scholarly journals A Distance Geometry Approach to the Singularity Analysis of 3R Robots

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Federico Thomas
Keyword(s):  
Relative Position ◽  
Distance Geometry ◽  
Singularity Analysis ◽  
Geometric Invariants ◽  
Projective Invariant ◽  
Singularity Locus

This paper shows how the computation of the singularity locus of a 3R robot can be reduced to the analysis of the relative position of two coplanar ellipses. Since the relative position of two conics is a projective invariant and the basic projective geometric invariants are determinants, it is not surprising that, using distance geometry, the computation of the singularity locus of a 3R robot can be fully expressed in terms of determinants. Geometric invariants have the benefit of simplifying symbolic manipulations. This paper shows how their use leads to a simpler characterization, compared to previous approaches, of the cusps and nodes in the singularity loci of 3R robots.

Singularity Analysis of 6-PUS Vertical Parallel Mechanism

2013 ◽  
Vol 568 ◽  
pp. 129-134 ◽  
Author(s):  
Chao Qun Wang ◽  
Hong Tao Wu
Keyword(s):  
Dynamic Characteristics ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Singularity Analysis ◽  
Stewart Platform ◽  
Analytic Singularity ◽  
Singularity Locus

Different from the general 6-SPS Stewart platform, 6-PUS parallel mechanism is a kind of fully parallel mechanism whose actuators are all fixed at the frame. The advantages of this mechanism are light movable mass, small inertia and good dynamic characteristics. This paper is focused on the singularity analysis of the 6-PUS parallel mechanism. Based on the Jacobian matrix which is derived from the kinematical equation, the analytic singularity locus equations are obtained and the three types singularities of the parallel mechanism are analyzed. Moreover, the position-singularity of the mechanism is discussed through some specific examples.

Orientation-singularity analysis and orientationability evaluation of a special class of the Stewart–Gough parallel manipulators

Robotica ◽  
2013 ◽  
Vol 31 (8) ◽  
pp. 1361-1372 ◽  
Author(s):  
Yi Cao ◽  
Clément Gosselin ◽  
Hui Zhou ◽  
Ping Ren ◽  
Weixi Ji
Keyword(s):  
Performance Index ◽  
Special Class ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Design Parameters ◽  
Graphical Representations ◽  
Practical Orientation ◽  
Discretization Algorithm ◽  
Half Angle ◽  
Singularity Locus

SUMMARYThis paper addresses the orientation-singularity analysis and the orientationability evaluation of a special class of the Stewart–Gough parallel manipulators in which the moving and base platforms are two similar semi-symmetrical hexagons. Based on the half-angle transformation, an analytical polynomial of degree 13 that represents the orientation-singularity locus of this special class of parallel manipulators at a given position is derived. Graphical representations of the orientation-singularity locus of this class of manipulators are illustrated with examples to demonstrate the results. Based on the description of the orientation-singularity and nonsingular orientation region of this class of parallel manipulators, a performance index, referred to as orientationability, which describes the orientation capability of this class of manipulators at a given position, is introduced. A discretization algorithm is proposed for computing the orientationability of the special class of parallel manipulators at a given position in the workspace. Moreover, the effects of the design parameters and position parameters on the orientationability are also investigated in detail. Based on the orientationability performance index, another performance index, referred to as practical orientationability, representing the practical orientation capability of the manipulators at a given position, is introduced. In this performance index, singularities, the limitations of active and passive joints and link interferences are all taken into consideration. Furthermore, the practical orientationability of the special class of parallel manipulators studied here is also analyzed over several plane sections of the position-workspace in detail.

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.

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.

Computational Micrograph Registration with Sieve Processes

1996 ◽  
Vol 54 ◽  
pp. 440-441
Author(s):  
P.J. Phillips ◽  
J. Huang ◽  
S. M. Dunn
Keyword(s):  
Planar Graph ◽  
Efficient Algorithm ◽  
Spatial Organization ◽  
Spatial Arrangement ◽  
Stereo Image ◽  
Image Model ◽  
Geometric Invariants ◽  
Point Set

In this paper we present an efficient algorithm for automatically finding the correspondence between pairs of stereo micrographs, the key step in forming a stereo image. The computation burden in this problem is solving for the optimal mapping and transformation between the two micrographs. In this paper, we present a sieve algorithm for efficiently estimating the transformation and correspondence.In a sieve algorithm, a sequence of stages gradually reduce the number of transformations and correspondences that need to be examined, i.e., the analogy of sieving through the set of mappings with gradually finer meshes until the answer is found. The set of sieves is derived from an image model, here a planar graph that encodes the spatial organization of the features. In the sieve algorithm, the graph represents the spatial arrangement of objects in the image. The algorithm for finding the correspondence restricts its attention to the graph, with the correspondence being found by a combination of graph matchings, point set matching and geometric invariants.

Revisiting Regression Artifacts Through Relative Position Matching

2006 ◽  
Author(s):  
Michael A. Harnar ◽  
James Griffith ◽  
William D. Crano
Keyword(s):  
Relative Position
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