Look at Fig. 92. It shows a frontal dimetric projection of a cube with circles inscribed in its faces.

Circles located on planes perpendicular to the x and z axes are represented by ellipses. The front face of the cube, perpendicular to the y-axis, is projected without distortion, and the circle located on it is depicted without distortion, i.e., described by a compass. Therefore, the frontal dimetric projection is convenient for depicting objects with curvilinear outlines, such as those shown in Fig. 93.

Construction of a frontal dimetric projection of a flat part with a cylindrical hole. The frontal dimetric projection of a flat part with a cylindrical hole is performed as follows.

1. Construct the outline of the front face of the part using a compass (Fig. 94, a).

2. Straight lines are drawn through the centers of the circle and arcs parallel to the y-axis, on which half the thickness of the part is laid. The centers of the circle and arcs located on the rear surface of the part are obtained (Fig. 94, b). From these centers a circle and arcs are drawn, the radii of which must be equal to the radii of the circle and arcs of the front face.

3. Draw tangents to the arcs. Remove excess lines and outline the visible contour (Fig. 94, c).

Isometric projections of circles. A square in isometric projection is projected into a rhombus. Circles inscribed in squares, for example, located on the faces of a cube (Fig. 95), are depicted as ellipses in an isometric projection. In practice, ellipses are replaced by ovals, which are drawn with four arcs of circles.

Construction of an oval inscribed in a rhombus.

1. Construct a rhombus with a side equal to the diameter of the depicted circle (Fig. 96, a). To do this, the isometric axes x and y are drawn through point O and segments equal to the radius of the depicted circle are laid on them from point O. Through points a, w, c and d, draw straight lines parallel to the axes; get a rhombus. The major axis of the oval is located on the major diagonal of the rhombus.

2. Fit an oval into the rhombus. To do this, arcs of radius R are drawn from the vertices of obtuse angles (points A and B), equal to the distance from the vertex of the obtuse angle (points A and B) to points a, b or c, d, respectively. Straight lines are drawn through points B and a, B and b (Fig. 96, b); the intersection of these lines with the larger diagonal of the rhombus gives points C and D, which will be the centers of the minor arcs; the radius R 1 of small arcs is equal to Ca (Db). Arcs of this radius conjugate the large arcs of the oval. This is how an oval is built, lying in a plane perpendicular to the z axis (oval 1 in Fig. 95). Ovals located in planes perpendicular to the x (oval 3) and y (oval 2) axes are constructed in the same way as oval 1, only the construction of oval 3 is carried out on the y and z axes (Fig. 97, a), and ovals 2 (see Fig. 95) - on the x and z axes (Fig. 97, b).

Constructing an isometric projection of a part with a cylindrical hole.

How to apply the discussed constructions in practice?

An isometric projection of the part is given (Fig. 98, a). It is necessary to draw a through cylindrical hole drilled perpendicular to the front edge.

The construction is carried out as follows.

1. Find the position of the center of the hole on the front face of the part. Isometric axes are drawn through the found center. (To determine their direction, it is convenient to use the image of a cube in Fig. 95.) On the axes from the center, segments equal to the radius of the depicted circle are laid (Fig. 98, a).

2. Construct a rhombus, the side of which is equal to the diameter of the depicted circle; draw a large diagonal of the rhombus (Fig. 98, b).

3. Describe large oval arcs; find centers for small arcs (Fig. 98, c).

4. Draw small arcs (Fig. 98, d).

5. Construct the same oval on the back face of the part and draw tangents to both ovals (Fig. 98, e).

Answer the questions

1. What figures are depicted in the frontal dimetric projection of circles located on planes perpendicular to the x and y axes?

2. Is a circle distorted in a frontal dimetric projection if its plane is perpendicular to the y-axis?

3. When depicting what parts is it convenient to use frontal dimetric projection?

4. What figures are used to represent circles in an isometric projection located on planes perpendicular to the x, y, z axes?

5. What figures in practice replace ellipses depicting circles in isometric projection?

6. What elements does the oval consist of?

7. What are the diameters of the circles depicted as ovals inscribed in rhombuses in Fig. 95 if the sides of these rhombuses are 40 mm?

Tasks for § 13 and 14

Exercise 42

In Fig. 99 axes are drawn to construct three rhombuses representing squares in an isometric projection. Look at Fig. 95 and write down on which face of the cube - the top, right side or left side will be located each rhombus, built on the axes given in Fig. 99. Which axis (x, y or z) will the plane of each rhombus be perpendicular to?

The standard establishes the following views obtained on the main projection planes (Fig. 1.2): front view (main), top view, left view, right view, bottom view, rear view.

Behind main view they accept the one that gives the most complete idea of ​​the shape and size of the object.

The number of images should be the smallest, but providing a complete picture of the shape and size of the item.

If the main views are located in a projection relationship, then their names are not indicated. For the best use of the drawing field, views can be placed outside the projection connection (Fig. 2.2). In this case, the image of the view is accompanied by a type designation:

1) the direction of view is indicated

2) above the image of the view a designation is applied A, as in Fig. 2.1.

Species are designated in capital letters Russian alphabet in a font 1...2 sizes larger than the font size of the dimensional numbers.

Figure 2.1 shows a part that requires four views. If these views are placed in a projection relationship, then they will take up a lot of space on the drawing field. You can arrange the necessary views as shown in Fig. 2.1. The drawing format is reduced, but the projection relationship is broken, so you need to designate the view on the right ().

2.2. Local species.

A local view is an image of a separate limited area of ​​the surface of an object.

It can be limited by the cliff line (Fig. 2.3 a) or not limited (Fig. 2.3 b).

In general, local species are designed in the same way as the main species.

2.3. Additional types.

If any part of an object cannot be shown in the main views without distorting the shape and size, then additional views are used.

An additional view is an image of the visible part of the surface of an object, obtained on a plane not parallel to any of the main projection planes.

If an additional view is performed in projection connection with the corresponding image (Fig. 2.4 a), then it is not designated.

If the image of an additional type is placed in free space (Fig. 2.4 b), i.e. If the projection connection is broken, then the direction of view is indicated by an arrow located perpendicular to the depicted part of the part and is indicated by a letter of the Russian alphabet, and the letter remains parallel to the main inscription of the drawing and does not turn behind the arrow.

If necessary, the image of an additional type can be rotated, then a letter and a rotation sign are placed above the image (this is a 5...6 mm circle with an arrow, between the wings of which there is an angle of 90°) (Fig. 2.4 c).

An additional type is most often performed as a local one.

3.Cuts.

A cut is an image of an object mentally dissected by one or more planes. The section shows what lies in the secant plane and what is located behind it.

In this case, the part of the object located between the observer and the cutting plane is mentally removed, as a result of which all surfaces covered by this part become visible.

3.1. Construction of sections.

Figure 3.1 shows three types of objects (without a cut). In the main view, the internal surfaces: a rectangular groove and a cylindrical stepped hole are shown with dashed lines.

In Fig. 3.2 shows a section obtained as follows.

Using a secant plane parallel to the frontal plane of projections, the object was mentally dissected along its axis passing through a rectangular groove and a cylindrical stepped hole located in the center of the object. Then the front half of the object, located between the observer and the secant plane, was mentally removed. Since the object is symmetrical, there is no point in giving a full cut. It is performed on the right, and the left view is left.

The view and the section are separated by a dash-dotted line. The section shows what happened in the cutting plane and what is behind it.

