A Complete Geometric Singular Characterization of the 6/6 Stewart Platform

2018 ◽  
Vol 10 (4) ◽  
Author(s):  
Michael Slavutin ◽  
Avshalom Sheffer ◽  
Offer Shai ◽  
Yoram Reich
Keyword(s):  
Three Dimensional ◽  
Parallel Line ◽  
Stewart Platform ◽  
New Approach ◽  
Singular Configurations ◽  
Geometric Relation ◽  
The Common ◽  
Singular Configuration ◽  
Special Case

This paper introduces the three-dimensional (3D) dual Kennedy theorem in statics, and demonstrates its application to characterize the singular configuration of the 6/6 Stewart Platform (6/6 SP). The proposed characterization is articulated as a simple geometric relation that is easy to apply and check. We find two lines that cross four of the six legs of the platform. Each one of these two lines has a parallel line that crosses the remaining two legs. Each pair of parallel lines defines a plane. The 6/6 SP is in a singular position if the intersection of these two planes is perpendicular to the common normal of the remaining two legs. The method developed for the singular characterization is also used for the analysis of the mobility and forces of the SP. Finally, the proposed method is compared to some known singular configurations, such as Hunt's and Fichter's singular configurations and the 3/6 Stewart Platform (3/6 SP) singularity. The relation between the reported characterizations of the 6/6 SP and other reported works is highlighted. Moreover, it is shown that the known 3/6 SP characterization is a special case of the results reported in the paper. Finally, a characterization of a platform that does not appear in the literature, 5/6 SP, is developed based on the new approach to demonstrate its utility.

A Geometric Singular Characterization of the 6/6 Stewart Platform

2016 ◽  
Author(s):  
Michael Slavutin ◽  
Avshalom Sheffer ◽  
Offer Shai
Keyword(s):  
Main Idea ◽  
Singularity Analysis ◽  
Stewart Platform ◽  
Parallel Lines ◽  
Analysis Methods ◽  
The Common ◽  
Singular Configuration ◽  
Intersection Line ◽  
Special Case

The paper introduces the 3D Kennedy theorem and applies it for characterizing of the singular configuration of 6/6 Stewart Platform (SP). The main idea underlying the proposed singular characterization is as follows: we search for two lines, which cross four of the six leg lines of the robot. For these two lines we find two parallel lines that cross the remaining leg lines 5 and 6. Each pair of parallel lines defines a plane. Let m be the intersection line of these two planes. The proposed singular characterization is: the 6/6 SP is in a singular configuration if and only if the line m is perpendicular to the common normal of leg lines 5 and 6. In addition, the method developed for the singular characterization is also used for the analysis of the mobility of SP. Finally, the proposed method is compared to other singularity analysis methods, such as of Hunt’s and Fichter’s singular configuration and the 3/6 Stewart Platform singularity. The relation between the reported characterizations of the 6/6 SP and other reported works is highlighted. Moreover, it is shown that the known 3/6 singular characterization is a special case of the work reported in the paper.

scholarly journals STRING THEORY EXTENSIONS OF EINSTEIN–MAXWELL FIELDS: THE STATIC CASE

2002 ◽  
Vol 17 (18) ◽  
pp. 2485-2500 ◽  
Author(s):  
ALFREDO HERRERA-AGUILAR ◽  
OLEG V. KECHKIN
Keyword(s):  
String Theory ◽  
Three Dimensional ◽  
Continuous Extension ◽  
Static Case ◽  
Dilaton Field ◽  
New Approach ◽  
Heterotic String Theory ◽  
Maxwell Fields ◽  
Dimensional Gravity ◽  
Special Case

We present a new approach for generating solutions in both the four–dimensional heterotic string theory with one vector field and the five–dimensional bosonic string theory, starting from static Einstein–Maxwell fields. Our approach allows one to construct classes of solutions which are invariant with respect to the total subgroup of three-dimensional charging symmetries of these string theories. The new solution-generating procedure leads to the extremal Israel–Wilson–Perjes subclass of string theory solutions in a special case and provides its natural continuous extension to the realm of nonextremal solutions. We explicitly calculate all string theory solutions related to three-dimensional gravity coupled to an effective dilaton field which arises after an appropriate charging symmetry invariant reduction of the static Einstein–Maxwell system.

scholarly journals Single source unsplittable flows with arc-wise lower and upper bounds

2021 ◽  
Author(s):  
Sarah Morell ◽  
Martin Skutella
Keyword(s):  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Common Source ◽  
Lower And Upper Bounds ◽  
New Approach ◽  
Math Program ◽  
Unsplittable Flow ◽  
The Common ◽  
Special Case ◽  
Single Path

