Ways of graphic representation of the product. Types of graphic images. Shape charts are built using two methods

In medical practice, graphic images are used to illustrate statistical data characterizing health and healthcare indicators.

When constructing graphic images, the following requirements must be observed:

1) data on the chart should be placed from left to right or from bottom to top;

2) the scales on the diagrams must be provided with size indicators;

3) the values ​​depicted graphically must have numerical designations on the graph itself or in the table attached to it;

4) geometric signs, figures, colors, shading should be explained;

5) each graph should have a clear, concise, if possible, short title that reflects its content.

There are the following types of graphic images:

1. Charts - are a way of displaying statistical data using lines and shapes.

2. Cartograms and cartograms - are a way of displaying the territorial distribution of statistical indicators using geographical maps.

The most common type of graphic images are diagrams, which, according to the method of construction, are divided into:

Linear;

planar;

Volumetric;

Curly.

Line charts are used both in studying the relationship between phenomena and in characterizing changes in phenomena over time. They are built in a rectangular coordinate system: horizontal (abscissa axis - x-axis) and vertical (y-axis - y-axis). The point of intersection of the axes serves as the reference point.

On the abscissa axis, on a chosen scale, time or other factor signs are plotted; then, from the points corresponding to certain moments or periods of time, the ordinates are restored, reflecting the dimensions of the studied effective feature. The vertices of the ordinates are connected by straight lines (Fig. 1).

Figure 1. An example of a line chart.

Several line charts can be built on one chart at the same time, which allows them to be visually compared (it is not recommended to build more than 4 charts, since more of them make it difficult to perceive).

A variety of line charts are radial diagrams (diagrams in polar coordinates). This type of diagram is used to depict seasonal fluctuations in phenomena that have a closed cyclical nature.

The number of axes corresponds to the number of parts into which a period of time is divided (for example, a year - with a monthly division of the year, 12 axes are taken). The average value is taken as the length of the radius of the circle, then the value corresponding to the level of the phenomenon is plotted on each axis. The obtained points are connected by straight lines (Fig. 2).

Figure 2. An example of a radial chart.

Planar charts are divided into: columnar; pyramidal; sector; intracolumnar.

Bar charts are built on the same principle as dynamic curves, but in them rectangles correspond to vertically or horizontally drawn lines. These diagrams are especially convenient when it is not the dynamics of phenomena that are illustrated, but their comparative magnitude in a certain period of time (Fig. 3).

Figure 3. An example of a bar chart.

Pyramidal charts are bar graphs, rotated bases to each other, resulting in bars are horizontal. Pyramid charts are often used to depict the age and sex structure of a population (Fig. 4).

Figure 4. An example of a pyramid chart.

Pie charts - represent a circle that is taken as a whole (360 o - 100%), and its individual sectors correspond to parts of the depicted phenomenon (Fig. 5).

Figure 5. An example of a pie chart.

Sectors must be arranged in ascending or descending order clockwise from 12 o'clock. Such charts are used to illustrate extensive indicators.

intracolumnar(bar, stacked, strip) charts are a rectangle or square, divided into parts. In this case, the length of the ribbons (columns) is taken as 100%, and their constituent parts correspond to the percentages of the phenomenon. This type of chart is used, as a rule, to compare the structure of a phenomenon (for example, morbidity) in several teams or in one team for different periods of time (Fig. 6).

Figure 6. An example of an intra-bar chart.

3D charts. When constructing this type of diagram (Fig. 7), statistical data is depicted in the form of geometric figures of three dimensions (cube, ball, pyramid).

Figure 7. An example of a 3D chart.

Curly charts. In this type of chart, statistical quantities are depicted using symbolic figures characteristic of a given phenomenon (for example, hospital beds; auxiliary vehicles). To build a diagram, a certain scale is set, for example, the image of one bed corresponds to 200 thousand actual beds.

Curly charts are built in two ways:

1) compared statistical values ​​are depicted either by figures of different sizes (see the figure on the left), or by a different number of figures of the same size (see the figure on the right).

In this case, rounded numerical data are usually used, therefore curly charts serve mainly to popularize statistical data, and are usually used to illustrate visibility indicators (Fig. 8).

Figure 8. An example of a shape chart.

Cartogram a geographical map or its scheme is called, on which the degree of distribution of a phenomenon in different parts of the territory is depicted with different colors or shading, and the coloring or shading becomes more intense, the greater the distribution of the phenomenon under study (Fig. 9, 10).

Distinguish:

1) background cartograms - where the differences in the value of the statistical indicator in different areas are expressed by the feature of the background given to each territory. In monophonic - the degree of hatching density, in color - the degree of color intensity, and they use only one color, but different shades - from the lightest to the darkest.

Figure 9. An example of a background cartogram.

2) dot cartograms - where the value of the statistical indicator is represented by the number of points placed on the contour map of a particular territory. Each dot denotes a certain (conditional) number of units of this characteristic (for example, 1000 inhabitants).

Figure 10. An example of a dot chart.

Cartogram such a graphic image is called when statistical data are plotted on a geographical map or its scheme in the form of bar, sector, curly and other charts (Fig. 11).

Figure 11. An example of a chart.

To category:

Basics of technical modeling

To the head of the circle on graphic training in the initial technical modeling

In the technical creative activity of younger students, work can be done according to a model, template, verbal description, but most often according to a technical drawing, a simple drawing or one’s own idea, where it becomes necessary to read technical drawings, simple drawings and other design and technological documentation. Therefore, mastering the techniques of reading graphic images is one of the main components of the graphic training of younger students. This means that it is necessary to teach schoolchildren to carefully consider and compare graphic images and real details or objects, to compare different images with each other and to represent a three-dimensional object according to its flat image. At the same time, it is important not only to teach schoolchildren to read drawings and drawings, but also to form the need to use them in independent work.

To facilitate the work of a primary school teacher, it is advisable to formulate a number of concepts of graphic preparation, which will be used in this book.

Graphic literacy can be defined as having knowledge in the field of technical drawing and the degree of proficiency in reading and executing design and technological documentation in accordance with the norms and rules of the Unified System for Design Documentation (ESKD) or the standards of the Council for Mutual Economic Assistance (ST CMEA).

Graphic knowledge - the concept of the methods of graphic representation of products, the norms and rules of ESKD and ST SEV, which are necessary for a person in the process of his work on design and technological documentation.

Graphic skills - the readiness of a person to accurately and consciously express his thoughts or read the thoughts of another person in design and technological documentation using the rules and regulations of ESKD. The process of acquiring graphic skills requires long practice and training based on graphic knowledge, which contributes to the development of students' spatial representations and largely depends on their individuality.

Graphic skills - possession of working methods with drawing tools, developed in the process of training. During schooling, students, as a rule, do not have time to develop skills in reading drawings and drawing them up. The acquisition of such skills is a long process associated with a high level of spatial and logical thinking.

Graphic information - information contained in the design and technological documentation. These include graphic conditional images in drawings, sketches, diagrams; symbols for grades of materials, coatings, etc.; technical conditions, etc.

Initial technical modeling is only the first inclusion of students in design and technological activities, where graphic training of schoolchildren is necessary, but it is carried out not in special classes, but in the labor process, that is, in parallel with the formation of the ability to manufacture products. And only that extremely simple graphic material that schoolchildren need in the process of specific practical work is subject to development. When selecting objects in circle classes, the leader needs to analyze in advance the shape and design of the technical objects that will be offered to children.

At the same time, it is important to take a small amount of details in an object, take into account the possibility of comparing the shape of an object with a geometric shape, and apply such methods of connecting parts that do not require additional graphic knowledge and skills. If volumetric products are made of paper and cardboard, then the development of any part must be a development of a simple geometric body (cube, straight prism, straight cylinder, cone).

In practical work, it is important to take into account the knowledge, skills and abilities that younger students master in the classroom, mathematics, fine arts and labor training.

Below is a brief list of knowledge and skills that primary school students master in the classroom at school1.

Knowledge: the concept of a point, line, segment, polygon, right angle, rectangle.

Skills: draw a line through a given point; draw ave straight lines intersecting at a given point; compare the size of the segments; measure the segment find the length of the sides of the polygon; draw a rectangle of given length and width; divide a polygon of a given shape by a segment into two polygons of a given shape; cut out various polygons from unlined paper; compare the shape of surrounding objects with the shape of polygons; mark up a flat part according to the template.