When examining the drawing you will notice the following:

1) the dashed lines, which in the main view indicate a rectangular groove and a cylindrical stepped hole, are outlined in the section with solid main lines, since they became visible as a result of mental dissection of the object;

2) in the section, the solid main line running along the main view, indicating the cut, has disappeared altogether, since the front half of the object is not depicted. The section located on the depicted half of the object is not marked, since it is not recommended to show invisible elements of the object with dashed lines on sections;

3) in the section, a flat figure located in the secant plane is highlighted by shading; shading is applied only in the place where the secant plane cuts the material of the object. For this reason, the back surface of the cylindrical stepped hole is not shaded, as well as the rectangular groove (when mentally dissecting the object, the cutting plane did not affect these surfaces);

4) when depicting a cylindrical stepped hole, a solid main line is drawn, depicting a horizontal plane formed by a change in diameters on the frontal plane of projections;

5) a section placed in the place of the main image does not change the images of the top and left views in any way.

When making cuts in drawings, you must follow the following rules:

1) make only useful cuts in the drawing (cuts chosen for reasons of necessity and sufficiency are called “useful”);

2) previously invisible internal outlines, depicted by dashed lines, should be outlined with solid main lines;

3) hatch the section figure included in the section;

4) mental dissection of an object should relate only to this cut and not affect the change in other images of the same object;

5) In all images, dashed lines are removed, since the internal contour is clearly readable in the section.

3.2 Designation of cuts

In order to know where the object has the shape shown in the cut image, the place where the cutting plane passed and the cut itself are indicated. The line indicating the cutting plane is called the cutting line. It is depicted as an open line.

In this case, select the initial letters of the alphabet ( A B C D E etc.). Above the section obtained using this cutting plane, an inscription is made according to the type A-A, i.e. two paired letters separated by a dash (Fig. 3.3).

Letters near section lines and letters indicating a section must be larger than the dimensional numbers in the same drawing (by one or two font numbers)

In cases where the cutting plane coincides with the plane of symmetry of a given object and the corresponding images are located on the same sheet in direct projection connection and are not separated by any other images, it is recommended not to mark the position of the cutting plane and not to accompany the cut image with an inscription.

Figure 3.3 shows a drawing of an object on which two cuts are made.

1. In the main view, the section is made by a plane, the location of which coincides with the plane of symmetry for a given object. It runs along the horizontal axis in the top view. Therefore this section is not marked.

2. Cutting plane A-A does not coincide with the plane of symmetry of this part, therefore the corresponding section is marked.

Letter designation cutting planes and sections are placed parallel to the main inscription, regardless of the angle of inclination of the cutting plane.

3.3 Hatching materials in sections and sections.

In sections and sections, the figure obtained in the secant plane is hatched.

GOST 2.306-68 establishes graphic designations for various materials (Fig. 3.4)

Hatching for metals is applied in thin lines at an angle of 45° to the contour lines of the image, or to its axis, or to the lines of the drawing frame, and the distance between the lines should be the same.

The shading on all sections and sections for a given object is the same in direction and pitch (distance between strokes).

3.4. Classification of cuts.

Incisions have several classifications:

1. Classification, depending on the number of cutting planes;

2. Classification, depending on the position of the cutting plane relative to the projection planes;

3. Classification, depending on the position of the cutting planes relative to each other.

Rice. 3.5

3.4.1 Simple cuts

A simple cut is a cut made by one cutting plane.

The position of the cutting plane can be different: vertical, horizontal, inclined. It is chosen depending on the shape of the object whose internal structure needs to be shown.

Depending on the position of the cutting plane relative to the horizontal plane of projections, sections are divided into vertical, horizontal and inclined.

Vertical is a section with a cutting plane perpendicular to the horizontal plane of projections.

A vertically located cutting plane can be parallel to the frontal plane of projections or the profile, thus forming, respectively, frontal (Fig. 3.6) or profile sections (Fig. 3.7).

A horizontal section is a section with a secant plane parallel to the horizontal plane of projections (Fig. 3.8).

An inclined cut is a cut with a cutting plane that makes an angle with one of the main projection planes that is different from a straight line (Fig. 3.9).

1. Based on the axonometric image of the part and the given dimensions, draw three of its views - the main one, the top and the left. Do not redraw the visual image.

7.2. Task 2

2. Make the necessary cuts.

3. Construct lines of intersection of surfaces.

4. Draw dimension lines and enter size numbers.

5. Outline the drawing and fill in the title block.

7.3. Task 3

1. Draw the given two types of object according to size and construct a third type.

2. Make the necessary cuts.

3. Construct lines of intersection of surfaces.

4. Draw dimension lines and enter size numbers.

5. Outline the drawing and fill in the title block.

For all tasks, draw views only in projection connection.

7.1. Task 1.

Let's look at examples of completing tasks.

Problem 1. Based on the visual image, construct three types of parts and make the necessary cuts.

7.2 Problem 2

Problem 2. Using two views, construct a third view and make the necessary cuts.

Task 2. Stage III.

1. Make the necessary cuts. The number of cuts should be minimal, but sufficient to read the internal contour.

1. Cutting plane A opens internal coaxial surfaces. This plane is parallel to the frontal plane of projections, so the section A-A combined with the main view.

2. The view on the left shows a sectional view exposing a Æ32 cylindrical hole.

3. Dimensions are applied on those images where the surface is readable better, i.e. diameter, length, etc., for example Æ52 and length 114.

4. If possible, do not cross extension lines. If the main view is selected correctly, then greatest number sizes will be on the main view.

Check:

1. So that each element of the part has a sufficient number of dimensions.
2. So that all protrusions and holes are dimensioned to other elements of the part (size 55, 46, and 50).
3. Dimensions.
4. Outline the drawing, removing all the lines of the invisible contour. Fill out the title block.

7.3. Task 3.

Construct three types of parts and make the necessary cuts.

8. Information about surfaces.

Constructing lines belonging to surfaces.

Surfaces.

In order to construct lines of intersection of surfaces, you need to be able to construct not only surfaces, but also points located on them. This section covers the most commonly encountered surfaces.

8.1. Prism.

A triangular prism is specified (Fig. 8.1), truncated by a frontally projecting plane (2GPZ, 1 algorithm, module No. 3). S Ç L= t (1234)

Since the prism projects relatively P 1, then the horizontal projection of the intersection line is already in the drawing, it coincides with the main projection of the given prism.

Cutting plane projecting relative to P 2, which means that the frontal projection of the intersection line is in the drawing, it coincides with the frontal projection of this plane.

The profile projection of the intersection line is constructed using two specified projections.

8.2. Pyramid

A truncated trihedral pyramid is given Ф(S,АВС)(Fig.8.2).

This pyramid F intersected by planes S, D And G .

2 GPZ, 2 algorithm (Module No. 3).

F Ç S=123

S ^P 2 Þ S 2 = 1 2 2 2 3 2

1 1 2 1 3 1 And 1 3 2 3 3 3 F .

F Ç D=345

D ^P 2 Þ = 3 2 4 2 5 2

3 1 4 1 5 1 And 3 3 4 3 5 3 are built according to their belonging to the surface F .

F Ç G = 456

G SP 2 Þ Г 2 = 4 2 5 6

4 1 5 1 6 1 And 4 3 5 3 6 3 are built according to their belonging to the surface F .

