Graphic work on. Calculation and graphic work: recommendations for implementation

TO SAOU SPO "Tambov Pedagogical College" METHODICAL INSTRUCTIONS for implementation practical work discipline "Engineering graphics" for students of the specialty "280707 Protection in emergency situations, rescue technician" (Works No. 1-6) TAMBOV, 2013 Author: TARASOV V.E., teacher of special disciplines of the State Autonomous Educational Institution of Secondary Professional Education "Tambov Pedagogical College "Reviewer: Lappa T.I.. Head of the Department of Physical Culture of the State Autonomous Educational Institution of Secondary Professional Education "Pedagogical College of G. Tambov" Guidelines for performing practical work in the discipline "Engineering Graphics" for students of the specialty "280707 Protection in Emergency Situations, Rescue Technician" (Works No. 1-6) Guidelines for performing graphic work in the course "Engineering Graphics" are intended for students of specialty 280707 "Protection in Emergency Situations". The manual contains the necessary theoretical and reference material for performing graphic works No. 1-6. Recommended by the scientific and methodological council of the college as a teaching aid. INTRODUCTION The program of the course "Engineering Graphics" for students majoring in secondary vocational education 280707 Emergency Protection, Rescue Technician determines the amount of knowledge required to complete mechanical engineering drawings and diagrams. Students perform most of the work independently, so when studying an engineering graphics course they are recommended to familiarize themselves with the requirements of ESKD standards for the execution of drawings. All graphic work by students must be completed in accordance with their version according to the serial number in the educational journal. The purpose of this publication is to familiarize students with fonts, lines, methods of constructing connections, depicting objects, arrangement of views, making cuts, sections and axonometric projections, drawing dimensions and maximum deviations, graphic designation of materials in graphic works and drawing electrical circuits. REQUIREMENTS MADE BY ESKD STANDARDS FOR THE PERFORMANCE OF GRAPHIC TASKS Unified System of Design Documentation (ESKD) - critical system permanent technical and organizational requirements that ensure the interchange of design documentation without its re-registration between industries and individual enterprises. It allows for increased unification in the design development of industrial product projects; simplification of document forms and reduction of their nomenclature, as well as graphic images: mechanized and automated creation of documentation and, most importantly, the readiness of industry to organize the production of any product at any enterprise in the most short term. The ESKD presents a set of state standards that establish interrelated unified rules and regulations on the procedure for the development and circulation of design documentation used by various organizations and enterprises. These uniform rules also apply to educational documentation, which may include graphic tasks performed by students, therefore all images must be made clearly, accurately and in accordance with the requirements of the Unified Design Document. Assignments are completed on sheets of drawing paper in A3 and A4 format (GOST 2.301-68). After drawing a frame on the sheet, in the lower right corner, mark the dimensions of the main inscription of the task, which is the same for all formats. The form of the main inscription is adopted in accordance with the requirements of GOST 2.104-68. Images must be made on the scale specified in the assignment, but in compliance with GOST 2.302-68. When filling out the main and other inscriptions, it is necessary to comply with the requirements of GOST 2.304-81. When applying dimensions, it is recommended to use GOST 2.307-68. When tracing an image, the thickness of the main lines should be 0.8 - 1.0 mm, and the thickness of the remaining lines should be in accordance with GOST 2.303-68. LIST OF REFERENCES 1. Bogolyubov S.K.Engineering graphics. - M.: Mechanical Engineering, 2004. -352s 2. GOST 2. 303-68. Lines. 3. GOST 2. 304-81. Drawing fonts. 4. GOST 2. 305-68. Images - views, sections, sections. 5. GOST 2. 301-68. Formats // ESKD. General rules execution of drawings. GOST 22.301-68 - GOST 2.321-84. M., 1988. 239 p. 6. GOST 2. 302-68. Scale. 7. GOST 2. 307-68. Drawing dimensions and maximum deviations. 8. Levitsky V.S. Mechanical engineering drawing/ V.S. Levitsky. M., 1998. 383 p. 9. Mechanical engineering drawing / G.P. Vyatkin, A.N. Andreeva, A.K. Boltukhin et al. M., 1985. 368 p. 10. Popova G.N. Mechanical engineering drawing / G.N. Popova, S.Yu. Alekseev. St. Petersburg, 1999. 453 p. 11. S.K. Bogolyubov Individual assignments for the drawing course: Practical. A manual for technical school students. - M.: Higher. school, 1989 - 368 pp.: ill. 12. Fedorenko V.A. Handbook of mechanical engineering drawing/ V.A. Fedorenko, A.I. Shoshin. L., 1986. 416 p. PRACTICAL WORK No. 1 DRAWING THE FORMAT AND BASIC LETTER FOR GRAPHIC AND TEXT DOCUMENTS Purpose of the work: to study graphic formats, types of main inscriptions on drawings All drawings must be made on sheets of paper of a standard format. The formats of paper sheets are determined by the dimensions of the outer frame of the drawing (Fig. 3). It is drawn with a continuous thin line. The drawing frame line is drawn as a solid thick main line at a distance of 5 mm from the outer frame. A 20 mm wide margin is left on the left for filing. The designation and dimensions of the sides of the formats are established by GOST 2.304-68. Data on the main formats are given in table. table with the given example. The drawing is drawn up with an internal frame (in the form of a solid main line), a margin of 20 mm is left from the borders of the format on the left side, and 5 mm on all other sides. In the lower right corner of the drawing, draw the main inscription (stamp) in accordance with GOST 2.104-68* in accordance with Figure 1. It is recommended to fill in the following columns for the main inscription in the conditions educational process(standard column designation retained): column 1 - name of the part or assembly unit (name of the topic on which the task was completed); Column 2 - designation of the document according to the system adopted at the college (name of the group, year, number on the list, number of the work performed - ZChS.31.2011.05.02.); Column 3 - designation of the part material (fill in only on part drawings); Column 4 - do not fill out; Column 5 - weight of the product (do not fill in); column 6 - image scale (in accordance with GOST 2.302-68* and GOST 2.109-73); column 7 - serial number sheet (on documents consisting of one sheet, the column is not filled in); column 8 - total quantity sheets of the document (the column is filled out only on the first sheet of the document); column 9 - name of the educational institution and group number; column 10 - the nature of the work performed by the person signing the document, for example: Developed by: (student) Checked by: (teacher) column 11 - clear spelling of the names of the persons signing the document; column 12 - signatures of persons whose surnames are indicated in column 11; Column 13 - date of signing of the document (indicate the month and year). Fig. 1 The text on the drawing margin and in the main inscription