Knowledge: terms used in connection with the comparison and measurement of segments and distances between points using a compass and straightedge; terms in connection with the introduction of letter designations; concepts about the perimeter of a polygon, the proportion of a figure, a circle, a circle, the center of a circle, the radius of a circle; terminology used in the classification of triangles; concept of axial symmetry.

Skills: draw a circle with a compass; connect the point of the outline of the circle with its center; determine the type of triangle; divide the figure into equal parts (shares); determine the shape of surrounding objects and their parts; mark a symmetrical flat part; plan the manufacture of simple 'flat parts in shape according to the finished drawing.

III class

Knowledge: the concept of the area of ​​​​a figure, a square centimeter and other measures of area.

Skills: divide the circle and other figures into 2, 3, 4, 6, 8 equal parts; build a figure with given dimensions on unlined paper; increase or decrease the figure several times; under the guidance of a teacher, mark up a flat part according to the drawing and a given scale (M 1: 2; M2: 1); read and execute the simplest electrical circuit; unfold a part with a simple shape.

Pedagogical work experience, the analysis of educational and methodological literature and programs for primary school made it possible to determine the approximate content of graphic training in the classroom for primary technical modeling with younger students:
1. Drawing tools and accessories.
2. Basic concepts about graphic images.
3. Drawing lines and some symbols.
4. Rules and techniques for reading a drawing of flat parts.
5. Basic graphic knowledge and skills with which marking is performed on the material.
6. Rules and techniques for increasing or decreasing details several times.
7. Rules for reading and sketching a flat part.
8. The order of reading images of three-dimensional parts of a simple form (visual images, scans and drawings).
9. The initial concept of an assembly drawing, consisting of 2-3 parts that are simple in shape.
10. Rules for reading and drawing up simple electrical circuits.

Recommendations for graphic training in the initial technical modeling are intended for primary school teachers, after-school educators and leaders of circles who conduct practical classes. The graphic literacy of the teacher and the head of the technical circle significantly exceeds the information that is communicated to children in the process of technical modeling. Considering that children from grades I to III can work in the same circle, it is important for the head of the circle to conduct classes in a differentiated way, clearly observing the availability of graphic information for students in each grade.

Extracurricular work on technology allows you to expand and deepen the graphic knowledge and skills of younger students to the extent necessary for the conscious practical work of students in the initial technical modeling.

We give an approximate content and methodology for the graphic training of younger students in the classroom for initial technical modeling.

Primary schoolchildren get acquainted with the basic drawing tools at the lessons of mathematics, labor training and know how to use them. However, it is very important to draw their attention to the fact that the success of graphic work largely depends on the quality of the tool, its proper preparation for work, and serviceability. It is necessary to explain to the children the conditions for storing each tool and fix the rules for using them. Paper for graphic works, younger students mainly use millimetric paper or sheets from a notebook in a cage. This facilitates the graphic work of younger students, reduces time and allows you to quickly move on to the manufacture of the intended products.

A technical drawing is a visual representation of an object, made by eye and by hand using the method of parallel projections (that is, those edges on an object that are parallel in nature are also parallel in a technical drawing). In the technical drawing, all structural elements (protrusions, holes, etc.) are depicted in compliance with proportions and dimensions by eye. Exact dimensions can be indicated by numbers. The volume of the object for a more visual display is done by shading. A technical drawing shows the shape of an object as a whole.

Drawing (Fig. 2) is a graphic representation of an object, made with the help of drawing tools on a certain scale, with exact dimensions. It contains data about the shape, size and material of the object. Both according to the drawing and the technical drawing, one can judge the device of the object as a whole and its parts, and the product can be made according to the dimensions and technical requirements. The drawing, as a rule, gives a series of images of individual sides of the object, which are located on strictly defined places on a sheet of paper. The drawing can more accurately show the design.

Rice. 1. Technical drawing of the boat model

Rice. 2. Drawing of a boat model

Rice. 3. Sketch of the boat model

A sketch (Fig. 3), just like a drawing, shows an object from several sides and is performed according to the same graphic rules. The lines on the sketch should be straight and clear. Dimensions are applied with exact numbers, indicate the scale and material from which the product will be made. A sketch differs from a drawing in that it is carried out without the help of drawing tools, by hand, without observing exact dimensions. The sketch should be treated as an important technical document. Directly according to the sketch, you can make both individual parts and the whole product. It must be remembered that an error in the sketch is a marriage in the work. When explaining to younger students the concepts of a drawing, a sketch, a technical drawing, it is necessary to highlight only their essential features that children encounter in practical activities, and clearly, using typical examples, show their differences. In the initial technical modeling, schoolchildren encounter the simplest drawing only in the process of studying it, reading it, but not drawing it. It is enough for them to know that the drawing is carried out with the help of drawing tools according to the exact dimensions.

However, from the first lessons of labor training and classes in technical circles, children should be taught to "talk with a pencil in hand." Ensure that students' thoughts are expressed in lines, symbols, silhouettes and contours. Systematically and consistently bring graphic images closer to their implementation in accordance with all the rules; to direct the minds of students to the development of designs in a graphical way.

Symbols for drawing lines and other initial elements of technical drawing that are communicated to younger students must comply with existing state all-union standards (GOST y) according to the Unified System for Design Documentation (ESKD), approved by the State Committee for Standards, Measures and Measuring Instruments under the Council of Ministers of the USSR in December 1967 and put into effect on January 1, 1971. All graphic works and all technical, methodological and educational literature can only correspond to their purpose if they are made in accordance with GOST according to ESKD or ST SEV.

Explaining to younger students, for example, the lines of the drawing (Fig. 4), we can say that the line of the visible contour is the main, solid, thick line, which has a thickness of about 1 mm (omitting fractions of a millimeter). And the invisible contour line and all other lines (axial, extension, fold line, etc.) are 2-3 times thinner than the main line (without specifying the thickness of each line, length, strokes and the distance between them). Thus, the information that younger students receive is close to the norm and corresponds to ESKD. They become acceptable to children in the process of working on initial technical modeling in the period preceding the study of a systematic course in drafting. In initial technical modeling, it is not necessary to introduce students to all types of lines, as well as to all their.appointments that they have. Students should be told only about those lines that they will meet in the process of work.

Rice. 4. Drawing lines and symbols: 1 - visible contour line; 2- line of invisible contour; 3- axial, center line; 4-fold line; 5- application of glue from the front side; 6- application of glue from the wrong side

Rice. 5. Parachute model

The visible contour line (Fig. 4) is clearly visible on any image. Schoolchildren get to know her already at the first lessons of labor training. It is necessary to teach children to special terminology and the correct name of this line - the main line, solid thick, indicating the contour of the product or workpiece (hole, protrusion, notch, which is visible). The symbol for the fold line is given in Figure 4, 4.

In the initial technical modeling, there are no special classes in graphic training, and the children receive the necessary information during the game and practical work on the manufacture of individual products. For example, a simple model of a parachute must be made from paper (Fig. 5). At the first stage, a square sheet of paper is depicted, its edges (contour) are indicated by a visible contour line. The corners of the square are first bent towards the center. To make the upcoming work operation clear, fold lines are drawn in the drawing at the fold points. The teacher explains to the children and shows with a specific example how the symbols (in this case, the designation of the fold line) help in the work. Then he shows a picture of that line on the blackboard.

At the next stage of work, the ends of the corners are bent along the fold lines to the sides of the square (Fig. 5, 2) and a parachute dome is obtained (Fig. 5, 3). Further, small holes are made in the corners, slings of thread are tied, and a small weight is attached to the slings (Fig. 5, 4). The parachute is ready.

In this case, children need to provide some information about the product. For example, a parachute comes to the aid of a pilot in a moment of danger. Parachutes drop food and cargo into remote, hard-to-reach areas. On large parachutes, the descent vehicles of spacecraft descend to the ground.

