Engineering graphics study guide bogdanov sciences. Engineering graphics (study guide). Approximate word search
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1 FEDERAL STATE EDUCATIONAL BUDGETARY INSTITUTION OF HIGHER PROFESSIONAL EDUCATION POVOLGA STATE UNIVERSITY OF TELECOMMUNICATIONS AND INFORMATICS E. A. Bogdanova Engineering instructions and computer graphics 1
2 FEDERAL COMMUNICATIONS AGENCY Federal State Educational Budgetary Institution of Higher Professional Education "POVOLGA STATE UNIVERSITY OF TELECOMMUNICATIONS AND INFORMATICS" Department of Economic and Information Systems E. A. Bogdanova ENGINEERING AND COMPUTER instructions for laboratory work
3 UDC BKK B73 Recommended for publication by the methodological council of PSUTI, minutes 20, from Mr. B Bogdanov, Е.А. Engineering and computer graphics: guidelines for laboratory work 1 Samara: PSUTI, p. Methodological instructions are intended for 1st year students of full-time study directions, and 3rd course of directions, as well as for students of 1st and 1st courses of correspondence courses of study directions and 3rd and 3rd courses of directions. laboratory work in the discipline Engineering and Computer Graphics., Bogdanova E.A.,
4 Contents Introduction. 4 1 Starting and exiting the KOMPAS-3D system Acquaintance with the main elements of the KOMPAS-3D interface. 6 3 Opening an existing document in the KOMPAS-3D system 10 Exercise 1. Working with the toolbar Exercise 2. Entering data into parameter string fields Using global, local and keyboard bindings .. 16 Exercise 3. Applying global and local bindings 17 Exercise 4. Usage keyboard bindings. 22 Independent work. 25 Test questions List of sources of information
5 Introduction The system of three-dimensional solid modeling KOMPAS 3D V14 / 15 is intended for automation of design and construction works in various fields of activity. It is successfully used in mechanical engineering, architecture, construction, drawing up plans and diagrams - wherever it is necessary to develop and produce graphic and text documents. KOMPAS-3D is a graphic editor that allows you to develop and issue various documents - sketches, drawings, diagrams, posters, etc. KOMPAS-3D allows you to work with all types of graphic primitives required for any construction. The KOMPAS-3D drawing model is focused on ESKD, which makes it possible to produce documentation that is fully compliant with standards without any additional shells and add-ons. When working with a text document, all the basic features are available: working with bitmap and vector Windows fonts, choosing font parameters (size, slant, style, color, etc.), choosing paragraph parameters, entering special characters and symbols, superscript and subscript characters , indices, fractions, insertion of pictures and graphic files KOMPAS-3D. The methodological instructions give a detailed description of how to perform the exercises included in laboratory work 1 on the topic: "Acquaintance with the basics of working in the KOMPAS-3D program". 5
6 Acquaintance with the basics of work in the KOMPAS-3D program Purpose of work 1) To study the main elements of the interface. 2) Get acquainted with the basic methods of working with the KOMPAS-3D program. 3) Study the basic types of bindings in KOMPAS-3D. 4) Learn to choose the types of bindings and apply them in specific situations. 1 Launching and exiting the KOMPAS-3D system a) Launching the program 1) Launching the program is carried out by clicking on the KOMPAS-3D V14 icon on the desktop. 2) If there is no icon on the desktop, then select it from the drop-down list of commands: Start KOMPAS 3D V14 or Start All Programs ASCON KOMPAS 3D V14. b) Exit the program To exit the program, click on the "Close" button. Opening a new document 1) To open a new document, click the "New" button on the "Standard Panel" or in the menu bar: File New. The "New Document" window will open on the screen. 2) Select "Drawing" from the proposed documents. Click. A new drawing sheet opens on the screen. Expand the document if necessary. 3) Do not close the document, it is necessary to get acquainted with the main elements of the program interface. 