is done in 3.5, 5 or 7 mm font, and the dimensional numbers are 3.5 or 5 mm. An example of filling out the main inscription is given in Figure 2. The work is performed in thin lines, then the final outline of the drawing is made with lines in accordance with their purpose. The outline begins with dash-dotted and solid thin lines, then the main solid lines are outlined: first curved sections, then straight ones. TASK: on a sheet of A4 drawing paper, draw the lines of the drawing frame and the main inscription. PRACTICAL WORK No. 2 IMPLEMENTING A DRAWING FONT Purpose of the work: To study the pits of drawing fonts, to gain skills in writing in a drawing font. GOST 2.304-81 establishes drawing fonts applied to drawings and other technical documents of all industries and construction. The font size determines the height h of capital letters in mm. The line thickness of the font d depends on the type and height of the font. GOST sets the following font sizes: (1.8); 2.5; 3.5; 5; 7; 10; 14; 20 (Tables 1, 2). The use of font 1.8 is not recommended and is allowed only for type B. The following font types are installed: Type A with a slope of 75° - d = (1/14)h; Type A without tilt - d = (1/14)h; Type B with an inclination of 75° - d = (1/10)h; Type B without tilt - d = (1/10)h. Font parameters are given in tables 1 and 2. Table 1 - Font parameters, mm Font parameters Designations3,55,07,010,014,0ABABABABABHeight of capital lettersh3,53,55,05,07,07,010101414Height of lowercase lettersc2,52,53,53,55, 05,07,07,01010Spacing between lettersa0,50,70,71,01,01,41,42,022,8Minimum line spacingb5,56,08,08,511,012,016,017,02224Minimum spacing between wordse1,52,12,13,03,04,24 ,26,06,08,4Thickness of font linesd0,250,350,350,50,50,70,71,01,01,4 Table 2 - Width of letters and numbers of type B font, mm Letters and numbersRelative size3,55,07,010,014,0Capital lettersB, V, I, J, K, L, N, O, P, R, T, U, C, H, L, E, Z 6d23469A, D, M, X, S, Yu7d2.53.55711Zh, F, Sh, Ш, ъ8d345.5812Э, Г, З, С5d1.82.53.557 Lowercase lettersA, b, c, d, d, f, h, i, j, k, l, n, o, p, r, y, x, h , c, b, e, i5d1. 82.53,557m, ъ, ы, ю6d23469ж, t, f, w, ш7d2.53.55711с4d1.62346Numbers2, 3, 5, 6, 7, 8, 9, 05d1.82.53,55713d11.523446d23469 TASK. Using size 10 type B font, write the letters of the alphabet shown (lowercase and uppercase), numbers from 0 to 10 and any two words. A sample of the task is shown in Figure 1. INSTRUCTIONS FOR COMPLETING THE TASK First you need to prepare a sheet of paper in standard A4 format with a frame at a distance of 5 mm from the edges at the top, right and bottom and 20 mm on the left. The sequence of completing the task of writing a standard type B font of size 10 is as follows: - draw all the auxiliary horizontal straight lines that define the boundaries of the lines of the font; - set aside a distance between lines equal to 15 mm; - set aside the font height h, i.e. 10 mm; - lay down segments equal to the width of the letters plus the distance between the letters; - draw inclined lines for the grid at an angle of 75° using two triangles: with an angle of 45° and with angles of 30° and 60°. Example of completing the task PRACTICAL WORK No. 3 DRAWING LINES Purpose of the work: to gain skills in drawing lines and using drawing tools All drawings are made with lines of various purposes, styles and thicknesses (Table 3). The thickness of the lines depends on the size, complexity and purpose of the drawing. According to GOST 2.303-68, lines are used to depict products in drawings various types depending on their purpose, which helps to identify the shape of the depicted product. Table 1 - Types of lines Inscription Line thickness in relation to the thickness of the main line Name Applications A solid thick main line is made with a thickness indicated by the letter s, ranging from 0.5 to 1.4 mm, depending on the complexity and size of the image in a given drawing, as well as on the format drawing. A solid thick line is used to depict the visible contour of an object, the contour of an extended section and part of a section. s/3-s/2 A solid thin line is used to depict dimension and extension lines, hatching sections, a contour line of an overlaid section, a leader line, a line for depicting boundary details (“furnishings”). s/3-s/2 A solid wavy line is used to depict break lines, the line demarcating the view and section s/3-s/2 The dashed line is used to depict an invisible contour. The length of the strokes must be the same. The length should be chosen, depending on the size of the image, from approximately 2 to 8 mm, the distance between strokes is 1...2 mm.s/3-s/2The dash-dotted thin line is used to depict axial and center lines, section lines, which are axes of symmetry for superimposed or offset sections. The length of the strokes must be the same and is selected depending on the size of the image, approximately from 5 to 30 mm. The distance between the strokes is recommended to be 2...3 mm.s/2-2s/3The dash-dotted thickened line is used to depict elements located in front of the secant plane (“superimposed projection”), lines indicating surfaces to be heat treated or coated.s/3 -s/2An open line is used to indicate a section line. The length of the strokes is taken 8...20 mm depending on the size of the image. s/3-s/2 A solid thin line with kinks is used for long break lines. s/3-s/2 A dash-dotted line with two dots is used to depict details in the extreme or intermediate positions; fold lines on developments The quality of the drawing largely depends on the quality and adjustment of the tools, as well as on their care. Drawing tools and accessories must be kept in full working order. After work, tools should be wiped and stored in a dry place. This prevents warping of wooden instruments and corrosion of metal ones. Before work, you should wash your hands and wipe the squares and crossbar with a soft rubber band. Pencils. The accuracy and precision of the drawing largely depends on the correct sharpening of the pencil. You can sharpen graphite using sandpaper. The student must have three brands of pencil: M-B, TM-HB and T-H. When making drawings with thin lines, it is recommended to use a pencil of grade T. You should trace the lines of the drawing with a pencil TM or M. A lead of grade M should be inserted into the compass. A circular compass is used for drawing circles. A needle is inserted into one leg of the compass and secured with a screw, and a pencil insert into the other. To measure dimensions and plot them on the drawing, use an insert with a needle. Calipers are used to draw circles of small diameter (from 0.5 to 10 mm). For ease of use, the rotating leg moves freely along the axis of the caliper. When drawing circles of large radii, an extension is inserted into the leg of the compass into which a pencil insert is secured. Lines are drawn in a certain direction: Horizontal lines are drawn from left to right, vertical lines are drawn from bottom to top, circles and curves are drawn clockwise. The center of the circle must necessarily be at the intersection of the strokes of the axial and center lines. Hatching in the drawings is performed in the form of parallel lines at an angle of 45° to the center line or to the contour line taken as the main one. The inclination of the hatch lines can be either left or right. Two touching figures are hatched in different directions . If a third figure is adjacent to two touching figures, then you can diversify the hatching by increasing or decreasing the distance between the