Practical and graphic work on drawing. Practical and graphic work on drawing “Modeling from a drawing”

Workbook

Introduction to the Subject of Drawing

The history of the emergence of graphic methods of images and drawings

Drawings in Rus' were made by “draftsmen”, a mention of which can be found in the “Pushkar Order” of Ivan IV.

Other images – drawings and drawings – were a bird’s eye view of the structure.

At the end of the 12th century. In Russia, large-scale images are introduced and dimensions are indicated. In the 18th century, Russian draftsmen and Tsar Peter I himself made drawings using the method of rectangular projections (the founder of the method is the French mathematician and engineer Gaspard Monge). By order of Peter I, the teaching of drawing was introduced in all technical educational institutions.

The entire history of the development of the drawing is inextricably linked with technical progress. Currently, the drawing has become the main document of business communication in science, technology, production, design, and construction.

It is impossible to create and check a machine drawing without knowing the basics of the graphic language. Which you will meet while studying the subject "Drawing"

Types of graphic images

Exercise: label the names of the images.

The concept of GOST standards. Formats. Frame. Drawing lines.

Exercise 1

Graphic work No. 1

"Formats. Frame. Drawing lines"

Examples of work performed

Test tasks for graphic work No. 1

Option #1.

1. What designation according to GOST has a format of size 210x297:

a) A1; b) A2; c) A4?

2. What is the thickness of the dash-dot line if in the drawing the solid main thick line is 0.8 mm:

a) 1mm: b) 0.8 mm: c) 0.3 mm?

______________________________________________________________

Option #2.

Select and underline the correct answers to the questions.

1. Where in the drawing is the main inscription located:

a) in the lower left corner; b) in the lower right corner; c) in the upper right corner?

2. How much should the axial and center lines extend beyond the contour of the image:

a) 3…5 mm; b) 5…10 mm4 c) 10…15 mm?

Option #3.

Select and underline the correct answers to the questions.

1. What arrangement of A4 format is allowed by GOST:

A) vertical; b) horizontal; c) vertical and horizontal?

2. . What is the thickness of a solid thin line if in the drawing the solid main thick line is 1 mm:

a) 0.3 mm: b) 0.8 mm: c) 0.5 mm?

Option number 4.

Select and underline the correct answers to the questions.

1. At what distance from the edges of the sheet is the drawing frame drawn:

a) left, top, right and bottom – 5 mm each; b) left, top and bottom – 10 mm, right – 25 mm; c) left – 20 mm, top, right and bottom – 5 mm each?

2. What type of line are the axial and center lines made in the drawings:

a) a solid thin line; b) dash-dotted line; c) dashed line?

Option #5.

Select and underline the correct answers to the questions.

1. What are the dimensions of the A4 format according to GOST:

a) 297x210 mm; b) 297x420 mm; c) 594x841 mm?

2. Depending on which line the thickness of the drawing lines is selected:

a) dash-dotted line; b) a solid thin line; c) a solid main thick line?

Fonts (GOST 2304-81)

Font types:

Font sizes:

Practical tasks:

Calculations of drawing font parameters

Test tasks

Option #1.

Select and underline the correct answers to the questions.

What value is taken as the font size:

a) the height of a lowercase letter; b) height of capital letter; c) the height of the spaces between the lines?

Option #2.

Select and underline the correct answers to the questions.

What is the height of the capital letter of rift No. 5:

a) 10 mm; b) 7 mm; c) 5 mm; d) 3.5 mm?

Option #3.

Select and underline the correct answers to the questions.

What is the height of lowercase letters that have protruding elements? c, d, b, r, f:

a) the height of the capital letter; b) the height of a lowercase letter; c) greater than the height of the capital letter?

Option number 4.

Select and underline the correct answers to the questions.

Are uppercase and lowercase letters different in writing? A, E, T, G, I:

a) differ; b) do not differ; c) do they differ in the spelling of individual elements?

Option #5.

Select and underline the correct answers to the questions.

What does the height of the numbers of a drawing font correspond to:

a) the height of a lowercase letter; b) the height of the capital letter; c) half the height of a capital letter?

Graphic work No. 2

"Drawing of a flat part"

Cards - tasks

1 option

Option 2

Option 3

Option 4

Geometric constructions

Dividing a circle into 5 and 10 parts

Dividing a circle into 4 and 8 parts

Dividing a circle into 3, 6 and 12 parts

Dividing a segment into 9 parts

Fixing the material

Practical work:

Based on these types, build a third one. Scale 1:1

Option #1

Option No. 2

Option #3

Option No. 4

Fixing the material

Write your answers in your workbook:

Option #1

Option No. 2

Practical work No. 3

"Modeling from a drawing."

