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 relook at Reissner's theory of plates in bending

Shear deformation and higher order theories of plates in bending are (generally) based on plate element equilibrium equations derived either through variational principles or other methods. They involve coupling of flexure with torsion (torsion-type) problem and if applied vertical load is along one face of the plate, coupling even with extension problem. These coupled problems with reference to vertical deflection of plate in flexure result in artificial deflection due to torsion and increased deflection of faces of the plate due to extension. Coupling in the former case is eliminated earlier using an iterative method for analysis of thick plates in bending. The method is extended here for the analysis of associated stretching problem in flexure.

A Kinematic Theory for Planar Hoberman and Other Novel Foldable Mechanisms

In this paper, we present a kinematic theory for Hoberman and other similar foldable linkages. By recognizing that the building blocks of such linkages can be modeled as planar linkages, different classes of possible solutions are systematically obtained including some novel arrangements. Criteria for foldability are arrived by analyzing the algebraic locus of the coupler curve of a PRRP linkage. They help explain generalized Hoberman and other mechanisms reported in the literature. New properties of such mechanisms including the extent of foldability, shape-preservation of the inner and outer profiles, multi-segmented assemblies and heterogeneous circumferential arrangements are derived. The design equations derived here make the conception of even complex planar radially foldable mechanisms systematic and easy. Representative examples are presented to illustrate the usage of the design equations and the kinematic theory.

High-Rate Vector Quantization for Noisy Channels With Applications to Wideband Speech Spectrum Compression

This paper considers the high-rate performance of source coding for noisy discrete symmetric channels with random index assignment (IA). Accurate analytical models are developed to characterize the expected distortion performance of vector quantization (VQ) for a large class of distortion measures. It is shown that when the point density is continuous, the distortion can be approximated as the sum of the source quantization distortion and the channel-error induced distortion. Expressions are also derived for the continuous point density that minimizes the expected distortion. Next, for the case of mean squared error distortion, a more accurate analytical model for the distortion is derived by allowing the point density to have a singular component. The extent of the singularity is also characterized. These results provide analytical models for the expected distortion performance of both conventional VQ as well as for channel-optimized VQ. As a practical example, compression of the linear predictive coding parameters in the wideband speech spectrum is considered, with the log spectral distortion as performance metric. The theory is able to correctly predict the channel error rate that is permissible for operation at a particular level of distortion.

Multi-UAV Task Allocation using Team Theory

A multiple UAV search and attack mission in a battlefield involves allocating UAVs to different target tasks efficiently. This task allocation becomes difficult when there is no communication among the UAVs and the UAVs sensors have limited range to detect the targets and neighbouring UAVs, and assess target status. In this paper, we propose a team theoretic approach to efficiently allocate UAVs to the targets with the constraint that UAVs do not communicate among themselves and have limited sensor range. We study the performance of team theoretic approach for task allocation on a battle field scenario. The performance obtained through team theory is compared with two other methods, namely, limited sensor range but with communication among all the UAVs, and greedy strategy with limited sensor range and no communication. It is found that the team theoretic strategy performs the best even though it assumes limited sensor range and no communication.

Scattering theory and linear optimal control: Regulator and servo problems

In this paper, several known computational solutions are readily obtained in a very natural way for the linear regulator, fixed end-point and servo-mechanism problems using a certain frame-work from scattering theory. The relationships between the solutions to the linear regulator problem with different terminal costs and the interplay between the forward and backward equations have enabled a concise derivation of the partitioned equations, the forward-backward equations, and Chandrasekhar equations for the problem. These methods have been extended to the fixed end-point, servo, and tracking problems.

Discrete control algorithms for a tubular ammonia reactor

The specific objective of this paper is to develop direct digital control strategies for an ammonia reactor using quadratic regulator theory and compare the performance of the resultant control system with that under conventional PID regulators. The controller design studies are based on a ninth order state-space model obtained from the exact nonlinear distributed model using linearization and lumping approximations. The evaluation of these controllers with reference to their disturbance rejection capabilities and transient response characteristics, is carried out using hybrid computer simulation.

