Time Optimal Transfer Function of a Mechanism

Volume 2 ◽  
2004 ◽  
Author(s):  
A. A. Goun ◽  
O. K. Sliva ◽  
Vyacheslav Murzin
Keyword(s):  
Transfer Function ◽  
Mechanical System ◽  
Optimization Problems ◽  
Mechanical Energy ◽  
Operating Time ◽  
Variational Calculus ◽  
Initial Position ◽  
Optimal Transfer ◽  
Time Optimal ◽  
Switch Design

A variety of optimization problems in theoretical mechanics are related to the problem of finding the quickest operating mechanism among all possible mechanisms. It can be formulated in the following way. Let us consider a mechanical system with one degree of freedom consisting of leading and lagging links with masses M1 and M2 respectively. Source of mechanical energy is attached to the leading link and its potential energy is known as a function of the position of the leading link. Positions of the leading - x and lagging links - y are related through the position function. Now the optimization problem can be formulated in the following way: find the position function such that the lagging link is transferred from initial position to the final position in the shortest time. We have obtained an analytic solution to this problem using variational calculus methods in the case then dissipative forces acting on the system can be neglected. We have shown that this problem is analogous to the classical brachistochtone problem. The qualitative feature of this result is that the optical mechanical system tends to accelerate the leading link first in order to maximize the power being extracted from the mechanical energy source. Analytical solution is applied for the optimization of the fast acting electric switch design. Leading link load and operating time reductions with the use of the optimal transfer function is demonstrated. This approach can be generalized for a variety of mechanisms where the operating time is critical.

Time Optimal Transfer Function of a Mechanism in the Presence of Dissipative Forces

2004 ◽  
Author(s):  
A. A. Goun ◽  
O. K. Sliva
Keyword(s):  
Dry Friction ◽  
Optimization Problems ◽  
Mechanical Energy ◽  
Operating Time ◽  
Variational Calculus ◽  
Viscous Friction ◽  
Optimal Position ◽  
Dissipative Forces ◽  
Time Optimal ◽  
Theoretical Mechanics

A variety of optimization problems in theoretical mechanics are related to the problem of finding the quickest operating mechanism among all possible mechanisms. Let us consider a mechanical system with one degree of freedom consisting of leading and lagging links with masses M1 and M2 respectively. Source of mechanical energy is attached to the leading link and its potential energy is known as a function of the position of the leading link. Positions of the leading - x and lagging links - y are related through the position function. Now the optimization problem can be formulated in the following way: find the position function such that the lagging link is transferred from initial to the final position in the shortest time. The analytic solution for this problem for the case when dissipative forces can be neglected was found using variational calculus method. In the case when dissipative forces can be described as viscous friction the problem can be solved using iterative methods. The differential equation that describes the stationary point of these iterations was obtained. The dependence of the optimal position function on the magnitude of friction is analyzed. In the case when dissipative forces are of the dry friction type the approach based on the variational calculus fails. We were able to find the optimal position function problem using Maximum Principle. New qualitative features of the solution arising due to dry friction are discussed. Approaches developed in this paper can be generalized for a variety of mechanisms where the operating time is critical.

A Numerical Scheme for a Class of Parametric Problem of Fractional Variational Calculus

2012 ◽  
Vol 7 (2) ◽  
Author(s):  
Om P. Agrawal ◽  
M. Mehedi Hasan ◽  
X. W. Tangpong
Keyword(s):  
Analytical Solutions ◽  
Numerical Scheme ◽  
Fractional Derivatives ◽  
Optimization Problems ◽  
Practical Interest ◽  
Variational Calculus ◽  
Functional Minimization ◽  
Orthogonal Functions ◽  
Order Problem ◽  
Parametric Problem

Fractional derivatives (FDs) or derivatives of arbitrary order have been used in many applications, and it is envisioned that in the future they will appear in many functional minimization problems of practical interest. Since fractional derivatives have such properties as being non-local, it can be extremely challenging to find analytical solutions for fractional parametric optimization problems, and in many cases, analytical solutions may not exist. Therefore, it is of great importance to develop numerical methods for such problems. This paper presents a numerical scheme for a linear functional minimization problem that involves FD terms. The FD is defined in terms of the Riemann-Liouville definition; however, the scheme will also apply to Caputo derivatives, as well as other definitions of fractional derivatives. In this scheme, the spatial domain is discretized into several subdomains and 2-node one-dimensional linear elements are adopted to approximate the solution and its fractional derivative at point within the domain. The fractional optimization problem is converted to an eigenvalue problem, the solution of which leads to fractional orthogonal functions. Convergence study of the number of elements and error analysis of the results ensure that the algorithm yields stable results. Various fractional orders of derivative are considered, and as the order approaches the integer value of 1, the solution recovers the analytical result for the corresponding integer order problem.

