scholarly journals INVESTIGATION OF THE THREE-LINK CRAWLING ROBOTS MOVEMENT ON THE NONDETERMINATED SURFACE

2018 ◽  
Vol 22 (4) ◽  
pp. 6-14
Author(s):  
S. F. Jatsun ◽  
L. Yu. Vorochaeva ◽  
A. V. Malchikov ◽  
А. S. Yatsun
Keyword(s):  
Mathematical Model ◽  
Robot Motion ◽  
Rough Terrain ◽  
Body Parts ◽  
Closed Space ◽  
Straight Line ◽  
Full Scale Tests ◽  
Electronic Compass ◽  
Theoretical Results ◽  
Wheel Track

Bionic principles of locomotion are the most promising for displacement and transporting equipment under the most difficult conditions. Robots gait based on the changing shape of the robots body and interaction with the surface by body parts, can find application when moving over rough terrain, in a closed space of technological and natural cavities, where the use of wheel-track or walking principle is not possible. In this paper, we propose the design of a three-link crawling robot equipped with two-coordinate active joints. The robot is equipped by supporting elements. Some supporting elements has adjustable friction coefficients, which allows realize various types of movement algorithms of the device. The article presents a mathematical model of a three-link crawling robot, which allows to study the process of robot movement, including case when the coefficients of friction of the surface under the supports are not equal to each other. In practice, the surface will most often have an inhomogeneous nondeterministic structure, which will lead to a deviation in straight-line motion. The paper proposes an algorithm and a diagram of an automatic control system that allows robot to move along a given path despite the indeterminate surface. This is achieved by using additional sensors: a digital electronic compass, an accelerometer, a GPS module. The paper presents the results of computational experiments and the results obtained during the full-scale tests of the prototype of a three-link robot motion. At the end of the article, a comparative analysis of the experimental and theoretical results confirming the adequacy of the developed mathematical model and computational algorithms is presented.

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

scholarly journals Effect of Rail Vehicle–Track Coupled Dynamics on Fatigue Failure of Coil Spring in a Suspension System

2021 ◽  
Vol 11 (6) ◽  
pp. 2650
Author(s):  
Sunil Kumar Sharma ◽  
Rakesh Chandmal Sharma ◽  
Jaesun Lee
Keyword(s):  
Mathematical Model ◽  
Fatigue Fracture ◽  
Suspension System ◽  
Railway Vehicle ◽  
Coil Spring ◽  
Internal Resonances ◽  
Rail Vehicle ◽  
Rail Vehicles ◽  
Stress Result ◽  
Wheel Track

In a rail vehicle, fatigue fracture causes a significant number of failures in the coil spring of the suspension system. In this work, the origin of these failures is examined by studying the rail wheel–track interaction, the modal analysis of the coil springs and the stresses induced during operation. The spring is tested experimentally, and a mathematical model is developed to show its force vs. displacement characteristics. A vertical 10-degree-of-freedom (DOF) mathematical model of a full-scale railway vehicle is developed, showing the motions of the car body, bogies and wheelsets, which are then combined with a track. The springs show internal resonances at nearly 50–60 Hz, where significant stresses are induced in them. From the stress result, the weakest position in the innerspring is identified and a few guidelines are proposed for the reduction of vibration and stress in rail vehicles.

A prey–predator model and control of a nematodes pest using control in banana: Mathematical modeling and qualitative analysis

2021 ◽  
pp. 2150089
Author(s):  
Sudhakar Yadav ◽  
Vivek Kumar
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Local Stability ◽  
Detection Method ◽  
Initial Release ◽  
Pest Detection ◽  
Predator Model ◽  
And Control ◽  
The Mathematical Model ◽  
Theoretical Results

This study develops a mathematical model for describing the dynamics of the banana-nematodes and its pest detection method to help banana farmers. Two criteria: the mathematical model and the type of nematodes pest control system are discussed. The sensitivity analysis, local stability, global stability, and the dynamic behavior of the mathematical model are performed. Further, we also develop and discuss the optimal control mathematical model. This mathematical model represents various modes of management, including the initial release of infected predators as well as the destroying of nematodes. The theoretical results are shown and verified by numerical simulations.

