scholarly journals Damped Least-Square Method Based on Chaos Anti-Control for Solving Forward Displacement of General 6-6-Type Parallel Mechanism

10.5772/56136 ◽  
2013 ◽  
Vol 10 (4) ◽  
pp. 186 ◽  
Author(s):  
Youxin Luo ◽  
Qiyuan Liu ◽  
Xiaoyi Che ◽  
Lingfang Li
Keyword(s):  
Parallel Mechanism ◽  
Least Square Method ◽  
Least Square ◽  
Forward Displacement ◽  
Damped Least Square Method

Displacement Analysis of the 3SPS-3CCS Mechanism Based on Hyper-Chaotic Damp Least Square Method

2011 ◽  
Vol 55-57 ◽  
pp. 2092-2098
Author(s):  
You Xin Luo ◽  
Qi Yuan Liu ◽  
Xiao Yi Che ◽  
Bin Zeng
Keyword(s):  
Mathematical Model ◽  
Real Number ◽  
Matrix Method ◽  
Parallel Mechanism ◽  
Least Square Method ◽  
Least Square ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Chaotic Sequences ◽  
Chaos System

The forward displacement analysis of parallel mechanism is attributed to find the solutions of complicated nonlinear equations and it is a very difficult process. Taking chaotic sequences as the initial values of the damp least square method, we can find all the solutions of equations quickly. Making use of existing chaos system and discovering new chaos system to generate chaotic sequences with good properties is the key to the damp least square method based on Chaos sequences. Based on utilizing hyper-chaotic Hénon mapping to obtain initial points, a new method of finding all real number solutions of the nonlinear questions is proposed. Using cosine matrix method, the author established the mathematical model of forward displacement for the generalized 3SPS-3CCS parallel robot mechanism and a numerical example is given. Compared to the quaternion method building mathematical model, the result shows cosine matrix method building mathematical model and hyper-chaotic damp least square method to find solution is brief and high calculation efficiency as the calculation is done in real number range. The proposed method has universality which can be used in forward displacement of other parallel mechanism.

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 4SPS-2CCS Generalized Stewart Parallel Robot Mechanism Based on Hyper-Chaotic Damp Least Square Method

2011 ◽  
Vol 230-232 ◽  
pp. 738-742
Author(s):  
You Xin Luo ◽  
Bin Zeng ◽  
Xiao Yi Che
Keyword(s):  
Nonlinear Equations ◽  
Parallel Mechanism ◽  
Least Square Method ◽  
Parallel Robot ◽  
Least Square ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
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. Taking chaotic sequences as the initial values of the damp least square method, we can find all the solutions of equations quickly. The paper investigated the initial points generated by hyper-chaotic Hénon mapping 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. Example showed 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.

Novel Algorithm for Computer-Aided Alignment of Wide Field of View Complex Optical System

2007 ◽  
Vol 364-366 ◽  
pp. 1066-1071
Author(s):  
Xiao Fei Yang ◽  
Chang Yuan Han
Keyword(s):  
Optical System ◽  
Main Idea ◽  
Least Square Method ◽  
Least Square ◽  
Field Of View ◽  
Wide Field ◽  
Alignment Algorithm ◽  
Singular Value Decomposition Method ◽  
Damped Least Square Method ◽  
Value Decomposition

With the advent of the new complex optical system, alignment technology is necessary. In this paper, is presented an alignment algorithm whose main idea is composed of damped least square method and singular value decomposition method. In addition, the how and why to enter the damped factor into algorithm is explained. According to this algorithm, an alignment software package was compiled and compared self-compiled software with alignment package of CODE V. Results show that, this self-compiled software is much more valid than alignment package of CODE V. For a field of view of 2° R-C system, average MTF over the field of view was greater than 0.3 at 50 line pairs /mm.

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.

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.

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