scholarly journals Time-optimal transfer of coherence

2012 ◽  
Vol 86 (5) ◽  
Author(s):  
Alberto Carlini ◽  
Tatsuhiko Koike
Keyword(s):  
Optimal Transfer ◽  
Time Optimal

On the Theory of the Acceleration Damper

1956 ◽  
Vol 23 (3) ◽  
pp. 373-378
Author(s):  
Carl Grubin
Keyword(s):  
Mechanical System ◽  
Momentum Transfer ◽  
Driving Force ◽  
Direct Problem ◽  
Mechanical Energy ◽  
Single Degree Of Freedom ◽  
Mass Particle ◽  
Single Degree ◽  
Vibrating System ◽  
At Resonance

Abstract The acceleration damper reduces the vibration of a mechanical system through momentum transfer by collision and conversion of mechanical energy into heat. A typical unit consists of a mass particle moving in a container fixed to the primary vibrating system. The direct problem is to determine the motion of a single-degree-of-freedom system with a damper, when the driving force is simple harmonic. The inverse is to determine the characteristics of a damper for reducing the vibration of the same system to a prescribed value. Numerical results indicate that the damper is most effective at resonance.

scholarly journals The Importance of Transfer Function in Solving Set-Union Knapsack Problem Based on Discrete Moth Search Algorithm

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 17 ◽  
Author(s):  
Yanhong Feng ◽  
Haizhong An ◽  
Xiangyun Gao
Keyword(s):  
Transfer Function ◽  
Knapsack Problem ◽  
Transfer Functions ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Continuous Optimization ◽  
Search Space ◽  
Discrete Search ◽  
Continuous Optimization Problems

Moth search (MS) algorithm, originally proposed to solve continuous optimization problems, is a novel bio-inspired metaheuristic algorithm. At present, there seems to be little concern about using MS to solve discrete optimization problems. One of the most common and efficient ways to discretize MS is to use a transfer function, which is in charge of mapping a continuous search space to a discrete search space. In this paper, twelve transfer functions divided into three families, S-shaped (named S1, S2, S3, and S4), V-shaped (named V1, V2, V3, and V4), and other shapes (named O1, O2, O3, and O4), are combined with MS, and then twelve discrete versions MS algorithms are proposed for solving set-union knapsack problem (SUKP). Three groups of fifteen SUKP instances are employed to evaluate the importance of these transfer functions. The results show that O4 is the best transfer function when combined with MS to solve SUKP. Meanwhile, the importance of the transfer function in terms of improving the quality of solutions and convergence rate is demonstrated as well.

The Motion of the Human Center of Mass and its Relationship to Mechanical Impedance

1966 ◽  
Vol 8 (5) ◽  
pp. 399-405 ◽  
Author(s):  
Edmund B. Weis ◽  
Frank P. Primiano
Keyword(s):  
Transfer Function ◽  
Mechanical System ◽  
Degrees Of Freedom ◽  
Center Of Mass ◽  
Mechanical Impedance ◽  
Second Order ◽  
Analysis Tool ◽  
Isotropic Theory ◽  
Spatial Degrees Of Freedom

This report concerns the development of a relationship between the human mechanical impedance and the coupling of the human center of mass to the environment. The mechanical impedance is a common analysis tool in biomechanics while the analysis of the coupling of the center of mass to the environment is technically more difficult, if not impossible. The development is based on linear, passive, isotropic theory and shows that the transfer function which expresses the relation between the motion of the center of mass and the motion of the source is similar to a linear second order mechanical system in each of the translational spatial degrees of freedom.

scholarly journals An algorithm to compute the transfer function of a mechanical system

2004 ◽  
Vol 21 (5) ◽  
pp. S1247-S1251
Author(s):  
L Ribichini ◽  
V Leonhardt ◽  
H Lück ◽  
K Danzmann
Keyword(s):  
Transfer Function ◽  
Mechanical System
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