Directions for use

To make a cardboard model, first cut out its blank. Determine the dimensions of the workpiece from the image of the part (Fig. 58). Mark (outline) the cutouts. Cut them along the outlined contour. Remove the cut out parts and bend the model according to the drawing. To prevent the cardboard from straightening after bending, draw lines on the outside of the bend with some sharp object.

The wire for modeling must be soft and of arbitrary length (10 – 20 mm).

Fixing the material

Option No. 1 Option No. 2

Fixing the material

In your workbook, draw a drawing of the part in 3 views. Apply dimensions.

Option No. 3 Option No. 4

Fixing the material

Working with cards

Fixing the material

Using colored pencils, complete the task on the card.

Amount (increasing)

Clipping

Reinforcement task

Oval -

Algorithm for constructing an oval

1. Construct an isometric projection of a square - rhombus ABCD

2. Let us denote the points of intersection of the circle and the square 1 2 3 4

3. From the top of the rhombus (D) draw a straight line to point 4 (3). We obtain segment D4, which will be equal to the radius of the arc R.

4. Let's draw an arc that will connect points 3 and 4.

5. At the intersection of segment B2 and AC, we obtain point O1.

When the segment D4 and AC intersect, we obtain point O2.

6. From the resulting centers O1 and O2 we will draw arcs R1 that will connect points 2 and 3, 4 and 1.

Fixing the material

Complete a technical drawing of the part, two views of which are shown in Fig. 62

Graphic work No. 9

Part sketch and technical drawing

1. What is called sketch?

Fixing the material

Exercise tasks

Practical work No. 7

"Reading Blueprints"

Graphic dictation

“Drawing and technical drawing of a part based on a verbal description”

Option #1

Frame is a combination of two parallelepipeds, of which the smaller one is placed with a larger base in the center of the upper base of the other parallelepiped. A through stepped hole runs vertically through the centers of the parallelepipeds.

The total height of the part is 30 mm.

The height of the lower parallelepiped is 10 mm, length 70 mm, width 50 mm.

The second parallelepiped has a length of 50 mm and a width of 40 mm.

The diameter of the bottom step of the hole is 35 mm, height 10 mm; diameter of the second stage is 20 mm.

Note:

Option No. 2

Support is a rectangular parallelepiped, to the left (smallest) face of which is attached a half-cylinder, which has a common lower base with the parallelepiped. In the center of the upper (largest) face of the parallelepiped, along its long side, there is a prismatic groove. At the base of the part there is a through hole of a prismatic shape. Its axis coincides in the top view with the axis of the groove.

The height of the parallelepiped is 30 mm, length 65 mm, width 40 mm.

Half-cylinder height 15 mm, base R 20 mm.

The width of the prismatic groove is 20 mm, the depth is 15 mm.

Hole width 10 mm, length 60 mm. The hole is located at a distance of 15 mm from the right edge of the support.

Note: When drawing dimensions, consider the part as a whole.

Option No. 3

Frame is a combination of a square prism and a truncated cone, which stands with its large base in the center of the upper base of the prism. A through stepped hole runs along the axis of the cone.

The total height of the part is 65 mm.

The height of the prism is 15 mm, the size of the sides of the base is 70x70 mm.

The height of the cone is 50 mm, the lower base is Ǿ 50 mm, the upper base is Ǿ 30 mm.

The diameter of the lower part of the hole is 25 mm, height 40 mm.

The diameter of the upper part of the hole is 15 mm.

Note: When drawing dimensions, consider the part as a whole.

Option No. 4

Sleeve is a combination of two cylinders with a stepped through hole that runs along the axis of the part.

The total height of the part is 60 mm.

The height of the lower cylinder is 15 mm, the base is Ǿ 70 mm.

The base of the second cylinder is 45 mm.

Bottom hole Ǿ 50 mm, height 8 mm.

Upper part of the hole Ǿ 30 mm.

Note: When drawing dimensions, consider the part as a whole.

Option No. 5

Base is a parallelepiped. In the center of the upper (largest) face of the parallelepiped, along its long side, there is a prismatic groove. There are two through cylindrical holes in the groove. The centers of the holes are spaced from the ends of the part at a distance of 25 mm.

The height of the parallelepiped is 30 mm, length 100 mm, width 50 mm.

Groove depth 15 mm, width 30 mm.

