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1 – 10 of over 1000Tao Song, Bo Pan, Guojun Niu and Yili Fu
This study aims to represent a novel closed-form solutions method based on the product of the exponential model to solve the inverse kinematics of a robotic manipulator. In…
Abstract
Purpose
This study aims to represent a novel closed-form solutions method based on the product of the exponential model to solve the inverse kinematics of a robotic manipulator. In addition, this method is applied to master–slave control of the minimally invasive surgical (MIS) robot.
Design/methodology/approach
For MIS robotic inverse kinematics, the closed-form solutions based on the product of the exponential model of manipulators are divided into the RRR and RRT subproblems. Geometric and algebraic constraints are used as preconditions to solve two subproblems. In addition, several important coordinate systems are established on the surgical robot and master–slave mapping strategies are illustrated in detail. Finally, the MIS robot can realize master–slave control by combining closed-form solutions and master–slave mapping strategy.
Findings
The simulation of the instrument manipulator based on the RRR and RRT subproblems is executed to verify the correctness of the proposed closed-form solutions. The fact that the accuracy of the closed-form solutions is better than that of the compensation method is validated by the contrastive linear trajectory experiment, and the average and the maximum tracking errors are 0.1388 mm and 0.3047 mm, respectively. In the animal experiment, the average and maximum tracking error of the left instrument manipulator are 0.2192 mm and 0.4987 mm, whereas the average and maximum tracking error of the right instrument manipulator are 0.1885 mm and 0.6933 mm. The successful completion of the animal experiment comprehensively demonstrated the feasibility and reliability of the master–slave control strategy based on the novel closed-form solutions.
Originality/value
The proposed closed-form solutions are error-free in theory. The master–slave control strategy is not affected by calculation error when the closed-form solutions are used in the surgical robot. And the accuracy and reliability of the master–slave control strategy are greatly improved.
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The purpose of this paper is to consider divergence of composite plate wings as well as slender wings with thin-walled cross-section of small-size airplanes. The main attention is…
Abstract
Purpose
The purpose of this paper is to consider divergence of composite plate wings as well as slender wings with thin-walled cross-section of small-size airplanes. The main attention is paid to establishing of closed-form mathematical solutions for models of wings with coupling effects. Simplified solutions for calculating the divergence speed of wings with different geometry are established.
Design/methodology/approach
The wings are modeled as anisotropic plate elements and thin-walled beams with closed cross-section. Two-dimensional plate-like models are applied to analysis and design problems for wings of large aspect ratio.
Findings
At first, the equations of elastic deformation for anisotropic slender, plate-like wing with the large aspect ratio are studied. The principal consideration is delivered to the coupled torsion-bending effects. The influence of anisotropic tailoring on the critical divergence speed of the wing is examined in closed form. At second, the method is extended to study the behavior of the large aspect ratio, anisotropic wing with box-like wings. The static equations of the wing with box-like profile are derived using the theory of anisotropic thin-walled beams with closed cross-section. The solutions for forward-swept wing with box-like profiles are given in analytical formulas. The formulas for critical divergence speed demonstrate the dependency upon cross-sectional shape characteristics and anisotropic properties of the wing.
Research limitations/implications
The following simplifications are used: the simplified aerodynamic theory for the wings of large aspect ratio was applied; the static aeroelastic instability is considered (divergence); according to standard component methodology, only the component of wing was modeled, but not the whole aircraft; the simplified theories (plate-lime model for flat section or thin-walled beam of closed-section) were applied; and a single parameter that defines the rotation of a stack of single layers over the face of the wing.
Practical implications
The simple, closed-form formulas for an estimation of critical static divergence are derived. The formulas are intended for use in designing of sport aircraft, gliders and small unmanned aircraft (drones). No complex analysis of airflow and advanced structural and aerodynamic models is necessary. The expression for chord length over the span of the wing allows for accounting a board class of wing shapes.
Social implications
The derived theory facilitates the use of composite materials for popular small-size aircraft, and particularly, for drones and gliders.
Originality/value
The closed-form solutions for thin-walled beams in steady gas flow are delivered in closed form. The explicit formulas for slender wings with variable chord and stiffness along the wing span are derived.
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Songtao Hu, Noel Brunetiere, Weifeng Huang, Xi Shi, Zhike Peng, Xiangfeng Liu and Yuming Wang
Face contact has a strong impact on the service life of non-contacting gas face seals; the current research which mainly focuses on the face contact had appeared during the…
Abstract
Purpose
Face contact has a strong impact on the service life of non-contacting gas face seals; the current research which mainly focuses on the face contact had appeared during the startup or shutdown operation. This paper aims to present a closed-form contact model of a gas face seal during the opened operation.
