Orientation-Singularity and Orientation Capability Analyses of the Stewart-Gough Manipulator

2005 ◽  
Author(s):  
Y. Cao ◽  
Z. Huang ◽  
Q. J. Ge
Keyword(s):  
Central Angle ◽  
Capability Index ◽  
Polynomial Expression ◽  
Moving Platform ◽  
Singularity Locus

In this paper, the orientation-singularity and orientation capability analyses of the Stewart-Gough manipulator are presented. Based on a particular kind of orientation representation of the manipulator, a polynomial expression of degree thirteen is derived, which represents the orientation-singularity locus of the manipulator at a given position, and examples are given to illustrate the result. The description of the orientation capability of the manipulator and the orientation capability index are discussed. In addition, effects of the geometry parameters of the moving platform, including the central angle, the ratio of the moving platform to the base one and the position of the moving platform on the orientation capability of the manipulator are also presented in this paper.

scholarly journals Position-Singularity Analysis of a Class of the 3/6-Gough-Stewart Manipulators Based on Singularity-Equivalent-Mechanism

10.5772/45664 ◽  
2012 ◽  
Vol 9 (1) ◽  
pp. 9 ◽  
Author(s):  
Hui Zhou ◽  
Yi Cao ◽  
Baokun Li ◽  
Meiping Wu ◽  
Jinghu Yu ◽  
...  
Keyword(s):  
Screw Theory ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Polynomial Expression ◽  
Moving Platform ◽  
Singularity Locus ◽  
Three Dimensional Space ◽  
Equivalent Mechanism

This paper addresses the problem of identifying the property of the singularity loci of a class of 3/6-Gough-Stewart manipulators for general orientations in which the moving platform is an equilateral triangle and the base is a semiregular hexagon. After constructing the Jacobian matrix of this class of 3/6-Gough-Stewart manipulators according to the screw theory, a cubic polynomial expression in the moving platform position parameters that represents the position-singularity locus of the manipulator in a three-dimensional space is derived. Graphical representations of the position-singularity locus for different orientations are given so as to demonstrate the results. Based on the singularity kinematics principle, a novel method referred to as ‘singularity-equivalent-mechanism' is proposed, by which the complicated singularity analysis of the parallel manipulator is transformed into a simpler direct position analysis of the planar singularity-equivalent-mechanism. The property of the position-singularity locus of this class of parallel manipulators for general orientations in the principal-section, where the moving platform lies, is identified. It shows that the position-singularity loci of this class of 3/6-Gough-Stewart manipulators for general orientations in parallel principal-sections are all quadratic expressions, including a parabola, four pairs of intersecting lines and infinite hyperbolas. Finally, the properties of the position-singularity loci of this class of 3/6-Gough-Stewart parallel manipulators in a three-dimensional space for all orientations are presented.

Position-singularity analysis of a special class of the Stewart parallel mechanisms with two dissimilar semi-symmetrical hexagons

Robotica ◽  
2012 ◽  
Vol 31 (1) ◽  
pp. 123-136 ◽  
Author(s):  
Baokun Li ◽  
Yi Cao ◽  
Qiuju Zhang ◽  
Zhen Huang
Keyword(s):  
Special Class ◽  
Screw Theory ◽  
Singularity Analysis ◽  
Parallel Mechanisms ◽  
Geometric Characteristics ◽  
Characteristic Plane ◽  
The Matrix ◽  
Grassmann Line Geometry ◽  
Moving Platform ◽  
Singularity Locus

SUMMARYIn this paper, for a special class of the Stewart parallel mechanism, whose moving platform and base one are two dissimilar semi-symmetrical hexagons, the position-singularity of the mechanism for a constant-orientation is analyzed systematically. The force Jacobian matrix [J]T is constructed based on the principle of static equilibrium and the screw theory. After expanding the determinant of the simplified matrix [D], whose rank is the same as the rank of the matrix [J]T, a cubic symbolic expression that represents the 3D position-singularity locus of the mechanism for a constant-orientation is derived and graphically represented. Further research shows that the 3D position-singularity surface is extremely complicated, and the geometric characteristics of the position-singularity locus lying in a general oblique plane are very difficult to be identified. However, the position-singularity locus lying in the series of characteristic planes, where the moving platform coincides, are all quadratic curves compromised of infinite many sets of hyperbolas, four pairs of intersecting lines and a parabola. For some special orientations, the quadratic curve can degenerate into two lines or even one line, all of which are parallel to the ridgeline. Two theorems are presented and proved for the first time when the geometric characteristics of the position-singularity curves in the characteristic plane are analyzed. Moreover, the kinematic property of the position-singularity curves is obtained using the Grassmann line geometry and the screw theory. The theoretical results are demonstrated with several numeric examples.

Orientation workspace analysis of a special class of the Stewart–Gough parallel manipulators

Robotica ◽  
2010 ◽  
Vol 28 (7) ◽  
pp. 989-1000 ◽  
Author(s):  
Yi Cao ◽  
Zhen Huang ◽  
Hui Zhou ◽  
Weixi Ji
Keyword(s):  
Special Class ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Discretization Method ◽  
Practical Orientation ◽  
Workspace Analysis ◽  
Half Angle ◽  
Polynomial Expression ◽  
Singularity Locus ◽  
Orientation Workspace