Hole diameters are 20 mm.

Note: When drawing dimensions, consider the part as a whole.

Option No. 6

Frame It is a cube, along the vertical axis of which there is a through hole: semi-conical at the top, and then turning into a stepped cylindrical one.

Cube edge 60 mm.

The depth of the semi-conical hole is 35 mm, the upper base is 40 mm, the bottom is 20 mm.

The height of the bottom step of the hole is 20 mm, the base is 50 mm. The diameter of the middle part of the hole is 20 mm.

Note: When drawing dimensions, consider the part as a whole.

Option No. 7

Support is a combination of a parallelepiped and a truncated cone. The cone with its large base is placed in the center of the upper base of the parallelepiped. In the center of the smaller side faces of the parallelepiped there are two prismatic cutouts. A through hole of cylindrical shape Ǿ 15 mm is drilled along the axis of the cone.

The total height of the part is 60 mm.

The height of the parallelepiped is 15 mm, length 90 mm, width 55 mm.

The diameters of the cone bases are 40 mm (lower) and 30 mm (upper).

The length of the prismatic cutout is 20 mm, width 10 mm.

Note: When drawing dimensions, consider the part as a whole.

Option No. 8

Frame is a hollow rectangular parallelepiped. In the center of the upper and lower base of the body there are two conical bosses. A through hole of cylindrical shape Ǿ 10 mm passes through the centers of the tides.

The total height of the part is 59 mm.

The height of the parallelepiped is 45 mm, length 90 mm, width 40 mm. The thickness of the walls of the parallelepiped is 10 mm.

The height of the cones is 7 mm, the base is Ǿ 30 mm and Ǿ 20 mm.

Note: When drawing dimensions, consider the part as a whole.

Option No. 9

Support is a combination of two cylinders with one common axis. A through hole runs along the axis: at the top it is prismatic in shape with a square base, and then cylindrical in shape.

The total height of the part is 50 mm.

The height of the lower cylinder is 10 mm, the base is Ǿ 70 mm. The diameter of the base of the second cylinder is 30 mm.

The height of the cylindrical hole is 25 mm, the base is Ǿ 24 mm.

The base side of the prismatic hole is 10 mm.

Note: When drawing dimensions, consider the part as a whole.

Test

Graphic work No. 11

“Drawing and visual representation of the part”

Using the axonometric projection, construct a drawing of the part in the required number of views on a scale of 1:1. Add dimensions.

Graphic work No. 10

“Sketch of a part with design elements”

Draw a drawing of a part from which parts have been removed according to the markings applied. The projection direction for constructing the main view is indicated by an arrow.

Graphic work No. 8

“Drawing of a part with transformation of its shape”

General concept of shape transformation. Relationship between drawing and markings

Graphic work

Making a drawing of an object in three views with transforming its shape (by removing part of the object)

Complete the technical drawing of the part, making, instead of the protrusions marked with arrows, notches of the same shape and size in the same place.

Logical thinking task

Topic “Design of drawings”

Crossword "Projection"

1.The point from which the projecting rays emanate during central projection.

2. What is obtained as a result of modeling.

3. Cube face.

4. The image obtained during projection.

5. In this axonometric projection, the axes are located at an angle of 120° to each other.

6. In Greek, this word means “double dimension.”

7. Side view of a person or object.

8. Curve, isometric projection of a circle.

9. The image on the profile projection plane is a view...

Rebus on the topic “View”

Rebus

Crossword "Axonometry"

Vertically:

1. Translated from French as “front view”.

2. The concept in drawing of what the projection of a point or object is obtained on.

3. The boundary between the halves of a symmetrical part in the drawing.

4. Geometric body.

5. Drawing tool.

6. Translated from Latin, “throw, throw forward.”

7. Geometric body.

8. The science of graphic images.

9. Unit of measurement.

10. Translated from Greek as “double dimension”.

11. Translated from French as “side view”.

12. In the drawing, “she” can be thick, thin, wavy, etc.

Technical Dictionary of Drawing

Workbook

Practical and graphic work on drawing

The notebook was developed by Anna Aleksandrovna Nesterova, teacher of the highest category of drawing and fine art, teacher of the Municipal Budget Educational Institution “Secondary School No. 1 of Lensk”

Introduction to the Subject of Drawing
Materials, accessories, drawing tools.

The course examines the sequence of performing some exercises from the textbook "Drawing" edited by A.D. Botvinnikova.

Stages of completing graphic work No. 4 of the first and second tasks, Fig. 98 and 99.

