scholarly journals Selecting Control Parameters of Mechanical Systems with Servoconstraints

2021 ◽  
Vol 264 ◽  
pp. 04085
Author(s):  
Kahramanjon Khusanov

The research results on the derivation of equations of motion (a mathematical model) of a mechanical system constrained by holonomic constraints of the first and second kind, which contains only tangential components of the constraint of the second kind, are presented in the article. These tangential components are taken as control parameters. Besides, the controllability of the plate, considered in the Appel problem, is investigated.

2013 ◽  
Vol 436 ◽  
pp. 166-173
Author(s):  
A. Mihaela Mîţiu ◽  
Daniel Constantin Comeagă ◽  
Octavian G. Donţu

In this paper are presented some aspects of transmissibility control of mechanical systems with 1 DOF so that the effects of vibration on their action to be minimized. Some technical solutions that can be used for this purpose is analyzed. Starting from the mathematical model of an electro-mechanical system with 1 DOF, are identified the parameters which influence the effectiveness of the transmissibility control system using an electrodynamic actuator who work in "closed loop".


Author(s):  
Darina Hroncová

Urgency of the research. Computer models mean new quality in the knowledge process. Using a computer model, the properties of the subject under investigation can be tested under different operating conditions. By experimenting with a com-puter model, we learn about the modelled object. We can test different machine variants without having to produce and edit prototypes. Target setting. The development of computer technology has expanded the possibility of solving mathematical models and allowed to gradually automate the calculation of mathematical model equations. It is necessary to insert appropriate inputs of the mathematical model and monitor and evaluate the output results through the computer output device The target was to describe the mathematical apparatus required for mathematical modeling and subsequently to compile a model for computer modeling. Actual scientific researches and issues analysis. When formulating a mathematical model for a computer, the laws and the theory we use are always valid under more or less idealized conditions, and operate with fictitious concepts such as, material point, ideal gas, intangible spring, and the like. However, with these simplifications, we describe a realistic phenomenon where the initial assumptions are only met to a certain extent. In order for the results not to be different from the modeled reality, it is to be assumed that a good computer model arises gradually, by verifying and modifying it, which is one of the advantages of MSC Adams. Uninvestigated parts of general matters defining. The question of building a real manipulator model. Based on the above simulation, it is possible to build a real model. The research objective. Using MSC Adams to simulate multiple body systems and verify its suitability for simulating ma-nipulator and robot models. In various versions of the assembled model we can monitor its behavior under different operating conditions. The statement of basic materials. In computer simulation, MSC Adams-View is used to simulate mechanical systems. It has an interactive environment for automated dynamic analysis of parameterized mechanical systems with an arbitrary struc-ture of rigid and flexible bodies with geometric or force joints, in which act gravity, inertia, experimentally designed contact, friction, aerodynamic, hydrodynamic or electromechanical forces and have integrated control, hydraulic, pneumatic or elec-tromechanical circuits. Conclusions. Working with a mathematical model on a computer opens space for specific synthesis of empirical and ana-lytical method of scientific knowledge. Working with the computer model carries the characteristic features of classical experi-mentation. It represents a qualitatively new way of solving tasks that can not be experimented with on a real object. The result is the equivalence of the computer model and the object being investigated with the features and expressions chosen as essen-tial, with accuracy sufficient to the exact purpose.


2004 ◽  
Vol 127 (3) ◽  
pp. 493-498 ◽  
Author(s):  
B. J. Alshaer ◽  
H. Nagarajan ◽  
H. K. Beheshti ◽  
H. M. Lankarani ◽  
S. Shivaswamy

Clearances exist in different kinds of joints in multibody mechanical systems, which could drastically affect the dynamic behavior of the system. If the joint is dry with no lubricant, impact occurs, resulting in wear and tear of the joint. In practical engineering design of machines, joints are usually designed to operate with some lubricant. Lubricated journal bearings are designed so that even when the maximum load is applied, the joint surfaces do not come into contact with each other. In this paper, a general methodology for modeling lubricated long journal bearings in multibody mechanical systems is presented. This modeling utilizes a method of solving for the forces produced by the lubricant in a dynamically loaded long journal bearing. A perfect revolute joint in a multibody mechanical system imposes kinematic constraints, while a lubricated journal bearing joint imposes force constraints. As an application, the dynamic response of a slider-crank mechanism including a lubricated journal bearing joint between the connecting rod and the slider is considered and analyzed. The dynamic response is obtained by numerically solving the constraint equations and the forces produced by the lubricant simultaneously with the differential equations of motion and a set of initial conditions numerically. The results are compared with the previous studies performed on the same mechanism as well a dry clearance joint. It is shown that in a multibody mechanical system, the journal bearing lubricant introduces damping and stiffness to the system. The earlier studies predict that the order of magnitude of the reaction moment is twice that of a perfect revolute joint. The proposed model predicts that the reaction moment is within the same order of magnitude of the perfect joint simulation case.


