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Developing general closed-form solutions for six-degrees-of-freedom (DOF) serial robots is a significant challenge. This paper thus aims to present a general solution for six-DOF robots based on the product of exponentials model, which adapts to a class of robots satisfying the Pieper criterion with two parallel or intersecting axes among its first three axes.

The proposed solution can be represented as uniform expressions by using geometrical properties and a modified Paden–Kahan sub-problem, which mainly adopts the screw theory.

A simulation and experiments validated the correctness and effectiveness of the proposed method (general resolution for six-DOF robots based on the product of exponentials model).

The Rodrigues rotation formula is additionally used to turn the complex problem into a solvable trigonometric function and uniformly express six solutions using two formulas.

The purpose of this paper is to suggest a new analytical methodology for transient analysis of DC‐DC power converters. The closed‐form solution obtained following this methodology is suitable both for design of passive elements of the converter and for the development of control techniques.

The methodology is based on a mixed use of Laplace transform and z‐transform. The expressions of variables of the set of equations, characteristic of a DC‐DC converter, are first evaluated in the Laplace domain for the generic switching interval. The solutions obtained are then z‐transformed in order that they match in each contiguous time interval, to form the complete transient response.

The new solution methodology allows the analytical determination of time constants of DC‐DC converters, also in presence of large duty‐cycle variations. Moreover, it is possible to evaluate easily the influence of passive elements on converter's behaviour, without several numerical simulations.

The analytical solution of linear systems is well known both in transient and in steady‐state conditions. However, when there is an infinite number of poles in the Laplace transform of the input signals, such as the case of switching power converters, the inversion in a closed form of the Laplace transform of the solution can be cumbersome. The methodology presented tries to overcome this problem by using an approach based on the z‐transform. Operating in this way, a closed‐form solution can be obtained both in transient and in steady‐state conditions, for all the main topologies of switching power converters. The procedure has been explained in detail for the sample case of boost DC‐DC converters.

The purpose of this paper is to propose a calibration method that can calibrate the relationships among the robot manipulator, the camera and the workspace.

The method uses a laser pointer rigidly mounted on the manipulator and projects the laser beam on the work plane. Nonlinear constraints governing the relationships of the geometrical parameters and measurement data are derived. The uniqueness of the solution is guaranteed when the camera is calibrated in advance. As a result, a decoupled multi‐stage closed‐form solution can be derived based on parallel line constraints, line/plane intersection and projective geometry. The closed‐form solution can be further refined by nonlinear optimization which considers all parameters simultaneously in the nonlinear model.

Computer simulations and experimental tests using actual data confirm the effectiveness of the proposed calibration method and illustrate its ability to work even when the eye cannot see the hand.

Only a laser pointer is required for this calibration method and this method can work without any manual measurement. In addition, this method can also be applied when the robot is not within the camera field of view.

The purpose of this paper is to develop the method for the calculation of residual stress and enduring deformation of helical springs.

For helical compression or tension springs, a spring wire is twisted. In the first case, the torsion of the straight bar with the circular cross-section is investigated, and, for derivations, the StVenant’s hypothesis is presumed. Analogously, for the torsion helical springs, the wire is in the state of flexure. In the second case, the bending of the straight bar with the rectangular cross-section is studied and the method is based on Bernoulli’s hypothesis.

For both cases (compression/tension of torsion helical spring), the closed-form solutions are based on the hyperbolic and on the Ramberg–Osgood material laws.

The method is based on the deformational formulation of plasticity theory and common kinematic hypotheses.

The advantage of the discovered closed-form solutions is their applicability for the calculation of spring length or spring twist angle loss and residual stresses on the wire after the pre-setting process without the necessity of complicated finite-element solutions.

The formulas are intended for practical evaluation of necessary parameters for optimal pre-setting processes of compression and torsion helical springs.

Because of the discovery of closed-form solutions and analytical formulas for the pre-setting process, the numerical analysis is not necessary. The analytical solution facilitates the proper evaluation of the plastic flow in torsion, compression and bending springs and improves the manufacturing of industrial components.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

In the past few years, Haar wavelet-based numerical methods have been applied successfully to solve linear and nonlinear partial differential equations. This study aims to propose a wavelet collocation method based on Haar wavelets to identify a parameter in parabolic partial differential equations (PDEs). As Haar wavelet is defined in a very simple way, implementation of the Haar wavelet method becomes easier than the other numerical methods such as finite element method and spectral method. The computational time taken by this method is very less because Haar matrices and Haar integral matrices are stored once and used for each iteration. In the case of Haar wavelet method, Dirichlet boundary conditions are incorporated automatically. Apart from this property, Haar wavelets are compactly supported orthonormal functions. These properties lead to a huge reduction in the computational cost of the method.

