A Laboratory Project on the Design and Machining of Bezier Surfaces

1994 ◽  
Vol 22 (1) ◽  
pp. 43-53 ◽  
Author(s):  
J. G. Gan ◽  
S. S. G. Lee ◽  
S. C. Tam ◽  
M. L. Tay
Keyword(s):  
Common Boundary ◽  
Scallop Height ◽  
Bézier Surfaces ◽  
The Common ◽  
Bezier Surfaces

This paper describes a six-hour laboratory project on the design and machining of Bezier surfaces. Students are required to design a pair of mutually orthogonal Bezier surfaces. In both cases, the surface is to lie completely within the stock material provided. In addition, C0 and C1 continuity has to be enforced at the common boundary. The coordinates of the second surface have to be rotated by 90 degrees so that the surface can be aligned to the axis of the cutter. The principal issues relating to the machining of multiple Bezier surfaces are discussed, viz. the determination of the cutter diameter and orientation, and the generation of the NC toolpath (i.e. the spacing between adjacent curves and their incremental movement) to achieve the specified scallop height and machining tolerance. An algorithm incorporating these aspects for the generation of the NC toolpath is presented.

scholarly journals Determination of Composite Properties in the Presence of Fiber Deboning and Matrix Damage by Using the Method of Cell

2020 ◽  
Author(s):  
Mohammad Ghalandari ◽  
Hossein Toozandehjani ◽  
Ibrahim Mahariq ◽  
Thabet Abeljawad
Keyword(s):  
Displacement Field ◽  
Fiber Composite ◽  
Composite Fiber ◽  
Common Boundary ◽  
Micro Cracks ◽  
Bearing Load ◽  
The Matrix ◽  
The Common ◽  
Composite Properties

In this study, the elastic properties of composite materials are investigated, considering the effects of separation of fiber-matrix joint boundary and matrix failure. In this method, by assuming periodic microstructure and using a linear approximation of the displacement field by applying continuity and equilibrium conditions, the composite fiber composite relation is determined. The effect of separation is assumed by introducing tangential and normal scalar parameters in the equations by assuming the displacement field jump at the common boundary. In order to express the effect of matrix micro-cracks, the fracture mechanics framework of continuous environments was used and the micro-cracks parallel to the fibers, perpendicular to the fibers and in the thickness direction with scalar parameters were expressed. At the end of the effect of these parameters the results are presented in graphs. The results show that the presence of defective joint at the joint boundary and the matrix micro-components reduce the hardness of the composite and thus it’s bearing load, which is more significant at the defective joint state.

Clay-sealings from the Fayum

1906 ◽  
Vol 26 ◽  
pp. 32-45
Author(s):  
J. G. Milne
Keyword(s):  
Irregular Shape ◽  
The Common

During the excavations of Messrs. Hogarth Grenfell and Hunt for the Egypt Exploration Fund in the winter of 1895–6 on the site of Karanis (Kom Ushim) in the Fayum, a considerable number of clay-sealings were found, mainly in the cellars of the Roman houses. These were recently put in my hands for investigation and offer some interesting material.The sealings have evidently come from various kinds of articles: in many instances the clay is too much broken for any determination of the shape which it had taken to be possible; but among the better preserved pieces are examples from the mouths of bottles, some of which have been squeezed down into the neck like a cork, others placed over a linen covering, sometimes tied down with cord: others are from the flat sides of wooden boxes, often showing the marks of cord: others again from parcels of irregular shape, in some cases seemingly wrapped in papyrus. The common points of all are that they consist of lumps of Nile-mud, and that they have been impressed, while the clay was damp, with signets, which were presumably those of the merchants who forwarded the goods upon which the sealings were placed.

