Synthesis and Singularity Analysis of N-UU Parallel Wrists: A Symmetric Space Approach

2017 ◽  
Vol 9 (5) ◽  
Author(s):  
Yuanqing Wu ◽  
Marco Carricato
Keyword(s):  
Symmetric Space ◽  
Mirror Symmetry ◽  
Singularity Analysis ◽  
Space Theory ◽  
Euclidean Group ◽  
Half Angle ◽  
Symmetric Submanifold ◽  
Spherical Mechanism ◽  
Space Approach ◽  
Angle Property

We report some recent advances in kinematics and singularity analysis of the mirror-symmetric N-UU parallel wrists using symmetric space theory. We show that both the finite displacement and infinitesimal singularity kinematics of a N-UU wrist are governed by the mirror symmetry property and half-angle property of the underlying motion manifold, which is a symmetric submanifold of the special Euclidean group SE(3). Our result is stronger than and may be considered a closure of Hunt's argument for instantaneous mirror symmetry in his pioneering exposition of constant velocity shaft couplings. Moreover, we show that the wrist can, to some extent, be treated as a spherical mechanism, even though dependent translation exists, and the singularity-free workspace of a N-UU wrist may be analytically derived. This leads to a straightforward optimal design for maximal singularity-free workspace.

Singularities of Single-DOF Spherical Mechanisms Identified by Means of Pole Axes’ Properties

2010 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Singularity Analysis ◽  
Systems Of Equations ◽  
Planar Mechanisms ◽  
Planar Mechanism ◽  
Geometric Conditions ◽  
Spherical Mechanisms ◽  
Spherical Mechanism ◽  
General Method

Instantaneous pole axes (IPAs) play, in spherical-mechanism kinematics, the same role as instant centers in planar-mechanism kinematics. IPA-based techniques have not been proposed yet for the singularity analysis of spherical mechanisms, even though instant-center-based algorithms have been already presented for planar mechanisms’ singularity analysis. This paper addresses the singularity analysis of single-dof spherical mechanisms by exploiting the properties of pole axes. A general method for implementing this analysis is presented. The presented method relies on the possibility of giving geometric conditions for any type of singularity, and it is the spherical counterpart of an instant-center-based algorithm previously proposed by the author for single-dof planar mechanisms. It can be used to generate systems of equations useful either for finding the singularities of a given mechanism or to synthesize mechanisms that have to match specific requirements about the singularities.

scholarly journals A Metric Space Approach on the Molecular vs. Chemical Similarity of Some Analgesic and Euphoric Compounds

2019 ◽  
Author(s):  
Demetrios Xenides ◽  
Dionisia Fostiropoulou ◽  
Dimitrios S Vlachos
Keyword(s):  
Metric Space ◽  
Clinical Findings ◽  
Space Theory ◽  
Chemical Similarity ◽  
Analgesic Drugs ◽  
Structural Indices ◽  
Space Approach

<p>There is a relentless effort on gaining information on the reason why some compounds could cause similar effects though they are or not structural similar. That is the chemical similarity that plays an equally important role and we approach it via metric space theory on a set of analgesic drugs and euphoric compounds. The findings of the present study are in agreement to these obtained via traditional structural indices moreover are in accord with clinical findings.</p>

Analytical method for the singularity analysis and exhaustive enumeration of the singularity conditions in single-degree-of-freedom spherical mechanisms

2012 ◽  
Vol 227 (8) ◽  
pp. 1830-1840 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Analytical Method ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Systems Of Equations ◽  
Single Degree Of Freedom ◽  
Planar Mechanism ◽  
Single Degree ◽  
Geometric Conditions ◽  
Spherical Mechanisms ◽  
Spherical Mechanism

In spherical-mechanism kinematics, instantaneous pole axes play the same role as, in planar-mechanism kinematics, instant centres. Their locations only depend on the mechanism configuration when spherical single-degree-of-freedom mechanisms are considered. Such a property makes them a tool to visualize and/or to analyse the instantaneous kinematics of those mechanisms. This article addresses the singularity analysis of single-degree-of-freedom spherical mechanisms by exploiting the properties of instantaneous pole axes. An exhaustive enumeration of the geometric conditions which occur for all the singularity types is given, and a general analytical method based on this enumeration is proposed for implementing the singularity analysis. The proposed analytical method can be used to generate systems of equations useful either for finding the singularities of a given mechanism or to synthesize mechanisms that have to match specific requirements about the singularities.

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 A Metric Space Approach on the Molecular vs. Chemical Similarity of Some Analgesic and Euphoric Compounds

2019 ◽  
Author(s):  
Demetrios Xenides ◽  
Dionisia Fostiropoulou ◽  
Dimitrios S Vlachos
Keyword(s):  
Metric Space ◽  
Clinical Findings ◽  
Space Theory ◽  
Chemical Similarity ◽  
Analgesic Drugs ◽  
Structural Indices ◽  
Space Approach

<p>There is a relentless effort on gaining information on the reason why some compounds could cause similar effects though they are or not structural similar. That is the chemical similarity that plays an equally important role and we approach it via metric space theory on a set of analgesic drugs and euphoric compounds. The findings of the present study are in agreement to these obtained via traditional structural indices moreover are in accord with clinical findings.</p>

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