scholarly journals Model of the dynamics of a wheeled vehicle for a complex of full-scale-mathematical modeling

2020 ◽  
Vol 1 (4) ◽  
pp. 46-60
Author(s):  
B.B. Kositsyn ◽  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Real Time ◽  
Block Diagram ◽  
Plane Motion ◽  
Full Scale ◽  
Practical Significance ◽  
Modes Of Operation ◽  
Wheeled Vehicle ◽  
Full Scale Tests

Introduction. The use of the method of full-scale-mathematical modeling in “real time” opens up wide opportunities associated with the analysis of the modes of operation of the “man – vehicle – environment” system, as well as the study of the loading of units and assemblies of vehicles. The existing research complexes of full-scale mathematical modeling are suitable for obtaining most of the indicators usually determined by full-scale tests. The difference lies in the ability to fully control the course of virtual testing, recording any parameters of the vehicle movement, taking into account the “human factor”, as well as complete safety of the experiment. Purpose of research. The purpose of this work is to create a mathematical model of the dynam-ics of a wheeled vehicle, suitable for use in such a complex of full-scale mathematical modeling and assessment of the load of transmission units in conditions close to real operation. Methodology and methods. The proposed model is based on the existing model of the dynamics of a wheeled vehicle developed at Bauman Moscow State Technical University. Within the framework of the model, the dynamics of a vehicle is described as a plane motion of a rigid body in a horizontal plane. The principle of possible displacements is applied to determine the normal reac-tions of the bearing surface. The interaction of the wheel with the ground in the plane of the support base is described using an approach based on the “friction ellipse” concept. To enable the driver and operator of the full-scale mathematical modeling complex to drive a virtual vehicle in “real time” mode, the mathematical model is supplemented with a control system that communicates between the control parameter set by the driver by pressing the accelerator and brake pedals and the control actions of the vehicle's transmission units, such as: an electric machine, an internal combustion en-gine, a hydrodynamic retarder and a brake system. The article presents a block diagram of the de-veloped control algorithm, as well as approbation of the system's operation in a complex of full-scale mathematical modeling. Results and scientific novelty. A mathematical model of the dynamics of a wheeled vehicle was developed. It opens up wide possibilities for studying the modes of operation of the “driver-vehicle-environment” system in “real time”, using a complex of full-scale mathematical modeling. Practical significance. A mathematical model of the dynamics of a wheeled vehicle was devel-oped. It is supplemented with an algorithm for the distribution of traction / braking torques between the transmission units, which provide a connection between the driver's pressing on the accelerator / brake pedal and the control parameters of each of the units.

Mobile Worm-Like Robots for Pipe Inspection

2015 ◽  
pp. 168-218 ◽  
Author(s):  
Sergey Fedorovich Jatsun ◽  
Andrei Vasilevich Malchikov
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Mobile Robots ◽  
Experimental Studies ◽  
Design Parameters ◽  
Robot Motion ◽  
Robot Dynamics ◽  
Confined Space ◽  
Pipe Inspection ◽  
The Mathematical Model

This chapter describes various designs of multilink mobile robots intended to move inside the confined space of pipelines. The mathematical model that describes robot dynamics and controlled motion, which allows simulating different regimes of robot motion and determining design parameters of the device and its control system, is presented. The chapter contains the results of numerical simulations for different types of worm-like mobile robots. The experimental studies of the in-pipe robots prototypes and their analyses are presented in this chapter.

scholarly journals Research on an Anthropomorphic Phantom for Evaluation of the Medical Device Electromagnetic Field Exposure SAR

2018 ◽  
Vol 8 (10) ◽  
pp. 1929 ◽  
Author(s):  
Shu Li ◽  
Zengwen Su ◽  
Hao Wang ◽  
Quan Wang ◽  
Haiping Ren
Keyword(s):  
Mathematical Model ◽  
Electromagnetic Radiation ◽  
Medical Device ◽  
Medical Devices ◽  
Debye Model ◽  
World Health ◽  
Endurance Capacity ◽  
Body Parts ◽  
Anthropomorphic Phantom ◽  
Field Exposure

