Robot Workspace of a Tool Plane: Part 1—A Ruled Surface and Other Geometry

1987 ◽  
Vol 109 (1) ◽  
pp. 50-60 ◽  
Author(s):  
J. K. Davidson ◽  
K. H. Hunt
Keyword(s):  
Intersection Point ◽  
Ruled Surface ◽  
Geometric Features ◽  
Sweeping Process ◽  
Tangent Point ◽  
Plane Part ◽  
Computer Generation ◽  
Robot Workspace

The sweeping process is used for conceptually describing plane-workspaces and for distinguishing certain forms of these workspaces for robots. The tangent point to the plane-workspace of a tool plane σ is identified as the intersection point of σ with that extreme-distance line which is also normal to σ. The quartic ruled surface, which is a new property of the dual torus, is identified and described. It contains information that uniquely identifies the 2-R manipulator which generates the dual torus. these geometric features are then used in developing the equations for computer generation of plane-workspace envelopes and boundaries for an n-R robot.

Robot Workspace of a Tool Plane: Part 2—Computer Generation and Selected Design Conditions for Dexterity

1987 ◽  
Vol 109 (1) ◽  
pp. 61-71 ◽  
Author(s):  
J. K. Davidson ◽  
P. Pingali
Keyword(s):  
Ruled Surface ◽  
End Effector ◽  
Plane Part ◽  
Computer Generation ◽  
Robot Workspace

In this paper the algorithm is completed for generation of envelope-surfaces for plane-workspaces of generally proportioned manipulators. Then the ruled surface Ψ is used for adapting the algorithm to 3-R manipulators for which the outermost two axes intersect (a2 = 0). The discriminant D is further developed, and it is used to classify 3-R manipulators, having a2 = 0, into seven Types. Manipulators, which are of Type 7, (i) can provide any orientation to a tool plane σ or (ii), with a fourth appropriately placed R joint and tool plane Σ, can also provide any attitude to the end effector. Design conditions are developed and presented which ensure that a manipulator will possess these properties of dexterity. The conditions are based on coupled motions at all three, or four, axes.

On Algorithms of Graphical Plotting of Geodesic Line on a Ruled Surface

2015 ◽  
Vol 3 (4) ◽  
pp. 15-18 ◽  
Author(s):  
Умбетов ◽  
Nurlan Umbetov ◽  
Джанабаев ◽  
Zh. Dzhanabaev
Keyword(s):  
Initial Point ◽  
Intersection Point ◽  
Ruled Surface ◽  
Engineering Practice ◽  
Geodesic Line ◽  
Axis Of Rotation ◽  
Characteristic Lines ◽  
Geodesic Lines ◽  
Internal Properties

Geodesic lines find interesting applications when solving many tasks of fundamental sciences (mathematicians, physics, etc.) and engineering practice. In differential geometry geodesic lines are characteristic lines for determination of internal properties of surface. However, the construction of geodesic line on a surface presents certain complications, mainly solved by the methods of calculating mathematics and descriptive geometry. In this article the development of a simple and comfortable algorithm of construction of geodesic line is considered on linear surfaces. In general case, the spatial model of algorithm of construction of geodesic line on a ruled surface is expressed in the following: a ruled surface we replace with averged surface, and at any side of the viewed verge, the intersection point of the geodesic with the rib of fracture (line of bending of dihedral angle) will be determined as the intersection of contiguous generatrix with the surface of cone of rotation – the congruence of directions of geodesic laying with the top at initial point, axis of rotation, incident to the considered generatrix, and the corner at the top of cone, equal to the doubled corner between the axis of rotation and direction of the geodesic laying. Next, as an initial parameters the contiguous with reviewed generatrix are accepted, determined higher point, lying on it, and the direction of geodesic is a corner between a segment obtained from geodesic and contiguous generatrix. Thus, repeatedly reiterating the described cycle, we will get the multitude number of points, making the required geodesic line.

