scholarly journals Kinematic analysis of Felix Baumgartner's stratospheric jump in 2012

2021 ◽  
Vol 10 (3) ◽  
Author(s):  
Josemaria Zavala ◽  
Jimmy Menendez
Keyword(s):  
Mathematical Model ◽  
Kinematic Analysis ◽  
Action Plan ◽  
Velocity Model ◽  
Scientific Achievement ◽  
Mathematical Exploration ◽  
Scientific Report ◽  
The Mathematical Model ◽  
Red Bull

The present investigation shows a kinematic analysis of Baumgartner’s stratospheric jump, based on a scientific report by Red Bull. The modeling was carried out using the different forces that intervened in the event (velocity, acceleration, etc.), making it possible to generate a mathematical model capable of extrapolating data and allowing us a better appreciation of such scientific achievement. All the mathematical exploration has been carried out with ten decimal places; however, they will be rounded to four in writing. The action plan was based on obtaining the velocities by placing points on a velocity model belonging to an approximate graph of a Red Bull scientific report, which was put into the GeoGebra Classic 5 program to find the velocities. After this, we proceeded to find the accelerations and the formula of the function that models them. Finally, this formula was integrated to acquire the mathematical model of the velocities. 

Kinematic Analysis of 5-UPS Parallel Machine Tool Based on Adams

2014 ◽  
Vol 644-650 ◽  
pp. 215-219 ◽  
Author(s):  
Lin Cai
Keyword(s):  
Mathematical Model ◽  
Machine Tool ◽  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Machine ◽  
Inverse Solution ◽  
Robot Kinematics ◽  
Vector Method ◽  
Parallel Machine Tool ◽  
The Mathematical Model

In this paper, the kinematics of 5-UPS parallel machine tool is analyzed, and a kinematic analysis method combining kinematic analysis and computer kinematics software is proposed. Under the premise that the parallel machine tool sector parameters is known, firstly we use the vector method to establish a mathematical model of inverse kinematics, and in accordance with a U-shaped processing trajectory the inverse solution is calculated; Secondly, three-dimensional model of the parallel machine tool is modeled in Adams, and kinematic constraints are set correctly; Finally, the inverse kinematics solution of the mathematical model is used as the Adams drive input, then the positive solutions is carried out. Compared through the Adams simulation results with U-machining path, it is verified that the inverse solution of the mathematical model and parallel machine tool bodies both are correct, it has certain significance for Parallel machine tools and other parallel robot kinematics analysis.

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.

Kinematic and Stiffness Analysis of an Origami-Type Carton

2013 ◽  
Author(s):  
C. Qiu ◽  
Vahid Aminzadeh ◽  
Jian S. Dai
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Angular Velocity ◽  
Kinematic Analysis ◽  
Stiffness Analysis ◽  
Revolute Joints ◽  
Stiffness Characteristics ◽  
The Individual ◽  
The Mathematical Model ◽  
Equivalent Mechanism

This paper investigates the stiffness characteristics of an origami-type carton, which can be modeled into an equivalent mechanism by considering creases as revolute joints and panels as links. Stiffness characteristics of a single crease is investigated regarding its relationships with folding angular velocity and crease length. Based on the kinematic analysis of carton folding, the aggregated stiffness is obtained by integrating the individual crease stiffness into the equivalent mechanism. Finally experiment results of carton folding manipulation are obtained, and comparisons between the mathematical model and experimental data show that the model predicts the carton’s behaviour well.

Displacement Analysis of a Spatial 7R Mechanism—A Generalized Lobster’s Arm

1979 ◽  
Vol 101 (2) ◽  
pp. 224-231 ◽  
Author(s):  
J. Duffy ◽  
S. Derby
Keyword(s):  
Mathematical Model ◽  
Kinematic Analysis ◽  
Input Output ◽  
Major Step ◽  
Displacement Analysis ◽  
The Mathematical Model ◽  
Output Equation

An input-output equation of degree 24 is derived for a spatial 7R mechanism with consecutive pair axes intersecting. This mechanism is essentially the mathematical model for the kinematic analysis of a lobster’s arm which is an open 6R chain with mutually perpendicular consecutive pair axes, the geometry of which was first described by Willis [4] in 1841. The analysis of this special 7R mechanism constitutes a major step towards the solution of the general 7R mechanism with seven axes arbitrarily oriented in space.