hatching lines. Non-metallic materials, including fibrous monolithic and slab (pressed) cross-sections are lined with a checkered pattern. TASK: Draw the given lines and images (in accordance with the task option, Figure 1, 2), observing their indicated location. The thickness of the lines should be carried out in accordance with GOST 2.303 - 68, do not apply dimensions. Complete the task on a sheet of A4 drawing paper. INSTRUCTIONS FOR COMPLETING THE TASK It is more convenient to begin the task by drawing a thin vertical line through the middle of the inner frame of the drawing, on which marks are made in accordance with the dimensions given in the task. Thin auxiliary horizontal lines are drawn through the designated points to facilitate the graphic part of the task. On the vertical axes intended for circles, points are marked through which the circles are drawn using the lines specified in the task. In training drawings, a solid main thick line is usually made with a thickness of s = 0.8...1 mm. Figure 1 - even numbers of options Figure 2 - odd numbers of options PRACTICAL WORK No. 4 EXECUTION OF A DRAWING OF A DETAIL WITH MATINGS Purpose of work: to study the implementation of mating curves, to draw a part with mates 1. Dividing circles into equal parts Dividing a circle into 4 and 8 equal parts 1) Two mutual perpendiculars to the diameter of the circle divide it into 4 equal parts (points 1, 3, 5, 7). 2) Next, divide the right angle into 2 equal parts (points 2, 4, 6, 8) (Figure 1 a). Dividing a circle into 3, 6, 12 equal parts 1) To find points dividing a circle of radius R into 3 equal parts, it is enough to draw an arc of radius R from any point on the circle, for example point A(1) (points 2,3) (Figure 1 b). 2) We describe arcs R from points 1 and 4 (Figure 1 c). 3) We describe arcs 4 times from points 1, 4, 7, 10 (Figure 1 d). abc where Figure 1 - Dividing circles into equal parts a - into 8 parts; b - into 3 parts; c - into 6 parts; g - into 12 parts; d - into 5 parts; e - into 7 parts. Dividing a circle into 5, 7, equal parts 1) From point A with radius R, draw an arc that intersects the circle at point n. From point n, a perpendicular is lowered onto the horizontal center line, obtaining point C. From point C with radius R1 = C1, an arc is drawn that intersects the horizontal center line at point m. From point 1 with radius R2=1m, draw an arc intersecting the circle at point 2. Arc 12=1/5 of the circumference. Points 3,4,5 are found by plotting segments equal to m1 with a compass (Figure 1e). 2) From point A we draw an auxiliary arc of radius R, which intersects the circle at point n. From it we lower the perpendicular to the horizontal center line. From point 1 with radius R=nc, 7 notches are made around the circle and 7 required points are obtained (Figure 1 e). 2. Construction of conjugations Conjugation is a smooth transition of one line to another. For accurate and correct execution drawings, you must be able to construct interfaces that are based on two provisions: 1. To interface a straight line and an arc, it is necessary that the center of the circle to which the arc belongs lies on the perpendicular to the straight line, restored from the interface point (Figure 2 a). 2. To conjugate two arcs, it is necessary that the centers of the circles to which the arcs belong lie on a straight line passing through the conjugation point (Figure 2 b). Figure 2 - Provisions on conjugations a - for a straight line and an arc; b - for two arcs. Conjugation of two sides of an angle with a circular arc and a given radius Conjugation of two sides of an angle (acute or obtuse) with an arc of a given radius is performed as follows: Parallel to the sides of the angle at a distance equal to the radius of the arc R, draw two auxiliary straight lines (Figure 3 a, b). The intersection point of these lines (point O) will be the center of an arc of radius R, i.e. mating center. From the center O, they describe an arc that smoothly turns into straight lines - the sides of the angle. The arc ends at the connecting points n and n1, which are the bases of the perpendiculars drawn from the center O to the sides of the angle. When constructing a mating of sides right angle It is easier to find the center of the mating arc using a compass (Figure 3 c). From the vertex of angle A, draw an arc of radius R equal to the conjugation radius. Conjugation points n and n1 are obtained on the sides of the angle. From these points, as from centers, arcs of radius R are drawn until they intersect each other at point O, which is the center of conjugation. From center O, describe a conjugation arc. Figure 3 - Conjugate angles a - acute; b - stupid; in - direct. Conjugation of a straight line with a circular arc Conjugation of a straight line with a circular arc can be performed using an arc with an internal tangency (Figure 4 b) and an arc with an external tangency (Figure 4 a). To construct a conjugation, draw a circle of radius R and a straight line AB using an external touch. A straight line ab is drawn parallel to a given straight line at a distance equal to the radius r (radius of the conjugate arc). From the center O, draw an arc of a circle with a radius equal to the sum of the radii R and r until it intersects the straight line ab at point O1. Point O1 is the center of the mating arc. The conjugation point c is found at the intersection of straight line OO1 with a circular arc of radius R. Conjugation point C1 is the base of the perpendicular dropped from the center O1 to this straight line AB. Using similar constructions, points O2, C2, C3 can be found. In Figure 6 b, an arc of radius R is paired with a straight arc AB of radius r with an internal tangency. The center of the conjugation arc O1 is located at the intersection of an auxiliary line drawn parallel to this line at a distance r with the arc of an auxiliary circle described from the center O with a radius equal to differences R-r . The conjugation point is the base of the perpendicular dropped from point O1 to this straight line. The mating point c is found at the intersection of straight line OO1 with the mating arc. ab Figure 4 - Conjugation of an arc with a straight line a - with external contact; b - with internal touch. Conjugation of an arc with an arc The conjugation of two circular arcs can be internal, external or mixed. With internal conjugation, the centers O and O1 of the mating arcs are located inside the mating arc of radius R (Figure 5 a). When externally conjugating mating arcs of radii R1 and R2 are located outside the mating arc of radius R (Figure 5 b). With a mixed conjugation, the center O1 of one of the mating arcs lies inside the mating arc of radius R, and the center O of the other mating arc lies outside it (Figure 5 c). abc Figure 5 - Arc mates a - internal; b - external; in - mixed. When drawing the contours of complex parts, it is important to be able to recognize certain types of interfaces in smooth transitions and be able to draw them. To acquire skills in constructing interfaces, perform exercises on drawing the contours of complex parts. To do this, it is necessary to determine the order in which the interfaces are constructed and only then begin to implement them. TASK: Draw images of the contours of the parts indicated in the drawing of the task, apply dimensions. Complete the task on a sheet of A4 drawing paper. Instructions for completing the task When performing each task, a certain sequence of geometric constructions must