Author(s):  
František Bures

A description of the original mathematical model of spatial oscillations of a four-axle autonomous traction module during its movement along straight and curved sections of the railway track is proposed. In this case, the design of a four-axle autonomous traction module is presented as a complex mechanical system, and the track is considered as an elastic-viscous inertial system. The equations of motion were compiled using the Lagrange method of the ІІ kind. For each of the solids, the kinetic energy is determined by the Koenig theorem. The potential energy component is obtained by the Clapeyron theorem, as the sum of the energies accumulated in the elastic elements of the system during their deformations. The dissipative energy was also taken into account when compiling the equations of motion. Generalized forces that have no potential, in this case, include the forces of interaction between wheels and rails, which are determined using the creep hypothesis. It is important to note that the model takes into account the forces in the bonds between the bodies of the system and the spatial displacements of the rigid bodies of the mechanical system, taking into account possible restrictions. Moreover, the mathematical model developed by the author is a system of differential equations of the 100th order. This mathematical model is the base for further theoretical studies of the dynamics of railway four-axle autonomous traction modules in single motion or when moving as part of a train. To solve the resulting system of differential equations, the author develops special software that allows for complex theoretical studies of spatial oscillations of a four-axle autonomous tractionmodule to determine the indicators of its dynamic loading and traffic safety. 


Author(s):  
B. J. Alshaer ◽  
H. M. Lankarani ◽  
S. Shivaswamy

Abstract Clearances exist in different kinds of joints in multibody mechanical systems, which could drastically affect the dynamic behavior of the system. If the joint is dry with no lubricant, impact occurs, resulting in wear and tear of the joint. In practical engineering design of machines, joints are usually designed to operate with some lubricant. Lubricated journal bearings are designed so that even when the maximum load is applied, the joint surfaces do not come into contact with each other. In this paper, a general methodology for modeling lubricated long journal bearings in multibody mechanical systems is presented. This modeling utilizes a new method of solving for the forces produced by the lubricant in a dynamically loaded long journal bearing. A perfect revolute joint in a multibody mechanical system imposes kinematic constraints, while a lubricated journal bearing joint imposes force constraints. As an application, the dynamic response of a crank-slider mechanism including a lubricated journal bearing joint between the connecting rod and the slider is considered and analyzed. The dynamic response is obtained by numerically solving the constraint equations and the forces produced by the lubricant simultaneously with the differential equations of motion and a set of initial conditions numerically. The results are compared with the previous studies performed on the same mechanism as well a dry clearance joint. It is shown that in a multibody mechanical system, the journal bearing lubricant introduces damping and stiffness to the system. The earlier studies previous predict that the order of magnitude of the reaction moment is twice that of a perfect revolute joint. The proposed model predicts that the reaction moment is within the same order of magnitude of the perfect joint simulation case.


2014 ◽  
Vol 11 (03) ◽  
pp. 1450017
Author(s):  
G. F. Torres del Castillo ◽  
O. Sosa-Rodríguez

It is shown that for a mechanical system with a finite number of degrees of freedom, subject to nonholonomic constraints, there exists an infinite number of Hamiltonians and symplectic structures such that the equations of motion can be written as the Hamilton equations, with the original constraints incorporated in the Hamiltonian structure.


1990 ◽  
Vol 57 (4) ◽  
pp. 1004-1010 ◽  
Author(s):  
John G. Papastavridis

This paper formulates the simplest possible, or canonical, form of the Lagrangean-type of equations of motion of holonomically constrained mechanical systems. This is achieved by introducing a new special set of n holonomic (system) coordinates in terms of which the m ( < n) holonomic constraints are expressed in their simplest, or uncoupled, form: the first m of these new coordinates vanish; the remaining (n-m) (nonvanishing) new coordinates of the (n-m) degree-of-freedom system are then independent. From the resulting equations of motion: (a) The last (n-m) are reactionless canonical equations (the holonomic counterpart of the linear or nonlinear equations, either of Maggi (in the old variables), or of Boltzmann/Hamel (in the new variables)) whose solution yields the motion, while (b) the first m supply the system reactions, in the old or new coordinates, once the motion is known. Special forms of these equations and a simple example are also given. The geometrical interpretation of the above, in modern vector/linear algebra language is summarized in the Appendix.


Author(s):  
Hiroaki Yoshimura

The paper illustrates the Lagrangian formalism of mechanical systems with nonholonomic constraints using the ideas of geometric mechanics. We first review a Lagrangian system for a conservative mechanical system in the context of variational principle of Hamilton, and we investigate the case that a given Lagrangian is hyperregular, which can be illustrated in the context of the symplectic structure on the tangent bundle of a configuration space by using the Legendre transformation. The Lagrangian system is denoted by the second order vector field and the Lagrangian one- and two-forms associated with a given hyperregular Lagrangian. Then, we demonstrate that a mechanical system with nonholonomic constraints can be formulated on the tangent bundle of a configuration manifold by using Lagrange multipliers. To do this, we investigate the Lagrange-d’Alembert principle from geometric points of view and we also show the intrinsic expression of the Lagrange-d’Alembert equations of motion for nonholonomic mechanical systems with nonconservative force fields.


Author(s):  
Firdaus E Udwadia ◽  
Phailaung Phohomsiri

We present the new, general, explicit form of the equations of motion for constrained mechanical systems applicable to systems with singular mass matrices. The systems may have holonomic and/or non-holonomic constraints, which may or may not satisfy D'Alembert's principle at each instant of time. The equation provides new insights into the behaviour of constrained motion and opens up new ways of modelling complex multi-body systems. Examples are provided and applications of the equation to such systems are illustrated.


2020 ◽  
pp. 19-25
Author(s):  
N.N Gorbatenko

A procedure is proposed for modeling automobile hydromechanical transmissions, based on representing them in the form of multi-mass mechanical systems and applying the Lagrange equations with indefinite multipliers to derive the equations of motion of concentrated masses. Keywords hydromechanical transmission, clutches, gear shifting, mathematical model, Lagrange equations with indefinite multipliers. [email protected]


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