8.3. Bodies bounded by surfaces of revolution.

Bodies of revolution are geometric figures bounded by surfaces of revolution (ball, ellipsoid of revolution, ring) or a surface of revolution and one or more planes (cone of revolution, cylinder of revolution, etc.). Images on projection planes parallel to the axis of rotation are limited by outline lines. These sketch lines are the boundary between the visible and invisible parts of geometric bodies. Therefore, when constructing projections of lines belonging to surfaces of revolution, it is necessary to construct points located on the outlines.

8.3.1. Rotation cylinder.

P 1, then the cylinder will be projected onto this plane in the form of a circle, and onto the other two projection planes in the form of rectangles, the width of which is equal to the diameter of this circle. Such a cylinder projects to P 1 .

If the axis of rotation is perpendicular P 2, then on P 2 it will be projected as a circle, and on P 1 And P 3 in the form of rectangles.

Similar reasoning for the position of the rotation axis perpendicular to P 3(Fig.8.3).

Cylinder F intersects with planes R, S, L And G(Fig.8.3).

2 GPZ, 1 algorithm (Module No. 3)

F ^P 3

R, S, L, G ^P 2

F Ç R = A(6 5 and )

F ^P 3 Þ Ф 3 = а 3 (6 3 =5 3 и = )

a 2 And a 1 are built according to their belonging to the surface F .

F Ç S = b (5 4 3 )

F Ç S = c (2 3 ) The reasoning is similar to the previous one.

F G = d (12 and

The problems in Figures 8.4, 8.5, 8.6 are solved similarly to the problem in Figure 8.3, since the cylinder

profile-projecting everywhere, and the holes are surfaces projecting relatively

P 1- 2GPZ, 1 algorithm (Module No. 3).

If both cylinders have the same diameters (Fig. 8.7), then their intersection lines will be two ellipses (Monge’s theorem, module No. 3). If the axes of rotation of these cylinders lie in a plane parallel to one of the projection planes, then the ellipses will be projected onto this plane in the form of intersecting line segments.

8.3.2. Cone of rotation

The problems in Figures 8.8, 8.9, 8.10, 8.11, 8.12 -2 GPZ (module No. 3) are solved using algorithm 2, since the surface of the cone cannot be projecting, and the cutting planes are always front-projecting.

Figure 8.13 shows a cone of rotation (body) intersected by two frontally projecting planes G And L. The intersection lines are constructed using algorithm 2.

In Figure 8.14, the surface of the cone of revolution intersects with the surface of the profile-projecting cylinder.

2 GPZ, 2 solution algorithm (module No. 3), that is, the profile projection of the intersection line is in the drawing, it coincides with the profile projection of the cylinder. The other two projections of the intersection line are constructed according to their belonging to the cone of rotation.

Fig.8.14

8.3.3. Sphere.

The surface of the sphere intersects with the plane and with all surfaces of revolution with it, along circles. If these circles are parallel to the projection planes, then they are projected onto them into a circle of natural size, and if they are not parallel, then in the form of an ellipse.

If the axes of rotation of the surfaces intersect and are parallel to one of the projection planes, then all intersection lines - circles - are projected onto this plane in the form of straight segments.

In Fig. 8.15 - sphere, G- plane, L- cylinder, F- frustum.

S Ç G = A- circle;

S Ç L=b- circle;

S Ç Ф =с- circle.

Since the axes of rotation of all intersecting surfaces are parallel P 2, then all intersection lines are circles on P 2 are projected onto line segments.

On P 1: circumference "A" is projected into the true value because it is parallel to it; circle "b" is projected onto a line segment, since it is parallel P 3; circle "With" is projected in the form of an ellipse, which is constructed according to its belonging to the sphere.

First the points are plotted 1, 7 And 4, which define the minor and major axes of the ellipse. Then builds a point 5 , as if lying on the equator of a sphere.

For other points (arbitrary), circles (parallels) are drawn on the surface of the sphere and, based on their affiliation, the horizontal projections of the points lying on them are determined.

9. Examples of completing tasks.

Task 4. Construct three types of parts with the necessary cuts and apply dimensions.

Task 5. Construct three types of parts and make the necessary cuts.

10.Axonometry

10.1. Brief theoretical information about axonometric projections

A complex drawing, composed of two or three projections, having the properties of reversibility, simplicity, etc., at the same time has a significant drawback: it lacks clarity. Therefore, wanting to give a more visual idea of ​​the subject, along with a comprehensive drawing, an axonometric drawing is provided, which is widely used in describing product designs, in operating manuals, in assembly diagrams, to explain drawings of machines, mechanisms and their parts.

Compare two images - an orthogonal drawing and an axonometric drawing of the same model. Which image is easier to read the form? Of course, in an axonometric image. (Fig. 10.1)

The essence of axonometric projection is that geometric figure along with axes rectangular coordinates, to which it is assigned in space, is parallelly projected onto a certain projection plane, called the axonometric projection plane, or picture plane.

If plotted on the coordinate axes x,y And z line segment l (lx,ly,lz) and project onto the plane P ¢ , then we get axonometric axes and segments on them l"x, l"y, l"z(Fig. 10.2)

lx, ly, lz- natural scale.

l = lx = ly = lz

l"x, l"y, l"z- axonometric scales.

The resulting set of projections on P¢ is called axonometry.

The ratio of the length of axonometric scale segments to the length of natural scale segments is called the indicator or coefficient of distortion along the axes, which are designated Kx, Ky, Kz.

Types of axonometric images depend on:

1. From the direction of the projecting rays (they can be perpendicular P"- then the axonometry will be called orthogonal (rectangular) or located at an angle not equal to 90° - oblique axonometry).

2. From the position of the coordinate axes to the axonometric plane.

Three cases are possible here: when all three coordinate axes make up some sharp corners(equal and unequal) and when one or two axes are parallel to it.

In the first case, only rectangular projection is used, (s ^P") in the second and third - only oblique projection (s P") .

If the coordinate axes OX, OY, OZ not parallel to the axonometric plane of projections P", then will they be projected onto it in life size? Of course not. In general, the image of straight lines is always smaller than actual size.

Consider an orthogonal drawing of a point A and its axonometric image.

The position of a point is determined by three coordinates - X A, Y A, Z A, obtained by measuring the links of a natural broken line OA X - A X A 1 – A 1 A(Fig. 10.3).

A"- main axonometric projection of a point A ;

A- secondary projection of the point A(projection of the projection of a point).

Distortion coefficients along the axes X", Y" and Z" will be:

k x = ; k y = ; k y =

In orthogonal axonometry, these indicators are equal to the cosines of the angles of inclination of the coordinate axes to the axonometric plane, and therefore they are always less than one.

They are connected by the formula

k 2 x + k 2 y + k 2 z= 2 (I)

In oblique axonometry, distortion indicators are related by the formula

k x + k y + k z = 2+ctg a (III)

those. any of them can be less than, equal to or greater than one (here a is the angle of inclination of the projecting rays to the axonometric plane). Both formulas are a derivation from Polke's theorem.

Polke's theorem: the axonometric axes on the drawing plane (P¢) and the scales on them can be chosen completely arbitrarily.

(Hence, the axonometric system ( O" X" Y" Z") in the general case is determined by five independent parameters: three axonometric scales and two angles between the axonometric axes).

The angles of inclination of the natural coordinate axes to the axonometric plane of projections and the direction of projection can be chosen arbitrarily, therefore many types of orthogonal and oblique axonometries are possible.