be observed: - axial, center lines, main descriptive lines; - arcs, roundings; - stroke, shading, extension lines; - dimensions. Variants of the task PRACTICAL WORK No. 5 PERFORMANCE OF VIEWS FROM AN AXONOMETRIC IMAGE OF A PART Purpose of the work: to gain skills in constructing projections of a part model. TASK: construct three types of parts based on this visual image in an axonometric projection in accordance with the task option. The task is performed on sheets of drawing paper in A3 or A2 format (GOST 2.301-68). After drawing a frame on the sheet, in the lower right corner, mark the dimensions of the main inscription of the task, which is the same for all formats. The form of the main inscription is adopted in accordance with the requirements of GOST 2.104-68. If necessary, images should be drawn to scale, GOST 2.302-68. When filling out the main and other inscriptions, it is necessary to comply with the requirements of GOST 2.304-81. When applying dimensions, it is recommended to use GOST 2.307-68. When tracing an image, the thickness of the main lines should be 0.8 - 1.0 mm, and the thickness of the remaining lines should be in accordance with GOST 2. 303-68 (ST SEV 1178-78). Objects in technical drawings are depicted using the method of rectangular projection onto six faces of a hollow cube. It is assumed that the depicted object is located between the observer and the corresponding face of the cube (see Fig. 1). The faces of the cube are taken as the main projection planes. There are six main projection planes: two frontal -1 and 6 (front view or main view, rear view), two horizontal -2 and 5 (top view and bottom view), two profile -3 and 4 (left view and right view) . The main projection planes are combined into one plane along with the images obtained on them. The image on the frontal plane of projections is taken as the main one in the drawing. The object is positioned relative to the frontal plane of projections so that the image on it - the main image - gives the most complete idea of ​​the shape and size of the object. Objects should be depicted in a functional position or in a position convenient for their manufacture. Items consisting of several parts should be depicted in a functional position. The question of which of the main views should be used in the product drawing must be resolved so that with the smallest number of views in combination with other images (local and additional views, sections and sections, extension elements), the drawing fully reflects the design of the product. Procedure for completing the task: 1) study GOST 2.305-68, 2.307-68; 2) carefully familiarize yourself with the design of the figure based on its visual representation and identify the main geometric bodies of which it consists; 3) select the appropriate area on a sheet of paper for each type of part; 4) finely draw all the lines of the visible and invisible contour with a pencil, mentally dividing the part into basic geometric bodies; 5) apply all necessary extension and dimension lines; 6) put dimensional numbers on the drawing; 7) fill out the main inscriptions and check the correctness of all constructions; 8) trace the drawing with a pencil. Variants of the task PRACTICAL WORK No. 6 PERFORMING A TECHNICAL DRAWING OF A SIMPLE DETAIL A technical drawing is a visual image that has the basic properties of axonometric projections or a perspective drawing, made without the use of drawing tools, on an eye scale, in compliance with proportions and possible shading of the shape. A technical drawing can be performed using the central projection method, and thereby obtain a perspective image of the object, or the parallel projection method (axonometric projections), constructing a visual image without perspective distortions. Technical drawing can be performed without revealing volume by shading, with shading of volume, as well as conveying the color and material of the depicted object. In technical drawings, it is allowed to reveal the volume of objects using the techniques of shading (parallel strokes), scribbling (strokes applied in the form of a grid) and dot shading. The most commonly used technique for identifying the volume of objects is shaking. It is generally accepted that light rays fall on an object from the top left. Illuminated surfaces are not shaded, while shaded surfaces are covered with shading (dots). When shading shaded areas, strokes (dots) are applied with the smallest distance between them, which makes it possible to obtain denser shading (dot shading) and thereby show shadows on objects. Table 1 shows examples of identifying the shape of geometric bodies and details using shading techniques. Fig. 1. Technical drawings revealing volume by shattering (a), shading (b) and dot shading (e) Table 1. Shading of the form using shattering techniques Technical drawings are not metrically defined images if dimensions are not indicated on them. technical drawing in a rectangular isometric projection(isometry) with a distortion coefficient on all axes equal to 1. When the true dimensions of the part are plotted along the axes, the drawing turns out to be 1.22 times larger than the real part. Methods for constructing an isometric projection of a part: 1. The method of constructing an isometric projection of a part from a form-generating face is used for parts whose shape has a flat face, called a form-generating face; The width (thickness) of the part is the same throughout; there are no grooves, holes or other elements on the side surfaces. The sequence of constructing an isometric projection is as follows: * constructing the axes of the isometric projection; * construction of an isometric projection of the formative face; * construction of projections of other faces by depicting the edges of the model; outline of the isometric projection (Fig. 1). Rice. 1. Construction of an isometric projection of a part, starting from the form-forming face 2. The method of constructing an isometric projection based on the sequential removal of volumes is used in cases where the displayed form is obtained as a result of removing any volumes from the original form (Fig. 2). 3. The method of constructing an isometric projection based on sequential increment (adding) of volumes is used to create an isometric image of a part, the shape of which is obtained from several volumes connected in a certain way with each other (Fig. 3). 4. Combined method of constructing an isometric projection. An isometric projection of a part whose shape is obtained as a result of a combination in various ways shaping is performed using a combined construction method (Fig. 4). An axonometric projection of a part can be performed with an image (Fig. 5, a) and without an image (Fig. 5, b) of invisible parts of the form. Rice. 2. Construction of an isometric projection of a part based on sequential removal of volumes Fig. 3. Construction of an isometric projection of a part based on sequential increments of volumes Fig. 4. Using a combined method for constructing an isometric projection of a part Fig. 5. Options for depicting isometric projections of a part: a - with the image of invisible parts; b - without images of invisible parts TASK: in accordance with the task option and the dimensions of the part, construct a technical drawing on A4 format of checkered paper in a rectangular isometric projection. Task options Option 1-2-3 Option 4-5-6 Option 7-8-9 Option 10-11-12 Option 13-14-15 Option 16-17-18 Option 19-20-21 Option 22-23-24 -25 1

