Specifity of Including of Structural Nonlinearity in Model of Dynamics of Cable-Driven Robot

2021 ◽  
Vol 22 (10) ◽  
pp. 547-552
Author(s):  
Ya. V. Kalinin ◽  
E. A. Marchuk
Keyword(s):  
Mathematical Model ◽  
Computer Model ◽  
Activation Functions ◽  
System Of Differential Equations ◽  
Unilateral Constraints ◽  
Cable System ◽  
Symbolic Computations ◽  
Structural Nonlinearity ◽  
The Mathematical Model ◽  
Cable Robots

The paper deals with a problem of modeling of the dynamics of a parallel cable-driven robot with the inclusion of structural nonlinearity of cables in a mathematical model. Mathematical model is implemented in a computer model with the possibility of using of symbolic calculations. Parallel cable robots as a type of robotics have been developing in the last two or three decades. The research in the theoretical field was being carried out and the mathematical model of the cable system was being refined with the spread of the practical use of cable robots. This is a non-trivial task to draw up a dynamic model of a cable-driven robot. Cable-driven robots are highly nonlinear systems, because of the main reason for the nonlinearity is the properties of the cable system. As an element of a mechanical system, the cable or the wire rope is a unilateral constraint, since the cable works only for stretching, but not for compression. Thus, the cables are structurally nonlinear elements of the system. On the other hand, cables have the property of sagging under their own weight. Thus, the cables are geometrically nonlinear elements of the system. Under the condition of a payload mass that is utterly greater than the mass of each cable, the cables can be considered strained without sagging and geometric nonlinearity can be neglected. Since symbolic computations can be used in a computer model which implements a mathematical model of the dynamics of a robot, in such a way it must provide the possibility of symbolic computations with the condition of structural nonlinearity. The main aim of this work is to develop a method that ensures the inclusion of the structural nonlinearity of the cable system in the mathematical model. It is supposed to consider the possibility of implementation of the computer model with symbolic computations. The problem of including a mathematical model of cables as unilateral constraints in the model of highly loaded cable robots is considered. The justification for including the activation functions in a system of differential equations of dynamics of cable-driven robot is formulated. A model of wire ropes as unilateral constraints is represented via including the activation functions in a system of differential equations. With using of the proposed method, numerical solution of a problem of forward dynamics has been obtained for high-loaded parallel cable-driven robot.

scholarly journals Internal forces analysis of gas permeable shelter with emphasis on short-delay blasting

2018 ◽  
Vol 56 ◽  
pp. 01014
Author(s):  
Aleksandr Leshchinskiy ◽  
Evgeniy Shevkun ◽  
Aleksandr Lovtsov ◽  
Olga Kostiunina
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mass Number ◽  
Large Displacements ◽  
Unilateral Constraints ◽  
Safe Operation ◽  
Short Delay ◽  
Heavy Trucks ◽  
Internal Forces ◽  
The Mathematical Model

A mathematical model of transformable gas permeable blasting shelter made from worn out tires of heavy trucks bound together with chains, ropes or cables is proposed. Large displacements and unilateral constraints are specific features of this model. An algorithm was developed to calculate the displacements of tires and internal forces in connecting elements of blasting shelter subjected to dynamic loading. The results of the numerical simulation of simple shelter are presented for assessment of the adequacy of the mathematical model. This algorithm can be used to determine the parameters of shelter such as mass, number of tires, diameter of connecting elements which ensure its safe operation under any sequence of explosions.

scholarly journals THE RESEARCH RESULTS OF THE LINEAR ELECTROMAGNETIC MOTOR MATHEMATICAL MODEL

2010 ◽  
Vol 2 (1) ◽  
pp. 99-102
Author(s):  
Marijanas Molis
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Supply Voltage ◽  
Traction Force ◽  
Electromagnetic Properties ◽  
System Of Differential Equations ◽  
Transitional Processes ◽  
Linear Electromagnetic Motor ◽  
The Mathematical Model ◽  
Secondary Element

Development of the mathematical model of the linear electromagnetic motor and the dependencies of the inductance and traction force on the secondary element position expressed by mathematical equations, are presented in this research article. The dependency of the inductance on the secondary element position was obtained, approximating the inductance change diagram obtained experimentally. Also, using the theory of electromechanical energy transformation, mathematical expressions of the dependency of the traction force on the secondary element position were obtained. Mathematical model of the linear electromagnetic motor is composed of the system of differential equations. The Runge – Kutta calculation method was used to solve these equations. The transitional processes of the current, speed and secondary element position obtained with the solution of the system of differential equations at different supply voltage also the transitional processes of the dynamic traction force obtained at 24 V supply voltage of the motor. All obtained results of the dependencies and transitional processes of the mathematical model are presented in the graphic form. In accordance with the obtained results of the mathematical model the conclusions were formulated, specifying electromagnetic properties of the linear electromagnetic motor.