The made parachute is a small and simple paper model, on the example of which the children got acquainted with the fold line. To fix the symbol of the fold line, you can ask schoolchildren the following questions: how is the fold line indicated? What is the difference between the image of the fold line and the image of the line of the visible contour (edge)? What is the name of the work step that should be performed if a fold line is indicated on the image? And so on. You can offer children exercises on how to make fold lines on checkered paper, when you need to bend a sheet of paper in half, diagonally, etc. To consolidate the ability to read the fold line on the drawing, the teacher invites the children to make a model of a flying arrow on their own. Figure 6 shows a step-by-step drawing according to which children complete this model. The teacher can draw it on the blackboard in advance or prepare a homemade table. The arrow is a simple model, but it flies well and can even perform aerobatics. Launch the arrow into flight with a smooth movement of the hand.

Rice. 6. Flying arrow model

The invisible contour line (Fig. 4.2) is a line denoting a real-life structural element (edge, notch, protrusion, hole, etc.), but invisible, located behind the surface that is being viewed. The invisible contour line is drawn with separate strokes and therefore it is called dashed. The invisible contour line can be seen on the drawing of the airframe model (Fig. 7, top view). Sections of the rack-fuselage, closed by wings and stabilizer, are indicated by dashed lines-lines of an invisible contour. This means that in fact the rail passes under the wings, but its contours in this area are hidden from view. This is even more characteristically shown at the end of the rail, where the lines of an invisible contour indicate the end of the rail-fuselage.

Rice. 7. Model of a sports glider: 1 - wooden rail; 2- cargo (rail section); 3- wings; 4- stabilizers; 5- keel

The airframe model (Fig. 7) is made of paper and wooden slats. A part of the same rail is glued to the rail - the nose of the fuselage - the nose weight. While the glue dries, mark out and cut out the wings, stabilizers and keel from thick paper. Where to glue the wings and stabilizers to the fuselage is shown in the top view.

In the process of assembling the airframe, so that it looks like in the visual image, according to the symbol, it should be clear to the student where the wings and stabilizers are attached to the fuselage. Rail - the nose load is attached to the lower part of the fuselage (it is hidden from view if you look at the model exactly from above). The edge of its front end coincides with the edge of the fuselage rail, so this section of the nose of the aircraft (the end of the rails) is indicated by a line of visible contour. And the rear end of the rail - the bow load - ends in front of the wings, it is hidden from view in the top view and is indicated by an invisible contour line.

About the launch of the glider and the flight control of such models is described in the paragraph "Making layouts and models of technical objects from flat parts".

Rice. 8. Making a symmetrical aircraft model

The axial line, center line is a dash-dotted line, which serves to designate both the axes of the structural elements of the part, and to designate the axis of the entire part. In the case when the center line is the basis of the part, it, as a rule, will also be the axis of symmetry.

Familiarization of younger students with axial symmetry takes place in the lessons of mathematics, fine arts and labor education. In the initial technical modeling classes, the concepts of axial symmetry are fixed on specific examples related to the practical activities of children. For example, so that the expressions symmetrical figure, symmetrical detail, etc. do not have a formal character in the representation of children, it is possible to make a model of an aircraft (Fig. 8). To do this, students fold a thick sheet of paper in half, then draw the contour of half of the plane according to the template. Without cutting along the fold line, they cut out the silhouette of the aircraft, bend the wings, stabilizers and get a paper model of the aircraft, which is symmetrical about a straight line. And the straight line (in this case, the fold line) is also the axis of symmetry of this model. The paper model must be centered, and it will fly.

To justify the expression: “These figures, details, drawings, etc. are arranged symmetrically,” you can fold this model along the existing fold line and use a pin or needle to prick a pattern on the wings, for example, stars (five main points), so, so that the needle pierces both layers of paper each time. Then unfold the wings of the plane, connect the dots to make a star, and the children will clearly see that the stars are arranged symmetrically. To verify this, you need to fold the plane again along the fold line and it will be seen that the points

the stars match. You can offer children pictures of various objects, geometric shapes, details and determine which of them will be symmetrical. You can place a pencil or the edge of a ruler on the images to check if they are symmetrical. You can make out which geometric figure or part can have two or more axes of symmetry, for example, an equilateral triangle, a square, an aircraft propeller, a nut, etc. In the process of making dials of various shapes for watches, you can ask schoolchildren to determine how many axes of symmetry can be drawn on dials of round (if the circle is divided only into four parts), square ^ and hexagonal shapes. On the dials, movable arrows are installed on the screw, washer and nut from the designer's set or mounted on a wire bent in the shape of the letter P. So, younger students use the basic concepts of axial symmetry in the process of making models of technical objects.

Among the lines that are used in technical drawing, there is a solid thin line. It can indicate a fold line, extension and dimension lines, and also serve as an auxiliary line. During the modeling process, students are rarely required to perform graphic work, and if necessary, they do it on checkered paper. But the head of the circle must show the techniques and methods for drawing lines: horizontal, vertical, as well as mutually perpendicular and parallel lines on unlined paper.

Figure 9 shows the technique of drawing parallel lines using a square and ruler. The square is moved along a fixed ruler (or T-square) and lines parallel to the first are drawn with a sharp pencil. At the same time, the vertical side of the square in this case is perpendicular to the ruler or T-square. And if you draw straight lines along the upper edge of the ruler and the vertical side of the square, then these lines will be perpendicular to each other. Students should be able to use these common techniques in practical work.

Reading and drawing dimensions is a very important part of the graphic activity. Children should be able to correctly read the dimensions in the drawing and technical drawing. The speed and accuracy of reading this image, and hence the manufacture of this product, largely depends on how accurately the rules for sizing are observed. Overall dimensions determine the product as a whole in width, length and height. In addition to overall dimensions, a part or product, as a rule, has structural elements (holes, protrusions, etc.), which also have their own dimensions. In technical drawing, dimensions are given in millimeters, while the name of the measurements is not indicated. If the dimensions are applied in centimeters (in construction drawing), then the name is indicated next to the number. Perpendicular to the segment whose size is indicated, extension lines are drawn (Fig. 10, /), then at a distance of 5-10 mm from the measured segment (contour), a dimension line is drawn parallel to it (Fig. 10, 1), which is limited on both sides arrows. Arrows with sharp ends rest against extension lines. Extension and dimension lines are solid thin lines. A dimension number is applied above the middle of the dimension line.

Rice. 9. Techniques for drawing parallel and perpendicular lines

In the work on the initial technical modeling, it is permissible to put down all dimensional numbers in centimeters, but with the obligatory indication of the names. Product dimensions that can be calculated should not be applied, since excessive dimensioning complicates the drawing and makes it difficult to read the graphic image.

To indicate the dimensions of parts that have a cylindrical shape, as well as the sizes of round holes and protrusions, a special diameter icon is used - a circle crossed out by a straight line inclined to the right. The dimension line with arrows at the ends in a circle is set so that it passes through the center and does not coincide with the axes of symmetry. If the circle is so small that the dimensional number does not fit in it or is poorly readable, then it is taken out of the circle. To indicate the size of the radius, the Latin letter R is always written in front of the dimension number. The dimension line is drawn from the center of this arc and ends with an arrow on one side, which rests on the arc or circle. Dimensional numbers in all cases should be written so that they are read from left to right. The designation of the angle value is shown in Figure 10, 6. But this does not mean that all the requirements of ESKD, including the application of dimensions, should be learned by younger students. Detailed information about the lines of the drawing is given only for the leader of the circle, since in preparation for classes he often has to examine and read drawings in various albums and magazines, where all graphic images are made according to ESKD. When parsing simple drawings, children often ask a variety of questions about graphic images, and the leader must give a short and intelligible, and most importantly, correct answer. In the process of practical exercises, younger students gradually memorize some information and master it. The leader of the circle draws the attention of the children to the fact that the dimensions on the finished drawings are affixed according to certain rules and therefore it is convenient to read them. In practical classes, younger students receive the following information about sizing: how dimensional numbers are applied, how dimensional lines are arranged, and when they use the signs of diameter and radius. During this period, it is better to work according to the drawing, technical drawing, and only then proceed to work according to your own plan, where it may be necessary to draw up a sketch of a simple flat part with dimensions.

Rice. 10. Application of dimensions: 1 - extension and dimension lines; 2 and 3 - designation of diameters; 4 and 5 - designation of radii; 6- designation of the angle

When modeling from paper and cardboard, it is often necessary to mark the places where glue is applied1. If the glue is applied from the wrong side, then these places are indicated by intermittent shading (Fig. 4, 6). For example, in a sports glider, the lower part of the keel is shaded with thin solid lines, which means that this place must be greased with glue from the front side. And for the Tu-134 aircraft, in the upper part of the keel, an additional valve is shaded with separate strokes, which means that here it is necessary to lubricate with glue on the reverse side (double valve).