They are divided into three groups:

1. All three distortion indicators are equal (k x = k y = k z). This type of axonometry is called isometric. 3k 2 =2; k= "0.82 - theoretical distortion coefficient. According to GOST 2.317-70, you can use K=1 - reduced distortion factor.

2. Any two indicators are equal (for example, kx=ky kz). This type of axonometry is called dimetry. k x = k z ; k y = 1/2k x 2 ; k x 2 +k z 2 + k y 2 /4 = 2; k = "0.94; k x = 0.94; ky = 0.47; kz = 0.94 - theoretical distortion coefficients. According to GOST 2.317-70, distortion coefficients can be given - k x =1; k y =0.5; k z =1.

3. 3. All three indicators are different (k x ¹ k y ¹ k z). This type of axonometry is called trimetry .

In practice, several types of both rectangular and oblique axonometry are used with the simplest relationships between distortion indicators.

From GOST 2.317-70 and various types axonometric projections, we will consider orthogonal isometry and dimetry, as well as oblique dimetry, as the most frequently used.

10.2.1. Rectangular isometry

In isometry, all axes are inclined to the axonometric plane at the same angle, therefore the angle between the axes (120°) and the distortion coefficient will be the same. Select scale 1: 0.82=1.22; M 1.22:1.

For ease of construction, the given coefficients are used, and then natural dimensions are plotted on all axes and lines parallel to them. The images thus become larger, but this does not affect the clarity.

The choice of axonometry type depends on the shape of the part being depicted. It is easiest to build rectangular isometry, which is why such images are more common. However, when depicting details that include quadrangular prisms and pyramids, their clarity decreases. In these cases, it is better to perform rectangular dimetry.

Oblique diameter should be selected for parts that have a large length with a small height and width (such as a shaft) or when one of the sides of the part contains greatest number important features.

Axonometric projections retain all the properties of parallel projections.

Consider the construction of a flat figure ABCDE .

First of all, let's construct the axes in axonometry. Figure 10.4 shows two ways to construct axonometric axes in isometry. In Fig. 10.4 A shows the construction of axes using a compass, and in Fig. 10.4 b- construction using equal segments.

Fig.10.5

Figure ABCDE lies in the horizontal projection plane, which is limited by the axes OH And OY(Fig. 10.5a). We construct this figure in axonometry (Fig. 10.5b).

How many coordinates does each point lying in the projection plane have? Two.

A point lying in the horizontal plane - coordinates X And Y .

Let's consider the construction t.A. From what coordinate will we start the construction? From coordinates X A .

To do this, measure the value on the orthogonal drawing OA X and put it on the axis X", we get a point A X " . A X A 1 Which axis is parallel? Axles Y. So from t. A X " draw a straight line parallel to the axis Y" and plot the coordinate on it Y A. Received point A" and will be an axonometric projection t.A .

All other points are constructed similarly. Dot WITH lies on the axis OY, which means it has one coordinate.

Figure 10.6 shows a pentagonal pyramid whose base is the same pentagon ABCDE. What needs to be completed to make a pyramid? We need to complete the point S, which is its top.

Dot S- a point in space, therefore it has three coordinates X S, Y S and Z S. First, a secondary projection is constructed S (S 1), and then all three dimensions are transferred from the orthogonal drawing. Connecting S" c A", B", C", D" And E", we obtain an axonometric image of a three-dimensional figure - a pyramid.

10.2.2. Circle isometry

Circles are projected onto a life-size projection plane when they are parallel to that plane. And since all planes are inclined to the axonometric plane, the circles lying on them will be projected onto this plane in the form of ellipses. In all types of axonometry, ellipses are replaced by ovals.

When depicting ovals, you must first of all pay attention to the construction of the major and minor axis. You need to start by determining the position of the minor axis, and the major axis is always perpendicular to it.

There is a rule: the minor axis coincides with the perpendicular to this plane, and the major axis is perpendicular to it, or the direction of the minor axis coincides with an axis that does not exist in this plane, and the major axis is perpendicular to it (Fig. 10.7)

The major axis of the ellipse is perpendicular to the coordinate axis that is absent in the plane of the circle.

The major axis of the ellipse is 1.22 ´ d env; the minor axis of the ellipse is 0.71 ´ d env.

In Figure 10.8 there is no axis in the plane of the circle Z Z ".

In Figure 10.9 there is no axis in the plane of the circle X, so the major axis is perpendicular to the axis X ".

Now let’s look at how an oval is drawn in one of the planes, for example, in the horizontal plane XY. There are many ways to construct an oval, let's get acquainted with one of them.

The sequence of constructing the oval is as follows (Fig. 10.10):

1. The position of the minor and major axis is determined.

2.Through the intersection point of the minor and major axis we draw lines parallel to the axes X" And Y" .

3.On these lines, as well as on the minor axis, from the center with a radius equal to the radius of a given circle, plot the points 1 And 2, 3 And 4, 5 And 6 .

4. Connecting the dots 3 And 5, 4 And 6 and mark the points of their intersection with the major axis of the ellipse ( 01 And 02 ). From the point 5 , radius 5-3 , and from the point 6 , radius 6-4 , draw arcs between points 3 And 2 and dots 4 And 1 .

5. Radius 01-3 draw an arc connecting the points 3 And 1 and radius 02-4 - points 2 And 4 . Ovals are constructed similarly in other planes (Fig. 10.11).

To simplify the construction of a visual image of the surface, the axis Z may coincide with the height of the surface, and the axis X And Y with axes of horizontal projection.

To plot a point A, belonging to the surface, we need to construct its three coordinates X A , Y A And Z A. A point on the surface of a cylinder and other surfaces is constructed in a similar way (Fig. 10.13).

The major axis of the oval is perpendicular to the axis Y ".

When constructing an axonometry of a part limited by several surfaces, the following sequence should be followed:

Option 1.

1. The part is mentally broken down into elementary geometric shapes.

2. The axonometry of each surface is drawn, the construction lines are saved.

3. A 1/4 cutout of the part is created to show the internal configuration of the part.

4. Hatching is applied in accordance with GOST 2.317-70.

Let's consider an example of constructing an axonometry of a part, the outer contour of which consists of several prisms, and inside the part there are cylindrical holes of different diameters.

Option 2. (Fig. 10.5)

1. A secondary projection of the part is constructed on the projection plane P.

2. The heights of all points are plotted.

3. A cutout of 1/4 of the part is constructed.

4. Hatching is applied.

For this part, option 1 will be more convenient for construction.

10.3. Stages of making a visual representation of a part.

1. The part fits into the surface of a quadrangular prism, the dimensions of which are equal to the overall dimensions of the part. This surface is called the wrapping surface.

An isometric image of this surface is performed. The wrapping surface is built according to overall dimensions (Fig. 10.15 A).

Rice. 10.15 A

2. Protrusions are cut out from this surface, located on the top of the part along the axis X and a prism 34 mm high is built, one of the bases of which will be the upper plane of the wrapping surface (Fig. 10.15 b).

Rice. 10.15 b

3. From the remaining prism, cut out a lower prism with a base of 45 ´35 and a height of 11 mm (Fig. 10.15 V).

Rice. 10.15 V

4. Two cylindrical holes are constructed, the axes of which lie on the axis Z. The upper base of the large cylinder lies on the upper base of the part, the second one is 26 mm lower. The lower base of the large cylinder and the upper base of the small one lie in the same plane. The lower base of the small cylinder is built on the lower base of the part (Fig. 10.15 G).

