Forward Displacement Analysis of the 4SPS-2CCS Generalized Stewart Platform Based on Hyper-Chaotic Neural Network Mathematical Programming Method

2008 ◽  
Author(s):  
Youxin Luo ◽  
Xiguang Huang ◽  
Bin Zeng
Keyword(s):  
Neural Network ◽  
Mathematical Programming ◽  
Stewart Platform ◽  
Programming Method ◽  
Chaotic Neural Network ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Mathematical Programming Method ◽  
Forward Displacement Analysis

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 6-SPS Mechanism Based on Hyper-Chaos Neural Network Mathematical Programming

2012 ◽  
Vol 507 ◽  
pp. 274-278
Author(s):  
You Xin Luo ◽  
Zhe Ming He ◽  
Xiao Song
Keyword(s):  
Neural Network ◽  
Mathematical Programming ◽  
Nerve Cell ◽  
Evolution Equations ◽  
Nonlinear Evolution Equations ◽  
Parallel Mechanisms ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Initial Node ◽  
Forward Displacement Analysis

The solutions of mechanism position fall squarely into the solutions of nonlinear evolution equations, which is an extremely difficult process. Using the chaotic sequence as the initial values of mathematical programming, all solutions of equations can be quickly found out. Neural network, which is a highly complicated nonlinear system, exist the chaos phenomenon. By eliminating the simulated annealing strategy of the transient chaos nerve cell, a kind of chaotic nerve cell that could permanently maintain chaos was investigated. With the hyper-chaos system and mathematical programming, the this new method for solving the nonlinear equation setting based on the initial node generating by the hyper-chaos mathematical programming of neural network was put forward. The mathematical model of forward displacement analysis of general 6-SPS parallel mechanisms is set up based on a quaternion.

The Kinematics of Redundant Tetrahedron Based Variable Geometry Truss Manipulators Based on Neural Network

2000 ◽  
Author(s):  
Li-Ju Xu ◽  
Jiang Wu
Keyword(s):  
Neural Network ◽  
Variable Geometry ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Influence Coefficients ◽  
Simulation Calculation ◽  
Variable Geometry Truss Manipulator ◽  
Variable Geometry Truss ◽  
Pseudo Inverse ◽  
Forward Displacement Analysis

Abstract The forward displacement analysis of redundant tetrahedron based variable geometry truss manipulators is obtained based on BP neural network, and then a solution to inverse displacement analysis problem is obtained. According to the above network model, the first- and second-order influence coefficients are derived, and the pseudo-inverse of Jacobian matrix is obtained by using a neural network. Finally the simulation calculation of kinematics for a seven celled tetrahedron-tetrahedron variable geometry truss manipulator is given for illustration.

Forward Displacement Analyses of the 4-4 Stewart Platforms

1992 ◽  
Vol 114 (3) ◽  
pp. 444-450 ◽  
Author(s):  
W. Lin ◽  
M. Griffis ◽  
J. Duffy
Keyword(s):  
Closed Form ◽  
Stewart Platform ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Half Angle ◽  
Stewart Platforms ◽  
Forward Displacement Analysis

A forward displacement analysis in closed-form is performed for each case of a class of Stewart Platform mechanisms. This class of mechanisms, which are classified into three cases, are called the “4-4 Stewart Platforms,” where each of the mechanisms has the distinguishing feature of six legs meeting either singly or pair-wise at four points in the top and base platforms. (This paper only addresses those 4-4 Platforms where both the top and base platforms are planar.) For each case, a polynomial is derived in the square of a tan-half-angle that measures the angle between two planar faces of a polyhedron embedded within the mechanism. The degrees of the polynomials for the first, second, and third cases are, respectively, eight, four, and twelve. All the solutions obtained from the forward displacement analyses for the three cases are verified numerically using a reverse displacement analysis.

Explicit Solution for the Forward Displacement Analysis of the Stewart Platform Manipulator

1996 ◽  
Author(s):  
Yao Jin ◽  
Fang Hai-Rong
Keyword(s):  
Explicit Solution ◽  
Computation Time ◽  
Stewart Platform ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Numerical Example ◽  
Forward Displacement Analysis ◽  
Explicit Expressions

Abstract A method is presented to directly solve the problem of the forward displacement analysis of the Stewart platform manipulator. With algebraic elimination and the use of only one extra sensor, the explicit expressions on the forward displacement solution is obtained so that the method may enable designers to get the best compromise between the supplementary cost and complexity of the manipulator and the computation time for solving the forward displacement analysis. A numerical example is given to illustrate the method presented.

scholarly journals Forward Displacement Analysis of a General 6-3 Stewart Platform Using Conformal Geometric Algebra

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Feng Wei ◽  
Shimin Wei ◽  
Ying Zhang ◽  
Qizheng Liao
Keyword(s):  
Geometric Algebra ◽  
Polynomial Equation ◽  
Stewart Platform ◽  
Conformal Geometric Algebra ◽  
Kinematic Constraint ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Sylvester Resultant ◽  
Univariate Polynomial ◽  
Forward Displacement Analysis

In this paper, a new algorithm for the forward displacement analysis of a general 6-3 Stewart platform (6-3SPS) based on conformal geometric algebra (CGA) is presented. First, a 6-3SPS structure is changed into an equivalent 2RPS-2SPS structure. Then, two kinematic constraint equations are established based on the geometric characteristics, one of which is built according to the point characteristic four-ball intersection in CGA. A 16th-degree univariate polynomial equation is derived from the aforementioned two equations by the Sylvester resultant elimination. Finally, a numerical example is given to verify the algorithm.

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