These types of exercises help develop spatial thinking. Graphic work No. 4 is a summary, generalization and consolidation of the skills acquired in the process of studying the topics “Vertexes, edges and faces of an object”, “Analysis of the geometric shape of an object”. Quality control of knowledge, skills and abilities acquired during practical exercises to determine the projections of a point on the surface of an object shown in a drawing and visual image.

This type of activity can be used both in technology and drawing lessons. Similar tasks can be assigned at home as independent work.

Requirements for the trainee

This course is designed for students in the 7th grade of a general education school; it can also be useful for students of technical specialties, for the simple reason that it contains elements of descriptive geometry. It also trains spatial imagination.

Necessary requirements for trainees: knowledge of the rules of orthogonal projection; oblique parallel projection.

The student must be able to: analyze the geometric shapes of an object; determine projections of edges, faces, vertices of an object; determine projections of points on the surface of an object; build an image along the axes of isometric and frontal dimetric projection of ribs, faces, ovals.

1. a) According to the teacher’s instructions, construct an axonometric projection of one of the parts (Fig. 98). On the axonometric projection, draw images of points A, B and C; label them. b) Answer the questions:

Rice. 98. Tasks for graphic work No. 4

1. What types of parts are shown in the drawing?
2. What geometric bodies combine to form each part?
3. Are there holes in the part? If so, what geometric shape does the hole have?
4. Find on each of the views all flat surfaces perpendicular to the frontal and then to the horizontal planes of projection.
1. Based on the visual representation of the parts (Fig. 99), complete the drawing in the required number of views. Draw on all views and mark points A, B and C.

Rice. 99. Tasks for graphic work No. 4

§ 13. The procedure for constructing images in drawings

13.1. A method for constructing images based on analysis of the shape of an object. As you already know, most objects can be represented as a combination of geometric bodies. Investigator, to read and execute drawings you need to know. how these geometric bodies are depicted.

Now that you know how such geometric bodies are depicted in a drawing, and have learned how vertices, edges and faces are projected, it will be easier for you to read drawings of objects.

Figure 100 shows a part of the machine - the counterweight. Let's analyze its shape. What geometric bodies do you know that it can be divided into? To answer this question, let us recall the characteristic features inherent in the images of these geometric bodies.

Rice. 100. Part projections

In Figure 101, a. one of them is highlighted in blue. What geometric body has such projections?

Projections in the form of rectangles are characteristic of a parallelepiped. Three projections and a visual image of the parallelepiped, highlighted in Figure 101, a in blue, are given in Figure 101, b.

In Figure 101, another geometric body is conventionally highlighted in gray. What geometric body has such projections?

Rice. 101. Part shape analysis

You encountered such projections when considering images of a triangular prism. Three projections and a visual image of the prism, highlighted in gray in Figure 101, c, are given in Figure 101, d. Thus, the counterweight consists of a rectangular parallelepiped and a triangular prism.

But a part has been removed from the parallelepiped, the surface of which is conventionally highlighted in blue in Figure 101, d. What geometric body has such projections?

You encountered projections in the form of a circle and two rectangles when considering images of a cylinder. Consequently, the counterweight contains a hole in the shape of a cylinder, three projections and a visual image of which are given in Figure 101. f.

Analysis of the shape of an object is necessary not only when reading, but also when making drawings. Thus, having determined the shape of which geometric bodies the parts of the counterweight shown in Figure 100 have, it is possible to establish an appropriate sequence for constructing its drawing.

For example, a drawing of a counterweight is built like this:

1. on all views, a parallelepiped is drawn, which is the basis of the counterweight;
2. a triangular prism is added to the parallelepiped;
3. draw an element in the form of a cylinder. In the top and left views it is shown with dashed lines, since the hole is invisible.

Draw the description of a part called a bushing. It consists of a truncated cone and a regular quadrangular prism. The total length of the part is 60 mm. The diameter of one base of the cone is 30 mm, the other is 50 mm. The prism is attached to a larger cone base, which is located in the middle of its base measuring 50X50 mm. The height of the prism is 10 mm. A through cylindrical hole with a diameter of 20 mm is drilled along the axis of the bushing.

13.2. The sequence of constructing views in a detail drawing. Let's consider an example of constructing views of a part - support (Fig. 102).

Rice. 102. Visual representation of the support

Before you start constructing images, you need to clearly imagine the general initial geometric shape of the part (whether it will be a cube, cylinder, parallelepiped, etc.). This form must be kept in mind when constructing views.