METHODOLOGICAL INSTRUCTIONS

on implementation test assignments

by discipline

OP.01 “Engineering graphics”

for specialty 02.23.03

Maintenance and repair road transport

For correspondence form training

(basic training)

Considered at the meeting of the Central Committee

Technical and economic direction

Protocol No.__ dated “___” ______2015.

Chairman of the Central Committee

O.V.Kobeleva

Methodical manual on “Engineering graphics” for the specialty

02/23/03 Maintenance and repair of motor vehicles for distance learning

Developer organization:

State educational institution secondary vocational education Kemerovo Vocational Technical College.

Kazannikova Valentina Grigorievna, teacher of the highest qualification category of the State Educational Institution of Secondary Professional Education of the Kemerovo Vocational Technical College.

Reviewers:

Shartynova Evgenia Sergeevna, teacher of engineering graphics of the highest qualification category at Kemerovo Vocational Technical College

Mashkina Valentina Vladimirovna, teacher of engineering graphics of the highest qualification category at the Kemerovo Municipal Construction College named after V.I. Zauzelkov

Introduction
Contents of the educational material of the discipline
General guidelines
Graphic works
Graphic work No. 1 Title page of the album of graphic works
Graphic work No. 2 Construction of mates, slope, taper
Graphic work No. 3 Complex drawings and axonometric images of geometric bodies with finding projections of points belonging to the surface of the body
Graphic work No. 4 Construction of the third projection of the model based on two given ones. Axonometric projection
Graphic work No. 5 Using these two types of model, construct a third view, the necessary sections, an axonometric projection with a cutout of the front quarter
Graphic work No. 6 Sketching a threaded part using a simple or complex cut
Graphic work No. 7 Execution threaded connections parts using a bolt and stud
Graphic work No. 8 Drawing of a cylindrical gear with a keyed connection between the shaft and wheels
Graphic work No. 9 Sketching parts of an assembly unit consisting of five or six parts
Information support
Application


INTRODUCTION

Academic discipline“Engineering graphics” is a general professional, formative basic knowledge, necessary for mastering special disciplines: the ability to read and execute drawings of parts, assembly drawings, drawings of circuits.

Guidelines for completing control tasks are compiled in accordance with work program discipline OP.01 “Engineering Graphics” in the specialty 02.23.03 Maintenance and repair of motor vehicles for distance learning, which provides for the student’s independent study of theoretical foundations and the completion of a number of test tasks in order to develop drawing skills. Carrying out graphic work helps to master drawing techniques, develop spatial thinking, without which active creative work students when completing coursework, diploma work and further work in their specialty.

As a result of mastering the discipline, the student should be able to:

Prepare design, technological and other documents technical documentation in accordance with the current regulatory framework;

Create images, cuts and sections on drawings;

Perform assembly drawing detailing;

Solve graphic problems.

As a result of mastering the discipline, the student should know:

Basic rules for constructing drawings and diagrams;

Methods of graphical representation of spatial images;

Capabilities of computer graphics application packages in professional activities;

Basic provisions of design, technological and other regulatory documentation;

Basics of construction graphics.

Methodological instructions include the content of the educational material of the discipline for independent study of theoretical material with reference to educational literature and the topics of tests, guidelines and tasks for graphic works, which the student performs under the guidance of a teacher during the lessons of the practical cycle and independently when preparing the test.

Each practical task of the manual includes methodological instructions, where methodological assistance is provided in completing the task, and samples of drawing design are provided for each work. All assignment options are made in the same style; the selection of assignments covers the material of the main sections of the program, which allows you to objectively assess the knowledge acquired by students while studying the discipline “Engineering Graphics”. A description of the procedure for completing a task facilitates and speeds up the process of completing it.

Under the heading "Please note" in methodological guidelines It is reported exactly what changes have occurred in the standard and what is important when executing the drawing.

The appendix includes the reference materials necessary for performing graphic work.

The final grade is obtained based on the results of checking each graphic work, the evaluation criteria of which are the following indicators:

Selecting the scale and location of the drawing format;

Layout of the drawing;

– the correctness of the task;

Dimensioning;

– drawing lines;

Filling out the title block.