Design/methodology/approach
Referring to the axial rub-impact model of rotor dynamics, a closed-form contact model is developed under a nonparallel plane contact condition that corresponds to the local face contact of sealing rings arising from some disturbances during the opened operation. The closed-form contact model and a direct numerical contact model are performed on Gaussian surfaces to compare the contact behavior.
Findings
The closed-form contact model is in a good agreement with the direct numerical contact model. However, the closed-form contact model cannot involve the influence of grooves on the sealing ends. The error is eliminated in some other types of gas face seals such as coned gas face seals. Besides non-contacting face seals, the closed-form model can be applied to the axial rub impact of rotor dynamics.
Originality value
A closed-form contact model of a gas face seal is established during the opened operation. The closed-form contact model is validated by a direct numerical contact model. The closed-form contact model also suits for axial rub-impact of rotor dynamics.
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Electric arc furnaces are very often modeled using combined models which cover separately deterministic and stochastic phenomena taking place in the furnace. The deterministic…
Abstract
Purpose
Electric arc furnaces are very often modeled using combined models which cover separately deterministic and stochastic phenomena taking place in the furnace. The deterministic part is expressed by nonlinear differential equations. A closed form of the solution to one of the most popular nonlinear differential equations used for the AC electric arc modeling does not exist for some values of the parameters. The purpose of this paper is to convert electric arc furnace equation for these parameters to the quadratic polynomial form which significantly simplifies solution.
Design/methodology/approach
The solution has been obtained in the time domain by a sequence of transformations of the original nonlinear equation which lead to a system of quadratic equations, for which a periodic solution can be found easily using harmonic balance method (HBM).
Findings
Quadratic polynomial form of electric arc furnace nonlinear equation in the case for which the solution to the nonlinear differential equation describing electric arc cannot be obtained in a closed form.
Research limitations/implications
The complete model of the arc requires extension of the deterministic solution obtained for the quadratic polynomial form using stochastic or chaotic component.
Practical implications
The obtained results simplify determination of the arc voltage or radius time waveforms if a closed form solution does not exist. The arc model can be used to evaluate the impact of arc furnaces on power quality during the planning stage of new plants. The proposed approach facilitates calculation of the arc characteristic.
Originality/value
In order to avoid problems occurring when a large number of harmonics is required or the system contains strong nonlinearities, a transformation of the original equation has been proposed. Nonlinearities present in the equation have been transformed into purely quadratic polynomial terms. It facilitates application of the classical HBM and allows to follow periodic solutions of the arc equation when its parameters are varied. It also enables better understanding of the phenomenon described by the equation and makes easier the extension of the arc model in order to cover the time-varying character of the arc waveforms.
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Tarikul Islam and Armina Akter
Fractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to…
Abstract
Purpose
Fractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to their importance in the nature of real world. In this article, the autors suggest a productive technique, called the rational fractional
Design/methodology/approach
The rational fractional
Findings
Achieved fresh and further abundant closed form traveling wave solutions to analyze the inner mechanisms of complex phenomenon in nature world which will bear a significant role in the of research and will be recorded in the literature.
Originality/value
The rational fractional
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Keywords
Dariusz Grabowski and Janusz Walczak
Electric arc furnaces are usually modelled using combined models which divide the phenomenon taking place in real objects into a deterministic and a stochastic or chaotic parts…
Abstract
Purpose
Electric arc furnaces are usually modelled using combined models which divide the phenomenon taking place in real objects into a deterministic and a stochastic or chaotic parts. The former is expressed by a nonlinear differential equation. The goal of this paper was to obtain a closed form of the solution to one of the most popular nonlinear differential equations used for the AC electric arc modelling.
Design/methodology/approach
The solution has been obtained in the time domain by a sequence of transformations of the original nonlinear equation which lead to a linear equation, for which a closed form solution is known.
Findings
The paper provides a set of parameters for which the solution to the nonlinear differential equation describing electric arc can be obtained in a closed form.
Research limitations/implications
There are still some parameter values for which the solution can be found only numerically. Moreover, due to the nature of the phenomena occurring in electric arc furnaces, in order to build a complete model of the arc the deterministic model must be extended using for example stochastic approach.