2 Acquaintance with the main elements of the KOMPAS-3D interface Consider the main elements of the KOMPAS-3D program window (Fig. 1). Remember their names. KOMPAS 3D is a program for the Windows operating system. Therefore, its window has the same controls as other Windows applications. Title. The title is located at the very top of the window. It displays the name of the program, its version number and the name of the current document. Main menu. The main menu is located at the top of the program window, just below the title. It contains all the main elements of the system menu: File, Editor, Select, View, etc. Each of the menus stores associated commands. Standard panel. The standard bar is located below the menu bar. This panel contains buttons for calling standard commands for operations with files and objects. The panel buttons allow you to access the most frequently used commands: New, Open, Save, Print, etc. (fig. 2). View panel. The View panel contains buttons that allow you to control the image: change the scale, move and rotate the image, change the form of the model presentation. Current status panel. This panel displays the system settings and the current document. The composition of the panel is different for different operating modes of the system. Message line. The line is located at the bottom of the program window. Serves to display various service information about objects displayed in the window (for example, brief information on the current action performed by the system). 6
7 Window title Menu bar View panel Current state panel Standard panel Compact panel Special control panel Message line Property panel panels (Fig. 3). Each button on the Switching panel corresponds to a toolbar of the same name. Toolbars contain a certain set of buttons grouped by functional attribute: "Geometry", "Dimensions", "Editing", etc. When you click the "Geometry" button on the switch panel, a toolbar opens, which contains commands that can be used to create geometric objects: lines, circles, arcs, etc. The properties panel automatically appears on the screen only after calling any command from the Toolbar or in the object editing mode (Fig. 1). Each drawing object that is created when working with the program has a certain set of parameters. For example, the parameters of a straight line segment are the coordinates of its start and end points, length, slope, and line style. Working with 7
8, the property bar when creating or editing drawing objects is reduced to activating the required fields and entering certain parameter values in them. The special control panel automatically appears on the screen only after calling any basic command from the Toolbar. The main buttons of this panel are the buttons "Create object" and "Cancel command" (Fig. 4) Button Contextual panel. geometry Toggle panel The context panel is displayed on the screen when you select objects in the document and contains the Create buttons. Interrupt calling the most frequently used object command of the used editing commands. The set of commands Toolbar on the panel depends on the type of selected object and the type of document. Model tree. The model tree is a graphical representation of the set Fig. 3 Fig. 4 of the objects that make up the model. Object icons automatically appear in the Model Tree immediately after these objects are created in the model. 3 Opening an existing document in the KOMPAS-3D system 1) Start the program. 2) To open an existing document, click the "Open Document" button on the control panel. The “Select files to open” dialog box will open on the screen (Fig. 5). 3) The existing documents that will be used in the laboratory work are located in the "Trainer" folder: Computer STUDENT (E :) Trainer) Open the "Trainer" folder, then the "Lab.work." 1". Fig. 5 8
9 5) In the full list of fragments, point to the document with the mouse. Click the "Open" button. 6) If necessary, switch the document window to full-screen mode by clicking the “Maximize” button and click the “Show all” button on the control panel (Fig. 2). The document will be displayed at its maximum size. Exercise 1. Working with the dashboard. The graphic part of the exercise file consists of two parts, one of them is the Sample (Fig. 6). The Sample shows what should be the result of the task. The sample is for demonstration purposes only. On the right side there is an area for completing the task, in which it is necessary to perform all the constructions described in the text part of the exercise. It is not necessary to put down dimensions in laboratory work. They are designed to build and control the teacher's work. After completing the exercise, the document is collapsed to open the document for the next exercise. The teacher checks the completed assignment at the end of the lesson, after which the student closes all documents without saving. Open the document Area for task execution Fig. 6 Task 1. Constructing a rectangle 1) On the switch panel, click the "Geometry" button. 2) To draw a rectangle, click the "Enter Rectangle" button on the toolbar. By default, a rectangle is drawn by specifying two vertices on any of its diagonals. 3) In response to the system query "Specify the first vertex of the rectangle or enter its coordinates" (in the message line), click at point p1. The system has fixed the first peak. 4) In response to the system query "Specify the second vertex of the rectangle", move the cursor to point p2 and fix it by clicking. The system has finished drawing the rectangle. 5) When performing the exercises, it becomes necessary to delete objects. To do this, click on the "Interrupt command" button on the special control panel (Fig. 4), with the mouse pointer, click on the created object (the object is highlighted in green) and press the "Delete" key. nine
