Descriptive geometry

They have fractional values (0.87, 0.47 etc.), so there are reduced factors as 1 or 0.5 which are used in drawings.

There are next types of axonometric projections according to the mutual ratio of these factors:

1.Isometric – when three factors are equal Kx Kx Kx .

2.Dimetric – when only two of three factors are equal Kx Kx Kx .

3.Trimetric – when all factors are different Kx Kx Kx .

There are orthogonal and oblique axonometric projections what depend on an angle of projection ray inclination.

Pohlke's theorem is a fundamental theorem of axonometric projection. It was established in 1853 by Karl Wilhelm Pohlke, German painter and teacher of Descriptive Geometry. The first proof of the theorem was published in 1864 by Hermann Amandus:

1.Orthogonal isometric projection.

2.Orthogonal dimetric projection.

3.Oblique frontal dimetric projection.

4.Oblique frontal izometric projection.

5.Oblique horizontal izometric projection.

First three types are used more often in the practice of technical drawing.

8.2. Orthogonal isometric projection

By this type of axonometric projections angles among axis lines are equal to 120 . A formula (8.4) is a formula for determination of distortion coefficients.

should be rounded to the nearest whole number for simplifying work with axonometric. So Kx K y Kz 1. In this case, the obtained representation is enlarged by 1.22.

A circle in axonometric projection is generally projected in an ellipse. When constructing an ellipse, it is necessary to know the direction of its axes and their dimensions.

Note: a minor axis of an ellipse is always perpendicular to the major one. When a circle projection is constructed (a circle lies in one of the co-ordinate planes), the minor axis of the ellipse is directed parallel to the axonometric axis which does not participate in the formation of the plane the drawing is in.

The following example of isometry of a complex body (fig. 8.1).

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A pyramid with some cutting planes was drawn in the orthogonal dim etric projection as an example (fig. 8.4).

Fig. 8.4. An orthogo nal dimetric projection of a straigh t pentagonal pyramid wit h some sections

As for a circl e in the orthogonal dimetric p rojection it has all three projections as an ellips . Two of them are the same and the third one is differen t. The biggest axis AB for all three ellipses is 1.06d. For circles in the horizontal an d profile planes of projection the smallest axis CE has the same direction w th axes x and z, respectively, and is equal to 0.35d. For a circle in the frontal plane of projection it is 0.95 d and the biggest axis AB is perpendi cular to th e axis y. The biggest axis a nd the smallest one are mutually perpendicular (fig. 8.5).

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APPENDIXES

UNIFIED SYSTEM FOR DESIGN DOCUMENTATION (USDD)

“Standardization is the process of formulating and applying rules for an orderly approach to a specific activity for the benefit and with the cooperation of all concerned, and in particular for the promotion of optimum overall economy taking due account of functional conditions and safety requirements.” (ISO – International Organization for Standardization)

These Complex rules are called Standard. Standard is a full complex of recommendations relevant to the preparation of technical product specifications.

Standards are set of different levels. There are local standards, national standards, regional standards and international standards.

Typical examples of the different levels of standards may include:

–Local Standards: SUA formats for writing various academic reports;

–National Standards: DIN (Deutsches Institut für Normung) (German), BS (UK), GOST (CIS), etc.;

–Regional Standards: Standards set for the East African Community, etc.;

–International Standards: ISO (International Organization for Standardization) DIN – an internationally accepted German national standard, BS – an internationally accepted British national standard.

The Republic of Belarus and countries from The Commonwealth of Independent States (CIS) use Unified System for Design Documentation (USDD).

The goal of USDD standards is to adopt unified regulations for completion, presentation and legalisation of engineering papers.

This is a set of the State Standards which are called GOST (it is abbreviation from Russian ГОСТ – State Standard).

GOST 2.301–68 Formats 2 – class by USDD

3.. group of standard which are relate to design drawings -68 – year when standard was established

Formats – The name of GOST

GOST 2.301–68 Formats

There are basic and additional formats.

This state standard such as the other international standards recommends an area of the largest sheet of paper as one square meter with sides in the ratio of 1:2. This format is called A0. The dimensions of the sheet of paper are 841 mm × 1189 mm. The size of A1 paper is a half the size of A0 while A2 is a half of A1 and so forth. Note that a higher order paper size (which is always smaller in size) is obtained by simply halving the preceding size along its longer side.

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And the third compone nt is the title block or the b sic inscri ptions. It is a table with som e information in the right b ottom corner of the format. There is the State Standard for it – GOST 2.104–2006 B asic insc iptions.

GOST 2.104–2 006 Basic inscrip tions (Title Block – UK)

The basic inscriptions are the rectangular frame th t is locat ed at the r ight hand bottom corner of s heet. It i cludes se veral sections for providing administrative and technical informat on. This able has following size (fig. A.2) and all its ite ms, which are usually filled, a re numbered and given belo w.

Fig. A.2. A basic in scription

1.N ame of the object, product, part of ma chine.

2.D ocument mark.

3.M aterial used to man ufacture this part.

4.Scale.

5.N umber of a group (Name of an organi ation).

6.Sheet num ber.

7.Total numb er of she ts.

8.Student’s name (Draughtsman’s name) (after Разраб. in ru ssian).

9.Signature o f a studen t (Draugh tsman’s s ignatures) (only this element has to be written by pen, all the other by pencil only).

10.Date of creation.

11. Name of the perso n who ha s to check this dra ing (Lecturer’s N ame, after Пров. in Russian.

12.Signature of a lecturer (This row is filled after c hecking by lecturer).

13.Date of checking (This row is filled at t e same ti me with c hecker’s s gnature).

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