The aim of this paper is to reconstruct the source control parameter arises in quasilinear parabolic partial differential equation using Haar wavelet-based numerical method. Haar wavelets possess various properties, for example, compact support, orthonormality and closed form expression. The main difficulty with the Haar wavelet is its discontinuity. Therefore, this paper cannot directly use the Haar wavelet to solve partial differential equations. To handle this difficulty, this paper represents the highest-order derivative in terms of Haar wavelet series and using successive integration this study obtains the required term appearing in the problem. Taylor series expansion is used to obtain the second-order partial derivatives at collocation points.

An efficient and accurate numerical method based on Haar wavelet has been proposed for parameter identification in quasilinear parabolic partial differential equations. Numerical results are obtained from the proposed method and compared with the existing results obtained from various finite difference methods including Saulyev method. It is shown that the proposed method is superior than the conventional finite difference methods including Saulyev method in terms of accuracy and CPU time. Convergence analysis is presented to show the accuracy of the proposed method. An efficient algorithm is proposed to find the wavelet coefficients at target time.

The outcome of the paper would have a valuable role in the scientific community for several reasons. In the current scenario, the parabolic inverse problem has emerged as very important problem because of its application in many diverse fields such as tomography, chemical diffusion, thermoelectricity and control theory. In this paper, higher-order derivative is represented in terms of Haar wavelet series. In other words, we represent the solution in multiscale framework. This would enable us to understand the solution at various resolution levels. In the case of Haar wavelet, this paper can achieve a very good accuracy at very less resolution levels, which ultimately leads to huge reduction in the computational cost.

I survey applications of Markov switching models to the asset pricing and portfolio choice literatures. In particular, I discuss the potential that Markov switching models have to fit financial time series and at the same time provide powerful tools to test hypotheses formulated in the light of financial theories, and to generate positive economic value, as measured by risk-adjusted performances, in dynamic asset allocation applications. The chapter also reviews the role of Markov switching dynamics in modern asset pricing models in which the no-arbitrage principle is used to characterize the properties of the fundamental pricing measure in the presence of regimes.

The purpose of this paper is to describe a general theoretical and finite element implementation framework for the constitutive modelling of biological soft tissues.

The model is based on continuum fibers reinforced composites in finite strains. As an extension of the isotropic hyperelasticity, it is assumed that the strain energy function is decomposed into a fully isotropic component and an anisotropic component. Closed form expressions of the stress tensor and elasticity tensor are first established in the general case of fully incompressible plane stress which orthotropic and transversely isotropic hyperelasticity. The incompressibility is satisfied exactly.

Numerical examples are presented to illustrate the model's performance.

The paper presents a constitutive model for incompressible plane stress transversely isotropic and orthotropic hyperelastic materials.

This paper presents a novel framework for solving elliptic partial differential equations (PDEs) over irregularly spaced meshes on bounded domains.

Second‐generation wavelet construction gives rise to a powerful generalization of the traditional hierarchical basis (HB) finite element method (FEM). A framework based on piecewise polynomial Lagrangian multiwavelets is used to generate customized multiresolution bases that have not only HB properties but also additional qualities.

For the 1D Poisson problem, we propose – for any given order of approximation – a compact closed‐form wavelet basis that block‐diagonalizes the stiffness matrix. With this wavelet choice, all coupling between the coarse scale and detail scales in the matrix is eliminated. In contrast, traditional higher‐order (n>1) HB do not exhibit this property. We also achieve full scale‐decoupling for the 2D Poisson problem on an irregular mesh. No traditional HB has this quality in 2D.

Similar techniques may be applied to scale‐decouple the multiresolution finite element (FE) matrices associated with more general elliptic PDEs.

By decoupling scales in the FE matrix, the wavelet formulation lends itself particularly well to adaptive refinement schemes.

The paper explains second‐generation wavelet construction in a Lagrangian FE context. For 1D higher‐order and 2D first‐order bases, we propose a particular choice of wavelet, customized to the Poisson problem. The approach generalizes to other elliptic PDE problems.

This paper presents a closed form analytic solution for the impulse response of an optimum FIR deconvolution filter intended for a pair of discrete pulses of arbitrary amplitude and sign, subject to the minimisation of Chebyshev maximum norm for the approximation error. The tradeoff between the approximation error and the degradation of signal‐to‐noise ratio, is examined.