10 6) Return the original construction. To do this, click the "Cancel" button on the control panel. Task 2. Drawing line segments 1) By default, the system draws a line segment by its two endpoints. Click the Line toolbar button. 2) In response to the request of the system "Specify the starting point of the segment or enter its coordinates", click at point p3. The system has locked the starting point of the line segment. 3) In response to the request of the system "Specify the end point of the segment", click at point p4. The system has finished drawing the segment. 4) To draw a horizontal line, sequentially click at points p5 and p6. Task 3. Constructing a circle 1) By default, the system draws a circle with a given center and passing through a specified point. 2) Click on the "Circle" button on the toolbar to activate the command for drawing circles. 3) In response to the request of the system "Specify the point of the center of the circle or enter its coordinates", click at point p7. The system has fixed the center point. 4) In response to the request of the system "Specify a point on the circle", move the cursor to point p8 and fix it by clicking the mouse. The system has finished drawing the circle. 5) The task is completed. Fold the document. Exercise 2. Entering data in the fields of the parameter string Open the document Task 1. Constructing a segment p2 p3 by coordinates 1) Activate the command "Segment". 2) Enter the section parameters manually using the keyboard. To do this, press the key
11 4) Press the key
12 Exercise 3. Applying global and local references Open the document Task 1. Drawing the centerline р1 - р2 1) To draw the centerline р1 - р2, turn on the "Line" button. 2) To change the style of the line, click in the field "Current style" in the "Property bar" (Fig. 8). 3) In the drop-down menu, click on the Pivot style. Please note that the line required for construction must be yellow or orange (Fig. 9). 4) Using the mouse, place the cursor approximately at the center of the circle (point p1). After the “Nearest point” global snapping is triggered (an additional, oblique cross will appear), click the left mouse button. The starting point of the line is fixed. 5) Similarly, using the snap, specify the end point of the p2 segment. The segment p1 - p2 is built. Field "Current style" Fig. 8 Fig. 9 Task 2. Construction of the segment p3 p4 1) The segment p3 - p4 begins at point p3 and passes tangentially to the circle centered at point p1. To draw it, change the line style to "Basic" and set the "Global Snaps", which allow you to quickly and accurately indicate existing points in the drawing. To do this, press the button "Setting global bindings" located on the "Current state panel" (Fig. 10). 2) The dialog box "Setting global bindings" will appear on the screen (Fig. 11). To set the desired combination of global snaps, enable the check boxes (if not present) in the dialog box: "Nearest point", "Midpoint", "Intersection", "Tangency", "Normal", "Show text". Click OK. 12
13 Setting global bindings Fig. 10 3) Fix the beginning of the line segment at point p3. 4) Move the cursor approximately to the point of tangency (point p4 on the "Pattern"). When the anchor cursor appears and the Tangency prompt appears, lock the point. 5) Similarly, construct the segments p5 - p6, p7 - p8, p9 - p10. The construction of the segments p7 - p8 and p9 - p10 should be started from the end points of the arc. Rice. 11 Task 3. Constructing an axial p11 - p12 1) Set the current line style to the “Axial” style. 2) Enter the segment p11 - p12, the beginning of which is in the middle of the segment p3 - p5. As soon as the prompt "Nearest point" appears - fix the position of point p11 by clicking the mouse. 3) Determine the middle of the arc p7 - p9. When the Midpoint prompt appears, lock the end point of line segment p12. Task 4. Construction of the segment p0 - p13 1) The segment p0 - p13 begins at point p0 - the point of intersection of the axes p1 - p2 and p11 - p12 and runs perpendicular to the segment p7 - p8. Place the cursor at point p0. Once the Nearest Point tooltip appears, lock the position of the line start point. 2) The end point of the segment p0 p13 is on the straight line p7 - p8. When the Normal prompt appears, click. For precise construction of a segment, use the "Zoom in" button on the "View Panel" (Fig. 12). Zoom in with a frame Fig. 12 3) Build a segment p0 - p14 on your own. 13
