Synthesis of workspaces of planar manipulators with arbitrary topology using shape representation and simulated annealing

This paper presents a general methodology for the synthesis of the external boundary of the workspaces of a planar manipulator with arbitrary topology. Both the desired workspace and the manipulator workspaces are identified by their boundaries and are treated as simple closed polygons. The paper introduces the concept of best match configuration and shows that the corresponding transformation can be obtained by using the concept of shape normalization available in image processing literature. Introduction of the concept of shape in workspace synthesis allows highly accurate synthesis with fewer numbers of design variables. This paper uses a new global property based vector representation for the shape of the workspaces which is computationally efficient because six out of the seven elements of this vector are obtained as a by-product of the shape normalization procedure. The synthesis of workspaces is formulated as an optimization problem where the distance between the shape vector of the desired workspace and that of the workspace of the manipulator at hand are minimized by changing the dimensional parameters of the manipulator. In view of the irregular nature of the error manifold, the statistical optimization procedure of simulated annealing has been used. A number of worked-out examples illustrate the generality and efficiency of the present method. (C) 1998 Elsevier Science Ltd. All rights reserved.

Gaussian Schell-model beams and general shape invariance

We present two six-parameter families of anisotropic Gaussian Schell-model beams that propagate in a shape-invariant manner, with the intensity distribution continuously twisting about the beam axis. The two families differ in the sense or helicity of this beam twist. The propagation characteristics of these shape-invariant beams are studied, and the restrictions on the beam parameters that arise from the optical uncertainty principle are brought out. Shape invariance is traced to a fundamental dynamical symmetry that underlies these beams. This symmetry is the product of spatial rotation and fractional Fourier transformation.

A Global Constraint On Relative Rotation To Avoid Lumped Compliant Mechanisms In Topology Optimization

Some of the well known formulations for topology optimization of compliant mechanisms could lead to lumped compliant mechanisms. In lumped compliance, most of the elastic deformation in a mechanism occurs at few points, while rest of the mechanism remains more or less rigid. Such points are referred to as point-flexures. It has been noted in literature that high relative rotation is associated with point-flexures. In literature we also find a formulation of local constraint on relative rotations to avoid lumped compliance. However it is well known that a global constraint is easier to handle than a local constraint, by a numerical optimization algorithm. The current work presents a way of putting global constraint on relative rotations. This constraint is also simpler to implement since it uses linearized rotation at the center of finite-elements, to compute relative rotations. I show the results obtained by using this constraint oil the following benchmark problems - displacement inverter and gripper.

A comparative study of side-band Fresnel holograms recorded with self-imaging and general objects

This paper deals with new results obtained in regard to the reconstruction properties of side-band Fresnel holograms (SBFH) of self-imaging type objects (for example, gratings) as compared with those of general objects. The major finding is that a distribution I2, which appears on the real-image plane along with the conventional real-image I1, remains a 2Z distribution (where 2Z is the axial distance between the object and its self-imaging plane) under a variety of situations, while its nature and focusing properties differ from one situation to another. It is demonstrated that the two distributions I1 and I2 can be used in the development of a novel technique for image subtraction.

Topology-Guided Tessellation Of Quadratic Elements

Topology-based methods have been successfully used for the analysis and visualization of piecewise-linear functions defined on triangle meshes. This paper describes a mechanism for extending these methods to piecewise-quadratic functions defined on triangulations of surfaces. Each triangular patch is tessellated into monotone regions, so that existing algorithms for computing topological representations of piecewise-linear functions may be applied directly to the piecewise-quadratic function. In particular, the tessellation is used for computing the Reeb graph, a topological data structure that provides a succinct representation of level sets of the function.

On The Topology Of Manifolds With Positive Isotropic Curvature

We show that a closed orientable Riemannian n-manifold, n >= 5, with positive isotropic curvature and free fundamental group is homeomorphic to the connected sum of copies of Sn-1 x S-1.