Rice. 10.15 G

5. A 1/4 part of the part is cut out to reveal its internal contour. The cut is made by two mutually perpendicular planes, that is, along the axes X And Y(Fig. 10.15 d).

Fig.10.15 d

6. The sections and the entire remaining part of the part are outlined, and the cut out part is removed. Invisible lines are erased and sections are shaded. The hatching density should be the same as in the orthogonal drawing. The direction of the dashed lines is shown in Fig.10.15 e in accordance with GOST 2.317-69.

The hatch lines will be lines parallel to the diagonals of the squares lying in each coordinate plane, the sides of which are parallel to the axonometric axes.

Fig.10.15 e

7. There is a peculiarity of shading of the stiffener in axonometry. According to the rules

GOST 2.305-68 in a longitudinal section, the stiffener in the orthogonal drawing is not

shaded, and shaded in axonometry. Figure 10.16 shows an example

shading of the stiffener.

10.4 Rectangular dimetry.

A rectangular dimetric projection can be obtained by rotating and tilting the coordinate axes relative to P ¢ so that the distortion indicators along the axes X" And Z" accepted equal value, and along the axis Y"- half as much. Distortion indicators" k x" And " k z" will be equal to 0.94, and " k y "- 0,47.

In practice, the given indicators are used, i.e. along the axes X" And Z" lay down the natural dimensions, and along the axis Y"- 2 times less than natural ones.

Axis Z" usually positioned vertically, axis X"- at an angle of 7°10¢ to the horizontal line, and the axis Y"-at an angle of 41°25¢ to the same line (Fig. 12.17).

1. A secondary projection of the truncated pyramid is constructed.

2. The heights of the points are constructed 1,2,3 And 4.

The easiest way to build an axis X ¢ , putting 8 on the horizontal line equal parts and down a vertical line 1 same part.

To build an axis Y" at an angle of 41°25¢, you need to put 8 parts on a horizontal line, and 7 of the same parts on a vertical line (Fig. 10.17).

Figure 10.18 shows a truncated quadrangular pyramid. To make it easier to construct it in axonometry, the axis Z must coincide with the height, then the tops of the base ABCD will lie on the axes X And Y (A and S Î X ,IN And D Î y). How many coordinates do points 1 and have? Two. Which? X And Z .

These coordinates are plotted in natural size. The resulting points 1¢ and 3¢ are connected to points A¢ and C¢.

Points 2 and 4 have two Z coordinates and Y. Since they have the same height, the coordinate Z is deposited on the axis Z". Through the received point 0 ¢ draw a line parallel to the axis Y, on which the distance is plotted on both sides of the point 0 1 4 1 reduced by half.

Received points 2 ¢ And 4 ¢ connect to dots IN ¢ And D" .

10.4.1. Constructing circles in rectangular dimensions.

Circles lying on coordinate planes in rectangular dimetry, as well as in isometry, will be depicted as ellipses. Ellipses located on planes between axes X" And Y",Y" And Z" in the reduced dimetry will have a major axis equal to 1.06d, and a minor axis equal to 0.35d, and in the plane between the axes X" And Z"- the major axis is also 1.06d, and the minor axis is 0.95d (Fig. 10.19).

Ellipses are replaced by four-cent ovals, as in isometry.

10.5. Oblique dimetric projection (frontal)

If we place the coordinate axes X And Y parallel to the P¢ plane, then the distortion indicators along these axes will become equal to one (k = t=1). Axis distortion index Y usually taken equal to 0.5. Axonometric axes X" And Z" make a right angle, axis Y" usually drawn as the bisector of this angle. Axis X can be directed either to the right of the axis Z", and to the left.

It is preferable to use the right-hand system, since it is more convenient to depict objects in dissected form. In this type of axonometry, it is good to draw parts that have the shape of a cylinder or cone.

For the convenience of depicting this part, the axis Y must be aligned with the axis of rotation of the cylinder surfaces. Then all circles will be depicted in natural size, and the length of each surface will be halved (Fig. 10.21).

11. Inclined sections.

When making drawings of machine parts, it is often necessary to use inclined sections.

When solving such problems, it is necessary first of all to understand: how the cutting plane should be located and which surfaces are involved in the section in order for the part to be read better. Let's look at examples.

Given a tetrahedral pyramid, which is dissected by an inclined frontally projecting plane A-A(Fig. 11.1). The cross section will be a quadrilateral.

First we construct its projections onto P 1 and on P 2. The frontal projection coincides with the projection of the plane, and we construct the horizontal projection of the quadrangle according to its membership in the pyramid.

Then we construct the natural size of the section. To do this, an additional projection plane is introduced P 4, parallel to a given cutting plane A-A, we project a quadrilateral onto it, and then combine it with the drawing plane.

This is the fourth main task of converting a complex drawing (module No. 4, p. 15 or task No. 117 from workbook in descriptive geometry).

Constructions are carried out in the following sequence (Fig. 11.2):

1. 1.On a free space in the drawing, draw a center line parallel to the plane A-A .

2. 2. From the points of intersection of the edges of the pyramid with the plane, we draw projecting rays perpendicular to the cutting plane. Points 1 And 3 will lie on a line perpendicular to the axial one.

3. 3.Distance between points 2 And 4 transferred from horizontal projection.

4. Similarly, the true size of the section of the surface of revolution is constructed - an ellipse.

Distance between points 1 And 5 -major axis of the ellipse. The minor axis of the ellipse must be constructed by dividing the major axis in half ( 3-3 ).

Distance between points 2-2, 3-3, 4-4 transferred from horizontal projection.

Let's consider more complex example, including polyhedral surfaces and surfaces of revolution (Fig. 11.3)

A tetrahedral prism is specified. There are two holes in it: a prismatic one, located horizontally, and a cylindrical one, the axis of which coincides with the height of the prism.

The cutting plane is front-projecting, so the frontal projection of the section coincides with the projection of this plane.

Quadrangular prism projecting to the horizontal plane of projections, and therefore the horizontal projection of the section is also in the drawing, it coincides with the horizontal projection of the prism.

The actual size of the section into which both prisms and the cylinder fall is constructed on a plane parallel to the cutting plane A-A(Fig. 11.3).

Sequence of performing an inclined section:

1. The section axis is drawn parallel to the cutting plane on the free field of the drawing.

2. A cross-section of the external prism is constructed: its length is transferred from the frontal projection, and the distance between the points from the horizontal one.

3. A cross section of the cylinder is constructed - part of the ellipse. First, characteristic points are constructed that determine the length of the minor and major axis ( 5 4 , 2 4 -2 4 ) and points limiting the ellipse (1 4 -1 4 ) , then additional points (4 4 -4 4 And 3 4 -3 4).

4. A cross section of the prismatic hole is constructed.

5. Hatching is applied at an angle of 45° to the main inscription, if it does not coincide with the contour lines, and if it does, then the hatching angle can be 30° or 60°. The hatching density on the section is the same as on the orthogonal drawing.

The inclined section can be rotated. In this case, the designation is accompanied by the sign. It is also allowed to show half of the inclined section figure if it is symmetrical. A similar arrangement of an inclined section is shown in Fig. 13.4. Point designations can be omitted when constructing an inclined section.

Figure 11.5 shows a visual representation of a given figure with a section by plane A-A .

Control questions

1. What is a species called?

2. How do you get an image of an object on a plane?

3.What names are assigned to the views on the main projection planes?

4.What is called the main species?

5.What is called additional view?

6. What is called a local species?

7.What is a cut called?