14 Task 5. Constructing a circle with a diameter of 15mm 1) Change the line style to "Basic". 2) Activate the "Circle" button. Place the cursor in the "Circle diameter" field on the "Property bar" and enter a value of 15. Then press the key<Епtеr>... 3) The created phantom of the future circle can be freely moved around the document field (with the mouse). To complete the construction of the circle, it is enough to indicate its center. For this purpose, it is necessary to enter "Local bindings". 4) Right-click anywhere in the drawing. 5) In the menu that appears, place the cursor on "Binding". In the drop-down list, specify the "Intersection" anchor (Fig. 13). Rice. 13 6) Place the cursor trap at approximately the point p0 - the point of intersection of the segments p1 - p2 and p11 - p12. 7) After the local snap "Intersection" is triggered, fix the point by clicking the mouse. Task 6. Constructing circles with a diameter of 5mm 1) Place the cursor in the "Circle diameter" field and enter the value of the diameter 5. 2) To automatically create axes of symmetry, enable the "With axes" button on the "Property bar" (Fig. 14). Rice. 14 3) Move the cursor to the line p0 - p13. Right-click to bring up the context menu of local bindings and select the Middle anchor from it. 4) To find the midpoint, set the cursor trap (without clicking) on the segment p0 - p13 at any point. After the local snap is triggered, fix the center of the circle with a mouse click. 5) Build a similar circle with the center in the middle of the segment p0 - p14 on your own. 6) There is no need to put down dimensions in the drawing! 7) Fold the document. fourteen
15 Exercise 4: Using Keyboard Bindings Keyboard bindings are precise cursor movement commands that you execute using the keyboard. Global and local bindings are used only when a command is activated. Keyboard bindings can be used in almost any mode of the program operation (Table 1) Tab. 1 Keybind
16 Task 3. Constructing an inner rectangle 1) Activate the "Enter rectangle" button. 2) Turn on the "No axes" button. 3) Using a keyboard command
17 Test questions 1) Name the main elements of the KOMPAS-3D interface. 2) List the main ways of constructing a line. 3) What are the main ways to define a rectangle? 4) List the ways to define a circle. 5) Explain the purpose of the geometric calculator. 6) Explain the purpose of global bindings. 7) How the global bindings are set. 8) What are the similarities and differences between global and local bindings? 9) How local bindings are set. 10) Explain the purpose of the keyboard bindings. 11) Name the reaction of the system when executing keyboard commands:
FEDERAL COMMUNICATIONS AGENCY Federal State Educational Budgetary Institution of Higher Professional Education "POVOLGA STATE UNIVERSITY OF TELECOMMUNICATIONS AND INFORMATICS"
Federal Communications Agency State Educational Institution of Higher Professional Education POVOLGA STATE UNIVERSITY OF TELECOMMUNICATIONS AND INFORMATICS ELECTRONIC LIBRARY
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MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION
Federal State Budgetary Educational Institution
higher professional education
"TYUMEN STATE OIL AND GAS UNIVERSITY"
Transport Institute
Department of Applied Mechanics
INSTRUCTIONS
Options for assignments for independent work in the course
"Descriptive geometry. Engineering graphics"
on the topic "Images"
for students of all directions and forms of study
Compiled by: N.G. Tuktarova,
A.N. Bogdanov,
I.A. Venediktova
Methodical instructions: options for assignments for independent work in the course “Descriptive geometry. Engineering graphics "on the topic" Images "for students of all directions and forms of education / comp .: N.G. Tuktarova, A.N. Bogdanova, I.A. Venediktov; Tyumen State Oil and Gas University. - 2nd ed., Rev. - Tyumen: Publishing Center BIK TyumGNGU 2012. - 31 p.
meeting of the Department of Applied Mechanics
"____" _________ 2012, minutes No. ____
annotation
Methodical instructions for independent work on the course “Descriptive geometry. Engineering Graphics "are intended for students of all directions and forms of education.
