Redundancy resolution using a tractrix and its application to real-time simulations of hyper-redundant manipulators, snakes and tying of knots

To realistically simulate the motion of flexible objects such as ropes, strings, snakes, or human hair,one strategy is to discretise the object into a large number of small rigid links connected by rotary or spherical joints. The discretised system is highly redundant and the rotations at the joints (or the motion of the other links) for a desired Cartesian motion of the end of a link cannot be solved uniquely. In this paper, we propose a novel strategy to resolve the redundancy in such hyper-redundant systems.We make use of the classical tractrix curve and its attractive features. For a desired Cartesian motion of the `head'of a link, the `tail' of the link is moved according to a tractrix,and recursively all links of the discretised objects are moved along different tractrix curves. We show that the use of a tractrix curve leads to a more `natural' motion of the entire object since the motion is distributed uniformly along the entire object with the displacements tending to diminish from the `head' to the `tail'. We also show that the computation of the motion of the links can be done in real time since it involves evaluation of simple algebraic, trigonometric and hyperbolic functions. The strategy is illustrated by simulations of a snake, tying of knots with a rope and a solution of the inverse kinematics of a planar hyper-redundant manipulator.

An algebraic formulation of exact force-, moment-isotropy in spatial parallel manipulators

In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions.We use the force and moment transformation matrices separately,and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation has been applied to a class of Stewart platform manipulators. We obtain multi-parameter families of isotropic manipulator analytically. In addition to computing the isotropic configurations of an existing manipulator,we demonstrate a procedure for designing the manipulator for isotropy at a given configuration.

Plane wave analysis of rectangular axial-inlet, axial-outlet and transverse-inlet, transverse-outlet air cleaners

In this work, one-dimensional flow-acoustic analysis of two basic configurations of air cleaners, (i) Rectangular Axial-Inlet, Axial-Outlet (RAIAO) and (ii) Rectangular Transverse-Inlet, Transverse-Outlet (RTITO), has been presented. This 1-D analytical approach has been verified with the help of 3-D FEM based software. Through subtraction of the acoustic performance of the bare plenum (without filter element) from that of the complete air cleaner box, the solitary performance of the filter element has been evaluated. Part of the present analysis illustrates that the analytical formulation remains effective even with offset positioning of the air pipes from the centre of the cross section of the air cleaner. The 1-D analytical tool computes much faster than its 3-D simulation counterpart. The present analysis not only predicts the acoustical impact of mean flow, but it also depicts the scenario with increased resistance of the filter element. Thus, the proposed 1-D analysis would help in the design of acoustically efficient air cleaners for automotive applications. (C) 2011 Institute of Noise Control Engineering.

A simple numerical method for three-dimensional analysis of simple expansion chamber mufflers of rectangular as well as circular cross-section with a stationary medium

Three-dimensional effects are a primary source of discrepancy between the measured values of automotive muffler performance and those predicted by the plane wave theory at higher frequencies. The basically exact method of (truncated) eigenfunction expansions for simple expansion chambers involves very complicated algebra, and the numerical finite element method requires large computation time and core storage. A simple numerical method is presented in this paper. It makes use of compatibility conditions for acoustic pressure and particle velocity at a number of equally spaced points in the planes of the junctions (or area discontinuities) to generate the required number of algebraic equations for evaluation of the relative amplitudes of the various modes (eigenfunctions), the total number of which is proportional to the area ratio. The method is demonstrated for evaluation of the four-pole parameters of rigid-walled, simple expansion chambers of rectangular as well as circular cross-section for the case of a stationary medium. Computed values of transmission loss are compared with those computed by means of the plane wave theory, in order to highlight the onset (cutting-on) of various higher order modes and the effect thereof on transmission loss of the muffler. These are also compared with predictions of the finite element methods (FEM) and the exact methods involving eigenfunction expansions, in order to demonstrate the accuracy of the simple method presented here.

The pursuit-evasion problem of two aircraft in a horizontal plane

The pursuit-evasion problem of two aircraft in a horizontal plane is modelled as a zerosum differential game with capture time as payoff. The aircraft are modelled as point masses with thrust and bank angle controls. The games of kind and degree for this differential game are solved.

The x¿n-x Plane for Analysis of Certain Second-Order Nonlinear Systems

Analysis of certain second-order nonlinear systems, not easily amenable to the phase-plane methods, and described by either of the following differential equations xÿn-2ÿ+ f(x)xÿ2n+g(x)xÿn+h(x)=0 ÿ+f(x)xÿn+h(x)=0 n≫0 can be effected easily by drawing the entire portrait of trajectories on a new plane; that is, on one of the xÿnÿx planes. Simple equations are given to evaluate time from a trajectory on any of these n planes. Poincaré's fundamental phase plane xÿÿx is conceived of as the simplest case of the general xÿnÿx plane.