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.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

RESEARCH OF INDICATORS OF A VEHICLE WITH A DIESEL WORKING ON DIESEL AND DIESEL GAS CYCLES USING THE MATHEMATICAL MODEL

2020 ◽  
pp. 14-19
Author(s):  
Serhii Kovbasenko ◽  
Andriy Holyk ◽  
Serhii Hutarevych
Keyword(s):  
Mathematical Model ◽  
Diesel Engine ◽  
Environmental Performance ◽  
Energy Performance ◽  
Dual Fuel ◽  
Fuel System ◽  
Compressed Natural Gas ◽  
Diesel Vehicles ◽  
Diesel Cycle ◽  
The Mathematical Model

The features of an advanced mathematical model of motion of a truck with a diesel engine operating on the diesel and diesel gas cycles are presented in the article. As a result of calculations using the mathematical model, a decrease in total mass emissions as a result of carbon monoxide emissions is observed due to a decrease in emissions of nitrogen oxides and emissions of soot in the diesel gas cycle compared to the diesel cycle. The mathematical model of a motion of a truck on a city driving cycle according to GOST 20306-90 allows to study the fuel-economic, environmental and energy indicators of a diesel and diesel gas vehicle. The results of the calculations on the mathematical model will make it possible to conclude on the feasibility of converting diesel vehicles to using compressed natural gas. Object of the study – the fuel-economic, environmental and energy performance diesel engine that runs on dual fuel system using CNG. Purpose of the study – study of changes in fuel, economic, environmental and energy performance of vehicles with diesel engines operating on diesel and diesel gas cycles, according to urban driving cycle modes. Method of the study – calculations on a mathematical model and comparison of results with road tests. Bench and road tests, results of calculations on the mathematical model of motion of a truck with diesel, working on diesel and diesel gas cycles, show the improvement of environmental performance of diesel vehicles during the converting to compressed natural gas in operation. Improvement of environmental performance is obtained mainly through the reduction of soot emissions and nitrogen oxides emissions from diesel gas cycle operations compared to diesel cycle operations. The results of the article can be used to further develop dual fuel system using CNG. Keywords: diesel engine, diesel gas engine, CNG

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

Mathematical Models of Papermaking

2001 ◽  
Vol 6 (1) ◽  
pp. 9-19 ◽  
Author(s):  
A. Buikis ◽  
J. Cepitis ◽  
H. Kalis ◽  
A. Reinfelds ◽  
A. Ancitis ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Initial Value Problems ◽  
Moisture Transfer ◽  
Bound Water ◽  
Drying Process ◽  
Initial Value ◽  
First Order ◽  
Heat And Moisture ◽  
The Mathematical Model ◽  
The Web

The mathematical model of wood drying based on detailed transport phenomena considering both heat and moisture transfer have been offered in article. The adjustment of this model to the drying process of papermaking is carried out for the range of moisture content corresponding to the period of drying in which vapour movement and bound water diffusion in the web are possible. By averaging as the desired models are obtained sequence of the initial value problems for systems of two nonlinear first order ordinary differential equations. 

The mathematical modelling of corrosion in hot dip galvanized steel reinforced concrete

2011 ◽  
Vol 2 (1) ◽  
pp. 1-12
Author(s):  
A. Hegyi ◽  
H. Vermeşan ◽  
V. Rus
Keyword(s):  
Mathematical Model ◽  
Reinforced Concrete ◽  
Numerical Model ◽  
Equation System ◽  
Galvanized Steel ◽  
Steel Reinforced Concrete ◽  
Numeric Model ◽  
Physical And Mathematical Models ◽  
Physical Phenomena ◽  
The Mathematical Model

Abstract In this paper we wish to present the numerical model elaborated in order to simulate some physical phenomena that influence the general deterioration of steel, whether hot dip galvanized or not, in reinforced concrete. We describe the physical and mathematical models, establishing the corresponding equation system, the initial and boundary conditions. We have also presented the numeric model associated to the mathematical model and the numeric methods of discretization and solution of the differential equations system that describes the mathematical model.

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