Variants of individual graphic assignments and samples of completed work on the topic "Images" are given.
INTRODUCTION
These methodological guidelines provide options for individual graphic assignments on the topic "Images", performed by students in the course "Descriptive geometry. Engineering graphics". On the topic "Images", drawings "Cuts, section", "Cuts" and an axonometric drawing are made.
On 4 ... 11 pages there are options for the task "Cuts, section", and on pages 13 ... 27 - "Cuts".
Before executing each drawing, it is necessary to work out the methodological instructions, follow the recommendations given in them.
The task "Cuts, section"
On a 1: 1 scale on the A3 format of whatman paper, draw front and top views of the object according to your option, providing a place for applying dimensions, build a left view. In the place of the front view, make a frontal cut or combine part of the front view with part of the frontal cut for symmetrical images. Draw a profile section in place of the view on the left, or combine a part of the view on the left with a part of the profile section, if the images have a plane of symmetry. In the free field of the drawing, make a section of the object with the indicated plane Σ (Σ 2). Apply dimensions in accordance with GOST 2.307-68, the necessary designations and inscriptions.
Quest "Cuts"
On the A3 format of Whatman paper at a scale of 1: 2, draw two specified types of products. Unspecified dimensions of the elements of the part are obtained by measuring them and determining the true value in proportion to the distortion of the image. In place of the front view, make a complex stepped cut. In the place of the left view, draw a profile section or combine a part of the left view with a part of the profile section for symmetric images. Give designations. Apply the dimensions specified in the options for the tasks, adding the dimensions required for the manufacture and control of the product.
Task for the execution of an axonometric drawing
On a scale of 1: 2 on the A3 format of whatman paper, draw a rectangular isometry with a cutout ≈ ¼ of the object according to the variant of the task "Cuts".
Draw up the drawings in accordance with the samples given in the guidelines in Figures 1 ... 3.
Literature
ESKD standards as of the moment.
Gordon V.O., Sementsov-Ogievsky M.A. Descriptive geometry course. - M .: Higher school, 2009 .-- 272 p.
Ivanov G.S. Descriptive geometry. - M .: Mechanical Engineering, 1995 .-- 224 p.
Levitsky V.S. Mechanical engineering and automation of the execution of drawings: Textbook. for universities / V.S. Levitsky. - 6th ed., Rev. and add. - M .: Higher. shk., 2004. - 435 p .: ill.
Chekmarev A.A., Osipov V.K. Handbook of mechanical engineering drawing. - 2nd ed., Rev. - M .: Higher. shk .; Ed. Center "Academy", 2009. - 493 p .: ill.
P.E. Nauk, A.N. Bogdanova Descriptive geometry: a tutorial. - Tyumen: TyumGNGU, 2009 .-- 128 p.
Bogdanova A.N., Nauk P.E. Engineering graphics .: Tutorial. - Tyumen: TyumGNGU, 2009 .-- 140 p.
Bogdanova A.N., Venediktova I.A., Tuktarova N.G. Intersection of surfaces: Methodical instructions. - Tyumen: TyumGNGU, 2012 .-- 12 p.
Bogdanova A.N., Venediktova I.A., Tuktarova N.G. Images: Methodological instructions. - Tyumen: TyumGNGU, 2012 .-- 23 p.
Venediktova I.A., Tuktarova N.G., Bogdanova A.N. Axonometric drawing: Methodical instructions. - Tyumen: TyumGNGU, 2012 .-- 16 p.
