Displacement Analysis of the 4SPS-2CCS Mechanism Based on Hyper-Chaotic Newton-Downhill Method

2011 ◽  
Vol 230-232 ◽  
pp. 733-737
Author(s):  
You Xin Luo ◽  
Xiao Yi Che ◽  
Bin Zeng
Keyword(s):  
Mathematical Model ◽  
Real Number ◽  
Matrix Method ◽  
Parallel Mechanism ◽  
Parallel Robot ◽  
Number Range ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Henon Mapping ◽  
Solutions Of Equations

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 Newton-downhill method, we can find all the solutions of equations quickly. 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 4SPS-2CCS 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 Newton-downhill method finding 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.

Displacement Analysis of the 3SPS-3CCS Mechanism Based on Hyper-Chaotic Newton-Downhill Method

2011 ◽  
Vol 467-469 ◽  
pp. 401-406 ◽  
Author(s):  
You Xin Luo ◽  
Xiao Yi Che ◽  
Bin Zeng
Keyword(s):  
Mathematical Model ◽  
Real Number ◽  
Matrix Method ◽  
Parallel Mechanism ◽  
Parallel Robot ◽  
Number Range ◽  
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 Newton-downhill 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 Newton-downhill 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 Newton-downhill method finding 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.

Displacement Analysis of the 3SPS-3CCS Mechanism Based on Hyper-Chaotic Three-Step Iterative Method

2011 ◽  
Vol 55-57 ◽  
pp. 2086-2091
Author(s):  
You Xin Luo ◽  
Xiao Yi Che ◽  
Qi Yuan Liu ◽  
Bin Zeng
Keyword(s):  
Mathematical Model ◽  
Iterative Method ◽  
Real Number ◽  
Matrix Method ◽  
Parallel Mechanism ◽  
Number Range ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Chaotic Sequences ◽  
Chaos System

The forward displacement analysis of parallel mechanism is transformed into find the solutions of complicated nonlinear equations and it is a very difficult process. Taking chaotic sequences as the initial values of the three-step iterative 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 three-step iterative 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 three-step iterative 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.

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 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.

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.

Forward displacement analysis of a 3-RPR spherical parallel mechanism

2013 ◽  
Vol 227 (8) ◽  
pp. 1864-1869 ◽  
Author(s):  
Duanling Li ◽  
Zhonghai Zhang ◽  
He Li
Keyword(s):  
Mathematical Model ◽  
Parallel Mechanism ◽  
Spherical Geometry ◽  
Parallel Mechanisms ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Spherical Parallel Mechanism ◽  
The Mathematical Model ◽  
Forward Displacement Analysis ◽  
Modeling Equation

The forward displacement analysis of spherical parallel mechanisms is a nonlinear problem and has attracted the attention of many researchers. A method is proposed to analyze the forward displacement of a 3-RPR spherical parallel mechanism. Firstly, based on spherical geometry and spherical trigonometry theory, a mathematical model is derived for the forward displacement analysis of the spherical parallel mechanism. After simplifying the mathematical model, the kinematical equations are then solved using the resultant elimination method. Using this method, one can obtain the three variables representing the position and pose of the moving platform directly. Finally, a numerical example is presented and Autodesk Inventor software is used to verify all the real solutions. The method of mathematical modeling, equation simplification, resultant elimination presented in this paper can be extended to solve similar problems effectively.

Mobility and Position Analysis of a Novel 3-DOF Translational Parallel Mechanism

2006 ◽  
Author(s):  
Daxing Zeng ◽  
Zhen Huang ◽  
Linlin Zhang
Keyword(s):  
Closed Form ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Continuation Method ◽  
Mobility Analysis ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Displacement Problem ◽  
Numerical Example ◽  
Forward Displacement Analysis

This paper presents the mobility analysis, the inverse and forward displacement analysis, and workspace of a novel 3-DOF 3-RPUR parallel manipulator. Closed-form inverse displacement solutions are obtained by the Denavit-Hartenberg method. The forward displacement problem is analyzed by using the continuation method and proved applying the result of the inverse displacement analysis. The workspace of the mechanism is also obtained. A numerical example is given in the paper.

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