scholarly journals The Determination of the Velocities after Impact for the Constrained Bar Problem

2009 ◽  
Vol 2009 ◽  
pp. 1-16
Author(s):  
André Fenili ◽  
Luiz Carlos Gadelha de Souza ◽  
Bernd Schäfer
Keyword(s):  
Mathematical Model ◽  
Numerical Integration ◽  
Equations Of Motion ◽  
Robotic Manipulators ◽  
Robotic Manipulator ◽  
Simple Mathematical Model ◽  
Governing Equations ◽  
Complex Problems ◽  
Constrained Equation

A simple mathematical model for a constrained robotic manipulator is investigated. Besides the fact that this model is relatively simple, all the features present in more complex problems are similar to the ones analyzed here. The fully plastic impact is considered in this paper. Expressions for the velocities of the colliding bodies after impact are developed. These expressions are important in the numerical integration of the governing equations of motion when one must exchange the set of unconstrained equations for the set of constrained equation. The theory presented in this work can be applied to problems in which robots have to follow some prescribed patterns or trajectories when in contact with the environment. It can also de applied to problems in which robotic manipulators must handle payloads.

A Simplified Model of Flow-Induced Oscillations of Collapsible Tubes Conveying Viscous Fluids

2006 ◽  
Author(s):  
X. Sheldon Wang
Keyword(s):  
Mathematical Model ◽  
Equations Of Motion ◽  
Small Deformation ◽  
Viscous Fluids ◽  
Simplified Model ◽  
Simple Mathematical Model ◽  
Governing Equations ◽  
Inertia Effects ◽  
Collapsible Tubes ◽  
Frictional Forces

In this paper, a simple mathematical model is formulated to study the static and dynamic instabilities of collapsible tubes conveying viscous fluids. The governing equations of motion for the pipe are derived under small deformation assumptions with the consideration of fluid frictional forces and inertia effects. In the case of steady flow, both buckling and flutter instabilities can be predicted based on the real and imaginary parts of the eigenvalues. In the case of pulsatile flow, the Bolotin method is employed to identify the dynamic stability regions.

scholarly journals Introducing a particular mathematical model for predicting the resistance and performance of prismatic planing hulls in calm water by means of total pressure distribution

2015 ◽  
Vol 12 (2) ◽  
pp. 73-94 ◽  
Author(s):  
P. Ghadimi ◽  
S. Tavakoli ◽  
M. A. Feizi Chekab ◽  
A. Dashtimanesh
Keyword(s):  
Mathematical Model ◽  
Pressure Distribution ◽  
Total Pressure ◽  
Center Of Gravity ◽  
Governing Equations ◽  
Calm Water ◽  
Hydrodynamic Study ◽  
Pass Through ◽  
And Performance

Mathematical modeling of planing hulls and determination of their characteristics are the most important subjects in hydrodynamic study of planing vessels. In this paper, a new mathematical model has been developed based on pressure distribution. This model has been provided for two different situations: (1) for a situation in which all forces pass through the center of gravity and (2) for a situation in which forces don not necessarily pass through the center of gravity. Two algorithms have been designed for the governing equations. Computational results have been presented in the form of trim angle, total pressure, hydrodynamic and hydrostatic lift coefficients, spray apex and total resistance which includes frictional, spray and induced resistances. Accuracy of the model has been verified by comparing the numerical findings against the results of Savitsky's method and available experimental data. Good accuracy is displayed. Furthermore, effects of deadrise angle on trim angle of the craft, position of spray apex and resistance have been investigated.

Infinite-dilution activity coefficients by comparative ebulliometry: A model of ebulliometer and the experimental equipment and procedure

1986 ◽  
Vol 51 (7) ◽  
pp. 1393-1402 ◽  
Author(s):  
Vladimír Dohnal ◽  
Marcela Novotná
Keyword(s):  
Mathematical Model ◽  
Activity Coefficients ◽  
Infinite Dilution ◽  
Calibration Error ◽  
Simple Mathematical Model ◽  
Experimental Equipment ◽  
Infinite Dilution Activity Coefficients ◽  
The Difference ◽  
Major Factors

The ebulliometric technique for determination of infinite-dilution activity coefficients is examined. A simple mathematical model of ebulliometer is formulated to derive and analyze corrections accounting for the difference between the composition of the ebulliometer charge and that of the equilibrium liquid. Our own experimental equipment employing the comparative ebulliometric setup is described along with the measuring procedure and calibration. Error analysis is carried out identifying major factors limiting the accuracy of the determination.

The Effect of Wall Motions on the Governing Equations of Contained Fluids

1990 ◽  
Vol 57 (3) ◽  
pp. 783-785 ◽  
Author(s):  
Roger Ohayon ◽  
Carlos A. Felippa
Keyword(s):  
Wave Equation ◽  
Finite Elements ◽  
Governing Equation ◽  
Equations Of Motion ◽  
Governing Equations ◽  
Displacement Potential ◽  
Classical Wave ◽  
Classical Wave Equation ◽  
Acoustic Fluid

The equations of motion for an acoustic fluid enclosed in a moving or flexible container are studied. It is shown that the determination of the reference state must account for the surface-integrated effect of the wall motions. The governing equation of transient motions about this state in the displacement potential does not generally reduce to the classical wave equation unless special adjustments are made. The results are relevant to finite elements formulations based on the displacement potential.