Topics of the section, classes Number of hours Literature
Section 1. Study geometric drawing
Topic 1.1. Basic information on the design of drawings Drawing formats - basic and additional. Drawing lines - style, name, purpose, thickness. Frame and title block. Scales - definition, designation and application.
Topic 1.2.Drawing font and making inscriptions on drawings. Information about standard fonts, sizes and designs of letters and numbers. Rules for making inscriptions on drawings. Graphic work No. 1 Title page of an album of student’s graphic works
Topic 1.3. Basic rules for applying dimensions Rules for applying dimensions. Linear and angular dimensions. Arrows. Rules for drawing extension and dimension lines and dimensional numbers. Signs used when applying dimensions.
Topic 1.4. Geometric constructions and techniques for drawing the contours of technical parts. Dividing a circle into equal parts. Mates used in the contours of technical parts. Conjugations of arcs with arcs, arcs with a line segment, line with a straight line. Slope and taper on technical parts: definition, rules for constructing a given value and designation. Graphic work No. 2Construction of mates, slope, taper
Section 2. Study of projection drawing (basics of descriptive geometry)
Topic 2.1. Projecting a point Projection methods. Planes and axes of projection. Projecting a point onto two and three projection planes. Point coordinates. Reading a drawing of points.
Topic 2.2. Projecting a straight line segment The location of a straight line segment relative to the projection planes. Projecting a straight line segment onto two and three projection planes. Reading drawings of a straight line segment.
Topic 2.3. Projecting a plane Image of a plane in a complex drawing. General and particular planes. Projections of points and lines located on a plane. Reading plane drawings.
Topic 2.4. Axonometric projections Types of axonometric projections. Axonometric axes. Distortion indicators. Images in axonometric projections of flat figures and three-dimensional bodies. Making images of flat figures and three-dimensional bodies.
Topic 2.5. Projection of geometric bodies Determination of surfaces of bodies. Projection of geometric bodies (prism, cone, cylinder, pyramid) onto three projection planes with a detailed analysis of the projections of elements of geometric bodies (vertices, edges, faces, axes and generatrices). Construction of projections of points belonging to the surfaces of geometric bodies. Graphic work No. 3 Complex drawings and axonometric images of geometric bodies with finding projections of points belonging to the surface of the body.
Topic 2.6. Section of geometric bodies by projecting planes. The concept of section. Section of bodies by projecting planes. Finding the actual value of a segment and a plane figure by methods of rotation, alignment and change of projection planes. Construction of the natural size of a section figure. Construction of developments of surfaces of truncated bodies. Image of truncated geometric bodies in axonometric projections Complex drawings of a truncated polyhedron or truncated body of revolution; development of the surface of truncated bodies; axonometry of truncated bodies
Topic 2.7. Mutual intersection of body surfaces General information about the line of intersection of surfaces of geometric bodies. Methods of finding points of the line of intersection. Complex drawing and axonometry of intersecting geometric bodies.
Topic 2.8. Model projections The sequence of constructing model drawings in a system of rectangular projections. Execution of complex drawings of models based on natural samples Graphic work No. 4 Construction of the third projection of the model based on two given ones. Axonometric projection
Section 3. Study of mechanical engineering drawing
Topic 3.1. Images on mechanical engineering drawings. Species - definitions, purpose, location and designation of main local and additional species. Sections - formation, purpose, location and designation. Local cuts. Connecting half a view with half a section. Sections taken out and superimposed. Designations and inscriptions. Graphic designation of materials in sections and sections Graphic work No. 5 Using these two types of model, construct a third view, the necessary sections, an axonometric projection with a cutout of the front quarter
Topic 3.2. Threads, threaded products Basic information about threads. Classification of threads. Thread parameters. Thread elements: runs, undercuts, grooves, chamfers. Conventional image and designation of threads Image of standard threaded fasteners according to their actual dimensions according to GOST (bolts, studs, nuts, washers). Image and designation of threads in the drawings
Topic 3.3. Sketches and working drawings of parts The shape of the part and its elements. Measuring tools and techniques for measuring parts. The concept of applying designations of surface roughness and material used to manufacture parts on a drawing. Purpose and procedure for completing a sketch of parts. Working drawing of the part. Reading working drawings. Graphic work No. 6 Sketching a part with a thread using a simple or complex cut
Topic 3.4. Detachable and permanent connections of parts. Types of detachable connections: threaded, keyed, toothed, etc. Their purpose. Illustration of connections using bolts, studs, screws. Types of permanent connections of parts. Conventional image and designation welds on the drawings. Execution of the drawing welded joint parts Graphic work No. 7 Making threaded connections of parts using a bolt and stud
Topic 3.5. Gear transmissions. Main types of transmissions. Design types of gears. Calculation and procedure for completing a gear drawing. Graphic work No. 8 Drawing of a cylindrical gear with a keyed connection between the shaft and wheels.
Topic 3.6. General information about products and drawing up assembly drawings. General drawing, its purpose and content. Sequence of execution of an assembly drawing. Execution of sketches of parts of an assembly unit. Linking of mating sizes. The procedure for making an assembly drawing based on sketches of parts. Selecting the number of images. Format selection. Dimensions on assembly drawings. Hatching on sections and sections. Simplifications used in assembly drawings. Specification, its purpose and filling procedure. Applying item numbers on the assembly drawing. Graphic work No. 9 Draw sketches of the parts of an assembly unit consisting of five or six parts.
Topic 3.7. Reading and detailing assembly drawings. Purpose and operation of the assembly unit. The number of standard and non-standard parts included in the assembly unit. Reading assembly drawings.
Section 4. Computer graphics
Topic 4.1 General information about the system computer-aided design
Section 5. Studying diagrams in the specialty Topic 5.1 Reading diagrams Types and types of diagrams. Conventional graphic symbols of circuit elements in drawings. Rules for implementing schemes in accordance with the requirements of the ESKD. Reading diagrams. Carrying out graphic work and drawings
Section 6. Study of elements of construction drawing
Topic 6.1 General information about construction drawing Types of construction drawings. Images on construction drawings. Axes grid. Drawing dimensions on construction drawings. Execution of graphic work: Execution of the workshop plan
Total

GENERAL GUIDELINES

As practice shows, the greatest effect of studying engineering graphics can be achieved when students complete individual graphic tasks, which are presented in these guidelines by task options. The option is selected by number in the list of the class magazine. All problems are solved after independent study of the corresponding section in the textbook. A link to educational literature is given in section 2 this manual, where the topics being studied, their content are indicated and pages on the textbooks available in the library of the technical school are given; below is an additional list of references.

Graphic tasks are performed on standard sheets of drawing paper, in pencil. Each sheet is framed and certified by the main inscription of Form 1 according to GOST 2.104-2006 (see Appendix 11). A sample of its filling is shown in Fig. 1. In an additional column measuring 14x70, which is located in the upper corner along the long side of the format, indicate the drawing code in an inverted position.

The code indicates the address of the drawing manufacturer and writes it in font No. 7:

KPTT – Kemerovo Vocational Technical College; name of the discipline: IG - engineering graphics; option number: 05 - fifth option; number of graphic work: 10 - graphic work No. 10.

For example: KPTT IG 05.10.00

For some sheets, instead of the last zeros, the part position number, circuit code, etc. are indicated.

In the main inscription in the “name” column the name of the graphic work is written. The scale of the image is indicated in the title block.

To set dimensions in drawings, use font No. 3.5.

Accepted designations:

Points on projections are designated by the same lowercase letters of the Russian alphabet with strokes indicating the projection plane (a, a", a");

Angles - lowercase Greek alphabet, indicating the degree (α, β).

All text inscriptions on the drawings are made in drawing font in accordance with GOST 2.304-81; for ease of use of this manual, Appendix No. 2 shows the design of letters and dimensions for font numbers 3.5; 5; 7 and 10. Upon completion of all graphic tasks, the sheets are bound into an album, the first sheet of which is front page(its number is not indicated on the sheet). The album is submitted to the teacher for review.