In the modeling process, it is often necessary to enlarge or reduce a drawing, drawing, template or pattern of a product. This is done in different ways: using knowledge of the scale or marking by cells of different areas. In order to increase any pattern (pattern) by cells, it is entered into a rectangle. The rectangle is drawn into squares and they are designated as shown in Figure 11 (model of the Mig-19 front-line fighter). Then a new rectangle is drawn on checkered or graph paper, for example twice as large if the pattern needs to be doubled. Designate the same number of cells on it and number them in the same way. In this rectangle, an enlarged pattern is drawn in cells. Care must be taken to ensure that the lines of the drawing are correctly located in the cells.

Rice. 11. Model aircraft MiG-19

The layout of the Mig-19 front-line fighter with a “lock” connection can be made from single-layer cardboard (boxboard) or velvet paper (two layers). At the same time, the attention of the children should be paid to ensure that the width of the slots corresponds to the thickness of the material from which the layout is made. Then the connection of the slots during assembly will be more dense. Children must transfer the contours of the enlarged parts (fuselage with keel, wings and stabilizers) onto the material, carefully cut and assemble the fighter according to the visual image.

For elementary school children who are not yet familiar with the scale, it is better to reduce or enlarge the images by cells, but you can tell that the scale is a number that shows how many times the image is larger or smaller than the part or product itself. On the drawings and technical drawings, the guys can see the following designations: M1: 2 (dimensions must be halved), M2: 1 (dimensions must be doubled).

Marking means transferring lines and points to the material (paper, fabric, wood, metal), which will indicate the contours of the future product or its parts. Markup can be done according to a template, drawing, technical drawing, verbal description, sample, etc. The guys get acquainted with marking on different materials in labor training lessons starting from grade I. First, they mark out the product or its parts of a rectangular shape, then in the form of circles, symmetrical parts using axial lines, etc. Children learn to divide the circle with a compass into 3, 6 and 12 equal parts in mathematics lessons starting from grade II. They know that mutually perpendicular axes divide the circle into four equal parts. So in the initial technical modeling classes, these skills and abilities are only consolidated and expanded. And if we take into account that in the first classes, younger students are eager to see the result of their work as soon as possible and by the end of classes they certainly want to have a ready-made craft, then most often they do the markup according to the existing templates, which are prepared in advance by the head of the circle, pioneer leaders or high school chefs . But very soon the guys have a desire to create themselves - to produce technical objects according to their own design.

Drawing up a sketch of a flat part on checkered paper consists in depicting one main view of the part, i.e., such a view in which its shape, dimensions and available structural elements (holes, protrusions, roundings) are visible. Regarding the order in which sketches are made, there are different recommendations in the methodological literature. Three of them are considered universally recognized. The first is the need to teach children to start any construction by drawing the axes of symmetry (where they are needed) and the dimensions of the object in order to best place it, and only then complete the structural elements of the object. Two other recommendations are related to the formation of students' methods of considering an object as a sum or difference of geometric shapes in flat parts and geometric bodies in volumetric ones. Drawing up a sketch (view) goes by building up parts of the object, that is, building from part to whole or, in the second case, from whole to part. Let us consider the case of formation of techniques for observing the shape of a flat object as a set of geometric shapes. For example, students were given the task of drawing up a sketch (from life) of a board for cutting products. The board will be made of plywood.

When considering a specific object - a board for cutting products (Fig. 12), it is necessary to teach the student to see (examining each part separately) of which geometric shapes this object consists. The main (working) part of the board, on which the products are cut, has the shape of a rectangle. The handle that holds the board (protrusion) also has the shape of a rectangle with a structural element in the form of a round hole. Starting to sketch a given object, the student draws a horizontal axis of symmetry for the object as a whole. Determines the dimensions of a larger rectangle (the working part of the board) and executes it by hand, placing the same parts on both sides of the axis of symmetry. Next, he “builds up” a smaller rectangle (the handle of the board) and, having determined by measuring the place for the center of the hole in the handle, draws a second (vertical) axis through it. The circle, like the entire sketch, the student performs according to approximate sizes, and the size numbers are applied accurately. On flat parts or products that have holes, when applying the size of the holes, the word hole is abbreviated in front of the diameter sign - holes. (and if there are several of them, then indicate their number). In the case under consideration, it is written as follows: otv. 0 10. Then the student rounds the corners, specifies the thickness of the lines, and the sketch is ready (Fig. 12, 2).

This work may be preceded by the following questions: is the product symmetrical or not? What is the line that marks the outline of an image called? Are the working part of the board and the ledge (handle) made from one piece of plywood or from separate parts? What symbol can be used to determine that the circle on the handle is a hole, and not a round protrusion? And so on. As experience shows, for the bulk of the circle members, sketching a flat detail on checkered paper is an affordable job. But the main task of this work is that in the process of making a sketch, schoolchildren better understand and see those basic initial rules for performing graphic works, according to which they are read. Then, in the process of making a product with the help of a sketch, students are convinced in practice that it is possible to read a graphic image only if it is made according to the rules. There are no special classes for sketching with the entire group of circle members, since the need for the ability to sketch is most often found in individual work with students in grade III. Third graders are not always satisfied with working on a template, a sample, a finished drawing. They want to improve products and even create them according to their own design. In this case, it is necessary to teach the children to make sketches of individual flat parts in accordance with the basic requirements. In the initial technical modeling, both flat and volumetric technical objects are made. And in individual work with students, the leader of the circle can, as an exception, show the student what a sketch of a three-dimensional detail is. It is too early to tell younger students about the rules for projection and formation of views, but in the language of direct and feedback between the student and the leader, expressions are inevitably encountered that determine, for example, the direction of the gaze on a technical object, the location of structural elements on the object, etc. These and others expressions and terms must be technically correct and used for their intended purpose. It is impossible to exclude any technical, graphic terms from the everyday life of circle members, and even more so to replace them with others, since this leads to the formation of incorrect technical ideas and adversely affects the overall development of children. Therefore, relying on the stock of geometric, graphical and technical concepts and terms that younger students have, it is important to work on revealing the origin, content and correct pronunciation of these terms.

Rice. 12. Board for cutting products: 1 - technical drawing; 2- sketch

So, for example, the actual size and the correct shape of the wings and stabilizers on aircraft models can only be determined if you look at the aircraft model exactly from above (when work is performed according to the model). If the work is carried out according to the drawing, for example, the model of the An-24 aircraft (Fig. 13), then the actual size of the wings and stabilizers is shown in place of the top view. Here it becomes necessary to correctly pronounce the name of the views and, if necessary, to explain that the image of the visible part of the surface of an object from the side of the observer is called a view. For example, the drawing of a matchbox (Fig. 14, 2) shows three main views: front view, top view, left view. The front view in this case is the main view. It gives the most complete picture of the subject. The observer is facing him.

Rice. 13. Model of the AI-24 aircraft: 1- fuselage; 2- wings; 3- stabilizers; 4- keel; 5- engines; 6- plank

If we rotate the object by 90°, we get a top view. The image of this view in the drawing is located below the front view.

If we turn the object (from the position of the front view) by 90° to the right side, we will see the left side of the object, that is, we will get a view from the left. The image of the view on the left in the drawing is located on the right side of the front view. The formation of views in the drawing can be understood using the trihedral angle (Fig. 14, 3). This image most clearly shows the formation of species. It is customary to consider the front view as the main one. The main view is the view that most fully characterizes a given product or object. But it happens when the object is most fully characterized by the view from the left (car, ship) or the view from above (airplane), then these views will be the main ones. It should be noted that in projection drawing there is an expression “left view”, but not “side view”, since according to the rules of projection, the left side of the object is depicted. And if you use the expression "side view", then the question arises: from which side? This complicates the exact language of the technique. It is also impossible to replace or abbreviate the names of species and say: from above, from the left, from the front - instead of: top view, left view, front view. A conversation with younger schoolchildren about the three types can only be 2* on material models. And if the circle members learn to correctly identify and pronounce the names of species so far only on models, then in the senior classes it will be easier for them to understand the projection connection of these species.