The general shape of the object shown in Figure 102 is a rectangular parallelepiped. It has rectangular cutouts and a triangular prism cutout. Let's start depicting the part with its general shape - a parallelepiped (Fig. 103, a).

Rice. 103. Sequence of constructing part views

By projecting the parallelepiped onto the planes V, H, W, we obtain rectangles on all three projection planes. On the frontal plane of projections the height and length of the part will be reflected, i.e. dimensions 30 and 34. On the horizontal plane of projections - the width and length of the part, i.e. dimensions 26 and 34. On the profile plane - width and height, i.e. dimensions 26 and 30.

Each dimension of the part is shown without distortion twice: height - on the frontal and profile planes, length - on the frontal and horizontal planes, width - on the horizontal and profile planes of projections. However, you cannot apply the same dimension twice in a drawing.

All constructions will be done first with thin lines. Since the main view and the top view are symmetrical, axes of symmetry are marked on them.

Now we will show the cutouts on the projections of the parallelepiped (Fig. 103, b). It makes more sense to show them first in the main view. To do this, you need to set aside 12 mm to the left and to the right from the axis of symmetry and draw vertical lines through the resulting points. Then, at a distance of 14 mm from the top edge of the part, draw horizontal straight segments.

Let's construct projections of these cutouts on other views. This can be done using communication lines. After this, in the top and left views you need to show the segments that limit the projections of the cutouts.

In conclusion, the images are outlined with the lines established by the standard and the dimensions are applied (Fig. 103, c).

1. Name the sequence of actions that make up the process of constructing types of an object.
2. What purpose are projection lines used for?

13.3. Constructing cuts on geometric bodies. Figure 104 shows images of geometric bodies, the shape of which is complicated by various kinds of cutouts.

Rice. 104. Geometric bodies containing cutouts

Parts of this shape are widely used in technology. To draw or read their drawing, you need to imagine the shape of the workpiece from which the part is made, and the shape of the cutout. Let's look at examples.

Example 1. Figure 105 shows a drawing of the gasket. What shape does the removed part have? What was the shape of the workpiece?

Rice. 105. Gasket shape analysis

Having analyzed the drawing of the gasket, we can come to the conclusion that it was obtained as a result of removing the fourth part of the cylinder from a rectangular parallelepiped (blank).

Example 2. Figure 106a shows a drawing of a plug. What is the shape of its blank? What resulted in the shape of the part?

Rice. 106. Constructing projections of a part with a cutout

After analyzing the drawing, we can come to the conclusion that the part is made from a cylindrical blank. There is a cutout in it, the shape of which is clear from Figure 106, b.

How to construct a projection of the cutout in the view on the left?

First, a rectangle is drawn - a view of the cylinder on the left, which is the original shape of the part. Then a projection of the cutout is constructed. Its dimensions are known, therefore, points a", b" and a, b, defining the projections of the cutout, can be considered as given.

The construction of profile projections a, b" of these points is shown by connection lines with arrows (Fig. 106, c).

Having established the shape of the cutout, it is easy to decide which lines in the left view should be outlined with solid thick main lines, which with dashed lines, and which to delete altogether.

1. Look at the images in Figure 107 and determine what shape the parts are removed from the blanks to obtain parts. Make technical drawings of these parts.

Rice. 107. Exercise tasks

1. Construct the missing projections of the points, lines and cuts given by the teacher on the drawings you completed earlier.

13.4. Construction of the third type. Sometimes you will have to complete tasks in which you need to build a third using two existing types.

In Figure 108 you see an image of a block with a cutout. There are two views: front and top. You need to build a view on the left. To do this, you must first imagine the shape of the depicted part.

Rice. 108. Drawing of a block with a cutout

Having compared the views in the drawing, we conclude that the block has the shape of a parallelepiped measuring 10x35x20 mm. A rectangular cutout is made in the parallelepiped, its size is 12x12x10 mm.

The view on the left, as we know, is placed at the same height as the main view to the right of it. We draw one horizontal line at the level of the lower base of the parallelepiped, and the other at the level of the upper base (Fig. 109, a). These lines limit the height of the view on the left. Draw a vertical line anywhere between them. It will be the projection of the back face of the block onto the profile projection plane. From it to the right we will set aside a segment equal to 20 mm, i.e. we will limit the width of the bar, and we will draw another vertical line - the projection of the front face (Fig. 109, b).

Rice. 109. Construction of the third projection

Let us now show the cutout in the part in the left view. To do this, put a 12 mm segment to the left of the right vertical line, which is the projection of the front edge of the block, and draw another vertical line (Fig. 109, c). After this, we delete all auxiliary construction lines and outline the drawing (Fig. 109, d).