SUMMARYThe workspace of a robotic manipulator is a very important issue and design criteria in the context of optimum design of robots, especially for parallel manipulators. Though, considerable research has been paid to the investigations of the three-dimensional (3D) constant orientation workspace or position workspace of parallel manipulators, very few works exist on the topic of the 3D orientation workspace, especially the nonsingular orientation workspace and practical orientation workspace. This paper addresses the orientation workspace analysis of a special class of the Stewart–Gough parallel manipulators in which the moving and base platforms are two similar semisymmetrical hexagons. Based on the half-angle transformation, a polynomial expression of 13 degree that represents the orientation singularity locus of this special class of the Stewart–Gough parallel manipulators at a fixed position is derived and graphical representations of the orientation singularity locus of this special class of the Stewart–Gough manipulators are illustrated with examples to demonstrate the result. Exploiting this half-angle transformation and the inverse kinematics solution of this special class of the Stewart–Gough parallel manipulators, a discretization method is proposed for computing the orientation workspace of this special class of the Stewart–Gough parallel manipulators taking limitations of active and passive joints and the link interference all into consideration. Based on this algorithm, this paper also presents a new discretization method for computing the nonsingular orientation workspace of this class of the manipulators, which not only can satisfy all the kinematics demand of this class of the manipulators but also can guarantee the manipulator is nonsingular in the whole orientation workspace, and the practical orientation workspace of this class of the manipulators, which not only can guarantee the manipulator is nonsingular and will never encounter any kinematic interference but also can satisfy the demand of the orientation workspace with a regular shape in practical application, respectively. Examples of a 6/6-SPS Stewart–Gough parallel manipulator of this special class are given to demonstrate these theoretical results.

Structure and property of the singularity loci of the 3/6-Stewart-Gough platform for general orientations

Robotica ◽  
2005 ◽  
Vol 24 (1) ◽  
pp. 75-84 ◽  
Author(s):  
Z. Huang ◽  
Y. Cao ◽  
Y. W. Li ◽  
L. H. Chen
Keyword(s):  
Singularity Analysis ◽  
Planar Mechanism ◽  
Structure And Property ◽  
Locus Equation ◽  
Polynomial Expression ◽  
Singularity Locus ◽  
Straight Lines ◽  
Stewart Gough Platform ◽  
Similar Issue ◽  
Equivalent Mechanism

This paper focuses on the structure and property of the singularity loci of the 3/6-Stewart-Gough platform for general orientations. Based on the singularity kinematics principle, a planar singularity-equivalent-mechanism is proposed, by which the complicated singularity analysis of that parallel mechanism is transformed into a simpler position analysis of the planar mechanism. All the possible positions of the planar mechanism form the singularity loci of the 3/6-Stewart-Gough manipulator. The result shows that the singularity equation become quite simple moreover the structure and property of the singularity loci are also identified and explained. For the most general orientations of the typical 3/6-Stewart-Gough platform, the singularity locus equation is a special irresolvable polynomial expression of degree three, which in infinite parallel principal sections includes a parabola, four pairs of intersecting straight lines and infinity of hyperbolas. This result is beneficial to analysis of the similar issue of other Stewart-Gough manipulators.

Development and evaluation of trans-Amadi groundwater parameters: The integration of finite element techniques

2019 ◽  
Author(s):  
Chem Int
Keyword(s):  
Finite Element ◽  
Polynomial Regression ◽  
Nitrate Concentration ◽  
Strong Relationship ◽  
Total Iron ◽  
Coefficient Of Determination ◽  
Port Harcourt ◽  
Polynomial Expression ◽  
The Relationship ◽  
Best Fit

Mathematical model was developed and evaluated to monitor and predict the groundwater characteristics of Trans-amadi region in Port Harcourt City. In this research three major components were considered such as chloride, total iron and nitrate concentration as well as the polynomial expression on the behavious on the concentration of each component was determined in terms of the equation of the best fit as well as the square root of the curve. The relationship between nitrate and distance traveled by Nitrate concentration by the model is given as Pc = 0.003x2 - 0.451x + 14.91with coefficient of determination, R² = 0.947, Chloride given as Pc = 0.000x2 - 0.071x + 2.343, R² = 0.951while that of Total Iron is given as Pc = 2E-05x2 - 0.003x + 0.110, R² = 0.930. All these show a strong relationship as established by Polynomial Regression Model. The finite element techniques are found useful in monitoring, predicting and simulating groundwater characteristics of Trans-amadi as well as the prediction on the variation on the parameters of groundwater with variation in time.

scholarly journals Fuzzy Evaluation Model of Process Improvement Capability with Costs Consideration

2021 ◽  
Vol 11 (10) ◽  
pp. 4344
Author(s):  
Kuen-Suan Chen ◽  
Shui-Chuan Chen ◽  
Ting-Hsin Hsu ◽  
Min-Yi Lin ◽  
Chih-Feng Wu
Keyword(s):  
Process Improvement ◽  
Quality Evaluation ◽  
Evaluation Model ◽  
Fuzzy Evaluation ◽  
Sampling Errors ◽  
Capability Index ◽  
Testing Method ◽  
Improvement Potential ◽  
Testing Accuracy

The Taguchi capability index, which reflects the expected loss and the yield of a process, is a useful index for evaluating the quality of a process. Several scholars have proposed a process improvement capability index based on the expected value of the Taguchi loss function as well as the corresponding cost of process improvement. There have been a number of studies using the Taguchi capability index to develop suppliers’ process quality evaluation models, whereas models for evaluating suppliers’ process improvement potential have been relatively lacking. Thus, this study applies the process improvement capability index to develop an evaluation model of the supplier’s process improvement capability, which can be provided to the industry for application. Besides, owing to the current need to respond quickly, coupled with cost considerations and the limits of technical capabilities, the sample size for sampling testing is usually not large. Consequently, the evaluation model of the process improvement capability developed in this study adopts a fuzzy testing method based on the confidence interval. This method reduces the risk of misjudgment due to sampling errors and improves the testing accuracy because it can incorporate experts and their accumulated experiences.

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