Rice. 14. Image of an object in parallel projections: 1- visual image of an object; 2- location of the main species; 3 - trihedral angle (formation of species)

The labor training program for technical labor in grade III provides for the manufacture of bulk products from cardboard, plywood, wood and wire, in which students must know the shapes of parts, reamers, patterns and how to connect parts to each other. Third graders should also be able to determine the shapes and sizes of parts from an assembly drawing. Proceeding from this, and based on the knowledge and skills that children receive in labor lessons, the leader of extra-curricular, out-of-school circle activities should ensure the consolidation and deepening of these knowledge and skills in the process of practical work in the manufacture of technical objects. So, for example, the initial concepts of an assembly drawing (such a drawing, where one image shows several parts interconnected into one product) can be fixed in the manufacture of an An-24 aircraft model (Fig. 13). At the same time, it is important that in the process of making a model, schoolchildren can always compare the product with an assembly drawing and a visual image, and also, at certain stages of work, analyze images showing the connection of individual parts and compare with the product. In such work, it is important to aim students at all the time trying to mentally separate the image of one detail from another and, perhaps, even try to depict a separate detail on checkered paper. Such work helps to prepare the thinking of schoolchildren for reading assembly drawings. Figure 13 shows separate parts of the An-24 aircraft model. Their drawings help the children to better understand the design in the manufacture of individual parts and assembling them into a single product.

To make an airplane model, you will need thick paper, glue, scissors and drawing accessories for marking on the material. The markup is performed according to a template, sketch or drawing, depending on the tasks that the leader sets for the students. In all cases, the paper is folded in half and the contour of half of the aircraft is outlined so that the fold line exactly coincides with the line of the visible contour of the lower part of the fuselage (Fig. 13). Then the model is cut out, the wings and stabilizers are folded along the fold lines. The keel is made in one layer of paper and glued into the tail section of the aircraft. Engines are made of paper folded in half. They are attached with glue-lubricated flaps to the bottom of the wing in the place where the leading edge of the wing has a bend. To fix the wings in a horizontal position, a paper strip is glued to them from above.

Before you start making electrified models, you can make with students an appliance that generates electricity and corresponds to a power plant with a generator and a transmission line going to the motor. Insulated wire is wound on two coils, and nails are inserted inside the coils (Fig. 15). Coils are placed at different ends of the table and connected with wire. If a compass is attached to one of them, and a permanent magnet is quickly brought to the other, the compass needle will deviate. When a magnet is brought up, its magnetic lines cross the turns of the coil and an electric current arises in it.

Rice. 15. Device "Power plant"

Through the wires, it reaches another coil and magnetizes it - the core, which makes the compass needle turn.

Training in initial technical modeling provides for the acquaintance of younger students with elementary electrical circuits. This knowledge is necessary for schoolchildren in the manufacture of electrified models and toys.

In general, the knowledge of younger schoolchildren about electricity and the use of electricity by a person expands in extracurricular activities, the schemes of objects that are modeled by circle members become somewhat more complicated, but the list of symbols for elements of electrical circuits does not expand compared to the third grade labor training program. Students in grades I-II also make the simplest electrified models, and in practice they know how to make an electrical circuit (battery, conductors, light bulb, switch), but it is not recommended to give them graphic symbols.

An electrical circuit consists of individual elements: a battery, conductors, a switch, a switch, consumers of electrical energy (a light bulb, an electric motor, an electric bell, etc.). Figure 16, 1 gives the symbols for these elements. An electrical circuit with one consumer (Fig. 16, 2) can be made even by first graders. At the same time, their attention must first of all be drawn to the fact that the current passes only through a closed electrical circuit. If at some point the wires are loosely connected, then the current will not flow through such a circuit and the bulb will not light up. Third graders can assemble a more complex working model of a traffic light (Fig. 17). They get acquainted with the ability to turn on one of the traffic light bulbs in turn. In this case, it is important to correctly connect the conductors to the terminals of the battery and the switch: one conductor goes to the switch from one terminal of the battery, and three conductors go to the three terminals of the switch through the traffic lights on the other.

Rice. 16. Electrical circuit: 1 - symbols of individual elements of the electrical circuit; 2 - electrical circuit with one consumer

When mastering the simplest electrical circuits, the main efforts of schoolchildren are aimed at acquiring the ability to read a circuit. The ability to quickly navigate the circuit and understand it correctly is necessary for students in order to assemble a circuit for the model. In addition, the ability to read an electrical circuit is used by them when checking the correct assembly of the circuit according to the circuit diagram. In the process of electrical modeling, the head of the circle systematizes the graphic knowledge that the children have in this area.

The whole complex of means and methods of graphic training of schoolchildren aims at active cognitive activity, the main task of which is to teach children to read graphic images, to help them master the techniques and methods of working on a drawing, diagram, etc. Reading a drawing means looking at a flat image of a product and, evaluating the totality of conditional images and designations, determine the shape of the product, dimensions, material, etc. That is, to make a mental analysis of the device of this product from the image and represent it in volume. The ability to determine the geometric shape of objects and analyze it is of great general educational importance and contributes to the development of technical thinking. All the objects around us have the form of geometric bodies or their combinations. The form of all parts, machines and mechanisms is based on certain geometric bodies and figures. Some of them are already familiar to younger students. If, for example, a student hears the word cube in a teacher's speech, he can easily imagine its shape. Consolidating and expanding the knowledge of younger students about geometric shapes and bodies, it is important to teach children to analyze these forms and mentally represent them. It is good to have visual aids of geometric bodies and geometric figures cut out of thick paper, equal in height and width to geometric bodies. Visually, by imposing a geometric figure on a geometric body, show and explain to schoolchildren that, for example, a circle is the base of a cylinder, and a rectangle is the side face of a tetrahedral regular straight prism. You can also visually show students the combination of bodies and shapes. By systematically and consistently bringing to the consciousness of younger schoolchildren that all objects and machines basically have geometric shapes, it is possible to teach children to understand the shape and design of objects and technical objects, as well as to mentally divide objects into geometric bodies, i.e. analyze the shape and design.

Rice. 17. Making a model of a three-lamp traffic light: 1- electric circuit of the model; 2- visual representation of the model

All surrounding objects, as well as machines, tools, fixtures and even toys, are made according to drawings, and, as mentioned above, all of them basically have geometric bodies or their parts, which means that between the ability to analyze a geometric shape and the ability to read the image of these items, i.e. drawing, there’s a certain connection.

Before starting to learn to read a drawing, it is necessary to ensure that schoolchildren recognize the symbols on the simplest drawings without additional effort. This is achieved through visual entertaining exercises. When the conditional images and designations become familiar to the eyes of the student, then, looking at the graphic image, he will quickly fix a specific designation, which implies a certain meaning. For example, a schoolchild sees a conventional designation of a radius, and an image of an arc of a circle, a circle, etc. appears in memory. A set of conventional images and designations associated with representations composes a mental image of the depicted product. And a mental analysis of the shape of its individual parts helps to suggest the device, the design of the product. The eyes at the time of the assumption continue to look at the graphic image and check, approve or reject the assumptions that have already arisen, that is, they control.

A way of visual, entertaining exercises to prepare the thinking of schoolchildren for reading drawings can be "Graphic Lotto". This game contributes to the correct assimilation of the names of geometric shapes, technical and graphic concepts, terms and symbols that are necessary in the initial technical modeling, as well as to consolidate and deepen the knowledge gained in the lessons of mathematics and labor training. "Graphic Lotto" may have options in form, volume and content. This can be one large wall-mounted tablet made by adults, or small cards (the same for all players) made by high school students according to the sketches of the game organizer. Each card is divided into cells, which depict geometric shapes, bodies and some conventional graphic symbols. The content of the card, which is shown in Figure 18, reflects part of the graphic material that occurs in the process of doing initial technical modeling. It corresponds to the program material in mathematics and labor education in the primary grades. The head of each specific technical circle selects the material for the cards independently, based on the tasks set, the age composition of the students and their general development. This means that you can make a lotto, taking only those topics that meet the objectives of a particular lesson. For example, fix the main symbols found on the simplest drawings (drawing lines, designation of radius, diameter, etc.).

