scholarly journals Generalized Whittaker's equations for holonomic mechanical systems

1978 ◽  
Vol 1 (2) ◽  
pp. 245-253
Author(s):  
Munawar Hussain

In this paper the classical theorem “a conservative holonomic dynamic system is invariantly connected with a certain differential form” is generalized to group variables. This general theorem is then used to reduce the order of a Hamiltonian system by the use of the integral of energy. Equations of motion of the reduced system so obtained are derived which are the so-called generalized Whittaker's equations. Finally an example is given as an application of the theory.

1998 ◽  
Vol 120 (1) ◽  
pp. 8-14 ◽  
Author(s):  
Marco A. Arteaga

Control design of flexible robot manipulators can take advantage of the structural properties of the model used to describe the robot dynamics. Many of these properties are physical characteristics of mechanical systems whereas others arise from the method employed to model the flexible manipulator. In this paper, the modeling of flexible-link robot manipulators on the basis of the Lagrange’s equations of motion combined with the assumed modes method is briefly discussed. Several notable properties of the dynamic model are presented and their impact on control design is underlined.


2003 ◽  
Vol 25 (3) ◽  
pp. 170-185
Author(s):  
Dinh Van Phong

The article deals with the problem of consistent initial values of the system of equations of motion which has the form of the system of differential-algebraic equations. Direct treating the equations of mechanical systems with particular properties enables to study the system of DAE in a more flexible approach. Algorithms and examples are shown in order to illustrate the considered technique.


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.


Author(s):  
Giovanni Carabin ◽  
Erich Wehrle ◽  
Renato Vidoni

We are in the era of the fourth industrial revolution. Which highlights adaptability, monitoring, digitisation and efficiency in manufacturing as a result of the design of new smart mechanical systems. A central role in Industry 4.0 is played by maintenance and, within this framework, we define and review condition-based predictive maintenance. Thereafter, we propose a new class of smart mechanical systems that self-optimise utilising both condition-based maintenance and dynamic system modification. Akin to smart structures, smart mechanical systems will recognise and predict faults or malfunctions and, subsequently, self-optimise to restore desirable system behaviour. Potential benefits include increased reliability and efficiency while reducing cost without the requirement of highly skilled technicians. Thus, small and medium-sized enterprises are a specific target of such technology due to their increasing level of automatisation within Industry 4.0.


2005 ◽  
Vol 33 (4) ◽  
pp. 319-338
Author(s):  
Ron P. Podhorodeski ◽  
Paul Sobejko

Analysis of the forces involved in mechanical systems requires an understanding of the dynamic properties of the system's components. In this work, a project on the determination of both the location of the centre of mass and inertial properties is described. The project involves physical testing, the proposal of approximate models, and the comparison of results. The educational goal of the project is to give students and appreciation of second mass moments and the validity of assumptions that are often applied in component modelling. This work reviews relevant equations of motion and discusses techniques to determine or estimate the centre of mass and second moment of inertia. An example project problem and solutions are presented. The value of such project problems within a first course on the theory of mechanisms is discussed.


Author(s):  
Ehsan Sarshari ◽  
Nastaran Vasegh ◽  
Mehran Khaghani ◽  
Saeid Dousti

Ziegler’s pendulum is an appropriate model of a non-conservative dynamic system. By considering gravity effect, new equations of motion are extracted from Newton’s motion laws. The instability of equilibriums is determined by linear stability analysis. Chaotic behavior of the model is shown by numerical simulations. Sliding mode controller is used for eliminating chaos and for stabilizing the equilibriums.


Author(s):  
F. Zhang ◽  
B. J. Gilmore ◽  
A. Sinha

Abstract Tolerance allocation standards do not exist for mechanical systems whose response are time varying and are subjected to discontinuous forcing functions. Previous approaches based on optimization and numerical integration of the dynamic equations of motion encounter difficulty with determining sensitivities around the force discontinuity. The Alternating Frequency/Time approach is applied here to capture the effect of the discontinuity. The effective link length model is used to model the system and to account for the uncertainties in the link length, radial clearance and pin location. Since the effective link length model is applied, the equations of motion for the nominal system can be applied for the entire analysis. Optimization procedure is applied to the problem where the objective is to minimize the manufacturing costs and satisfy the constraints imposed on mechanical errors and design variables. Examples of tolerance allocation are presented for a single cylinder internal combustion engine.


Author(s):  
S. J. Lee ◽  
B. J. Gilmore ◽  
M. M. Ogot

Abstract Uncertainties due to random dimensional tolerances within stochastic dynamic mechanical systems lead to mechanical errors and thus, performance degradation. Since design standards do not exist for these systems, analysis and design tools are needed to properly allocate tolerances. This paper presents probabilistic models and methods to allocate tolerances on the link lengths and radial clearances such that the system meets a probabilistic and time dependent performance criterion. The method includes a general procedure for sensitivity analysis, using the effective link length model and nominal equations of motion. Since the sensitivity analysis requires only the nominal equations of motion and statistical information as input, it is straight forward to implement. An optimal design problem is formulated to allocate random tolerances. Examples are presented to illustrate the approach and its generality. This paper provides a solution to the tolerance allocation problem for stochastic dynamically driven mechanical systems.


Author(s):  
Yu Wang

Abstract A model is developed for analyzing mechanical systems with a pair of bodies with topological changes in their kinematic constraints. It is built upon the concept of Poincaré map rather than following the traditional methods of differential equations. The model provides a set of well-defined and naturally-discrete equations of motion and is capable of giving physical insights of dynamic characteristics of deadbeat convergence of multiple collisions and periodic or chaotic responses. The development of dynamic model and a local stability analysis are presented in Part 1, and the global analysis and numerical simulation are discussed in Part 2.


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