The Research of Chaos Mapping Method with Infinite Collapses to Mechanism Synthesis

2011 ◽  
Vol 204-210 ◽  
pp. 79-82
Author(s):  
Qi Yuan Liu ◽  
You Xin Luo ◽  
Bin Zeng
Keyword(s):  
Mapping Method ◽  
Initial Guess ◽  
New Method ◽  
One Dimensional ◽  
Newton Iterative Method ◽  
All Solutions ◽  
Sensitive Dependence ◽  
Approximate Synthesis ◽  
Chaos Sequences ◽  
First Time

Many questions in natural science and engineering are transformed into nonlinear equations to be found, Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point. The property of chaos sequences produced by one dimensional simple chaos mapping method with infinite collapses in finite interval was analyzed. For the first time, a new method based on utilizing one dimensional chaos mapping method with infinite collapses to obtain locate initial points to find all solutions of the nonlinear questions was proposed. The numerical examples in linkage synthesis and approximate synthesis show that the new method is correct and effective.

The Research of Lorenz Chaos Mapping Method to Mechanism Synthesis

2011 ◽  
Vol 467-469 ◽  
pp. 407-410
Author(s):  
You Xin Luo ◽  
Qi Yuan Liu
Keyword(s):  
Mapping Method ◽  
Initial Guess ◽  
New Method ◽  
Mechanism Synthesis ◽  
One Dimensional ◽  
Newton Iterative Method ◽  
All Solutions ◽  
Sensitive Dependence ◽  
Approximate Synthesis ◽  
First Time

Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point. The property of chaos serials produced by Lorenz chaos mapping method was analyzed. For the first time, a new method to find all solutions based on utilizing Lorenz chaos mapping to obtain locate initial points to find all solutions of the nonlinear questions was proposed. The numerical examples in linkage synthesis and approximate synthesis show that the new method is correct and effective.

The Research of Chebyshev Chaos Mapping Method to Mechanism Synthesis

2011 ◽  
Vol 467-469 ◽  
pp. 416-420
Author(s):  
You Xin Luo ◽  
Qi Yuan Liu ◽  
Xiao Yi Che
Keyword(s):  
Mapping Method ◽  
Initial Guess ◽  
New Method ◽  
Mechanism Synthesis ◽  
Science And Engineering ◽  
Newton Iterative Method ◽  
All Solutions ◽  
Sensitive Dependence ◽  
Approximate Synthesis ◽  
First Time

Many questions in natural science and engineering are transformed into nonlinear equations to be found. Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point. The property of chaos serials produced by Chebyshev chaos mappings was analyzed. For the first time, a new method to find all solutions based on utilizing Chebyshev chaos mappings to obtain locate initial points to find all solutions of the nonlinear questions was proposed. The numerical examples in linkage synthesis and approximate synthesis show that the new method is correct and effective.

The Research of Sinai Chaos Mapping Method to Mechanism Synthesis

2011 ◽  
Vol 467-469 ◽  
pp. 411-415
Author(s):  
You Xin Luo ◽  
Qi Yuan Liu ◽  
Bin Zeng
Keyword(s):  
Mapping Method ◽  
Initial Guess ◽  
New Method ◽  
Mechanism Synthesis ◽  
Science And Engineering ◽  
Newton Iterative Method ◽  
All Solutions ◽  
Sensitive Dependence ◽  
Approximate Synthesis ◽  
First Time

Many questions in natural science and engineering are transformed into nonlinear equations to be found, Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point. The property of chaos serials produced by Sinai chaos mapping method was analyzed. For the first time, a new method to find all solutions based on utilizing Sinai chaos mapping to obtain locate initial points to find all solutions of the nonlinear questions was proposed. The numerical examples in linkage synthesis and approximate synthesis show that the new method is correct and effective.

The Research of Composite Nonlinear Discrete Chaos Dynamical Systems to Mechanism Synthesis

2011 ◽  
Vol 204-210 ◽  
pp. 160-164
Author(s):  
Qi Yuan Liu ◽  
You Xin Luo ◽  
Bin Zeng
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Initial Guess ◽  
New Method ◽  
Newton Iterative Method ◽  
All Solutions ◽  
Sensitive Dependence ◽  
Approximate Synthesis ◽  
Discrete Chaos ◽  
First Time

Many questions in natural science and engineering are transformed into nonlinear equations to be found. Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point.　A composite discrete chaos dynamical system was constructed by two special discrete chaos dynamical systems and initial points were produced by proposed chaos system. For the first time, a new method based on composite discrete chaos dynamical system to obtain locate initial points to find all solutions of the nonlinear questions was proposed. The numerical examples in linkage synthesis and approximate synthesis show that the new method is correct and effective.

Meshed Chaos Mapping-Based Newton Iteration Method of Mechanism Synthesis

2011 ◽  
Vol 55-57 ◽  
pp. 688-691
Author(s):  
Xiao Yi Che ◽  
Qi Yuan Liu ◽  
You Xin Luo ◽  
Bin Zeng
Keyword(s):  
Kinematic Analysis ◽  
Mapping Method ◽  
Initial Guess ◽  
Mechanism Synthesis ◽  
Newton Iterative Method ◽  
All Solutions ◽  
Sensitive Dependence ◽  
Approximate Synthesis ◽  
Newton Iteration Method ◽  
First Time

Kinematic analysis is fundamental for the mechanism synthesis. The kinematic analysis of mechanism is attributed to find the solutions of the nonlinear equations and this process is very difficult. Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point. For the first time, a new method based on utilizing meshed chaos mapping method to obtain locate initial points to find all solutions of the nonlinear questions was proposed. The numerical examples in linkage synthesis and approximate synthesis show that the method is correct and effective.