Rice. 18. Approximate graphic lotto map: 1- straight and broken lines: 2-square (geometric figure); 3-cylinder (geometric body); 4- cone (geometric body); 5-right angle; 6-linear and square centimeters; 7 lines of visible and invisible contour; 8-radius designation;

The host of the game (leader, educator, high school student) has a second card, on which the names (terms) of all images are written, corresponding to the serial number. The first games: the host clearly and correctly pronounces the name of the image, and each player recognizes the corresponding image on his card and raises his hand to name the number of the cell in which it is placed. The one who first raised his hand gets the right to answer. If the respondent makes a mistake, the facilitator invites another to correct the mistake. The duration of the game is by agreement. As the game progresses, the leader can give the answering a certain number of points for the correct answer. The one who scores the most points wins. After the students have consolidated the concepts and memorized the visual symbols, the game can be played differently, i.e. the leader calls the cell number, and the players must give the correct and complete name of the image or symbol that is in it, preferably with explanations. Further, the course of the game remains the same, and when evaluating the answers, the leader must take into account not only the correctness, but also the completeness of the answers, as well as additions to them.

After the mathematical and graphic names, terms and symbols have been mastered by schoolchildren and fixed, you can choose (appoint) a leader from the circles, and lead the game to the winner in terms of speed, clarity and completeness of answers. Whoever gives the wrong answer is out of the game. Activity is taken into account as follows: if a player who plays three questions in a row does not raise his hands, then he is not ready for an answer and automatically leaves the game. The winner is the one who turns out to be the most knowledgeable and the most active, i.e. one or two people (by agreement) who are still in the game after everyone else has already dropped out.

The selection (by content) of the most appropriate material for making cards is done by the head of the circle or the teacher of the group. The course of the game is discussed with the students and their most interesting proposals are taken into account. The content of the material that is included in the game "Graphic Lotto" should cover educational material and provide some new information for elementary grades that is necessary to prepare students for design and technological activities. The leader informs them of new information for the children in such a volume that is necessary for meaningful practical work. On the card, the material is placed without any sequence and taking into account increasing complexity, so that students do not have

The whole group or circle plays "Graphic Lotto". You can play this game with the guys, taking into account age, especially at the first stage, and take into account the curriculum in mathematics and labor, gradually expanding and deepening the material used. Before the game is advisable. show the lotto cards to the students, answer the children's questions. Then the leader pronounces all the names, terms and demonstrates visual aids. For example, if the leader has slats of different and the same size, then it is very easy to show different angles, triangles, squares, rectangles, polygons, or, for example, a closed broken line, etc. The image of symbols can be shown on the blackboard with the involvement of children for exercises etc. During the conversation, the teacher, the head of the circle draws the attention of students to the correct pronunciation of names, terms and conventional graphic symbols. So that the terms are not divorced from the real ideas of schoolchildren, it is important to systematically analyze together with students the shape of bodies and figures, to show their difference on visual aids (material models), surrounding objects and technical objects. In practical work, the leader encourages the desire of younger students to use one or another term in speech, this contributes to the formation of correct ideas and has a positive effect on overall technical development. In addition, having the necessary theoretical knowledge and experience, each teacher, educator and leader of the circle independently determines the volume and content of the game, sets tasks and finds appropriate solutions in relation to specific conditions and the contingent of schoolchildren. As experience has shown, the game in the "Graphic Lotto" is active among schoolchildren, arouses children's interest in the competition and at the same time helps to accumulate a stock of ideas about symbols and images of objects. The main task of the "Graphic Lotto" is to prepare students' thinking for reading the simplest drawings.

When reading assembly drawings, the order remains the same. A child should not be allowed to try to read a drawing without adhering to a certain system. When reading a drawing randomly, younger students can consider a randomly selected part of a stump without comparing it with others. Experience shows that a unified approach to the formation of methods for reading graphic images of different content (technical drawing, part drawing and assembly drawing) is most appropriate and it is better to read them in the same order.

In conclusion, it must be said once again that the material presented is intended primarily for the teacher - the head of the technical circle, who, implementing the basic didactic principles of systematicity and consistency, accessibility and feasibility, visibility and awareness, will improve the elementary graphic training of younger students in the labor process.

The formation of primary graphic knowledge and skills in primary schoolchildren in out-of-class technical classes is not an end in itself, and special classes in graphic training should not be conducted. However, in the process of practical work in the manufacture of specific products, students are faced with the need to work with design and technological documentation (technical drawing, simple drawing, sketch, etc.). And it is important for the class leader to scientifically and methodically soundly consolidate the knowledge of students, improve them, and sometimes provide new information about the simplest elements of graphic literacy (symbols of the simplest drawing, electrical circuits, etc.) that are needed in the manufacture of a particular product and at a particular stage work.

The experience of advanced teachers and leaders of technical circles shows that at each practical lesson, no more than 5-7 minutes are allotted for graphic training of younger students (conversation, demonstration of visual aids, analysis of a graphic image, etc.). Systematic work on the formation of graphic knowledge and skills of younger students contributes to the successful assimilation of general labor knowledge and skills, the development of figurative thinking, the implementation of the first steps in the design and technological activities of younger students and prepares them for an earlier perception of the simplest technical information.

Despite the wide variety of statistical graphs, there are general rules for their construction.

When constructing a graph, it is important to find such display methods that best suit the content and logical nature of the displayed indicators.

Each graph consists of a graphic image and auxiliary elements.

Graphic image (the basis of the graph)- these are geometric signs, that is, a set of points, lines, figures, with the help of which statistical indicators are depicted. It is important to choose the right graphic image, which should correspond to the purpose of the graph and contribute to the greatest expressiveness of the displayed statistical data. So, for example, in Figure 4.4, the graphic image is a series of columns, in Figure 4.7 - a series of squares, etc.

Auxiliary elements make it possible to read the graph, understand and use it. These include: 1) chart explication; 2) spatial reference points; 3) scale landmarks; 4) chart field.

Let's consider each of them.

Graph explication- a verbal description of its content. It includes the general title of the graph, captions along the scales and explanations for individual parts of the graph.

The title of the graph should briefly and clearly reflect the main content (theme) of the data depicted on the graph; it indicates the object limited in space and time to which the data refers. If the title is part of the text (in a book, article, thesis, etc.), then it is usually placed under the bottom edge of the graph. If the graph is presented separately from the text, the title is written at the top of the graph in larger letters and numbers than all other labels on the graph.

In the graphics, in addition to the title, verbal explanations of the conventional signs and the meaning of individual elements of the graphic image are necessarily given. This includes the names and numbers of scales, the names of broken lines, numbers characterizing the values ​​of individual parts of the graph, references to sources, etc.

Explanatory inscriptions that reveal the meaning of individual elements of the graphic image can be placed either on the chart itself (on the graphic image or next to it) in the form of so-called labels (see Fig. 4.8), or in the form of a key placed outside the graphic image ( Fig. 4.5). The latter method is usually used in cases where there is not enough space on the graph, and the explanations are long.

Spatial landmarks of the graph are set in the form of a system of coordinate grids. Coordinate systems are rectilinear (Cartesian) and curvilinear. For plotting, usually only the first and, occasionally, the first and fourth quadrants are used. Curvilinear coordinates are a circle divided by 360º. In the practice of graphic representation, polar coordinates are also used. They are necessary for cyclic movement in time.

scale landmarks statistical graphics are determined by the scale and scale system. Scale A statistical graph is a measure of the conversion of a numerical value into a graphic one. For example, 1 cm of column height is equal to 50 thousand rubles of the authorized capital of a commercial bank. If the graph is built in the form of areas or volumes, units of areas or volumes serve as scales (For example, 1cm2 = 100km2 of the territory of the region).

The scales are chosen so that the difference between the displayed values ​​is clearly visible on the graph, but at the same time the possibility of their comparison is not lost.

If not one, but two scales are plotted on the graph (in a rectangular coordinate system), the ratio of their fields is chosen so that the sides of the space occupied by the graph vertically and horizontally are related as and. A scale scale is a line, the individual points of which can be read as certain numbers. The scale is of great importance in the chart. It distinguishes three elements: a line (or scale carrier), a certain number of dots marked with dashes, which are located on the scale carrier in a certain order, a digital designation of numbers corresponding to individual marked points. As a rule, not all marked points are supplied with a digital designation, but only some of them located in a certain order. According to the rules, the numerical value must be placed strictly against the corresponding points, and not between them (Fig. 4.1).