scholarly journals A numerical solution by alternative Legendre polynomials on a model for novel coronavirus (COVID-19)

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Elham Hashemizadeh ◽  
Mohammad Ali Ebadi
Keyword(s):  
Mathematical Model ◽  
Numerical Solution ◽  
Legendre Polynomials ◽  
Algebraic System ◽  
The Novel ◽  
Kutta Method ◽  
System Of Differential Equations ◽  
Runge Kutta Method ◽  
Novel Coronavirus ◽  
The Mathematical Model

Abstract Coronavirus disease (COVID-19) is an infectious disease caused by a newly discovered coronavirus. This paper provides a numerical solution for the mathematical model of the novel coronavirus by the application of alternative Legendre polynomials to find the transmissibility of COVID-19. The mathematical model of the present problem is a system of differential equations. The goal is to convert this system to an algebraic system by use of the useful property of alternative Legendre polynomials and collocation method that can be solved easily. We compare the results of this method with those of the Runge–Kutta method to show the efficiency of the proposed method.

scholarly journals COMPUTER SIMULATION AND ANALYTICAL SOLUTION OF FOUR BAR MECHANISM

2020 ◽  
pp. 120-128
Author(s):  
Darina Hroncová
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Mathematical Models ◽  
Computer Model ◽  
Analytical Methods ◽  
Kinematic Analysis ◽  
Linkage Mechanism ◽  
The Creation ◽  
Four Bar Linkage ◽  
The Mathematical Model

Urgency of the research. The use of computers in technical practice leads to the extension of the possibility of solving mathematical models. This makes it possible to gradually automate complex calculations of equations of mathematical models. It is necessary to input the relevant inputs of the mathematical model, to build a simulation computer model and to monitor and evaluate the output results using a computer's output device. Target setting. The possibilities of modeling a four-bar linkage mechanism by classical analytical methods and methodsusing computer modeling are presented in this paper.The problem is to describe the creation of a computer model and to show the mathematical model and its solution in the classical ways. Actual scientific researches and issues analysis. The inspiration for the creation of the article was the study of the mechanisms in the work [1-3] and the study of other resources available in library and journal materials, as well as prepared study materials for students of Technical university Kosice. Uninvestigated parts of general matters defining. The question of building a real mechanism model. The possibilities to building a real model, based on the result of simulation. The research objective. The aim of this paper is to develop a functional model of the mechanism in ADAMS/View and Matlab and its complete kinematic analysis.The statement of basic materials.The task was to create a computer model in MSC Adams and Matlab and to perform a four-bar linkage mechanism kinematic analysis. At the same time the classical procedure of analytical methods of kinematic analysis was described. Kinematic сharacteristics of driven members and their selected points were determined. The movement of the parts of the mechanism in its significant points was analyzed. The results of the solution were shown in both programs in graphical form. Kinematic analysis was performed by both vector and graphical methods. Finally, the results with a graphical representation of parameters such as angular displacement, angular velocity and angular acceleration of mechanism members are presented in this work. The results of these solutions are created in the form of graphs. To ensure that the results do not differ from the model real, a good computer model gradually was created by its verification and modification, which is one of the advantages of MSC Adams. The practical applicability of the mathematical model was limited by the existence of an analytical solution. Conclusions. The development of computer technology has expanded the limit of solvability of mathematical models and made it possible to gradually automate the calculation of equations of mathematical models. In a computer model the auto-mated calculation can be treated as a real object sample. In various variations of calculation, we can monitor and measure the behavior of an object under different conditions, under the influence of different inputs. Graphical and vector methods were used for classical analytical methods. MSC Adams and Matlab were used for the automated calculations.

scholarly journals APPLICATION OF THE SIR MODEL TO COVID-19: social distance and (no-)evolution of the pandemic in state of the Tocantins

2020 ◽  
Vol 6 (3) ◽  
pp. a16en
Author(s):  
Élis Gardel da Costa Mesquita ◽  
Janeisi de Lima Meira ◽  
José de Ribamar Leonel Dias Neto
Keyword(s):  
Mathematical Model ◽  
Decision Making ◽  
Social Distance ◽  
Sir Model ◽  
System Of Differential Equations ◽  
Public Power ◽  
The Social ◽  
Isolation Index ◽  
The Mathematical Model ◽  
Reproduction Factor