Practical implications
The obtained results enable determination of exact waveforms of the arc voltage or radius without application of numerical algorithms for ODE solving. The arc model can be used to evaluate the impact of arc furnaces on power quality during the planning stage of new plants. The proposed approach facilitates calculation of the arc characteristic.
Originality/value
The importance of having a closed form of the solution instead of the numerical ones comes from new possible ways of extension of the arc model in order to cover the time‐varying nature of the arc waveforms. So far the equation has been solved only using numerical algorithms.
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The purpose of this paper is to propose the new dependences of cycles to failure for a given initial crack length upon the stress amplitude in the linear fracture approach. The…
Abstract
Purpose
The purpose of this paper is to propose the new dependences of cycles to failure for a given initial crack length upon the stress amplitude in the linear fracture approach. The anticipated unified propagation function describes the infinitesimal crack-length growths per increasing number of load cycles, supposing that the load ratio remains constant over the load history. Two unification functions with different number of fitting parameters are proposed. On one hand, the closed-form analytical solutions facilitate the universal fitting of the constants of the fatigue law over all stages of fatigue. On the other hand, the closed-form solution eases the application of the fatigue law, because the solution of nonlinear differential equation turns out to be dispensable. The main advantage of the proposed functions is the possibility of having closed-form analytical solutions for the unified crack growth law. Moreover, the mean stress dependence is the immediate consequence of the proposed law. The corresponding formulas for crack length over the number of cycles are derived.
Design/methodology/approach
In this paper, the method of representation of crack propagation functions through appropriate elementary functions is employed. The choice of the elementary functions is motivated by the phenomenological data and covers a broad region of possible parameters. With the introduced crack propagation functions, differential equations describing the crack propagation are solved rigorously.
Findings
The resulting closed-form solutions allow the evaluation of crack propagation histories on one hand, and the effects of stress ratio on crack propagation on the other hand. The explicit formulas for crack length over the number of cycles are derived.
Research limitations/implications
In this paper, linear fracture mechanics approach is assumed.
Practical implications
Shortening of evaluation time for fatigue crack growth. Simplification of the computer codes due to the elimination of solution of differential equation. Standardization of experiments for crack growth.
Originality/value
This paper introduces the closed-form analytical expression for crack length over number of cycles. The new function that expresses the damage growth per cycle is also introduced. This function allows closed-form analytical solution for crack length. The solution expresses the number of cycles to failure as the function of the initial size of the crack and eliminates the solution of the nonlinear ordinary differential equation of the first order. The different common expressions, which account for the influence of the stress ratio, are immediately applicable.
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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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Originality/value
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.
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To give a closed‐form solution of the relative pose determination problem based on monocular vision during final approach phase of spacecraft Rendzvous and Docking.
Abstract
Purpose
To give a closed‐form solution of the relative pose determination problem based on monocular vision during final approach phase of spacecraft Rendzvous and Docking.
Design/methodology/approach
Based on the assumption of scaled orthographic projection, the model of perspective projection is simplified by representing the relative attitude using unit quaternion. Then a closed‐form solution is derived. Subsequently, this study correct the approximate solution to compensate the error caused by the assumption of scaled orthographic projection.
Findings
Extensive simulation studies were conducted for the validation of the proposed algorithm using Matlab™. When there are no relative attitudes between RVD spacecrafts, target distance for camera=2‐20 m. The simulation results show that the largest relative error of corrected relative position parameters is about 0.12 percent. When distance between RVD spacecrafts exceeds 5 m, the largest error of corrected relative attitude parameters are less than 0.3°. When the distance between spacecrafts are constant, the relative attitude parameters are changed, respectively, the simulition results show the largest relative error of relative position is 1 percent, and largest error of estimated relative attitude is 1.2°, when a relative attitude angle reaches 20°.
Originality/value
The proposed algorithm avoids the multiple results problem in determining the relative position and attitude parameters and the closed‐form solution is simple and effective, is more suitable for on‐board implementation.
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Bahaa S. Al Janabi, E. Hinton and Dj. Vuksanovic
This paper presents a parametric study of the free vibrations of square plates with various thickness‐to‐span ratios and different boundary conditions. The numerical analysis of…
Abstract
This paper presents a parametric study of the free vibrations of square plates with various thickness‐to‐span ratios and different boundary conditions. The numerical analysis of these problems has been undertaken using the finite element method. In particular, a nine‐noded, quadrilateral Mindlin plate element has been adopted. The effects of rotatory inertia and shear deformation are included in this model. Results obtained by the finite element analysis are compared with results from various sources. It is suggested that this study might be used to supplement existing benchmark tests.