8. What symbols and inscriptions are installed for sections?

9. What is the difference between simple cuts and complex ones?

10.What conventions are followed when making broken cuts?

11. Which incision is called local?

12. Under what conditions is it permissible to combine half the view and half the section?

13. What is called a section?

14. How are the sections arranged in the drawings?

15. What is called a remote element?

16. How are repeating elements shown in a drawing in a simplified manner?

17. How do you conventionally shorten the image of long objects in a drawing?

18. How do axonometric projections differ from orthogonal ones?

19. What is the principle of formation of axonometric projections?

20. What types of axonometric projections are established?

21. What are the features of isometry?

22. What are the features of dimetry?

Bibliography

1. Suvorov, S.G. Mechanical engineering drawing in questions and answers: (reference book) / S.G. Suvorov, N.S. Suvorova. - 2nd ed. reworked and additional - M.: Mechanical Engineering, 1992.-366 p.

2. Fedorenko V.A. Handbook of mechanical engineering drawing / V.A. Fedorenko, A.I. Shoshin, - Ed. 16-ster.; m Reprint. from the 14th edition 1981-M.: Alliance, 2007.-416 p.

3. Bogolyubov, S.K. Engineering graphics: Textbook for environments. specialist. textbook establishments for special purposes tech. profile/ S.K. Bogolyubov.-3rd ed., revised. and additional - M.: Mechanical Engineering, 2000.-351 p.

4. Vyshnepolsky, I.S. Technical drawing e. Textbook. for the beginning prof. education / I.S. Vyshnepolsky. - 4th ed., revised. and additional; Grif MO.- M.: Higher. school: Academy, 2000.-219 p.

5. Levitsky, V.S. Mechanical engineering drawing and automation of drawings: textbook. for colleges/V.S.Levitsky.-6th ed., revised. and additional; Grif MO.-M.: Higher. school, 2004.-435p.

6. Pavlova, A.A. Descriptive geometry: textbook. for universities/ A.A. Pavlova-2nd ed., revised. and additional; Grif MO.- M.: Vlados, 2005.-301p.

7. GOST 2.305-68*. Images: views, sections, sections/Unified system of design documentation. - M.: Standards Publishing House, 1968.

8. GOST 2.307-68. Application of dimensions and maximum deviations/Unified system

design documentation. - M.: Standards Publishing House, 1968.

Rectangular isometry called an axonometric projection, in which the distortion coefficients along all three axes are equal, and the angles between the axonometric axes are 120. In Fig. Figure 1 shows the position of the axonometric axes of rectangular isometry and methods for their construction.

Rice. 1. Construction of axonometric axes of rectangular isometry using: a) segments; b) compass; c) squares or protractor.

For practical constructions, the distortion coefficient (K) along the axonometric axes according to GOST 2.317-2011 is recommended to be equal to one. In this case, the image is larger in comparison with the theoretical or exact image with distortion coefficients of 0.82. The magnification is 1.22. In Fig. Figure 2 shows an example of an image of a part in a rectangular isometric projection.

Rice. 2. Isometric part.

Construction of plane figures in isometry

A regular hexagon ABCDEF is given, located parallel to the horizontal projection plane H (P 1).

a) Construct isometric axes (Fig. 3).

b) The coefficient of distortion along the axes in isometry is equal to 1, therefore, from the point O 0 along the axes we plot the natural values ​​of the segments: A 0 O 0 = AO; О 0 D 0 = ОD; K 0 O 0 = KO; O 0 P 0 = OR.

c) Lines parallel to the coordinate axes are drawn in isometry also parallel to the corresponding isometric axes in full size.

In our example, sides BC and FE parallel to the axis X.

In isometry, they are also drawn parallel to the X axis in full size B 0 C 0 = BC; F 0 E 0 = FE.

d) By connecting the resulting points, we obtain an isometric image of the hexagon in the H plane (P 1).

Rice. 3. Isometric projection of a hexagon in a drawing

and in the horizontal plane of projection

In Fig. Figure 4 shows projections of the most common flat figures in various projection planes.

The most common shape is a circle. The isometric projection of a circle is generally an ellipse. An ellipse is constructed from points and traced along a pattern, which is very inconvenient in drawing practice. Therefore, ellipses are replaced with ovals.

In Fig. 5, a cube is constructed in isometry with circles inscribed in each face of the cube. When making isometric constructions, it is important to correctly position the axes of the ovals depending on the plane in which the circle is supposed to be drawn. As can be seen in Fig. The 5 major axes of the ovals are located along the larger diagonal of the rhombuses into which the faces of the cube are projected.

Rice. 4 Isometric image of flat figures

a) on the drawing; b) on the H plane; c) on plane V; d) on plane W.

For rectangular axonometry of any type, the rule for determining the main axes of the oval ellipse into which a circle lying in any projection plane is projected can be formulated as follows: the major axis of the oval is located perpendicular to the axonometric axis that is absent in this plane, and the minor coincides with the direction of this axis. The shape and size of the ovals in each plane of isometric projections are the same.

Axonometric views of machine parts and assemblies are often used in design documentation in order to clearly show design features parts (assembly), imagine what the part (assembly) looks like in space. Depending on the angle at which the coordinate axes are located, axonometric projections are divided into rectangular and oblique.

You will need

• Drawing program, pencil, paper, eraser, protractor.

Instructions

Rectangular projections. Isometric projection. When constructing a rectangular isometric projection, take into account the distortion coefficient along the X, Y, Z axes, equal to 0.82, while , parallel to the projection planes, are projected onto the axonometric projection planes in the form of ellipses, the axis of which is equal to d, and the axis is 0.58d, where d – diameter of the original circle. For ease of calculations, isometric projection without distortion along the axes (distortion coefficient is 1). In this case, the projected circles will look like ellipses with an axis equal to 1.22d and a minor axis equal to 0.71d.

Dimetric projection. When constructing a rectangular dimetric projection, the distortion coefficient along the X and Z axes is equal to 0.94, and along the Y axis – 0.47. To dimetric projection in a simplified manner, they are performed without distortion along the X and Z axes and with a distortion coefficient along the Y axis = 0.5. A circle parallel to the frontal projection plane is projected onto it in the form of an ellipse with a major axis equal to 1.06d and a minor axis equal to 0.95d, where d is the diameter of the original circle. Circles parallel to two other axonometric planes are projected onto them in the form of ellipses with axes equal to 1.06d and 0.35d, respectively.

Oblique projections. Frontal isometric view. When constructing a frontal isometric projection, the standard establishes the optimal angle of inclination of the Y axis to the horizontal at 45 degrees. Allowed angles of inclination of the Y axis to the horizontal are 30 and 60 degrees. The distortion coefficient along the X, Y and Z axes is 1. Circle 1, located on the frontal projection plane, is projected onto it without distortion. Circles parallel to the horizontal and profile planes of projections are made in the form of ellipses 2 and 3 with a major axis equal to 1.3d and a minor axis equal to 0.54d, where d is the diameter of the original circle.

Horizontal isometric projection. A horizontal isometric projection of a part (assembly) is built on axonometric axes located as shown in Fig. 7. It is allowed to change the angle between the Y axis and the horizontal by 45 and 60 degrees, leaving unchanged the angle of 90 degrees between the Y and X axes. The distortion coefficient along the X, Y, Z axes is 1. A circle lying in a plane parallel to the horizontal projection plane is projected as circle 2 without distortion. Circles parallel to the frontal and profile planes of projections, type of ellipses 1 and 3. The dimensions of the axes of the ellipses are related to the diameter d of the original circle by the following dependencies:
ellipse 1 – major axis is 1.37d, minor axis is 0.37d; ellipse 3 – major axis is 1.22d, minor axis is 0.71d.