AbstractIn a digraph with a source and several destination nodes with associated demands, an unsplittable flow routes each demand along a single path from the common source to its destination. Given some flow x that is not necessarily unsplittable but satisfies all demands, it is a natural question to ask for an unsplittable flow y that does not deviate from x by too much, i.e., $$y_a\approx x_a$$ y a ≈ x a for all arcs a. Twenty years ago, in a landmark paper, Dinitz et al. (Combinatorica 19:17–41, 1999) proved that there exists an unsplittable flow y such that $$y_a\le x_a+d_{\max }$$ y a ≤ x a + d max for all arcs a, where $$d_{\max }$$ d max denotes the maximum demand value. Our first contribution is a considerably simpler one-page proof for this classical result, based upon an entirely new approach. Secondly, using a subtle variant of this approach, we obtain a new result: There is an unsplittable flow y such that $$y_a\ge x_a-d_{\max }$$ y a ≥ x a - d max for all arcs a. Finally, building upon an iterative rounding technique previously introduced by Kolliopoulos and Stein (SIAM J Comput 31:919–946, 2002) and Skutella (Math Program 91:493–514, 2002), we prove existence of an unsplittable flow that simultaneously satisfies the upper and lower bounds for the special case when demands are integer multiples of each other. For arbitrary demand values, we prove the weaker simultaneous bounds $$x_a/2-d_{\max }\le y_a\le 2x_a+d_{\max }$$ x a / 2 - d max ≤ y a ≤ 2 x a + d max for all arcs a.

A New Approach for Singularity Analysis and Closeness Measurement to Singularities of Parallel Manipulators

2012 ◽  
Vol 4 (4) ◽  
Author(s):  
Xin-Jun Liu ◽  
Chao Wu ◽  
Jinsong Wang
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Challenging Problem ◽  
Performance Indices ◽  
New Approach ◽  
Singular Configurations ◽  
Different Types ◽  
Force Transmissibility ◽  
Singular Configuration

Singularity analysis is one of the most important issues in the field of parallel manipulators. An approach for singularity analysis should be able to not only identify all possible singularities but also explain their physical meanings. Since a parallel manipulator is always out of control at a singularity and its neighborhood, it should work far from singular configurations. However, how to measure the closeness between a pose and a singular configuration is still a challenging problem. This paper presents a new approach for singularity analysis of parallel manipulators by taking into account motion/force transmissibility. Several performance indices are introduced to measure the closeness to singularities. By using these indices, a uniform “metric” can be found to represent the closeness to singularities for different types of nonredundant parallel manipulators.

Some Characterization of Spiral Surfaces

2021 ◽  
Vol 65 (3) ◽  
pp. 81-92
Keyword(s):  
Vector Field ◽  
Three Dimensional ◽  
Gauss Map ◽  
Dimensional Euclidean Space ◽  
Weingarten Surface ◽  
Spiral Surfaces ◽  
Spiral Surface ◽  
Special Case ◽  
Canonical Vector

In this paper we will study special spiral surfaces in the three dimensional Euclidean space and we give some characterization of these surfaces. More specifically, we investigate the Chang-Yau operator acting on the Gauss map of spiral surfaces. We also give some results about canonical vector field of these surfaces, i.e., we study incomperssibility of canonical vector field in two types of spiral surfaces. Moreover, we give some necessary conditions for a spiral surface to be a Weingarten surface. Existence of umbilical point is another problem that we investigate about it for a special case of spiral surfaces of the first type.

scholarly journals Total Recall: Lateral Habenula and Psychedelics in the Study of Depression and Comorbid Brain Disorders

2020 ◽  
Vol 21 (18) ◽  
pp. 6525
Author(s):  
Matas Vitkauskas ◽  
Ajay S. Mathuru
Keyword(s):  
Brain Disorders ◽  
Future Directions ◽  
Lateral Habenula ◽  
New Approach ◽  
Early Results ◽  
New Directions ◽  
The Common ◽  
Induced Changes ◽  
Deep Brain

Depression impacts the lives and daily activities of millions globally. Research into the neurobiology of lateral habenula circuitry and the use of psychedelics for treating depressive states has emerged in the last decade as new directions to devise interventional strategies and therapies. Several clinical trials using deep brain stimulation of the habenula, or using ketamine, and psychedelics that target the serotonergic system such as psilocybin are also underway. The promising early results in these fields require cautious optimism as further evidence from experiments conducted in animal systems in ecologically relevant settings, and a larger number of human studies with improved spatiotemporal neuroimaging, accumulates. Designing optimal methods of intervention will also be aided by an improvement in our understanding of the common genetic and molecular factors underlying disorders comorbid with depression, as well as the characterization of psychedelic-induced changes at a molecular level. Advances in the use of cerebral organoids offers a new approach for rapid progress towards these goals. Here, we review developments in these fast-moving areas of research and discuss potential future directions.