Phase-plane techniques for the solution of transient-stability problems

The paper presents a graphical-numerical method for determining the transient stability limits of a two-machine system under the usual assumptions of constant input, no damping and constant voltage behind transient reactance. The method presented is based on the phase-plane criterion,1, 2 in contrast to the usual step-by-step and equal-area methods. For the transient stability limit of a two-machine system, under the assumptions stated, the sum of the kinetic energy and the potential energy, at the instant of fault clearing, should just be equal to the maximum value of the potential energy which the machines can accommodate with the fault cleared. The assumption of constant voltage behind transient reactance is then discarded in favour of the more accurate assumption of constant field flux linkages. Finally, the method is extended to include the effect of field decrement and damping. A number of examples corresponding to each case are worked out, and the results obtained by the proposed method are compared with those obtained by the usual methods.

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.

Techniques for Analysis of Certain Nonlinear Systems

This paper suggests the use of simple transformations like ÿ=kx, kx2 for second-order nonlinear differential equations to effect rapid plotting of the phase-plane trajectories. The method is particularly helpful in determining quickly the trajectory slopes along simple curves in any desired region of the phase plane. New planes such as the tÿ-x, tÿ2-x are considered for the study of some groups of nonlinear time-varying systems. Suggestions for solving certain higher-order nonlinear systems are also made.

Algebraic Approaches to Space-Time Code Construction for Multiple-Antenna Communication

A major challenge in wireless communications is overcoming the deleterious effects of fading, a phenomenon largely responsible for the seemingly inevitable dropped call. Multiple-antennas communication systems, commonly referred to as MIMO systems, employ multiple antennas at both transmitter and receiver, thereby creating a multitude of signalling pathways between transmitter and receiver. These multiple pathways give the signal a diversity advantage with which to combat fading. Apart from helping overcome the effects of fading, MIMO systems can also be shown to provide a manyfold increase in the amount of information that can be transmitted from transmitter to receiver. Not surprisingly,MIMO has played, and continues to play, a key role in the advancement of wireless communication.Space-time codes are a reference to a signalling format in which information about the message is dispersed across both the spatial (or antenna) and time dimension. Algebraic techniques drawing from algebraic structures such as rings, fields and algebras, have been extensively employed in the construction of optimal space-time codes that enable the potential of MIMO communication to be realized, some of which have found their way into the IEEE wireless communication standards. In this tutorial article, reflecting the authors’interests in this area, we survey some of these techniques.

Approximate synthesis formulas for microstrip line with aperture in ground plane

Approximate closed-form expressions for the propagation characteristics of a microstrip line with a symmetrical aperture in its ground plane are reported in this article. Well-known expressions for the characteristic impedance of a regular microstrip line have been modified to incorporate the effect of this aperture. The accuracy of these expressions for various values of substrate thickness, permittivity and line width has been studied in detail by fullwave simulations. This has been further verified by measurements. These expressions are easier to compute and find immense use in the design of broadband filters, tight couplers, power dividers, transformers, delay lines, and matching circuits. A broadband filter with aperture in ground plane is demonstrated in this article. (c) 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2012.

Image Encryption with Space-filling Curves

Conventional encryption techniques are usually applicable for text data and often unsuited for encrypting multimedia objects for two reasons. Firstly, the huge sizes associated with multimedia objects make conventional encryption computationally costly. Secondly, multimedia objects come with massive redundancies which are useful in avoiding encryption of the objects in their entirety. Hence a class of encryption techniques devoted to encrypting multimedia objects like images have been developed. These techniques make use of the fact that the data comprising multimedia objects like images could in general be seggregated into two disjoint components, namely salient and non-salient. While the former component contributes to the perceptual quality of the object, the latter only adds minor details to it. In the context of images, the salient component is often much smaller in size than the non-salient component. Encryption effort is considerably reduced if only the salient component is encrypted while leaving the other component unencrypted. A key challenge is to find means to achieve a desirable seggregation so that the unencrypted component does not reveal any information about the object itself. In this study, an image encryption approach that uses fractal structures known as space-filling curves- in order to reduce the encryption overload is presented. In addition, the approach also enables a high quality lossy compression of images.

Bases and Ideal Generators for Projective Monomial Curves

In this article we study bases for projective monomial curves and the relationship between the basis and the set of generators for the defining ideal of the curve. We understand this relationship best for curves in P-3 and for curves defined by an arithmetic progression. We are able to prove that the latter are set theoretic complete intersections.