A General Theory for Synthesizing Crank-Type Four-Bar Function Generators With Transmission Angle Control

1978 ◽  
Vol 45 (2) ◽  
pp. 415-421 ◽  
Author(s):  
Krishna C. Gupta
Keyword(s):  
General Theory ◽  
Least Square ◽  
Angle Variation ◽  
Numerical Examples ◽  
Transmission Angle ◽  
Function Generators

In this paper, the author proposes a general theory for synthesizing crank-type (i.e., crank-rocker and double-crank) four-bar function generators in which the transmission angle variation over a full crank revolution is in a specified range. Precision point as well as least-square designs have been considered in the paper. Applications of the theory are illustrated by means of numerical examples.

Design of Four-Bar Function Generators With Mini-Max Transmission Angle

1977 ◽  
Vol 99 (2) ◽  
pp. 360-365 ◽  
Author(s):  
K. C. Gupta
Keyword(s):  
Extreme Values ◽  
New Method ◽  
Numerical Examples ◽  
Transmission Angle ◽  
Function Generators ◽  
Synthesis Procedure

A new method of designing four-bar function generators with optimum transmission angle is presented. Transmission angles are considered optimum, in a mini-max sense, when their extreme values deviate equally from 90 deg. Numerical examples are given to illustrate the synthesis procedure.

Optimization of Crank-and-Rocker Linkages with Size and Transmission Constraints

1979 ◽  
Vol 101 (1) ◽  
pp. 51-57 ◽  
Author(s):  
F. Freudenstein ◽  
Meng Sang Chew
Keyword(s):  
Logical Analysis ◽  
Direct Solution ◽  
Angle Variation ◽  
Numerical Examples ◽  
Transmission Angle ◽  
Transmission Constraints

An algebraic procedure suitable for pocket calculators is derived for the determination of the proportions of a plane crank-and-rocker linkage in which the ratio of largest to smallest link and the transmission-angle variation are prescribed. A logical analysis of the relative lengths of the links leads to a direct solution without algorithms or iteration. The results are illustrated with tables and numerical examples.

Performance Criteria for High-Speed Crank-and-Rocker Linkages—Part II: Spherical Crank-and-Rocker Linkages

1979 ◽  
Vol 101 (1) ◽  
pp. 26-31 ◽  
Author(s):  
H. Funabashi ◽  
F. Freudenstein
Keyword(s):  
High Speed ◽  
Dynamic Performance ◽  
Performance Criteria ◽  
Link Length ◽  
Angle Variation ◽  
Numerical Examples ◽  
Transmission Angle ◽  
The Dead ◽  
Sine Functions

In Part I proportions were derived for high-speed plane crank-and-rocker mechanisms. In this part, the corresponding developments are given for spherical crank-and-rocker mechanisms. The ratios of the sine functions of the transmission angles and of the rocker accelerations—both at the dead-center positions—remain the static and dynamic performance criteria of the linkage. The results are illustrated by numerical examples, which show the influence of these ratios on the transmission-angle variation, rocker acceleration and the ratio of minimum to maximum link length.

The Constrained Least-Square Optimization of Spherical Four-Bar Path Generators

1992 ◽  
Vol 114 (3) ◽  
pp. 394-405 ◽  
Author(s):  
J. Angeles ◽  
Z. Liu
Keyword(s):  
Numerical Procedure ◽  
Orthogonal Decomposition ◽  
Least Square ◽  
System Of Nonlinear Equations ◽  
Overdetermined System ◽  
Optimization Scheme ◽  
Numerical Examples ◽  
Speed Up ◽  
General Basis ◽  
Four Bar Linkage

In this paper, the optimization of the spherical RRRR four-bar linkage for the problem of path generation is addressed. The problem is formulated as a two-loop minimization of the error between the path-generating point in the coupler curve and the prescribed position, while decoupling the linkage parameters from the configuration variables, namely, the input angles. The synthesis problem consists of evaluating a set of input angles {ψk}1m defining m linkage configurations and the linkage parameters independently. This leads to a constrained overdetermined system of nonlinear equations. The orthogonal decomposition algorithm, introduced elsewhere, is employed to solve the problem. Continuation and damping techniques are used in the numerical procedure to ensure convergence and speed up its rate. The optimization scheme is developed on a general basis and can handle the problem for any number of given path points. Three numerical examples are included.

scholarly journals PROJECTION METHODS FOR INTEGRAL EQUATIONS IN EPIDEMIC

2002 ◽  
Vol 7 (2) ◽  
pp. 229-240 ◽  
Author(s):  
L. Hacia
Keyword(s):  
Mathematical Modeling ◽  
Numerical Methods ◽  
General Theory ◽  
Integral Equations ◽  
Projection Methods ◽  
Volterra Integral Equations ◽  
Temporal Development ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Spatio Temporal

In this paper numerical methods for mixed integral equations are presented. Studied equations arise in the mathematical modeling of the spatio‐temporal development of an epidemic. The general theory of these equations is given and used in the projection methods. Projection methods lead to a system of algebraic equations or to a system of Volterra integral equations. The considered theory is illustrated by numerical examples.

XIV.—Studies in Practical Mathematics. VIII. On the Iterative Methods of Lin and Friedman for Factorizing Polynomials

1954 ◽  
Vol 64 (2) ◽  
pp. 190-199
Author(s):  
A. C. Aitken
Keyword(s):  
General Theory ◽  
Iterative Methods ◽  
Point Of View ◽  
Tentative Conclusion ◽  
Numerical Examples ◽  
Practical Mathematics

SynopsisThe methods of S. N. Lin (1943) and B. Friedman (1949) for approximating to the factors of a polynomial by iterated division are studied from the point of view of convergence. The general theory, hitherto lacking, is supplied. The matrices which transform the errors in coefficients from one iterate to the next are explicitly found, and the criterion of convergence derived. Numerical examples are given. The tentative conclusion is that the methods are less simple in theory and less adaptable than the method of penultimate remainder, which admits of accelerative devices.

Kernel Fuzzy c-Regression Based on Least Absolute Deviation with Modified Huber Function

2019 ◽  
Vol 23 (3) ◽  
pp. 571-576 ◽  
Author(s):  
Yusuke Oi ◽  
Yasunori Endo ◽  
◽  
Keyword(s):  
Objective Function ◽  
Regression Models ◽  
Least Square ◽  
Least Absolute Deviation ◽  
Absolute Deviation ◽  
Numerical Examples

The fuzzy c-regression models are useful for datasets with various correlations. To deal with nonlinear datasets, a kernel fuzzy c-regression (KFCR) method was previously proposed. However, this method is weak for outliers because its objective function is based on the least square principle. We introduce the least absolute deviation (LAD) method with a modified Huber function into the KFCR (LAD-KFCR) to overcome the abovementioned problem. We verify the usefulness of the proposed LAD-KFCR method through numerical examples.

scholarly journals Lattice Methods for Pricing American Strangles with Two-Dimensional Stochastic Volatility Models

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xuemei Gao ◽  
Dongya Deng ◽  
Yue Shan
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Stochastic Volatility ◽  
Least Square ◽  
Two Dimensional ◽  
Stochastic Volatility Models ◽  
Lattice Method ◽  
Numerical Examples ◽  
One Dimensional ◽  
Volatility Models

The aim of this paper is to extend the lattice method proposed by Ritchken and Trevor (1999) for pricing American options with one-dimensional stochastic volatility models to the two-dimensional cases with strangle payoff. This proposed method is compared with the least square Monte-Carlo method via numerical examples.

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