Forward Displacement Analysis of Nine-Link Barranov Truss Based on Anti-Control of Chaos Newton Downhill Method

2011 ◽  
Vol 230-232 ◽  
pp. 749-753
Author(s):  
You Xin Luo ◽  
Ying Yang
Keyword(s):  
Body Motion ◽  
Control Of Chaos ◽  
Vector Method ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Real Solutions ◽  
Chaotic Sequences ◽  
Motion System ◽  
Constrained Equations ◽  
Forward Displacement Analysis

The anti-control of chaos Newton downhill method finding all real solutions of nonlinear equations was proposed and the forward displacement analysis on the 25th nine-link Barranov truss was completed. Four constrained equations were established by vector method with complex numbers according to four loops of the mechanism and four supplement equations were also established by increasing four variables and the relation of sine and cosine function. The established eight equations are that of forward displacement analysis of the mechanism. Combining Newton downhill method with chaotic sequences, anti-control of chaos Newton downhill method based on utilizing anti-control of chaos in body motion system to obtain locate initial points to find all real solutions of the nonlinear questions was proposed. The numerical example was given.The result shows that all real solutions have been quickly obtained, and it proves the correctness and validity of the proposed method.

Forward Displacement Analysis of Nine-Link Barranov Truss Based on Chaos Improved Newton Iterative Method

2011 ◽  
Vol 230-232 ◽  
pp. 743-748
Author(s):  
You Xin Luo ◽  
Bin Zeng
Keyword(s):  
Iterative Method ◽  
Vector Method ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Real Solutions ◽  
Newton Iterative Method ◽  
Chaotic Sequences ◽  
Constrained Equations ◽  
New Type ◽  
Forward Displacement Analysis

The chaos improved Newton iterative method finding all real solutions of nonlinear equations was proposed and the forward displacement analysis on the 25th nine-link Barranov truss was completed. Four constrained equations were established by vector method with complex numbers according to four loops of the mechanism and four supplement equations were also established by increasing four variables and the relation of sine and cosine function. The established eight equations are that of forward displacement analysis of the mechanism. Combining improved Newton iterative method with chaotic sequences, chaos improved Newton iterative method based on utilizing new type chaos system introduced by Chen to obtain locate initial points to find all real solutions of the nonlinear questions was proposed. The numerical example was given. The result shows that all real solutions have been quickly obtained, and it proves the correctness and validity of the proposed method.

Displacement Analysis of Nine-Link Barranov Truss Based on Hyper-Chaotic Least Square Method

2012 ◽  
Vol 507 ◽  
pp. 260-264
Author(s):  
You Xin Luo ◽  
Qi Yuan Liu
Keyword(s):  
Solution Method ◽  
Least Square Method ◽  
Least Square ◽  
Vector Method ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Real Solutions ◽  
Chaotic Sequences ◽  
Constrained Equations ◽  
Forward Displacement Analysis

Four constrained equations were established by vector method with complex numbers according to four loops of the mechanism and four supplement equations were also established by increasing four variables and the relation of sine and cosine function. The established eight equations are that of forward displacement analysis of the 30th 2-coupled–degree nine-link Barranov truss mechanism. Combining least square method with hyper-chaotic sequences, hyper-chaotic least square method based on utilizing two-dimensional discrete hyper-chaotic system to obtain locate initial points to find all real solutions of the nonlinear questions was proposed. The numerical example of forward displacement analysis was given. Comparison was also done with other finding solution method. The result shows that all real solutions have been quickly obtained, and it proves the correctness and validity of the proposed method.

Forward Displacement Analysis of Non-Plane Two Coupled Degree Nine-Link Barranov Truss Based on Hyper-Chaotic Newton Downhill Method

2010 ◽  
Vol 20-23 ◽  
pp. 659-664 ◽  
Author(s):  
You Xin Luo ◽  
Qi Yuan Liu
Keyword(s):  
Discrete System ◽  
Solution Method ◽  
Complex Numbers ◽  
Vector Method ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Real Solutions ◽  
Chaotic Sequences ◽  
Constrained Equations ◽  
Forward Displacement Analysis

The hyper-chaotic Newton downhill method finding all real solutions of nonlinear equations was proposed and the forward displacement analysis on the 33th non-plane 2-coupled–degree nine-link Barranov truss was completed. Four constrained equations were established by vector method with complex numbers according to four loops of the mechanism and four supplement equations were also established by increasing four variables and the relation of sine and cosine function. The established eight equations are that of forward displacement analysis of the mechanism. Combining Newton downhill method with hyper-chaotic sequences, hyper-chaotic Newton-downhill method based on utilizing hyper-chaotic discrete system to obtain locate initial points to find all real solutions of the nonlinear questions was proposed. The numerical example was given. Comparison was also done with other finding solution method. The result shows that all real solutions have been quickly obtained, and it proves the correctness and validity of the proposed method.