A medical device will emit electromagnetic radiation to its surrounding environment either actively or passively. However, clinicians are unaware as to whether the ambient electromagnetic radiation will exceed the human body’s endurance capacity. In this paper, the mathematical model of electromagnetic parameters devoted to Specific Absorption Rate (SAR) testing of medical devices was established using a Debye Model. Body liquids featuring dielectric properties including the conductivity and permittivity of tissues at various body parts were simulated on the basis of results derived from the model. A simplified anthropomorphic phantom for the SAR test was founded on the basis of geometric parameters by following the principles of resemblance and consistent conductivity. A full-band electromagnetic mathematical model of brain, muscle, heart, lungs, stomach, and kidneys was set up. Electromagnetic radiation levels of a wearable Electrocardiograph monitoring device were measured and found that the maximum electric field intensity was up to 30 V/m, and the electromagnetic radiation SAR value was 0.96 W/kg, which were equivalent to the electromagnetic radiation exposure of the occupational group. The results established that electromagnetic radiation of certain medical devices exceeded the allowed values specified by the World Health Organization (WHO). Therefore, further studies within the field of medicine are required to decide whether additional evaluation measures should be required.

scholarly journals General fractional financial models of awareness with Caputo–Fabrizio derivative

2020 ◽  
Vol 12 (11) ◽  
pp. 168781402097552
Author(s):  
Amr MS Mahdy ◽  
Yasser Abd Elaziz Amer ◽  
Mohamed S Mohamed ◽  
Eslam Sobhy
Keyword(s):  
Mathematical Model ◽  
Fixed Point ◽  
Numerical Simulations ◽  
Caputo Derivative ◽  
Existence And Uniqueness ◽  
Financial Models ◽  
Whole Number ◽  
Fractional System ◽  
Set Up ◽  
Theoretical Results

A Caputo–Fabrizio (CF) form a fractional-system mathematical model for the fractional financial models of awareness is suggested. The fundamental attributes of the model are explored. The existence and uniqueness of the suggest fractional financial models of awareness solutions are given through the fixed point hypothesis. The non-number request subordinate gives progressively adaptable and more profound data about the multifaceted nature of the elements of the proposed partial budgetary models of mindfulness model than the whole number request models set up previously. In order to confirm the theoretical results and numerical simulations studies with Caputo derivative are offered.

scholarly journals Research and Application of Mathematical Model of Transmission Grating Signal Lissajous Figure

2018 ◽  
Vol 232 ◽  
pp. 03046
Author(s):  
Luqing Hu ◽  
Xianqing Lei ◽  
Xiaoyi Wang ◽  
Yadong Zhang ◽  
Xiaolin Zuo
Keyword(s):  
Mathematical Model ◽  
Measurement System ◽  
Electrical Signal ◽  
Two Phase ◽  
Lissajous Figure ◽  
Transmission Grating ◽  
Straight Line ◽  
Voltage Signal ◽  
Working Principle ◽  
Grating Pair

In this paper, the working principle of the grating measurement system is combined with the Fourier analysis method of Moiré fringe to establish the mathematical model of the grating signal Lissajous figure to know the quality of the grating signal intuitively. The Mathematica numerical analysis software is used to obtain the graphics of the model, and the correctness of the relationship between the parameters of the grating measurement system and the Lissajous figure equation of the grating signal is verified. The influence of the grating pair angle α on the output voltage signal and Lissajous figure of the grating measurement system is studied. The results show that the intensity of the two-phase output electrical signal decreases gradually with the increase of the deviation of the angle α of the grating pair, but the equal-amplitude of the two-phase output electrical signal does not change; Meanwhile, the shape of the grating signal Lissajous figure gradually changes from the ideal circle to the non-ideal ellipse, until a straight line with a strip slope of 135° is formed.

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