Frontal dimetric projection. An oblique frontal dimetric projection of a part (assembly) is built on axonometric axes similar to the axes of the frontal isometric projection, but from it by a distortion coefficient along the Y axis, which is equal to 0.5. On the X and Z axes, the distortion coefficient is 1. It is also possible to change the angle of the Y axis to the horizontal to values ​​of 30 and 60 degrees. A circle lying in a plane parallel to the frontal axonometric plane of projections is projected onto it without distortion. Circles parallel to the planes of horizontal and profile projections are drawn in the form of ellipses 2 and 3. The dimensions of the ellipses on the size of the diameter of the circle d are expressed by the dependence:
the major axis of ellipses 2 and 3 is 1.07d; the minor axis of ellipses 2 and 3 is 0.33d.

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note

Axonometric projection (from ancient Greek ἄξων “axis” and ancient Greek μετρέω “I measure”) is a method of depicting geometric objects in a drawing using parallel projections.

Helpful advice

The plane onto which the projection is made is called axonometric or picture. An axonometric projection is called rectangular if, during parallel projection, the projecting rays are perpendicular to the picture plane (=90) and oblique if the rays make an angle of 0 with the picture plane

Sources:

• Handbook of Drawing
• axonometric projection of a circle

The image of an object in the drawing should give a complete idea of ​​its shape and design features and can be done using rectangular projection, linear perspective and axonometric projection.

Instructions

Remember that dimetry is one of the types of axonometric projection of an object, in which the image is rigidly tied to the natural Oxyz coordinate system. Dimetry in that two distortion coefficients along the axes are equal and different from the third. Dimetry rectangular and frontal.

With a rectangular diameter, the z axis is vertical, the x axis with a horizontal line is at an angle of 7011`, and the y angle is 410 25`. The reduced distortion coefficient along the y-axis is ky = 0.5 (real 0.47), kx = kz = 1 (real 0.94). GOST 2.317–69 recommends using only the given coefficients when constructing images in a rectangular dimetric projection.

To draw a rectangular dimetric projection, mark the vertical Oz axis on the drawing. To construct the x-axis, draw in the drawing a rectangle with legs 1 and 8 units, the vertex of which is point O. The hypotenuse of the rectangle will become the x-axis, which deviates from the horizon at an angle of 7011`. To construct the y-axis, also draw right triangle with the vertex at point O. The size of the legs in this case is 7 and 8 units. The resulting hypotenuse will be the y-axis, deviating from the horizon at an angle of 410 25`.

When constructing a dimetric projection, the size of the object is increased by 1.06 times. In this case, the image is projected into an ellipse in the xOy and yO coordinate planes with a major axis equal to 1.06d, where d is the diameter of the projected circle. The minor axis of the ellipse is 0.35 d.

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note

Many industries use drawings. The rules for depicting objects and drawing up drawings are regulated by the “Unified System of Design Documentation” (ESKD).

To make any part, you need to design it and produce drawings. The drawing should show the main and auxiliary views of the part, which, if read correctly, provide all the necessary information about the shape and dimensions of the product.

Instructions

How, designing new parts, studying state and industry standards according to which design documentation is carried out. Find all GOSTs and OSTs that will be needed when drawing the part. To do this, you need standards numbers by which you can find them on the Internet in electronic form or in the enterprise archive in paper form.

Before you start drawing, select the required sheet on which it will be located. Consider the number of projections of the part that you need to depict in the drawing. For parts of simple shape (especially for bodies of revolution), the main view and one projection are sufficient. If the designed part has a complex shape, a large number of through and blind holes, grooves, then it is advisable to make several projections, as well as provide additional local views.

Draw the main view of the part. Choose the view that will give the most complete idea of ​​the shape of the part. Make other views if necessary. Draw cuts and sections showing the internal holes and grooves of the part.

Apply dimensions in accordance with GOST 2.307-68. Overall dimensions are better than the size of the part, so put these dimensions so that they can be easily identified on the drawing. Enter all dimensions with tolerances or indicate the quality according to which the part should be manufactured. Remember that in real life, produce a part with exact dimensions. There will always be a deviation upward or downward, which should be within the tolerance range for the size.

Be sure to indicate the surface roughness of the part in accordance with GOST 2.309-73. This is very important, especially for precision instrument-making parts that are part of assembly units and are connected by fit.

Write down the technical requirements for the part. Indicate its manufacture, processing, coating, operation and storage. In the title block of the drawing, do not forget to indicate the material from which the part is made.

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When designing and practically debugging power supply systems, it is necessary to use various schemes. Sometimes they are given in ready-made form, attached to the technical system, but in some cases you have to draw the diagram yourself, restoring it based on installation and connections. How accessible it will be to understand depends on the correct drawing of the diagram.

Instructions

Use the Visio computer program to draw a power supply diagram. For accumulation, you can first diagram an abstract supply circuit, including an arbitrary set of elements. In accordance with standards and requirements unified system The design concept is drawn in a single-line drawing.

Select Page Options settings. In the “File” menu, use the appropriate command, and in the window that opens, set the required format for the future image, for example, A3 or A4. Also select portrait or landscape drawing orientation. Set the scale to 1:1, and the unit of measurement to millimeters. Complete your selection by clicking on the “OK” button.

Using the "Open" menu, find the stencil library. Open the set of main inscriptions and transfer the frame, inscription shape and additional columns to the sheet of the future drawing. Fill in the necessary columns that explain the diagram.

Draw the actual supply circuit diagram using stencils from the program, or use other blanks at your disposal. Convenient to use a specially designed drawing kit electrical diagrams various supply circuits.

Since many components of the power supply circuit of individual groups are often of the same type, draw similar ones by copying already drawn elements, and then make adjustments. In this case, select the elements of the group with the mouse and move the copied fragment to the desired place in the diagram.

Finally, move the input circuit components from the stencil set. Carefully fill out the explanatory notes for the diagram. Save the changes with the desired name. If necessary, print the finished power supply diagram.

Constructing an isometric projection of a part allows you to obtain the most detailed understanding of the spatial characteristics of the image object. Isometric with cutout of part of the part in addition to appearance shows the internal structure of an object.

You will need

• - a set of drawing pencils;
• - ruler;
• - squares;
• - protractor;
• - compass;
• - eraser.

Instructions

Draw the axes with thin lines so that the image is located in the center of the sheet. In a rectangular isometry The angles between the axes are one hundred degrees. In a horizontal oblique isometry the angles between the X and Y axes are ninety degrees. And between the X and Z axes; Y and Z - one hundred thirty-five degrees.

Start from the top surface of the part being depicted. From the corners horizontal surfaces draw vertical lines down and mark the corresponding linear dimensions from the part drawing on these lines. IN isometry linear dimensions along all three axes remain unity. Consistently connect the resulting points on vertical lines. The outer contour of the part is ready. Draw images of holes, grooves, etc. on the edges of the part.

Remember that when depicting objects in isometry the visibility of curved elements will be distorted. Circumference in isometry is depicted as an ellipse. Distance between ellipse points along axes isometry equal to the diameter of the circle, and the axes of the ellipse do not coincide with the axes isometry.