Forward Displacement Analysis of a Kind of 2-Coupled–degree Nine-Link Barranov Truss Based on Hyper-Chaotic Least Square Method

2011 ◽  
Vol 230-232 ◽  
pp. 754-758
Author(s):  
You Xin Luo ◽  
Qi Yuan Liu ◽  
Xiao Yi Che
Keyword(s):  
Solution Method ◽  
Least Square Method ◽  
Least Square ◽  
Vector Method ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Real Solutions ◽  
Constrained Equations ◽  
Parameter Coupling ◽  
Forward Displacement Analysis

The hyper-chaotic least square method finding all real solutions of nonlinear equations was proposed and the forward displacement analysis on the 31th 2-coupled–degree nine-link Barranov truss was completed. Four constrained equations were established by vector method with complex numbers according to four loops of the mechanism and four supplement equations were also established by increasing four variables and the relation of sine and cosine function. The established eight equations are that of forward displacement analysis of the mechanism. Combining least square method with hyper-chaotic sequences, hyper-chaotic least square method based on utilizing parameter coupling hyper-chaotic discrete system to obtain locate initial points to find all real solutions of the nonlinear questions was proposed. The numerical example was given. Comparison was also done with other finding solution method. The result shows that all real solutions have been quickly obtained, and it proves the correctness and validity of the proposed method.

scholarly journals Forward Displacement Analysis of a Non-Plane Two Coupled Degree Nine-Link Barranov Truss Based on the Hyper-Chaotic Least Square Method

10.5772/45665 ◽  
2012 ◽  
Vol 9 (1) ◽  
pp. 8 ◽  
Author(s):  
Youxin Luo ◽  
Zouxin Mou ◽  
Bing He
Keyword(s):  
Least Square Method ◽  
Least Square ◽  
Vector Method ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
The Real ◽  
Real Solutions ◽  
Constrained Equations ◽  
Sine And Cosine Functions ◽  
Forward Displacement Analysis

The hyper-chaotic least square method for finding all of the real solutions of nonlinear equations was proposed and the following displacement analysis on the 33rd non-plane 2-coupled–degree nine-link Barranov truss was completed. Four constrained equations were established by a vector method with complex numbers according to four loops of the mechanism, and four supplement equations were also established by increasing four variables and the relation of the sine and cosine functions. The established eight equations are those of the forward displacement analysis of the mechanism. In combining the least square method with hyper-chaotic sequences, a hyper-chaotic least square method based on utilizing a hyper-chaotic discrete system to obtain and locate initial points so as to find all the real solutions of the nonlinear questions was proposed. A numerical example was given. A comparison was also done with another means of finding a solution method. The results show that all of real solutions were quickly obtained, and it proves the correctness and validity of the proposed method.

Forward Displacement Analysis of the 6-SPS Stewart Mechanism Based on Quaternion and Hyper-Chaotic Damp Least Square Method

2011 ◽  
Vol 230-232 ◽  
pp. 759-763 ◽  
Author(s):  
You Xin Luo ◽  
Qi Yuan Liu ◽  
Xiao Yi Che ◽  
Bin Zeng
Keyword(s):  
Neural Network ◽  
Parallel Mechanism ◽  
Least Square Method ◽  
Least Square ◽  
Chaotic Neural Network ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Chaotic Sequences ◽  
Chaos System ◽  
Forward Displacement Analysis

The forward displacement analysis of parallel mechanism can be transformed into solving complicated nonlinear equations and it is a very difficult process. Taking chaotic sequences as the initial values of damp least square method, all the solutions of equations can be found and the solving efficiency is related to modeling methods. Making use of existing chaos system and discovering new chaos system to generate chaotic sequences with good properties is the key to the chaos sequences-based damp least square method. Based on the connection topology of chaotic neural network composed of the four chaotic neurons, hyper-chaos exists in the chaotic neural network system. Combining hyper-chaos with damp least square method, a new method to find all solutions of nonlinear questions was proposed, in which initial points are generated by utilizing hyper-chaotic neural network. For the first time, based on quaternion, the model of the forward displacements of 6-SPS parallel mechanism is built up. The result is verified by a numerical example.