Geometric Design and Fabrication of Developable Bezier Surfaces

1992 ◽  
Author(s):  
R. M. C. Bodduluri ◽  
B. Ravani
Keyword(s):  
Geometric Design ◽  
Developable Surface ◽  
Developable Surfaces ◽  
Surface Patches ◽  
Bézier Surfaces ◽  
Point Representation ◽  
Cad Cam ◽  
C2 Continuity ◽  
Type Construction ◽  
Bezier Surfaces

Abstract In this paper we study Computer Aided Geometric Design (CAGD) and Manufacturing (CAM) of developable surfaces. We develop direct representations of developable surfaces in terms of point as well as plane geometries. The point representation uses a Bezier curve, the tangents of which span the surface. The plane representation uses control planes instead of control points and determines a surface which is a Bezier interpolation of the control planes. In this case, a de Casteljau type construction method is presented for geometric design of developable Bezier surfaces. In design of piecewise surface patches, a computational geometric algorithm similar to Farin-Boehm construction used in design of piecewise parametric curves is developed for designing developable surfaces with C2 continuity. In the area of manufacturing or fabrication of developable surfaces, we present simple methods for both development of a surface into a plane and bending of a flat plane into a desired developable surface. The approach presented uses plane and line geometries and eliminates the need for solving differential equations of Riccatti type used in previous methods. The results are illustrated using an example generated by a CAD/CAM system implemented based on the theory presented.

About the possibility of identification of articles from steels, aluminum, copper and alloys on their basis on the expanded micro-impurity elemental composition

2021 ◽  
pp. 51-56
Author(s):  
Yu. B. Sazonov ◽  
D. Yu. Ozherelkov ◽  
R. Sh. Latypov ◽  
E. E. Gorshkov
Keyword(s):  
Spectral Analysis ◽  
Chemical Composition ◽  
Elemental Composition ◽  
Chemical Elements ◽  
Copper Alloys ◽  
Minimal Amount ◽  
Elementary Composition ◽  
Geometric Size ◽  
The Common

Possibility of determination of the fragments and articles made of different grades of steel aluminium and copper alloys and their affiliation to the common melt was examined via the methods of photoelectric spectral analysis based on composition of micro-impurities. Chemical elements with micro-impurities were revealed; they allow to determine affiliation of metal fragments to one melt. Ultimately possible deviations of micro-impurities within one melt were obtained. The technique allowing to establish affiliation of fragments to the common melt based on their elementary composition of micro-impurities with minimal amount of measurements was suggested based on the obtained results. The minimal geometric size of a sample available for analysis was determined; it allows to classify the examined fragments to one melt based on the results of investigation of expanded elementary composition of micro-impurities. Practical opportunities of this technique were displayed on the example of the alloys with different chemical composition.

scholarly journals The contemporary cartographic presentation of geographical names of objects lying on the border between Poland and the Czech Republic

2015 ◽  
Vol 47 (3) ◽  
pp. 159-174
Author(s):  
Maciej Zych
Keyword(s):  
Czech Republic ◽  
Topographic Maps ◽  
National Register ◽  
The Czech Republic ◽  
Common Boundary ◽  
Mountain Ranges ◽  
Single Region ◽  
The Common ◽  
Mountain Basins ◽  
Own Name

Abstract The aim of this paper is the analysis of the names used on cartographic publications in Poland and the Czech Republic for transboundary geographical objects lying on the common boundary. After the analysis of the Czech and Polish topographic maps that are available on the national geoportals, maps of the divisions into natural regions, and toponymic databases (Polish the National Register of Geographical Names, and Czech Geonames – the Database of geographic names of the Czech Republic) it was established that 360 named geographic objects lie on this boundary. This number includes: 123 hydronyms (names of rivers and other streams), 224 oronyms (139 names of summits, 22 names of mountain passes, 35 names of mountain ranges and ridges, 15 names of highlands, plateaus and uplands, 7 names of mountain basins, valleys and depressions, 3 names of lowlands, and 3 names of rocks), 9 names of forests, 1 name of mountain meadow (alp), and 3 names of tracks. 212 of these objects (59%) have names in both languages – Polish and Czech, however, in 99 cases (47% of objects that have name in both Polish and Czech languages) the Polish and Czech toponyms entirely do not correspond to each other. From the remaining objects 67 (18%) have only the Czech name, and 81 (23%) only the Polish name. In some natural regions, the limits of their ranges set by the Czech and Polish geographers vary widely, for example a single region on one side of the boundary corresponds to two or more regions on other side of the boundary. In other cases illustrations of incorrectness are more sophisticated, like the river that has different course according to the Czech or Polish maps (stream regarded as a main watercourse in one country, which has its own name, in another country is considered as a tributary one with a different name). In the summary, it should be stated that in the large part of the Polish and Czech names of the geographical objects lying on the common boundary were drawn regardless of the names used in the neighboring country.