Dispersion and vaporization of biofuels and conventional fuels in a crossflow pre-mixer

In lean premixed pre-vaporized (LPP) combustion, controlled atomization, dispersion and vaporization of different types of liquid fuel in the premixer are the key factors required to stabilize the combustion process and improve the efficiency. The dispersion and vaporization process for biofuels and conventional fuels sprayed into a crossflow pre-mixer have been simulated and analyzed with respect to vaporization rate, degree of mixedness and homogeneity. Two major biofuels under investigation are Ethanol and Rapeseed Methyl Esters (RME), while conventional fuels are gasoline and jet-A. First, the numerical code is validated by comparing with the experimental data of single n-heptane and decane droplet evaporating under both moderate and high temperature convective air now. Next, the spray simulations were conducted with monodispersed droplets with an initial diameter of 80 mu m injected into a turbulent crossflow of air with a typical velocity of 10 m/s and temperature of around 800K. Vaporization time scales of different fuels are found to be very different. The droplet diameter reduction and surface temperature rise were found to be strongly dependent on the fuel properties. Gasoline droplet exhibited a much faster vaporization due a combination of higher vapor pressure and smaller latent heat of vaporization compared to other fuels. Mono-dispersed spray was adopted with the expectation of achieving more homogeneous fuel droplet size than poly-dispersed spray. However, the diameter histogram in the zone near the pre-mixer exit shows a large range of droplet diameter distributions for all the fuels. In order to improve the vaporization performance, fuels were pre-heated before injection. Results show that the Sauter mean diameter of ethanol improved from 52.8% of the initial injection size to 48.2%, while jet-A improved from 48.4% to 18.6% and RME improved from 63.5% to 31.3%. The diameter histogram showed improved vaporization performance of jet-A. (C) 2011 Elsevier Ltd. All rights reserved.

Study of symmetrical and related components through the theory of linear vector spaces

The paper proposes a study of symmetrical and related components, based on the theory of linear vector spaces. Using the concept of equivalence, the transformation matrixes of Clarke, Kimbark, Concordia, Boyajian and Koga are shown to be column equivalent to Fortescue's symmetrical-component transformation matrix. With a constraint on power, criteria are presented for the choice of bases for voltage and current vector spaces. In particular, it is shown that, for power invariance, either the same orthonormal (self-reciprocal) basis must be chosen for both voltage and current vector spaces, or the basis of one must be chosen to be reciprocal to that of the other. The original �¿, ��, 0 components of Clarke are modified to achieve power invariance. For machine analysis, it is shown that invariant transformations lead to reciprocal mutual inductances between the equivalent circuits. The relative merits of the various components are discussed.

Microwave cavity resonators. Some perturbation effects and their applications

Lagrange's equation is utilized to show the analogy of a lossless microwave cavity resonator with the conventional LC network. A brief discussion on the resonant frequencies of a microwave cavity resonator and the two degenerate companion modes H01 and E11 appearing in a cavity is given. The first order perturbation theory of a small deformation of the wall of a cavity is discussed. The effects of perturbation, such as the change in the resonant frequency and the Q of a cavity, the change in the electromagnetic field configurations and hence mixing of modes are also discussed. An expression for the coupling coefficient between the two degenerate modes H01 and E11 is derived with the help of the field equations. Results indicate that in the absence of perturbation the above two degenerate modes can co-exist without losing their individual identities. Several applications of the perturbation theory, such as the measurement of the dielectric properties of matter, study of ferromagnetic resonance, etc., are described.

Group Actions and Elementary Number Theory

Abstract | In this article the shuffling of cards is studied by using the concept of a group action. We use some fundamental results in Elementary Number Theory to obtain formulas for the orders of some special shufflings, namely the Faro and Monge shufflings and give necessary and sufficient conditions for the Monge shuffling to be a cycle. In the final section we extend the considerations to the shuffling of multisets.

Galois Theory and Solvable Equations of Prime Degree

In this article we review classical and modern Galois theory with historical evolution and prove a criterion of Galois for solvability of an irreducible separable polynomial of prime degree over an arbitrary field k and give many illustrative examples.