GRAPHIC WORKS

GRAPHIC WORK No. 1

Accent placement: GRAPHICAL WORKS

GRAPHIC WORKS - independent work students containing any graphic images, performed on assignment and under the guidance of the teacher. G. r. can be used in the study of all theoretical uch. items at all stages schooling, starting from simple drawings and ending with complex conditional types of graphics. images: drawings, diagrams, graphs, etc. G. r. can be assigned as a class exercise (for example, sketching from life), as homework (for example, drawing from sketches), as a test (for example, in the section “Projection drawing”). G. r. may also be part of a c.-l. another work illustrating its individual provisions, or used as a method with the help of which a class is determined. from the required quantities (graphical calculations).

Main types of G. r. study and varieties of graphics. images used in teaching: drawing, diagram, plan, map, diagram, graph, technical. drawing, drawing, sketch.

Drawing- depiction of objects and phenomena, done by hand graphic. means: line, combination of strokes, etc. Types of graphics, provided by the program for drawing: a) drawing from life - an image of objects based on the direct perception of them by the person drawing; b) thematic drawing - an image made based on simple scenes from the surrounding reality or on literary themes. works. G. r. by thematic drawing is performed on the basis of observations, ideas, memory; groups of depicted objects and phenomena are united by a selected or given plot; c) decorative drawing - depiction of ornaments, patterns, etc. The main attention is paid to drawing from life. In grades 1-2, flat objects of rectangular, round and other shapes, placed for drawing in a frontal position, serve as natural objects. Getting acquainted with the phenomena of perspective, students in grades 3-4 draw three-dimensional objects of cylindrical, conical, spherical and other shapes, students in grades 5-7 draw groups of objects, conveying the features of shape, proportion, color, position in space, illumination. G. r. in decorative drawing, students are prepared for all kinds of design work: album cover, poster, wall newspaper, sketch and details of the festive decoration of the school premises, etc. Drawings are widely used in all classes as graphics. images of instruments, experiments performed, Ph.D. objects (see also Drawing at school).

Diagram- graphic display of compared values ​​using lines, geometric. figures and other means. Most widespread have a trace. types of diagrams: a) linear, which are constructed on a coordinate field; the quantities being compared are depicted by straight line segments of the appropriate length (usually ordinates), their ends are connected by straight lines, forming a broken line; b) columnar or strip, where the data is represented by rectangles of the same width, located vertically (column, Fig. 1) or horizontally (tape); the height or length of the rectangles is proportional to the quantities they represent; c) pie charts are circles divided into sectors, the values ​​of which are proportional to the sizes of the individual parts of the image (Fig. 2); d) illustrated diagrams made using figures - signs of different sizes, on which digital data is applied.

Diagrams are used when it is necessary to show in a visual form ratio of k.-l. quantities in the topic being studied, e.g. the process of development and growth (line and bar charts), the division of the whole into parts (sector), etc. Sometimes the charts are located on the account. maps (see Educational maps), for example. to show the growth of industry in different geographies. or economical areas. Such cards are called. map diagrams. G. r. for making diagrams on contour maps are usually used in geography, history, and social studies lessons.

Plan - conventional image on a plane in orthogonal projection a small part of the earth's surface, buildings, structures, etc. The plans can depict: terrain, settlement, residential or industrial. building (image of the building in a horizontal section) or part of it (workshops, laboratory), etc. It is advisable to set the student G. r. to carry out plans from nature, including measurements, choice of scale, sketch photography, for example, a plan of a school site, an educational site. workshops (with equipment layout), etc.

Scheme- graphic an image that conveys in a simplified or conditional form the most essential features subjects, the main thing and the main thing in the phenomena being studied. Symbols of parts, mechanisms, equipment, devices for certain types of circuits are standardized, for example. for kinematic, electrical diagrams, for pipeline diagrams. With the help of diagrams, they show all kinds of classifications, divisions, connections and relationships, the progress of the process, the interaction of parts, the structure (in general terms) and the principle of operation of machines, mechanisms, structures, installations, etc. For example, when studying chemistry - a diagram of a gas plant, blast furnace process diagram, synthetic ammonia production diagram, aluminum production diagram (Fig. 3); physics - simple electrical, hydraulic, pneumatic. schemes. Sometimes the diagrams are located on the account. maps, for example to designate routes of communication, import or export of products from one geographical location. or economical district in another (on geographical maps), movements of armies (on historical maps), etc. Such cards are called. maps. G. r. "For making diagrams on contour maps, they are usually used in geography and history lessons."

Schedule- visual graphic display of functional dependence. In mathematics, the graph of a function is geometric. the location of points in the plane whose coordinates satisfy the equation of this function. The method for constructing graphs depends on the selected coordinate system. In most cases, graphs are constructed based on a Cartesian (rectangular) coordinate system. To depict functions of the angular argument, a polar coordinate system is convenient, for example. luminous intensity distribution graph different types lamps. The ability to quickly find function values ​​from argument values ​​provides graphs with great practicality. use in folklore x-ve. Students study the construction of graphs in a mathematics course and use them for graphics. problem solving. Graphs are used in the study of other subjects, e.g. in physics: a graph showing temperature changes in water, "heating - boiling - cooling", a "immersion - pressure" graph, a "temperature - time" graph, a "path - time" graph; in chemistry: temperature - solubility graph (Fig. 4). In addition to constructing graphs, students learn to read them, for example, when reading the “heating - boiling - cooling” graph, students must imagine what characterizes the middle part of the graph, which is obtained in the form of a horizontal section of a straight line. It is also necessary to teach how to use graphs to determine intermediate values ​​of functions, for example. Using the graph point specified between the divisions on the temperature axis, set the weight amount of the dissolved substance, etc.

Technical drawing- a visual representation of an object, done by hand using the axonometric method. design (Fig. 5). Technical A drawing with dimensions is used in labor lessons in school. workshops as the most accessible (easy to read) type of graphic. images. G. r. in technical Drawing is done in drawing, mechanical engineering, etc. lessons.

Drawing- image of products and structures or their components, made according to the rules of descriptive geometry and technical. drawing. The most commonly used method is orthogonal design, less often - axonometric (Fig. 6) and perspective. Basic rules for the execution of drawings, symbols, design are established by state standards. Depending on the design stage, mechanical engineering drawings are divided into design (intended for drawing up working drawings) and working (intended for the manufacture, repair and control of products and their components). Depending on the content, the drawings are divided into the following. types: a) drawings of parts containing images of parts of products, as well as the necessary data for their manufacture and control (Fig. 7); b) assembly drawings containing images of products, groups or assemblies and the necessary data for their assembly and control; c) dimensional drawings containing outline or simplified images of products or their components and overall dimensions; d) installation drawings containing outline or simplified images of products or their components, as well as the necessary data for their installation at the installation site; e) tabular - summary drawings containing data necessary for the manufacture and control or use of a number of similar products and their components, differing in size, material, coating, coloring or other data.

