. The effect of copper on the activity of oxygen dissolved in liquid gallium is found to be in good agreement with that predicted by a recent quasichemical model in which it was assumed that each oxygen is interstitially coordinated to four metal atoms and that the nearest neighbour metal atoms lose approximately half their metallic cohesive energies.

Solubility and activity of oxygen in liquid indium and copper indium alloys

The solubility of oxygen in liquid indium in the temperature range 650–820 °C and in liquid copper-indium alloys at 1100 °C in equilibrium with indium sesquioxide has been measured by a phase equilibration technique. The solubility of oxygen in pure indium is given by the relation log(at.% O) = −4726/T + 3.73 (±0.08) Using the recently measured values for the standard free energy of formation of In2O3 and assuming that oxygen obeys Sievert's law up to saturation, the standard free energy of solution of molecular oxygen in liquid indium is calculated as View the MathML sourceΔG°= −51 440 + 8.07 T (±500) cal where the standard state for dissolved oxygen is an infinitely dilute solution in which activity is equal to atomic per cent. The effect of indium additions on the activity coefficient of oxygen dissolved in liquid copper was measured by a solid oxide galvanic cell. The interaction parameter ϵ0In is given by View the MathML source The experimentally determined variation of the activity coefficient of oxygen in dilute solution in Cu-In alloys is in fair agreement with that predicted by a quasichemical model in which each oxygen atom is assumed to be interstitially coordinated to four metal atoms and the nearest neighbour metal atoms are assumed to lose approximately half their metallic cohesive energies.

Aids in the design of microstrip components I: Getsinger's chart

Charts relating the capacitance to the width, spacing, thickness and height above the ground plane of coupled microstrips have been obtained. These are used to design hairpin line and hybrid hairpin line filters as well as multiplexers using microstrip comb line filters. The experimental results agree reasonably well with the design specifications. Getsinger's original charts for parallel coupled bars between parallel plates have been formulated for the microstrip case. Corresponding charts relating the capacitances to the width, spacing, thickness and height above the ground plane of coupled microstrips have been obtained. Examples of the use of these charts are shown in the design of hairpin lines and hybrid hairpin line filters as well as multiplexers using comb line filters. The hairpin line/hybrid hairpin line filters were designed to operate at a central frequency of 9÷5 GHz with 11 per cent bandwidth and 0÷5 dB ripple. The three filters constituting the comb line filters have center frequencies of 2÷4, 3÷0 and 3÷6 GHz. The components so designed were fabricated and tested. The dielectric used for the microstrip was teflon. Experimental curves for the attenuation (insertion loss) and VSWR are given. The design specifications arc satisfied quite well.

Monitoring Himalayan cryosphere using remote sensing techniques

In the Himalayas, large area is covered by glaciers, seasonal snow and changes in its extent can influence availability of water in the Himalayan Rivers. In this paper, changes in glacial extent, glacial mass balance and seasonal snow cover have been discussed. Field and satellite based investigations suggest, most of the Himalayan glaciers are retreating though the rate of retreat is varying from glacier to glacier, ranging from few meters to almost 50 meters per year, depending upon the numerous glacial, terrain and meteorological parameters. Retreat was estimated for 1868 glaciers in eleven basins distributed across the Indian Himalaya since 1962 to 2001/02. Estimates show an overall reduction in glacier area from 6332 to 5329 sq km, an overall deglaciation of 16 percent.Snow line at the end of ablation season on the Chhota Shigri glacier suggests a change in altitude from 4900 to 5200 m from late 1970’s to the present. Seasonal snow cover monitoring of the Himalaya has shown large amounts of snow cover depletion in early part of winter, i.e. from October to December. For many basins located in lower altitude and in south of Pir Panjal range, snow ablation was observed through out the winter season. In addition, average stream runoff of the Baspa basin during the month of December shows an increase by 75 per cent. This combination of glacial retreat, negative mass balance, early melting of seasonal snow cover and winter time increase in stream runoff suggest an influence of climate change on the Himalayan cryosphere.

Error, Confidence, and Cost in Engineering Computations

The questions that one should answer in engineering computations - deterministic, probabilistic/randomized, as well as heuristic - are (i) how good the computed results/outputs are and (ii) how much the cost in terms of amount of computation and the amount of storage utilized in getting the outputs is. The absolutely errorfree quantities as well as the completely errorless computations done in a natural process can never be captured by any means that we have at our disposal. While the computations including the input real quantities in nature/natural processes are exact, all the computations that we do using a digital computer or are carried out in an embedded form are never exact. The input data for such computations are also never exact because any measuring instrument has inherent error of a fixed order associated with it and this error, as a matter of hypothesis and not as a matter of assumption, is not less than 0.005 per cent. Here by error we imply relative error bounds. The fact that exact error is never known under any circumstances and any context implies that the term error is nothing but error-bounds. Further, in engineering computations, it is the relative error or, equivalently, the relative error-bounds (and not the absolute error) which is supremely important in providing us the information regarding the quality of the results/outputs. Another important fact is that inconsistency and/or near-consistency in nature, i.e., in problems created from nature is completely nonexistent while in our modelling of the natural problems we may introduce inconsistency or near-inconsistency due to human error or due to inherent non-removable error associated with any measuring device or due to assumptions introduced to make the problem solvable or more easily solvable in practice. Thus if we discover any inconsistency or possibly any near-inconsistency in a mathematical model, it is certainly due to any or all of the three foregoing factors. We do, however, go ahead to solve such inconsistent/near-consistent problems and do get results that could be useful in real-world situations. The talk considers several deterministic, probabilistic, and heuristic algorithms in numerical optimisation, other numerical and statistical computations, and in PAC (probably approximately correct) learning models. It highlights the quality of the results/outputs through specifying relative error-bounds along with the associated confidence level, and the cost, viz., amount of computations and that of storage through complexity. It points out the limitation in error-free computations (wherever possible, i.e., where the number of arithmetic operations is finite and is known a priori) as well as in the usage of interval arithmetic. Further, the interdependence among the error, the confidence, and the cost is discussed.

Compositionally modulated Pb(Mg1/3Nb2/3)O-3-PbTiO3 relaxor thin films deposited by pulsed excimer laser ablation technique

Thin films of (1-x)Pb(Mg1/3Nb2/3)O-3 - xPbTiO(3) (x = 0.1 to 0.3)(PMN-PT) were deposited on the platinum coated silicon substrate by pulsed excimer laser ablation technique. A template layer of LaSr0.5Co0.5O3 (LSCO) was deposited on platinum substrate prior to the deposition of PMN-PT thin films. The composition and the structure of the films were modulated via proper variation of the deposition parameter such as substrate temperature, laser fluence and thickness of the template layers. We observed the impact of the thickness of LSCO template layer on the orientation of the films. A room temperature dielectric constant varying from 2000 to 4500 was noted for different composition of the films. The dielectric properties of the films were studied over the frequency range of 100 Hz - 100 kHz over a wide range of temperatures. The films exhibited the relaxor- type behavior that was characterized by the frequency dispersion of the temperature of dielectric constant maxima (T-m) and also diffuse phase transition. C1 Indian Inst Sci, Mat Res Ctr, Bangalore, Karnataka 560012 India.