Microdiffraction analysis of precipitate crystallography and morphology in Al alloys

1990 ◽  
Vol 48 (4) ◽  
pp. 954-955
Author(s):  
B.C. Muddle ◽  
G.R. Hugo
Keyword(s):  
Point Group ◽  
Hexagonal Lattice ◽  
Intersection Point ◽  
Saed Pattern ◽  
Point Symmetry ◽  
Hexagonal Symmetry ◽  
Precipitate Crystal ◽  
The Matrix ◽  
The Subject ◽  
Electron Microdiffraction

Electron microdiffraction has been used to determine the crystallography of precipitation in Al-Cu-Mg-Ag and Al-Ge alloys for individual precipitates with dimensions down to 10 nm. The crystallography has been related to the morphology of the precipitates using an analysis based on the intersection point symmetry. This analysis requires that the precipitate form be consistent with the intersection point group, defined as those point symmetry elements common to precipitate and matrix crystals when the precipitate crystal is in its observed orientation relationship with the matrix.In Al-Cu-Mg-Ag alloys with high Cu:Mg ratios and containing trace amounts of silver, a phase designated Ω readily precipitates as thin, hexagonal-shaped plates on matrix {111}α planes. Examples of these precipitates are shown in Fig. 1. The structure of this phase has been the subject of some controversy. An SAED pattern, Fig. 2, recorded from matrix and precipitates parallel to a <11l>α axis is suggestive of hexagonal symmetry and a hexagonal lattice has been proposed on the basis of such patterns.

Face Completion Using Semantic Segmentation and Geometric Features

2018 ◽  
Vol 11 (6) ◽  
pp. 304
Author(s):  
Javier Pinzon-Arenas ◽  
Robinson Jimenez-Moreno ◽  
Ruben Hernandez-Beleno
Keyword(s):  
Semantic Segmentation ◽  
Geometric Features

OFFLINE YORÙBÁ HANDWRITTEN WORD RECOGNITION USING GEOMETRIC FEATURE EXTRACTION AND SUPPORT VECTOR MACHINE CLASSIFIER

2020 ◽  
Vol 5 (2) ◽  
pp. 504
Author(s):  
Matthias Omotayo Oladele ◽  
Temilola Morufat Adepoju ◽  
Olaide ` Abiodun Olatoke ◽  
Oluwaseun Adewale Ojo
Keyword(s):  
Support Vector Machine ◽  
Feature Extraction ◽  
Word Recognition ◽  
Support Vector Machine Classifier ◽  
Recognition Accuracy ◽  
Recognition System ◽  
Support Vector ◽  
Geometric Features ◽  
Total Length ◽  
Yoruba Language

Yorùbá language is one of the three main languages that is been spoken in Nigeria. It is a tonal language that carries an accent on the vowel alphabets. There are twenty-five (25) alphabets in Yorùbá language with one of the alphabets a digraph (GB). Due to the difficulty in typing handwritten Yorùbá documents, there is a need to develop a handwritten recognition system that can convert the handwritten texts to digital format. This study discusses the offline Yorùbá handwritten word recognition system (OYHWR) that recognizes Yorùbá uppercase alphabets. Handwritten characters and words were obtained from different writers using the paint application and M708 graphics tablets. The characters were used for training and the words were used for testing. Pre-processing was done on the images and the geometric features of the images were extracted using zoning and gradient-based feature extraction. Geometric features are the different line types that form a particular character such as the vertical, horizontal, and diagonal lines. The geometric features used are the number of horizontal lines, number of vertical lines, number of right diagonal lines, number of left diagonal lines, total length of all horizontal lines, total length of all vertical lines, total length of all right slanting lines, total length of all left-slanting lines and the area of the skeleton. The characters are divided into 9 zones and gradient feature extraction was used to extract the horizontal and vertical components and geometric features in each zone. The words were fed into the support vector machine classifier and the performance was evaluated based on recognition accuracy. Support vector machine is a two-class classifier, hence a multiclass SVM classifier least square support vector machine (LSSVM) was used for word recognition. The one vs one strategy and RBF kernel were used and the recognition accuracy obtained from the tested words ranges between 66.7%, 83.3%, 85.7%, 87.5%, and 100%. The low recognition rate for some of the words could be as a result of the similarity in the extracted features.

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