This article is a study about the behavior and spread of the Covid-19 pandemic, in the state of Tocantins, based on data reported from March 18 to June 10. A modification of the mathematical model SIR was used, in which some auxiliary compartments were added. We analyzed epidemic aspects such as the speed of the contagion curve and its impacts on the health system. As the data are made available daily, a discretization of the system of differential equations that make up the model was performed, and based on the availability of known data, we investigated the correlation between the social isolation index and the basic reproduction factor.  Through a very simple interpolation, approximate contagion rates were obtained, enabling us to evaluate the behavior of the evolution of contagion curves and those that depend on them, which allows us to anticipate scenarios based on the trend lines of the data generated, thus helping decision making public power.

scholarly journals Mathematical model of orientation of a ferromagnetic particle in magnetic field

2018 ◽  
Vol 224 ◽  
pp. 02041
Author(s):  
Eugene Masyutkin ◽  
Vasilii Masyagin ◽  
Boris Avdeyev
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Homogeneous Magnetic Field ◽  
System Of Differential Equations ◽  
Medium Resistance ◽  
The Moment ◽  
Fourth Order Method ◽  
Driving Torque ◽  
The Mathematical Model ◽  
Angle Of Rotation

A mathematical model of the rotational motion of a particle with pronounced ferromagnetic properties, due to the moment of forces from the side of an external homogeneous magnetic field is deduced in the article. The basis of the model is the equation for the moment of forces effecting on a solid body. The driving torque is the magnetic moment, calculated through the strength of the external field and the magnetization of the material. The counter–torque is the moment of medium resistance, which mainly depends on the viscosity of the medium in which the simulated body is located. The dependences of the angle of rotation and angular velocity on time are determined. The mathematical model is represented as a system of differential equations. The developed mathematical model was solved by a Runge – Kutta fourth order method. The obtained results are presented in the form of graphs.

scholarly journals COMPUTER MODEL OF THE ORBITAL CABLE SYSTEM

2020 ◽  
Vol 2020 (1) ◽  
pp. 143-144
Author(s):  
Andrey Maslyuchenko ◽  
Svetlana Senotova
Keyword(s):  
Mathematical Model ◽  
Computer Model ◽  
Cable System ◽  
Graphic Editor

A computer model of the orbital cable system was developed in the Blender graphic editor based on a mathematical model.

scholarly journals A Computer Model of the Spread of the Pandemic and its Analysis

2021 ◽  
Vol 10 (5) ◽  
Author(s):  
Avtandil Bardavelidze ◽  
Irakli Basheleishvili ◽  
Khatuna Bradvelidze
Keyword(s):  
Mathematical Model ◽  
Computer Model ◽  
Software Package ◽  
The State ◽  
System Of Differential Equations ◽  
Structural Diagram ◽  
Infected People ◽  
Vector Matrix ◽  
Spatial State ◽  
Epidemic Diseases

The paper describes and analyzes a mathematical model of the variable state of the incidence of epidemic diseases, which is of great importance for determining the quantity of vaccines and antiviral drugs to be produced.    The information model according to the system of differential equations of the spread of the pandemic is illustrated in a structural diagram. The model is presented in a vector-matrix form and the state of equilibrium of the model in the spatial state is proved.The model of the spread of the pandemic was developed, whose implementation with a Matlab software package resulted in obtaining the curves of variation of the state. The developed computer model of the incidence of epidemic diseases can be used to make a projection of the number of infected people, as well as intensity of the process of disseminating information and ideas in the community.

scholarly journals Methodology for predicting oily mixture properties in the mathematical modeling of molecular distillation

2017 ◽  
Vol 68 (2) ◽  
pp. 193 ◽  
Author(s):  
M. F. Gayol ◽  
M. C. Pramparo ◽  
S. M. Miró Erdmann
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Mathematical Model ◽  
Molecular Distillation ◽  
Computer Code ◽  
Deodorizer Distillate ◽  
System Of Differential Equations ◽  
Prediction Of Properties ◽  
Implicit Finite Difference ◽  
The Mathematical Model

A methodology for predicting the thermodynamic and transport properties of a multi-component oily mixture, in which the different mixture components are grouped into a small number of pseudo components is shown. This prediction of properties is used in the mathematical modeling of molecular distillation, which consists of a system of differential equations in partial derivatives, according to the principles of the Transport Phenomena and is solved by an implicit finite difference method using a computer code. The mathematical model was validated with experimental data, specifically the molecular distillation of a deodorizer distillate (DD) of sunflower oil. The results obtained were satisfactory, with errors less than 10% with respect to the experimental data in a temperature range in which it is possible to apply the proposed method.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

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