Rice. 4.1. Grid

Graphical and numerical intervals can be equal or unequal. If, throughout the scale, equal graphic intervals correspond to equal numerical intervals, such a scale is called uniform. If unequal graphical intervals correspond to equal numerical intervals, and vice versa, the scale is called non-uniform.

The scale of a uniform scale is the length of a segment (graphic interval), taken as a unit and measured in any measure. The smaller the scale, the denser the points that have the same value are located on the scale. To build a scale means to place points on a given scale carrier and designate them with the corresponding numbers according to the conditions of the problem. Of the non-uniform, the logarithmic scale is of the greatest importance. The method of its construction is somewhat different, since on this scale the segments are proportional not to the displayed values, but to their logarithms. So at base 10 lg1=0; log10=1; lg100=2 etc.

The scale carrier can be either a straight line or a curved line. In accordance with this, rectilinear scales (for example, a millimeter ruler) and curvilinear - arc and circular (clock dial) are distinguished.

Chart field- the space in which the geometric signs forming the graph are placed. The graph field is characterized by its format, i.e. size and proportions (aspect ratio).

For example, a sheet of paper on which the graph is located should be proportional. It is believed that the most convenient proportion for perception by the human eye is a rectangle, i.e. 1:1.474 (about 5:7). This combination is accepted in the standard for writing paper intended for copiers with A4 format, i.e. 210 mm: 297 mm.

Approximately the same proportions should be maintained in the sizes of most of the actual graphic images. In this case, the long side of the graph (grid) can be located horizontally (wide graph) and vertically (high graph).

Getting down to the graphical representation of statistical data, it is necessary first of all to choose the form of the graph and determine the methodology and technique for its construction.

What is a drawing?

Drawing- this is a document containing an image of a product (electrical circuit or architectural structure), as well as other data (dimensions, scale, technical requirements) necessary for its manufacture (construction) and control.

For example, in order to make a “Frame” part, you need to know its shape, dimensions, and the material from which it will be made. All of the above data must contain a drawing (Fig. 1).

The drawings depict various products: parts (for example: a ruler, a knitting needle), assembly units (for example: a paint roller, a fountain pen), kits (for example: a set of carpentry tools, a set of felt-tip pens), complexes (for example: a turning and milling shop, a moon rover ).

Product- any item or set of items to be manufactured.

Detail (from French detail)- a product made of a material that is homogeneous in name and brand, without the use of assembly operations. For example, a knitting needle is a part because it is made of a homogeneous material - aluminum alloy, without any assembly operations (screwing, riveting).

assembly unit- a product, the components of which are to be connected to each other by assembly operations (screwing, riveting, welding, stitching). For example: car, machine.

Set (from lat. completus - complete)- a set of any items that meet a specific purpose. For example: a manicure set, a cooking station, a personal computer.

Complex (from lat. complexus - connection, combination)- a set of something (products, buildings) that form a single whole. For example, a town-planning complex or a system block.

You can depict all the listed types of products if you master the methods and rules for the implementation and execution of technical documentation. And if this is not required for the future specialty, then what will the study of the subject give each of you? The answer is simple: the study of ICG will contribute to the development of figurative and logical thinking, ingenuity, attention, perseverance and accuracy, which are so necessary for people of various professions. In addition, knowledge of the drawing will allow you to carry out minor repairs to household appliances at home.

On the history of the emergence of graphic methods of images and drawing

The technique uses many methods by which various graphic images are obtained. The most commonly used of them were created and improved over many centuries.

Unfortunately, history has not preserved many historical documents by which it is possible to trace the evolution of graphic ways of displaying information. However, it is clear that their foundations were laid in ancient times.

Considering the history of the development of images adopted in technology, one should turn to the origins - primitive drawings and ancient pictograms. It is in them that the graphic language originates, is born and formed, the basis of which are the methods of images. You know from history that drawing appeared as a means of communication between people long before the creation of writing. Subsequently, drawing writing developed on its basis. In ancient times, many peoples transmitted any information (reports about military campaigns, business and political messages, hunting messages, magic spells, love messages) using drawings. On fig. 2a shows hieroglyphic writing, made with the help of symbols - hieroglyphs. The decoding of some hieroglyphs is shown in fig. 2b. Ancient hieroglyphs, as a rule, are contour drawings. It is this feature of the image that makes it “related” to the contour images of the drawing.

The surviving rock paintings testify to the origin of the cartographic method of transmitting information, which has been improved over many centuries.

One of the oldest maps (2500 BC) is the so-called Babylonian drawing, made on a clay tablet.

Drawings, plans, drawings of the Middle Ages do not indicate any noticeable development of the existing methods of images. However, there is reason to believe that the architectural drawing was born during this period.

In the Renaissance, the laws of perspective were discovered, the practical foundations for displaying technical information in new graphic ways were laid. The great Leonardo da Vinci (1452-1519) left to his descendants graphic images of an aircraft, throwing machines. They were executed in a special way, which his contemporaries called "conical perspective". This method has not lost its relevance to this day. It is now called "linear perspective" and is used in architecture, drawing, painting, and design.

Despite the fact that the drawing does not give a complete picture of the internal structure and the actual dimensions of the depicted object, for a long time it was used as the main technical document with which various structures were built. So, for example, the St. Sophia Cathedral in Kyiv (XI century), famous for its architecture, was erected according to drawings. In ancient Russia, Novgorod and Moscow churches and many other remarkable monuments of antiquity were built according to the drawings.

Over time, perspective drawings were transformed into a special kind of graphic image - technical drawings.

The development of image methods in Russia proceeded in an original way. On miniatures of the XIV-XV centuries. we can see images that are reminiscent of modern axonometric images and technical drawings currently used in technical graphics (Fig. 3).

Drawings in Russia were made by "drawers" (draughtsmen), a mention of which can be found in Ivan IV's "Pushkar order". Other images - drawings, drawings, were a view of the structure "from a bird's eye view" and were widely used by Russian craftsmen and builders. An example is the drawing-plan of a part of the Kremlin, made by P. Godunov at the beginning of the 17th century. (Fig. 4).

In Russia, there were graphic methods that made it possible to depict a car, an architectural structure from several sides, in order to get a better idea of ​​their shape and size. But since these images were not projectively connected to each other, they were difficult to use. At the end of the XVII century. scale images are being introduced in Russia (Fig. 5). The drawings begin to indicate scales and dimensions.

The development of technology has made it necessary to improve the methods and methods of graphic images. In the XVIII century. conditional (sometimes primitive) drawing gives way to another type of graphic image - a drawing. Russian draftsmen and Tsar Peter I himself made drawings using a method that would later be called 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. New types of images appeared, called profiles (profile in front, top) (Fig. 6), which became the prototypes of modern images in the system of three projections used in the drawings.

The largest Russian mechanics and inventors performed the drawings with great skill. Drawings of bridges across the Neva, a semaphore telegraph, a waterway and other projects made by I.P. Kulibin. Of interest are the methods of displaying the shape of the product on the drawings used by: Fedor Borzov when creating a lifting gate, R. Glinkov when designing parts of a spinning and carding machine (Fig. 7), I.I. Polzunov during the invention of the steam engine, father and son Cherepanov during the construction of the first steam locomotive in Russia.

Drawings and drawings of the 17th-18th centuries that have come down to us. testify not only to the high art of their implementation, but also to the use of the method of rectangular projection long before its theoretical substantiation.

A great contribution to the development of technical graphics was made by Ya.A. Sevastyanov, who published a work in 1818, which made it possible to make the drawings more informative.

The development of technical graphics was devoted to the works of professors A.I. Dobryakov, N.A. Rynin, D.I. Kargin, N.F. Chetvertukhin and others.

Over time, the images improved, changed, became convenient for work and gradually transformed into images of a modern drawing.

The entire history of the development of the drawing is continuously connected with technical progress. At present, the drawing has become the main document of business communication in science, technology, production, design, and construction.

For many years, drawings were made by hand using a "circle" - a compass, a "square" - a square and various round-shaped gear, which took a lot of time. At the beginning of the 20th century, work began on the mechanization of the designer's workplace. As a result of it, drawing machines, drawing and writing instruments of various systems appeared, which made it possible to speed up the process of making drawings. Currently, automated methods for making drawings have been created, which greatly simplified this process and accelerated the development of design documentation. However, it is impossible to create and check a computer drawing without knowing the basics of the graphic language, which you will learn while studying the subject "Engineering Computer Graphics".