All actions must be performed using drawing tools - ruler, pencil, compass and protractor. Use several pencils of different hardnesses. Hard - for thin lines, hard - for dotted and dash-dotted lines, soft - for main lines. Do not forget to draw and fill out the main inscription and frame in accordance with GOST. Also construction isometry can be performed in specialized software such as Compass, AutoCAD.

Sources:

• isometric drawing

There are not many people these days who have never had to draw or draw something on paper in their lives. The ability to make a simple drawing of any design is sometimes very useful. You can spend a lot of time explaining “on your fingers” how this or that thing is made, while one glance at its drawing is enough to understand it without any words.

You will need

• – sheet of whatman paper;
• – drawing accessories;
• - drawing board.

Instructions

Select the sheet format on which the drawing will be drawn - in accordance with GOST 9327-60. The format should be such that the main information can be placed on the sheet kinds details in the appropriate scale, as well as all necessary cuts and sections. For simple parts, choose A4 (210x297 mm) or A3 (297x420 mm) format. The first can be positioned with its long side only vertically, the second - vertically and horizontally.

Draw a frame for the drawing, 20 mm from the left edge of the sheet, 5 mm from the other three. Draw the main inscription - a table in which all data about details and drawing. Its dimensions are determined by GOST 2.108-68. The width of the main inscription remains unchanged - 185 mm, the height varies from 15 to 55 mm depending on the purpose of the drawing and the type of institution for which it is being carried out.

Select the main image scale. Possible scales are determined by GOST 2.302-68. They should be chosen so that all the main elements are clearly visible in the drawing. details. If some places are not visible clearly enough, they can be taken out a separate species, shown with the necessary magnification.

Select main image details. It should represent the direction of viewing the part (direction of projection) from which its design is most fully revealed. In most cases, the main image is the position in which the part is on the machine during the main operation. Parts that have an axis of rotation are located on the main image, as a rule, so that the axis has a horizontal position. The main image is located at the top left of the drawing (if there are three projections) or close to the center (if there is no side projection).

Determine the location of the remaining images (side view, top view, sections, sections). Kinds details are formed by its projection onto three or two mutually perpendicular planes (Monge's method). In this case, the part must be positioned in such a way that most or all of its elements are projected without distortion. If any of these types is informationally redundant, do not perform it. The drawing should have only those images that are necessary.

Select the cuts and sections to be made. Their difference from each other is that it also shows what is located behind the cutting plane, while the section displays only what is located in the plane itself. The cutting plane can be stepped or broken.

Proceed directly to drawing. When drawing lines, follow GOST 2.303-68, which defines kinds lines and their parameters. Place the images at such a distance from each other that there is enough space for setting dimensions. If the cutting planes pass along the monolith details, hatch the sections with lines running at an angle of 45°. If the hatch lines coincide with the main lines of the image, you can draw them at an angle of 30° or 60°.

Draw dimension lines and mark down the dimensions. In doing so, be guided by the following rules. The distance from the first dimension line to the outline of the image must be at least 10 mm, the distance between adjacent dimension lines must be at least 7 mm. The arrows should be about 5 mm long. Write numbers in accordance with GOST 2.304-68, take their height to be 3.5-5 mm. Place the numbers closer to the middle of the dimension line (but not on the image axis) with some offset relative to the numbers placed on adjacent dimension lines.

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Sources:

• Electronic textbook on engineering graphics

The ratio of angles and planes of any object visually changes depending on the object’s position in space. That is why the part in the drawing is usually performed in three orthogonal projections, to which a spatial image is added. Usually this . When performing it, vanishing points are not used, as when constructing a frontal perspective. Therefore, the dimensions do not change as they move away from the observer.

You will need

• - ruler;
• - compass;
• - paper.

Instructions

Define the axes. To do this, draw a circle of arbitrary radius from point O. Its central angle is 360º. Divide the circle into 3 equal ones, using the OZ axis as the base radius. In this case, the angle of each sector will be equal to 120º. The two radii exactly represent the OX and OY axes you need.

Determine the position. Divide the angles between the axes in half. Connect point O to these new points with thin lines. Center position circle depends on conditions. Mark it with a dot and draw a perpendicular to it in both directions. This line will determine the position of the large diameter.

Calculate the diameters. They depend on whether you apply a distortion factor or not. This coefficient for all axes is 0.82, but quite often it is rounded and taken as 1. Taking into account the distortion, the major and minor diameters of the ellipse are 1 and 0.58 of the original, respectively. Without applying the coefficient, these dimensions are 1.22 and 0.71 of the diameter of the original circle.

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To create a three-dimensional image, you can construct not only an isometric, but also a dimetric projection, as well as a frontal or linear perspective. Projections are used in detail drawings, while perspectives are used primarily in architecture. A circle in dimetry is also depicted as an ellipse, but there is a different arrangement of axes and different distortion coefficients. When performing various types of perspectives, changes in size with distance from the observer are taken into account.

In order to obtain an axonometric projection of an object (Fig. 106), it is necessary to mentally: place the object in the coordinate system; select an axonometric projection plane and place the object in front of it; choose the direction of parallel projecting rays, which should not coincide with any of the axonometric axes; direct the projecting rays through all points of the object and coordinate axes until they intersect with the axonometric plane of projections, thereby obtaining an image of the projected object and coordinate axes.

On the axonometric plane of projections, an image is obtained - an axonometric projection of an object, as well as projections of the axes of coordinate systems, which are called axonometric axes.

An axonometric projection is an image obtained on an axonometric plane as a result of parallel projection of an object along with a coordinate system, which visually displays its shape.

The coordinate system consists of three mutually intersecting planes that have a fixed point - the origin (point O) and three axes (X, Y, Z) emanating from it and located at right angles to each other. The coordinate system allows you to make measurements along the axes, determining the position of objects in space.

Rice. 106. Obtaining an axonometric (rectangular isometric) projection

Many axonometric projections can be obtained, differently placing the object in front of the plane and choosing different directions of the projecting rays (Fig. 107).

The most commonly used is the so-called rectangular isometric projection (in the future we will use its abbreviated name - isometric projection). An isometric projection (see Fig. 107, a) is a projection in which the distortion coefficients along all three axes are equal, and the angles between the axonometric axes are 120°. An isometric projection is obtained using parallel projection.

Rice. 107. Axonometric projections established by GOST 2.317-69:
a - rectangular isometric projection; b - rectangular dimetric projection;
c - oblique frontal isometric projection;
d - oblique frontal dimetric projection

Rice. 107. Continued: d - oblique horizontal isometric projection

In this case, the projecting rays are perpendicular to the axonometric plane of projections, and the coordinate axes are equally inclined to the axonometric plane of projections (see Fig. 106). If you compare the linear dimensions of an object and the corresponding dimensions of the axonometric image, you can see that in the image these dimensions are smaller than the actual ones. Values ​​showing the ratio of the sizes of projections of straight segments to their actual sizes are called distortion coefficients. The distortion coefficients (K) along the axes of the isometric projection are the same and equal to 0.82, however, for ease of construction, the so-called practical distortion coefficients are used, which are equal to unity (Fig. 108).

Rice. 108. Position of axes and coefficients of distortion of isometric projection

There are isometric, dimetric and trimetric projections. Isometric projections include those projections that have the same distortion coefficients on all three axes. Dimetric projections are those projections in which two coefficients of distortion along the axes are the same, and the value of the third differs from them. Trimetric projections are projections in which all distortion coefficients are different.