Sketch- a drawing of a temporary nature, carried out, as a rule, without the use of drawing tools, without exact adherence to scale (Fig. 8). Sketches are commonly used in design and manufacturing.

A special place in the graphic. preparation for studying is occupied by G. r. by drawing. They are a means of consolidating learning. material and form the ability to depict objects using orthogonal and axonometric design methods. In the process of performing these G. r. technical drawing skills, the ability to use tools and accessories, and “freehand” skills when performing sketches are developed. Content, volume and time distribution of G. r. in drawing are determined by the curriculum (see Drawing at school).

General requirements for G. r. in drawing is compliance with the rules of state standards. Therefore, from the very beginning of G. r. are carried out on sheets of standard formats, established types and sizes of lines, inscriptions on the line. are made in a standard font.

Most useful view G. r. is the execution of drawings or sketches from life, during which the most complete perception of the object of the image occurs, the greatest independence of learning is manifested in resolving issues related to the choice of image method, and intensive training of spatial thinking occurs. A very valuable methodological The technique is the inclusion of G. r. in exercises for reading drawings, for example, performing sections, sections, additional views specified in the drawing. For the development of polytechnics. ideas and practical skills need to connect the topics of G. r. with life, practice, production (see Graphic literacy).

K. A. Yankovsky. Moscow.


Sources:

  1. Pedagogical encyclopedia. Volume 1. Ch. ed. - A.I. Kairov and F.N. Petrov. M., "Soviet Encyclopedia", 1964. 832 columns. with illustration, 7 p. ill.

INSTRUCTION CARD. Graphic work No. 1 “Drawing font”

Graphic work No. 1 “Drawing font”

Purpose of the work: Learn how to make a drawing font and fill out the main inscription with a drawing font

Task for work:

1. Carefully study the sample worksheet

2. On A4 graph paper, make the main inscription (Fig. 1)

3. Use standard font size 10 GOST B to write the letters of the Russian alphabet and numbers. Two lines - uppercase, two lines - lowercase, a line with numbers.

A sample sheet is shown in Fig. 1

The inscriptions on the drawings must comply with the font standard. To learn how to write correctly in a standard font, you need to study GOST 2.304-68 and perform exercises in writing letters and numbers on a grid with a line inclined at an angle of 75° (A4 graph paper). The grid marks the width of the letters and the distance between them.

The sheet is positioned vertically, we put 10 mm on the top and left and draw two lines for writing capital letters. Line height 10 mm, distance between lines 7 mm. For each letter, first draw auxiliary lines with a width equal to the width of the letters, the distance between the letters is 2 mm. We enter letters into the auxiliary lines (Fig. 2)

Most lowercase letters contain elements of the letter O, so you need to learn how to write this letter correctly. Middle part About 1/3 of the height should be straight (Fig. 2)

The drawing must maintain the required ratios of line thicknesses of different types. It is recommended to choose the following line thicknesses: for solid main line S=1 mm, for dashed line – from S|2 to S|3, for solid thin line S|3, for dashed-dotted line S|3. The thickness of the auxiliary lines should be approximately S|3.


Fig.2 Drawing letters

Get good higher education It's not so easy for us. To do this, you will need not only to attend lectures, seminars and workshops, but also to complete various independent tasks, such as essays or coursework. In this article I would like to talk about what calculation and graphic work is.

About the concept

First of all, you need to understand the concept itself. Often, when a student hears the abbreviation RGR for the first time, he becomes confused. But there’s nothing to worry about, that’s the abbreviated name for calculation and graphic work. This is a student designed for a more complete assimilation of the material he has completed in a particular subject. It is also worth mentioning that RGR can be part of course work, that is, its practical component. The essence of this type of work is to provide not only theoretical, but also practical material. Thus, the RGR will necessarily contain certain calculations, possibly graphs, tables, diagrams.

What should it be?

What important elements does the RGR consist of?

  1. Justification of the chosen topic. This is a theoretical component where the student must talk about the importance of the work he has done.
  2. Characteristic
  3. Carrying out basic calculations.
  4. Providing the results obtained in a convenient form: tables, graphs, diagrams.
  5. Conclusions and possibly recommendations.

Structure

Calculation and graphic work must have its own structure. It is not possible to submit material for consideration in any form. So, the RGR should consist of the following points:

  1. Table of contents. Here the student provides information about all sections of his work.
  2. Exercise. At this stage, it is necessary to fully “voice” the task given to the student.
  3. Initial data. The student provides all existing source data that may be needed to carry out the calculations.
  4. This is followed by sections that will contain practical solutions and analysis of the results obtained.
  5. Providing calculation results in the most convenient form for understanding.
  6. Conclusions.
  7. References.
  8. Applications (if any).

Highlights

There is also a list of special requirements that the student must comply with when preparing calculation and graphic work.

Design of tables and figures

Economics, statistics, theoretical mechanics... Calculation and graphic work can be performed in almost any subject where there are calculations (regardless of the student’s specialty of study). However, it is worth remembering that it is necessary not only to correctly format the text itself, but also to provide all the tables, figures and diagrams.

Informatics

What might computational and graphical work in computer science look like? So, it’s worth saying that there are no specific frameworks here. It all depends on the level of the material taught at the university for a given specialty. So, for humanities students the RGR in computer science will be one, for programmers it will be completely different. This could be simply a demonstration of PC skills (for example, in Word or Excel), or maybe programming, use for work various systems calculus, performing all kinds of transfers between different ones, etc.

BJD

As part of the Life Safety course, some universities also offer students to complete RGR. And again, I would like to say that work in different specialties will differ from each other. After all, each profession has its own precautions and requirements. Calculation and graphic work on heavy-duty railways - what can be studied or researched here? Thus, you can calculate the most comfortable working conditions for a group of workers, you can plan the placement of jobs in a workshop or enterprise, you can analyze, etc. In fact, there are a huge number of topics to consider.

Other items

It is worth saying that calculation and graphic work can be written on almost any subject: economics, electronics, logistics, theoretical mechanics, etc. However, the goal of this work will always remain the same: to teach the student not only to correctly carry out the necessary calculations, but also to be able to correctly present them for consideration.