Forward Displacement Analysis of the 6-SPS Stewart Mechanisms Based on Hyper-Chaotic Damp Least Square Method

2011 ◽  
Vol 55-57 ◽  
pp. 2099-2103
Author(s):  
You Xin Luo ◽  
Qi Yuan Liu ◽  
Xiao Yi Che ◽  
Bin Zeng ◽  
Zhe Ming He
Keyword(s):  
Neural Network ◽  
Direction Cosine ◽  
Least Square Method ◽  
Least Square ◽  
Chaotic Neural Network ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Chaotic Sequences ◽  
Chaos System ◽  
Forward Displacement Analysis

The forward displacement analysis of the 6-SPS Stewart mechanism can be transformed into solving complicated nonlinear equations and it is a very difficult process. Taking chaotic sequences as the initial values of damp least square method, all the solutions of equations can be found quickly and making use of existing chaos system and discovering new chaos system to generate chaotic sequences with good properties is the key to the Chaos sequences-based damp least square method. Based on the connection topology of chaotic neural network composed of the four chaotic neurons, hyper-chaos exists in the chaotic neural network system. Combining hyper-chaos with damp least square method, a new method to find all solutions of nonlinear questions was proposed, in which initial points are generated by utilizing hyper-chaotic neural network. Based on direction cosine matrix and Euler parameters, the model of the forward displacements of 6-SPS parallel mechanism with seven variables is built up. The result is verified by a numerical example.

Forward Displacement Analysis of the 4SPS-2CCS Generalized Stewart Parallel Robot Mechanism Based on Hyper-Chaotic Sequences

2011 ◽  
Vol 230-232 ◽  
pp. 728-732
Author(s):  
You Xin Luo ◽  
Xiao Yi Che ◽  
Bin Zeng
Keyword(s):  
Nonlinear Equations ◽  
Parallel Mechanism ◽  
Initial Point ◽  
Parallel Robot ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Chaotic Sequences ◽  
Calculation Step ◽  
Solutions Of Equations ◽  
Forward Displacement Analysis

The forward displacement analysis of parallel mechanism is attributed to find the solution of complex nonlinear equations which is a very difficult process. Take chaotic sequences as the initial value of Newton iterative method, we can find all the solutions of equations quickly. The paper investigated the initial point generated by hyper-chaotic circuit system and provided a new method and calculation step of finding the all real number solutions of nonlinear equations. Using quaternion, the mathematical model of forward displacement for the generalized 4SPS-2CCS Stewart parallel robot mechanism was established and an example was given. Compared to the topological continuations method the result shows the calculation is brief and general. It can be used in forward displacement of other parallel mechanism. The research builds the theory basis for dimensional design, trajectory planning and controlling of this type of manipulator.

Generation and Forward Displacement Analysis of RP_R-PR-RP_R Analytic Planar Parallel Manipulators

2002 ◽  
Vol 124 (2) ◽  
pp. 294-300 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Fourth Degree ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Kinematic Chains ◽  
Real Solutions ◽  
Planar Parallel Manipulator ◽  
Forward Displacement Analysis ◽  
Planar Parallel Manipulators

Analytic manipulators are manipulators for which a characteristic polynomial of fourth degree or lower can be obtained symbolically. Six types of RP_R-PR-RP_R analytic planar parallel manipulators (APPMs) are first generated using the component approach and the method based on the structure of the univariate equation. Of the six types, four are composed of Assur II kinematic chains while the other two are composed of Assur III kinematic chains. The forward displacement analysis (FDA) of two types of RP_R-PR-RP_R APPMs composed of Assur III kinematic chains is then performed. The FDA of each of the two types of APPMs composed of Assur III kinematic chains is reduced to the solution of a univariate cubic equation and a quadratic equation in sequence. It is also proven that the maximum number of real solutions to the FDA is 4 for the RP_R-PR-RP_R planar parallel manipulator with one aligned platform and one orthogonal platform. Examples with 4 real solutions for the RP_R-PR-RP_R planar parallel manipulator with one aligned platform and one orthogonal platform or 6 real solutions for the RP_R-PR-RP_R planar parallel manipulator with two aligned platforms are given at the end of this paper.

scholarly journals Inverse Displacement Analysis of a General 6R Manipulator Based on the Hyper-Chaotic Least Square Method

10.5772/50909 ◽  
2012 ◽  
Vol 9 (1) ◽  
pp. 7 ◽  
Author(s):  
Youxin Luo ◽  
Wei Yi ◽  
Qiyuan Liu
Keyword(s):  
Nonlinear Equations ◽  
Discrete System ◽  
Least Square Method ◽  
Least Square ◽  
Displacement Analysis ◽  
The Real ◽  
Real Solutions ◽  
Chaotic Sequences ◽  
The Matrix ◽  
Constrained Equations

The hyper-chaotic least square method for finding all real solutions of nonlinear equations was proposed and the inverse displacement analysis of a general 6R manipulator was completed. Applying the D-H method, a 4 × 4 matrix transform was obtained and the first type twelve constrained equations were established. Analysing the characteristics of the matrix, the second type twelve constrained equations were established by adding variables and restriction. Combining the least square method with hyper-chaotic sequences, the hyper-chaotic least square method based on utilizing a hyper-chaotic discrete system to obtain and locate initial points to find all the real solutions of the nonlinear questions was proposed. The numerical example was given for two type constrained equations. The results show that all the real solutions have been obtained, and it proves the correctness and validity of the proposed method.

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