The third projection can be constructed based on an analysis of the geometric shape of the object. Let's look at how this is done. Figure 110a shows two projections of the part. We need to build a third one.

Rice. 110. Construction of the third projection from two data

Judging by these projections, the part is composed of a hexagonal prism, a parallelepiped and a cylinder. Mentally combining them into a single whole, let’s imagine the shape of the part (Fig. 110, c).

We draw an auxiliary straight line in the drawing at an angle of 45° and proceed to construct the third projection. You know what the third projections of a hexagonal prism, parallelepiped and cylinder look like. We draw sequentially the third projection of each of these bodies, using connection lines and axes of symmetry (Fig. 110, b).

Please note that in many cases there is no need to construct a third projection in the drawing, since rational execution of images involves constructing only the necessary (minimum) number of views sufficient to identify the shape of the object. In this case, the construction of the third projection of the object is only an educational task.

1. You have become familiar with different ways to construct the third projection of an object. How are they different from each other?
2. What is the purpose of using a constant line? How is it carried out?

1. In the drawing of the part (Fig. 111, a) the view on the left is not drawn - it does not show images of a semicircular cutout and a rectangular hole. As instructed by the teacher, redraw or transfer the drawing onto tracing paper and complete it with the missing lines. What lines (solid main or dashed) do you use for this purpose? Draw the missing lines also in Figures 111, b, c, d.

Rice. 111. Tasks for drawing missing lines

1. Redraw or transfer onto tracing paper the data in Figure 112 of the projection and construct profile projections of the parts.

Rice. 112. Exercise tasks

1. Redraw or transfer onto tracing paper the projections indicated to you in Figure 113 or 114 by the teacher. Construct the missing projections in place of the question marks. Perform technical drawings of parts.

Rice. 113. Exercise tasks

Rice. 114. Exercise tasks

a) Construction of the third type based on two given ones.

Construct a third type of part based on two data, put down dimensions, and make a visual representation of the part in an axonometric projection. Take the task from Table 6. Sample of completing the task (Fig. 5.19).

Methodical instructions.

1. The drawing begins with the construction of axes of symmetry of the views. The distance between views, as well as the distance between views and the drawing frame, is taken to be: 30-40 mm. The main view and the top view are constructed. The two constructed views are used to draw the third view - the view on the left. This view is drawn according to the rules for constructing third projections of points for which two other projections are given (see Fig. 5.4 point A). When projecting a part with a complex shape, you have to simultaneously construct all three images. When constructing the third view in this task, as well as in subsequent ones, you can not draw projection axes, but use the “axisless” projection system. One of the faces (Fig. 5.5, plane P) can be taken as the coordinate plane, from which the coordinates are measured. For example, having measured a segment on the horizontal projection for point A, expressing the coordinate Y, we transfer it to the profile projection, we obtain the profile projection A 3. As a coordinate plane, you can also take the plane of symmetry R, ​​the traces of which coincide with the axial line of the horizontal and profile projection, and from it the coordinates Y C, Y A can be measured, as shown in Fig. 5.5, for points A and C.

Rice. 5.4 Fig. 5.5

2. Each detail, no matter how complex it may be, can always be divided into a number of geometric bodies: prism, pyramid, cylinder, cone, sphere, etc. Projecting a part comes down to projecting these geometric bodies.

3. The dimensions of objects should be applied only after constructing the view on the left, since in many cases it is in this view that it is advisable to apply part of the dimensions.

4. For a visual representation of products or their components, axonometric projections are used in technology. It is recommended to first study the chapter “Axonometric projections” in the descriptive geometry course.

For a rectangular axonometric projection, the sum of the squares of the distortion coefficients (indicators) is equal to 2, i.e.

k 2 + m 2 + n 2 =2,

where k, m, n are coefficients (indicators) of distortion along the axes. In isometric

projections, all three distortion coefficients are equal to each other, i.e.

k = m = n = 0.82

In practice, for the simplicity of constructing an isometric projection, the distortion coefficient (indicator) equal to 0.82 is replaced by the reduced distortion coefficient equal to 1, i.e. construct an image of an object, enlarged by 1/0.82 = 1.22 times. The X, Y, Z axes in an isometric projection make 120° angles with each other, while the Z axis is directed perpendicular to the horizontal line (Fig. 5.6).

