A matrix method of displacement analysis of the general spatial 7R mechanism

1987 ◽  
Vol 8 (10) ◽  
pp. 957-967 ◽  
Author(s):  
Chen Wei-rong
Keyword(s):  
Matrix Method ◽  
Displacement Analysis

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.

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.

Feasibility Study of a Platform Type of Robotic Manipulators from a Kinematic Viewpoint

1984 ◽  
Vol 106 (2) ◽  
pp. 191-198 ◽  
Author(s):  
D. C. H. Yang ◽  
T. W. Lee
Keyword(s):  
Feasibility Study ◽  
Theoretical Investigation ◽  
Matrix Method ◽  
Closed Loop ◽  
Kinematic Chain ◽  
Robotic Manipulators ◽  
Design Parameters ◽  
Inverse Control ◽  
Displacement Analysis ◽  
Number Synthesis

This paper presents a theoretical investigation on the feasibility of using a platform mechanism as a robotic manipulator. The existence of this type of closed-loop kinematic chain is first investigated via a kinematic number synthesis. A displacement analysis then follows, which gives inverse control equations in terms of motion and design parameters, using the [4 × 4] matrix method. Basic kinematic characteristics and limitations, such as the extreme ranges of motion and rotatability as well as workspace are investigated.

On the Displacement Analysis of Open-Loop Systems by the Direction Cosine Matrix Method

1987 ◽  
Author(s):  
Y. Youm ◽  
T. Yih
Keyword(s):  
Matrix Method ◽  
Direction Cosine ◽  
Open Loop ◽  
Open Loop System ◽  
Displacement Analysis ◽  
Transformation Matrices ◽  
Joint Axis ◽  
Cosine Transformation ◽  
Direction Cosine Matrix ◽  
Unit Vectors

Abstract In this paper, displacement analysis of a general spatial open-loop system and a computer algorithm for the workspace of the system are developed by applying the direction cosine matrix method. In using this method, one global coordinate system and two joint local coordinate systems must be predefined in order to formulate the direction cosine transformation matrices of the unit vectors of each joint axis and link vector. The 3 × 3 direction cosine transformation matrices for each joint axis and link vector are established based on the known geometric configurations, the preceding unit vectors, and the cofactor property of the direction cosine matrix. The use of cofactor property will provide a unique solution for the transformation matrix. A computer algorithm is developed to illustrate the workspace of spatial n-R open-loop systems projected onto the coordinate X-Y, Y-Z, and X-Z planes. Numerical examples are demonstrated for an industrial robot, an application to human upper extremity, and a hypothetical 9-link open-loop system.

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 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.

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