GRDB: A general purpose relational database system

This article discusses the design and development of GRDB (General Purpose Relational Data Base System) which has been implemented on a DEC-1090 system in Pascal. GRDB is a general purpose database system designed to be completely independent of the nature of data to be handled, since it is not tailored to the specific requirements of any particular enterprise. It can handle different types of data such as variable length records and textual data. Apart from the usual database facilities such as data definition and data manipulation, GRDB supports User Definition Language (UDL) and Security definition language. These facilities are provided through a SEQUEL-like General Purpose Query Language (GQL). GRDB provides adequate protection facilities up to the relation level. The concept of “security matrix” has been made use of to provide database protection. The concept of Unique IDentification number (UID) and Password is made use of to ensure user identification and authentication. The concept of static integrity constraints has been used to ensure data integrity. Considerable efforts have been made to improve the response time through indexing on the data files and query optimisation. GRDB is designed for an interactive use but alternate provision has been made for its use through batch mode also. A typical Air Force application (consisting of data about personnel, inventory control, and maintenance planning) has been used to test GRDB and it has been found to perform satisfactorily.

Gauge theory of a group of diffeomorphisms. I. General principles

Any (N+M)-parameter Lie group G with an N-parameter subgroup H can be realized as a global group of diffeomorphisms on an M-dimensional base space B, with representations in terms of transformation laws of fields on B belonging to linear representations of H. The gauged generalization of the global diffeomorphisms consists of general diffeomorphisms (or coordinate transformations) on a base space together with a local action of H on the fields. The particular applications of the scheme to space-time symmetries is discussed in terms of Lagrangians, field equations, currents, and source identities. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

The credit risk(+) model with general sector correlations

We consider an enhancement of the credit risk+ model to incorporate correlations between sectors. We model the sector default rates as linear combinations of a common set of independent variables that represent macro-economic variables or risk factors. We also derive the formula for exact VaR contributions at the obligor level.

Elementary particles, general relativity and f-mesons

Abstract is not available.

Paraxial Maxwell beams: transformation by general linear optical systems

Extending the work of earlier papers on the relativistic-front description of paraxial optics and the formulation of Fourier optics for vector waves consistent with the Maxwell equations, we generalize the Jones calculus of axial plane waves to describe the action of the most general linear optical system on paraxial Maxwell fields. Several examples are worked out, and in each case it is shown that the formalism leads to physically correct results. The importance of retaining the small components of the field vectors along the axis of the system for a consistent description is emphasized.

spin Precession of a Charged Particle in a Magnetic Field Including the Effects of General Relativity

Abstract is not available.

Crystal Physics, Diffraction, Theoretical and General Crystallography

A formula has been derived for the mean-square error in the phases of crystal reflections determined through the multiwavelength anomalous scattering method. The error is written in terms of a simple function of the positions in the complex plane of the 'centres' corresponding to the different wavelengths. For the case of three centres, the mean-square error is inversely proportional to the area of the triangle formed by them. The theoretical values are in good agreement with those obtained by earlier workers from computer simulations. The present method makes it easier to optimize the number and the actual wavelengths to be employed in the multiwavelength method. The maximum benefits of this method are expected in experiments employing synchrotron radiation or neutrons.

Velocity ratio in the analysis of linear dynamical systems

The transfer matrix method is known to be well suited for a complete analysis of a lumped as well as distributed element, one-dimensional, linear dynamical system with a marked chain topology. However, general subroutines of the type available for classical matrix methods are not available in the current literature on transfer matrix methods. In the present article, general expressions for various aspects of analysis-viz., natural frequency equation, modal vectors, forced response and filter performance—have been evaluated in terms of a single parameter, referred to as velocity ratio. Subprograms have been developed for use with the transfer matrix method for the evaluation of velocity ratio and related parameters. It is shown that a given system, branched or straight-through, can be completely analysed in terms of these basic subprograms, on a stored program digital computer. It is observed that the transfer matrix method with the velocity ratio approach has certain advantages over the existing general matrix methods in the analysis of one-dimensional systems.