In a dimetric projection, two distortion coefficients are equal to each other, and the third in a particular case is taken equal to 1/2 of them, i.e.,

k = n = 0.94; and m =1/2 k = 0.47

In practice, for the simplicity of constructing a dimetric projection, the distortion coefficients (indicators) equal to 0.94 and 0.47 are replaced with the given distortion coefficients equal to 1 and 0.5, i.e. construct an image of an object, enlarged by 1/0.94 = 1.06 times. The Z axis in rectangular diameter is directed perpendicular to the horizontal line, the X axis is at an angle of 7°10", the Y axis is at an angle of 41°25". Since tg 7°10" ≈ 1/8, and tg 41°25" ≈ 7/8, these angles can be constructed without a protractor, as shown in Fig. 5.7. In rectangular dimetry, natural dimensions are laid out along the X and Z axes, and with a reduction factor of 0.5 along the Y axis.

The axonometric projection of a circle is generally an ellipse. If the circle lies in a plane parallel to one of the projection planes, then the minor axis of the ellipse is always parallel to the axonometric rectangular projection of the axis that is perpendicular to the plane of the depicted circle, while the major axis of the ellipse is always perpendicular to the minor one.

In this task, it is recommended to visualize the part in an isometric projection.

b) Simple cuts.

Construct the third type of part based on two data, make simple cuts (horizontal and vertical planes), put down dimensions, make a visual representation of the part in an axonometric projection with a 1/4 part cut out. Take the task from Table 7. Sample of completing the task (Fig. 5.20).

Complete the graphic work on a sheet of A3 drawing paper.

Methodical instructions.

1. When completing the task, pay attention to the fact that if the part is symmetrical, then it is necessary to combine half the view and half the section in one image. At the same time, in sight don't show invisible contour lines. The boundary between the appearance and the section is the dash-dot axis of symmetry. Section image details located from the vertical axis of symmetry to the right(Fig. 5.8), and from the horizontal axis of symmetry – from below(Fig. 5.9, 5.10) regardless of which projection plane it is depicted on.

Rice. 5.9 Fig. 5.10

If the projection of an edge belonging to the external outline of the object falls on the axis of symmetry, then the incision is made as shown in Fig. 5.11, and if an edge belonging to the internal outline of the object falls on the axis of symmetry, then the cut is made as shown in Fig. 5.12, i.e. in both cases, the projection of the edge is preserved. The boundary between the section and the view is shown with a solid wavy line.

Rice. 5.11 Fig. 5.12

2. On images of symmetrical parts, in order to show the internal structure in an axonometric projection, a cutout is made of 1/4 of the part (the most illuminated and closest to the observer, Fig. 5.8). This cut is not associated with the incision on orthogonal views. So, for example, on a horizontal projection (Fig. 5.8), the axes of symmetry (vertical and horizontal) divide the image into four quarters. By making an incision on the frontal projection, it is as if the lower right quarter of the horizontal projection is removed, and in the axonometric image the lower left quarter of the model is removed. The stiffening ribs (Fig. 5.8), which fall into the longitudinal section on orthogonal projections, are not shaded, but shaded in axonometry.

3. The construction of the model in axonometry with a cutout of one quarter is shown in Fig. 5.13. The model constructed in thin lines is mentally cut by the frontal and profile planes passing through the Ox and Oy axes. The quarter of the model enclosed between them is removed, revealing the internal structure of the model. When cutting the model, the planes leave a mark on its surface. One such trace lies in the frontal, the other in the profile plane of the section. Each of these traces is a closed broken line consisting of segments along which the cut plane intersects with the faces of the model and the surface of the cylindrical hole. Figures lying in the section plane are shaded in axonometric projections. In Fig. Figure 5.6 shows the direction of the hatch lines in an isometric projection, and Fig. 5.7 – in dimetric projection. Hatching lines are drawn parallel to the segments that cut off identical segments on the axonometric axes Ox, Oy and Oz from point O in an isometric projection, and identical segments on the Ox and Oz axes in the dimetric projection and on the Oy axis - a segment equal to 0.5 segments on the axis Ox or Oz.

4. In this task, it is recommended to visualize the part in a dimetric projection.

5. When determining the true type of section, one must use one of the methods of descriptive geometry: rotation, alignment, plane-parallel movement (rotation without specifying the position of the axes) or changing projection planes.