Planar Four-Linkage Guide Mechanism Synthesis Based on Mechanical Chaos System Methods

2011 ◽  
Vol 55-57 ◽  
pp. 1009-1012
Author(s):  
Xiao Yi Che ◽  
Zhe Ming He ◽  
You Xin Luo ◽  
Qi Yuan Liu
Keyword(s):  
Initial Guess ◽  
Mechanism Synthesis ◽  
One Dimensional ◽  
Function Generation ◽  
Newton Iterative Method ◽  
All Solutions ◽  
Sensitive Dependence ◽  
Simple Realization ◽  
Chaos Sequences ◽  
First Time

The problem of four-linkage guide mechanism synthesis is transformed into nonlinear equations to be found, Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess points. For the first time, the mechanical chaos methods of mechanism synthesis and all solutions of the nonlinear questions of mechanism synthesis were found by utilizing chaos sequences of chaos motions of mechanical system to obtain locate initial points. As an example the problem of function generation for planar four-linkage guide mechanism was considered. This makes that multi-projects selecting could be possible. This method is adaptive to planar multi-linkage and spatial mechanism. This provides a new simple realization method for mechanics design.

The Research of Two-Dimensional Probability Hyper-Chaotic Mapping Newton Iterative Method to Mechanism Synthesis

2010 ◽  
Vol 20-23 ◽  
pp. 670-675
Author(s):  
You Xin Luo ◽  
Bin Zeng
Keyword(s):  
Iterative Method ◽  
Discrete Systems ◽  
Initial Guess ◽  
Two Dimensional ◽  
Chaotic Mapping ◽  
Newton Iterative Method ◽  
All Solutions ◽  
Sensitive Dependence ◽  
Approximate Synthesis ◽  
First Time

Many questions in natural science and engineering are transformed into nonlinear equations to be found. Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point. The probability characteristic of hyper-chaotic sequences produced by two dimensional hyper-chaotic discrete systems was analyzed. For the first time, a new method to find all solutions based on utilizing　two dimensional probability hyper-chaotic discrete mapping to obtain initial points to find all solutions of the nonlinear questions was proposed. The numerical examples in linkage synthesis and approximate synthesis show that the method is correct and effective.

The Research of Equal Probability Newton Iterative Method to Mechanism Synthesis & Approximate Synthesis

2013 ◽  
Vol 364 ◽  
pp. 24-27
Author(s):  
Xiao Yi Che ◽  
You Xin Luo ◽  
Ling Fang Li
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Random Number ◽  
Initial Guess ◽  
Equal Probability ◽  
Newton Iterative Method ◽  
All Solutions ◽  
Sensitive Dependence ◽  
Approximate Synthesis ◽  
First Time

Many questions in natural science and engineering are transformed into nonlinear equations to be found, Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point. For the first time, utilizing an equal probability random number to produce initial value, a new method to find all solutions based on utilizing equal probability random number to obtain locate initial points to find all solutions of the nonlinear equations was proposed. The numerical examples in linkage synthesis and approximate synthesis show that the method is correct and effective.

The Research of Newton Iteration Method Based on Hyperchaos Chen System to Mechanism Synthesis

2011 ◽  
Vol 204-210 ◽  
pp. 169-173
Author(s):  
Qi Yuan Liu ◽  
You Xin Luo ◽  
Bin Zeng ◽  
Zhe Ming He
Keyword(s):  
Iterative Method ◽  
Initial Guess ◽  
Chen System ◽  
Science And Engineering ◽  
Newton Iterative Method ◽  
All Solutions ◽  
Sensitive Dependence ◽  
Approximate Synthesis ◽  
Newton Iteration Method ◽  
First Time

Many questions in natural science and engineering are transformed into nonlinear equations to be found. Newton iterative method is an important technique to one dimensional and multi-dimensional variables and iterative process exhibits sensitive dependence on initial guess point. For the first time, a new method based on utilizing hyperchaos Chen systems to obtain locate initial points to find all solutions of the nonlinear questions and taking improved Newton iterative method was proposed and it has higher solving efficiency compared with chaos Chen systems. The numerical examples in linkage synthesis and approximate synthesis show that the proposed method is correct and effective.

Fractal–Based Newton Method and Mechanism Synthesis & Approximate Synthesis

2012 ◽  
Vol 155-156 ◽  
pp. 420-423
Author(s):  
You Xin Luo ◽  
Ling Fang Li
Keyword(s):  
Nonlinear Equations ◽  
Initial Guess ◽  
Mechanism Synthesis ◽  
Initial Value ◽  
Science And Engineering ◽  
Newton Iterative Method ◽  
All Solutions ◽  
Sensitive Dependence ◽  
Approximate Synthesis ◽  
First Time

Many questions in natural science and engineering are transformed into nonlinear equations to be found, Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point. For the first time, utilizing a fractal iteration system to produce initial value, a new method to find all solutions of the nonlinear equations was proposed. The numerical examples in linkage synthesis and approximate synthesis show that the method is correct and effective.

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