CGA-based novel modeling method for solving the forward displacement analysis of 3-RPR planar parallel mechanism

2022 ◽  
Vol 168 ◽  
pp. 104595
Author(s):  
Ganmin Zhu ◽  
Shimin Wei ◽  
Ying Zhang ◽  
Qizheng Liao
Keyword(s):  
Parallel Mechanism ◽  
Modeling Method ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Forward Displacement Analysis

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.

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 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.

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 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.

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 Three New Classes of Analytic Spherical Parallel Manipulators

1998 ◽  
Author(s):  
Xian-Wen Kong
Keyword(s):  
Characteristic Polynomial ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Dual Solutions ◽  
Fourth Degree ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
The Third ◽  
Spherical Parallel Manipulator ◽  
Forward Displacement Analysis

Abstract The analytic manipulator is a manipulator the characteristic polynomial of which is of fourth degree or lower. Three new classes of analytic spherical parallel manipulators with prismatic actuators are proposed. The first is the spherical parallel manipulator with non-similar planar platforms, the second is the spherical parallel manipulator with similar planar platforms, and the third is the spherical parallel manipulator with orthogonal platforms. The forward displacement analysis of these new classes of spherical parallel manipulators is investigated in sequence. Polynomials of degree 4, 2 and 2 in one unknown respectively can be obtained to inscribe this problem. Due to dual solutions of other unknowns, a maximum of eight solutions might be possible for each of the new analytic spherical parallel manipulators.

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