In Fig. 5.14 shows the construction of projections and the true view of the section of a quadrangular prism by the frontally projecting plane G by changing the projection planes. The frontal projection of the section will be a line coinciding with the trace of the plane. To find the horizontal projection of the section, we find the points of intersection of the edges of the prism with the plane (points A, B, C, D), connecting them, we get a flat figure, the horizontal projection of which will be A 1, B 1, C 1, D 1.

symmetry, parallel to the axis x 12, will also be parallel to the new axis and be at a distance from it equal to b 1.In the new system of projection planes, the distances of points to the axis of symmetry are kept the same, as in the previous system, so to find them you can set aside distances ( b 2) from the axis of symmetry. By connecting the obtained points A 4 B 4 C 4 D 4, we obtain the true view of the section by plane G of the given body.

In Fig. Figure 5.16 shows the construction of the true cross-section of a truncated cone. The major axis of the ellipse is determined by points 1 and 2, the minor axis of the ellipse is perpendicular to the major axis and passes through its middle, i.e. point O. The minor axis lies in the horizontal plane of the base of the cone and is equal to the chord of the circle of the base of the cone passing through point O.

The ellipse is limited by the straight line of intersection of the cutting plane with the base of the cone, i.e. a straight line passing through points 5 and 6. Intermediate points 3 and 4 are constructed using the horizontal plane G. In Fig. Figure 5.17 shows the construction of a section of a part consisting of geometric bodies: a cone, a cylinder, a prism.

Rice. 5.16

Rice. 5.17

c) Complex cuts (complex step cut).

Construct the third type of part based on two data, make the indicated complex cuts, construct an inclined section using the plane specified in the drawing, put down dimensions, and make a visual representation of the part in an axonometric projection (rectangular isometry or dimetry). Take the task from Table 8. Sample of completing the task (Fig. 5.21). Complete the graphic work on two sheets of A3 drawing paper.

Methodical instructions.

1. When performing graphic work, you need to pay attention to the fact that a complex step section is depicted according to the following rule: the cutting planes are, as it were, combined into one plane. The boundaries between the cutting planes are not indicated, and this section is designed in the same way as a simple section made not along the axis of symmetry.

2. In the assignment, some of the dimensions, due to the lack of a third image, are not placed appropriately, so the dimensions must be applied in accordance with the instructions given in the “Applying Dimensions” section, and not copied from the assignment.

3. In Fig. 5.21. shows an example of making a part image in rectangular isometry with a complex cutout.

d) Complex cuts (complex broken cut).

Construct the third type of part based on two data, make the indicated complex broken section, and add dimensions. Take the task from Table 9. Sample of completing the task (Fig. 5.22).

Complete the graphic work on a sheet of A4 drawing paper.

Methodical instructions.

In Fig. Figure 5.18 shows an image of a complex broken section obtained by two intersecting profile-projecting planes. To obtain a section in an undistorted form when cutting an object with inclined planes, these planes, together with the section figures belonging to them, are rotated around the line of intersection of the planes to a position parallel to the plane of projections (in Fig. 5.18 - to a position parallel to the frontal plane of projections). The construction of a complex broken section is based on the method of rotation around a projecting straight line (see the course on descriptive geometry). The presence of kinks in the section line does not affect the graphic design of a complex section - it is designed as a simple section.

Options for individual assignments. Table 6 (Construction of the third type).

Examples of task completion.

Rice. 5.22

Rice. 99. Tasks for graphic work No. 4

3) Are there any holes in the part? If so, what geometric shape does the hole have?

4) Find on each of the views all flat surfaces perpendicular to the frontal and then to the horizontal projection planes.

2. Based on the visual representation of the parts (Fig. 99), make a drawing in the required number of views. Draw on all views and mark points A, B and C.

13. The order of constructing images in drawings

13.1. A method for constructing images based on analysis of the shape of an object. As you already know, most objects can be represented as a combination of geometric bodies. Therefore, to read and complete drawings, you need to know how these geometric bodies are depicted.

Now that you know how such geometric bodies are depicted in a drawing, and have learned how vertices, edges and faces are projected, it will be easier for you to read drawings of objects.

Figure 100 shows a part of the machine - the counterweight. Let's analyze its shape. What geometric bodies do you know that it can be divided into? To answer this question, let us recall the characteristic features inherent in the images of these geometric bodies.

In Figure 101, and one of them is highlighted in brown. What geometric body has such projections?

Projections in the form of rectangles are characteristic of a parallelepiped. Three projections and a visual image of the parallelepiped, highlighted in Figure 101, and in brown, are given in Figure 101, 6.

In Figure 101, in gray conditionally, another geometric body is highlighted. What geometric body has such projections?

You encountered such projections when considering images of a triangular prism.