scholarly journals A note on the implications of factorial invariance for common factor variable equivalence

2016 ◽  
Author(s):  
Michael Maraun ◽  
Moritz Heene
Keyword(s):  
Common Factor ◽  
Random Variables ◽  
Random Variable ◽  
Factorial Invariance ◽  
Technical Examination ◽  
The Common ◽  
Factor Variable

There has come to exist within the psychometric literature a generalized belief to the effect that a determination of the level of factorial invariance that holds over a set of k populations Δj, j = 1..s, is central to ascertaining whether or not the common factor random variables ξj, j = 1..s, are equivalent. In the current manuscript, a technical examination of this belief is undertaken. The chief conclusion of the work is that, as long as technical, statistical senses of random variable equivalence are adhered to, the belief is unfounded.

scholarly journals ADAPTIVE ALGORITHM FOR DETERMINING THE PARAMETERS OF AN INACCESSIBLE POINT OF AN OBJECT

2021 ◽  
pp. 58-70
Author(s):  
Aleksandr Brailov ◽  
Vitaliy Panchenko
Keyword(s):  
Adaptive Algorithm ◽  
Minimum Distance ◽  
Three Dimensional ◽  
Geometrical Model ◽  
Multiple Variables ◽  
The Common ◽  
Relative Errors ◽  
The Given ◽  
Real Experimental Data

In the present research the optimizing approach to the determination of the parameters of an inaccessible point of an object is developed. The common issues are revealed and essential steps of their resolution are identified. The essence of the problem is an objective contradiction between a requirement for the location of points A and B of the centers of the sighting tubes of optical devices in the same horizontal plane P1 and the lack of a real possibility to perform such to achieve this an identical one-level arrangement without error. The aim of the study is to develop strategies for determining the position of an inaccessible point of an object in the minimum domain between intersecting sighting rays as well as an adaptive algorithm for determining the values of the parameters of an inaccessible point under the given absolute and relative errors. To achieve this aim, the following problems are formulated and solved in the paper: 1. Develop strategies for determining the position of the inaccessible point of the object in the minimum domain between the intersecting sighting rays. 2. Develop an adaptive algorithm for determining the values of the parameters of an inaccessible point based on the specified absolute and relative errors. In the proposed optimizing approach, the three-dimensional geometrical model with crossed directional rays for the determination of coordinates of the inaccessible point of an object is developed. It is discussed that points С and C', coordinated of which to be determined, locates in domain [CDM, CEM], [C'D'M, C'E'M] of the minimum distance ρmin between crossed directional rays. The optimizing problem of the determination of coordinates of an inaccessible point of an object in space is reduced to a problem of the determination of the minimum distance between two crossed directional rays. It’s known from the theory of function of multiple variables that function ρ = f (tC'D', tC'E') reaches its extremum ρmin when its partial derivatives by each variable are equal to zero. Three strategies for selecting the position of the inaccessible point C (xC, yC, zC) in the found minimum region [CDM, CEM] are proposed. The required point C' (xC', yC', zC') can be located, for example, in the middle of the minimum segment [C'D'M, C'E'M]. The essence of the adaptive algorithm is in optimizing the variation of the initial values of data α, α', β, γ, γ', AB, at which the absolute and relative errors of the coordinates of the inaccessible point satisfy the error values set by the customer (0.0001-1.2%) The proposed approach is verified using real experimental data.

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