Characterization of photosystem II with the atomic-force microscope

1992 ◽  
Vol 50 (2) ◽  
pp. 1146-1147
Author(s):  
Kathleen M. Marr ◽  
Mary K. Lyon
Keyword(s):  
Photosystem Ii ◽  
Atomic Force Microscope ◽  
Three Dimensional ◽  
Biologically Active ◽  
Atomic Force ◽  
Freeze Etching ◽  
Image Averaging ◽  
Oxygen Evolving ◽  
Averaging Techniques

Photosystem II (PSII) is different from all other reaction centers in that it splits water to evolve oxygen and hydrogen ions. This unique ability to evolve oxygen is partly due to three oxygen evolving polypeptides (OEPs) associated with the PSII complex. Freeze etching on grana derived insideout membranes revealed that the OEPs contribute to the observed tetrameric nature of the PSIl particle; when the OEPs are removed, a distinct dimer emerges. Thus, the surface of the PSII complex changes dramatically upon removal of these polypeptides. The atomic force microscope (AFM) is ideal for examining surface topography. The instrument provides a topographical view of individual PSII complexes, giving relatively high resolution three-dimensional information without image averaging techniques. In addition, the use of a fluid cell allows a biologically active sample to be maintained under fully hydrated and physiologically buffered conditions. The OEPs associated with PSII may be sequentially removed, thereby changing the surface of the complex by one polypeptide at a time.

convergent-beam diffraction from surfaces

1987 ◽  
Vol 45 ◽  
pp. 30-33
Author(s):  
J. A. Eades ◽  
A. E. Smith ◽  
D. F. Lynch
Keyword(s):  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
Three Dimensions ◽  
Plane Figure ◽  
Transmission Electron ◽  
Convergent Beam ◽  
Beam Patterns ◽  
Beam Diffraction

It is quite simple (in the transmission electron microscope) to obtain convergent-beam patterns from the surface of a bulk crystal. The beam is focussed onto the surface at near grazing incidence (figure 1) and if the surface is flat the appropriate pattern is obtained in the diffraction plane (figure 2). Such patterns are potentially valuable for the characterization of surfaces just as normal convergent-beam patterns are valuable for the characterization of crystals.There are, however, several important ways in which reflection diffraction from surfaces differs from the more familiar electron diffraction in transmission.GeometryIn reflection diffraction, because of the surface, it is not possible to describe the specimen as periodic in three dimensions, nor is it possible to associate diffraction with a conventional three-dimensional reciprocal lattice.

Construction of plastic contact deformation maps on ceramics: a case study on aluminum nitride

1996 ◽  
Vol 54 ◽  
pp. 636-637
Author(s):  
D. L. Callahan
Keyword(s):  
Plastic Deformation ◽  
Aluminum Nitride ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Bright Field Image ◽  
Perfectly Plastic ◽  
Contrast Analysis ◽  
Deformation Patterns

Modern polishing, precision machining and microindentation techniques allow the processing and mechanical characterization of ceramics at nanometric scales and within entirely plastic deformation regimes. The mechanical response of most ceramics to such highly constrained contact is not predictable from macroscopic properties and the microstructural deformation patterns have proven difficult to characterize by the application of any individual technique. In this study, TEM techniques of contrast analysis and CBED are combined with stereographic analysis to construct a three-dimensional microstructure deformation map of the surface of a perfectly plastic microindentation on macroscopically brittle aluminum nitride.The bright field image in Figure 1 shows a lg Vickers microindentation contained within a single AlN grain far from any boundaries. High densities of dislocations are evident, particularly near facet edges but are not individually resolvable. The prominent bend contours also indicate the severity of plastic deformation. Figure 2 is a selected area diffraction pattern covering the entire indentation area.

Characterization of a monolayer graphitic structure

1994 ◽  
Vol 52 ◽  
pp. 760-761
Author(s):  
X. Lin ◽  
X. K. Wang ◽  
V. P. Dravid ◽  
J. B. Ketterson ◽  
R. P. H. Chang
Keyword(s):  
Three Dimensional ◽  
Single Layer ◽  
Synthesis Process ◽  
Graphitic Structure ◽  
Positive Gaussian Curvature ◽  
Graphitic Sheet ◽  
Structural And Electronic Properties ◽  
New Material ◽  
Hexagonal Network

For small curvatures of a graphitic sheet, carbon atoms can maintain their preferred sp2 bonding while allowing the sheet to have various three-dimensional geometries, which may have exotic structural and electronic properties. In addition the fivefold rings will lead to a positive Gaussian curvature in the hexagonal network, and the sevenfold rings cause a negative one. By combining these sevenfold and fivefold rings with sixfold rings, it is possible to construct complicated carbon sp2 networks. Because it is much easier to introduce pentagons and heptagons into the single-layer hexagonal network than into the multilayer network, the complicated morphologies would be more common in the single-layer graphite structures. In this contribution, we report the observation and characterization of a new material of monolayer graphitic structure by electron diffraction, HREM, EELS.The synthesis process used in this study is reported early. We utilized a composite anode of graphite and copper for arc evaporation in helium.

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