Graphical language is often referred to as the international technical language of communication because technically literate people can read drawings made in different countries of the world.

Types of graphic images Drawing - done by hand, dimensions are not maintained. Sketch - is done by hand and the projections are maintained "by eye". A drawing is a graphic representation of an object or part of it with exact dimensions. Assembly drawing - depicts the product as a whole, assembled. Reamers - images of products that are "cut out" from a whole sheet of material and bent along certain lines. Schemes are conditional images showing the principle of operation of devices. A technical drawing is a graphic illustration made by hand with approximate observance of proportions. Axonometric projections are visual images made exactly in size according to certain rules. Visual images - show the detail as a whole, in volume.

Definition of the term "axonometric projection" An axonometric projection is an image obtained by parallel projection of an object along with the axes of rectangular coordinates onto a plane. z x y z x y z z x y The principle of constructing axonometric projections on the example of a cube x y Р Р

The origin of the name The word "axonometry" itself comes from the Greek words "axon" - axis and "metrio" - to measure, that is, it literally translates as follows: "measurement along the axes." If the dimensions of the part during projection are distorted along all three axes with the same coefficient of distortion, then the projection is called isometric (from the Greek isos - the same). If, during projection, the dimensions of the part are distorted equally along two axes, then the projection is called dimetric (from the Greek di-double). If the dimensions of the part are distorted along all three axes with different distortion coefficients, then the projection is called three metric.

Types of axonometric projections oblique frontal dimetric projection If the projecting parallel rays are directed to the plane, directed to the projection plane P at an angle less than 90 °, at an angle less than 90 °, and the object is turned to us by the front face (“face to face”), then we get z y x p 45 °

Types of axonometric projections If the faces of the part are inclined to the plane P at equal angles, and the projection onto it is carried out by parallel rays perpendicular to the projection plane, then we get a visual image called a rectangular isometric projection z x y 90 °

Projection of Plane Figures A rectangle is a projection of a parallelepiped and a cylinder, a prism. A triangle is a projection of a trihedral pyramid and a prism. A polygon is a projection of polyhedral bodies A square is a projection of the faces of a cube A circle is a projection of a ball and one of the projections of a cylinder

Oblique frontal dimetric projection An oblique frontal dimetric projection (abbreviated as frontal dimetry) is built as follows: x 1 y z The dimensions are set aside: a) along the X and Z axes - true (1: 1) b) along the Y axis and lines parallel to it - reduced in twice (1:2) 45°

The image of flat figures in the dimeter Triangle a y z x To build the projection of the triangle, you need to: 2. On the X axis, set aside the length of the base a, divide it in half - find the point O, from which draw a line parallel to the Y axis (projection of the height of the triangle) and set aside half on it its lengths .. a / 2 a / 2 a / 2 a / 2 a / 2 a / 2 a / 2 a / 2 o h h / 2 3. Connect the obtained vertices of the triangle with line segments - this is its projection in dimetry Construct axonometric axes.

Rectangular isometric view. A rectangular isometric projection (abbreviated: isometry) is built as follows: 1. The axonometric axes are arranged as follows: z z x y

A convenient way to build axes for isometric projection. For a simple construction of isometric axes (without a protractor), you can use this method: draw a vertical line-axis Z draw an auxiliary horizontal line from the origin to the left and right along it, set aside 5 identical segments (we get points A and B) Set aside from these points vertically down 3 of the same segments (we get points C and D) connect these points with point O - we get the X and Y axes at the right angle to each other about A B C D

To build an isometric projection of a part, you need: Example of constructing an isometric projection according to the drawing 1 Analyze the geometric shape of the part Drawing of the part The part is a structure of two parallelepipeds of different sizes, the smaller of which is located on the larger one and the centers of their bases coincide

An example of building an isometric projection according to the drawing z x y Isometric projection of a part. The lines of the invisible contour are drawn with a dashed line 3. Set aside along the X and Y axes the dimensions corresponding to the length and width of the base of the lower parallelepiped 4. From the ends of these segments, draw straight lines parallel to the Y and X axes until they intersect 5. Draw line segments from the obtained vertices of the lower base, parallel to the Z axis and equal to the height of the lower parallelepiped 6. Connect the resulting points - you get a large parallelepiped 7. Find the center of symmetry of the upper base of this parallelepiped and similarly construct a second parallelepiped relative to it - a smaller one 2. Draw axonometric axes

Features of constructing projections of parts with cylindrical holes If a part has holes in the form of cut cylinders, then the construction of their axonometric projections becomes somewhat more complicated. An important point in this case is the choice of the type of projection - it depends on the location of the hole.

Selecting the projection type for parts with cylindrical holes It is advisable to choose frontal dimetry as a type of visual representation if the hole is located on the front face of the part - then the hole will not change its shape and its construction will be quite simple. This is how the frontal dimetric projection of the part shown in Figure 11 looks like.

An example of constructing a projection of a part with a round hole on the front face To build the projection of a part, you need to: 1. Construct a frontal dimetric projection in the usual way - from the front or back face. 2. Draw with a compass the projection of the hole on the original face - a circle of the desired radius from the center O. 3. From this center of the circle O, draw the axis of the hole parallel to the Y axis, that is, at an angle of 45 ° to the X axis .. 4. Set aside from the point O along the axis a straight line segment equal to half the depth of the hole (distortion along the Y axis) - we get the point O 1 - the center of the opposite part of the hole. 5. From point O 1, draw a circle of the desired radius with a compass and highlight with a solid line that part of it where it falls inside the first circle, mark the rest of it with a dashed line, like the walls of the cylinder .. z y x o o1o1 dashed line.

Distortion of round holes in isometry If in dimetry a round hole on the front face of the part was not distorted, then in isometry we are faced with a distortion of the shape of a round hole, regardless of which face of the part it is located on. In any case, the circle turns into an ellipse, but to simplify the construction process, it is permissible to replace it with an oval.

Construction of an oval y x o x y o a a z b b 1. Construct axonometric axes. 2. On the corresponding pair of axes, set aside segments a and b, the length of which determines the position of the center of the variable circle O 1. o 1 o 1 o 1 o 1 3. Draw straight lines through the points obtained, parallel to the axes, at their intersection is the center of the future oval O From points O 1 on both sides to put on the existing straight lines segments equal to the radius of the original circle r and get points A, B, C, D r r 5. From the obtained points A, B, C, D, draw straight lines parallel to the axes X and Y to their intersection - we get a rhombus PQRS, into which an oval should be inscribed. Draw its axes OS and PR D A B C S P Q R 6. Place the needle of the compass at point Q, and the second leg at point C and draw an arc of radius QC from it to point D. Similarly, an arc AB is drawn from point S. K M 7. From points K and M (at the intersection of the major axis of the ellipse and the radii of large arcs QC and SA), draw small arcs AD and BC - you get the required oval. The accuracy of the coincidence of the ends of the arcs depends on the thoroughness of the construction. To build an oval, you need:

An example of constructing an isometric projection of a part with a round hole on one of the faces x z y o Part drawing Part projection To build a projection of a part with a round hole on one of the faces, you must: 1. Draw axonometric axes. 2. Construct a visual image of the part in isometry in a standard way. 3. On the face of the part where the hole is located, mark the position of its center O 1 and build an oval according to the previously discussed rules. 4. Draw the axis of the cylindrical hole, set aside on it the depth of the hole O 1 O 2 5. Regarding the center O 2, it is similar to build an oval corresponding to the back of the hole. And highlight with a solid line that part of it where it falls inside the front of the hole. designating the side walls of the hole. All lines of the invisible contour are drawn with a dashed line O1O1 O2O2

In this case, you can apply the following method: cut out its front quarter from the constructed projection of the part, cutting it with two planes perpendicular to each other, parallel to the frontal and profile planes, thereby making the previously hidden structural elements visible. Axonometric projections of a part with a quarter cut.

Technical drawing A graphic representation of a part, made by hand and with approximate observance of proportions and dimensions, is a technical drawing. It is assumed that the light falls on the object from the top left. The strokes are applied the thicker, the darker the surface of the object. To enhance the effect of the volume of an object, hatching is applied to technical drawings.