Determination of elastodynamic errors in joints of industrial robots

Robotica ◽  
1988 ◽  
Vol 6 (3) ◽  
pp. 213-219 ◽  
Author(s):  
Ilija Nikolić
Keyword(s):  
Numerical Integration ◽  
Equations Of Motion ◽  
Industrial Robots ◽  
Dynamic Equations ◽  
Minimal Configuration ◽  
Dynamic Errors ◽  
Elastic Joints

SUMMARYThis paper presents a method for automatic forming and solving dynamic equations of motion of manipulator with elastic joints and rigid segments. For the minimal configuration of a cylindrical manipulator the numerical integration of these equations is performed, and vibrations in the joints are obtained as dynamic errors with respect to the prescribed trajectory.

Vibration Control of Beams with Negative Capacitive Shunting of Interdigital Electrode Piezoceramics

2005 ◽  
Vol 11 (3) ◽  
pp. 331-346 ◽  
Author(s):  
Chul H. Park ◽  
Amr Baz
Keyword(s):  
Mathematical Model ◽  
Boundary Conditions ◽  
Vibration Control ◽  
Equations Of Motion ◽  
Vibration Modes ◽  
Frequency Range ◽  
Governing Equations ◽  
Interdigital Electrode ◽  
Beam System ◽  
Cantilevered Beam

A pair of interdigital electrode (IDE) piezoceramics is used to simultaneously suppress multimode vibrations of a cantilevered beam. This is achieved by connecting the IDE piezoceramics in parallel to a negative capacitive shunt circuit. The governing equations of motion of an IDE piezo/beam system and associated boundary conditions are derived using the Hamilton principle. The obtained mathematical model is validated experimentally Attenuations ranging between 5 and 20 dB are obtained for all the vibration modes over the frequency range of 0-3000 Hz. The presented theoretical and experimental techniques provide invaluable tools for designing simple and effective passive vibration dampers for structures with closely packed modes.

A Nonlinear and Non-Ideal Wind Generator Supporting Structure

2006 ◽  
Vol 5-6 ◽  
pp. 433-442 ◽  
Author(s):  
Reyolando Manoel Lopes Rabelo da Fonseca Brasil ◽  
L.C.S. Feitosa ◽  
José Manoel Balthazar
Keyword(s):  
Mathematical Model ◽  
Energy Supply ◽  
Degrees Of Freedom ◽  
Transverse Direction ◽  
Equations Of Motion ◽  
Power Source ◽  
Sommerfeld Effect ◽  
Simple Mathematical Model ◽  
Supporting Structure ◽  
Tower Vibration

We present a simple mathematical model of a wind turbine supporting tower. Here, the wind excitation is considered to be a non-ideal power source. In such a consideration, there is interaction between the energy supply and the motion of the supporting structure. If power is not enough, the rotation of the generator may get stuck at a resonance frequency of the structure. This is a manifestation of the so-called Sommerfeld Effect. In this model, at first, only two degrees of freedom are considered, the horizontal motion of the upper tip of the tower, in the transverse direction to the wind, and the generator rotation. Next, we add another degree of freedom, the motion of a free rolling mass inside a chamber. Its impact with the walls of the chamber provides control of both the amplitude of the tower vibration and the width of the band of frequencies in which the Sommerfeld effect occur. Some numerical simulations are performed using the equations of motion of the models obtained via a Lagrangian approach.

CUSTOMIZED SCALAR DYNAMIC EQUATIONS FOR ROBOTIC MANIPULATORS

1996 ◽  
Vol 20 (4) ◽  
pp. 401-420
Author(s):  
Oleg Vinogradov
Keyword(s):  
Rigid Body ◽  
Computer Simulations ◽  
Robotic Manipulators ◽  
Robotic Manipulator ◽  
Dynamic Equations ◽  
Governing Equations ◽  
Scalar Form ◽  
Kinematic Constraints ◽  
One Dimensional ◽  
A Chain

A robotic manipulator is considered as a reduction of a topologically uniform 3D-chain which is defined as a system of one-dimensional links connected by spherical joints. It has been shown in (4) that for the introduced chain the dynamic equations can be derived in an explicit scalar form. Such a chain can be viewed as a generic manipulator so that any specific type of the latter can be obtained from this chain by imposing additional kinematic constraints. It is shown in the paper that for practically all joints the governing equations for the chain and the constraints equations can be solved together resulting in an explicit scalar form of equations for a given manipulator. This form of equations has a potential for more efficient computer simulations. An application of the results to a 3-DOF rigid-body manipulator is given.

Bearing Capacity of Strip Footings in Frozen Soils

1975 ◽  
Vol 12 (3) ◽  
pp. 393-407 ◽  
Author(s):  
B. Ladanyi
Keyword(s):  
Mathematical Model ◽  
Bearing Capacity ◽  
Frozen Soil ◽  
Simple Mathematical Model ◽  
Frozen Soils ◽  
Present Solution ◽  
Strip Footings ◽  
Allowable Bearing Pressure ◽  
Circular Footing

The first part of this paper discusses some basic requirements for the determination of the allowable bearing pressure for frozen soils, with a particular reference to the delayed deformations due to creep and consolidation, which occur simultaneously in frozen soils containing large amounts of unfrozen water.In the second part of the paper, it is shown how the creep settlement and failure of a strip footing in frozen soil can be predicted by using a simple mathematical model of an expanding cylindrical cavity. With the help of a previously obtained solution, valid for a circular footing, and an appropriate empirical depth factor, the present solution is then extended to cover also the bearing capacity of footings of any shape and at any depth of embedment.

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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