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Educational edition
INSTRUCTIONS
Options for assignments for independent work
Compiled by:
TUKTAROVA Nuria Gazisovna,
BOGDANOVA Alevtina Nikolaevna,
VENEDIKTOVA Irina Alexandrovna
Signed to print. Format 60x90 1/16. CONV. print l. 1.9.
Circulation 30 copies. Order no.
Library and publishing complex
federal state budgetary educational
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Tyumen State Oil and Gas University.
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P. E. Nauk, A. N. Bogdanova
DESCRIPTION
GEOMETRY
Tutorial
FEDERAL EDUCATION AGENCY
STATE EDUCATIONAL INSTITUTION OF HIGHER PROFESSIONAL EDUCATION
"TYUMEN STATE OIL AND GAS UNIVERSITY"
P. E. Nauk, A. N. Bogdanova
Descriptive
geometry
Tutorial
Tyumen 2009
Sciences, P.E. Bogdanova A.N. Descriptive geometry: a tutorial. - 2nd ed. / P.E. Nauk, A.N. Bogdanov. - Tyumen: TyumGNGU, 2009 .-- 128 p.
The textbook is intended for teaching students on the section "Descriptive geometry" in the program of the discipline "Descriptive geometry. Engineering graphics". The educational material consists of six educational modules, which are compiled in accordance with the state educational standards of specialties.
Each educational module includes a didactic goal and tasks, theoretical material, questions for self-control and tasks for individual work with a detailed analysis of one typical task on the topic under consideration, tests of the module control of the student's knowledge. Depending on the chosen specialty, it is possible to vary the set of educational modules.
In the manual, explanatory three-dimensional graphic models are widely used to intensify learning by increasing the degree of visualization of educational and practical material.
By analogy with the standard tests of the module control of students 'knowledge, an application with tests for the final control of students' knowledge was developed separately from the manual.
Certification of the level of education of each student in the section "Descriptive geometry" is carried out on the basis of final control tests. Testing time is 20 minutes. Students who have completed all the tasks for individual work, presented on the relevant topics, are allowed to the final testing.
For the convenience of working with the manual, a glossary of terms and a description of conventional symbols are provided.
For all students whose curriculum includes this discipline.
Reviewers: Yu.I. Nekrasov, Candidate of Technical Sciences, Professor of the Tyumen State Oil and Gas University;
E.V. Varnakova, Candidate of Technical Sciences, Associate Professor of the Tyumen Law Institute of the Ministry of Internal Affairs of the Russian Federation
ISBN 978-5-9961-0062-0 |
GOU VPO "Tyumen State |
Oil and Gas University ", 2009 |
NS R e n i t e s
1. Points are designated by capital letters of the Latin alphabet: A, B, C, D,. ... ...
or in Arabic numerals: 1, 2, 3,. ... ... ; the center of the projection is indicated by the letter S.
2. Straight and curved lines, arbitrarily located relative to the projection planes, are denoted by lowercase letters of the Latin alphabet: a, b, c, d,. ... ...
Lines that occupy a special position are indicated by: h - horizontal line of the level (horizontal);
f - front line of the level (frontal); p - profile line of the level;
x is the abscissa axis; y - ordinate axis; z is the axis of the applicate;
s - direction of parallel projection.
The following designations are also used for lines: AB - straight line defined by points A and B; [AB] - line segment bounded by points A and B; | AB | - natural size of the segment [AB];
ex, ey, ez or e with ex = ey = ez are unit (scale) segments.
3. Surfaces are designated by capital letters of the Greek alphabet: Г - gamma,
- delta, - theta, - lambda, - xi, - pi, - sigma, F - phi, - psi, - omega.
To indicate the method of specifying the surface, next to their letter designations, the designations of the elements defining them are written in parentheses: Г (А, В, С); (a, M);
The projection planes are designated by the letter P with the addition of a subscript or superscript:
P1 - horizontal projection plane; P2 - frontal projection plane; P3 - profile plane of projections;
Pa - axonometric projection plane.
4. Corners are indicated in lowercase Greek letters: The following conventions are also used:
ABC - angle with apex at point B;
a, G - the angle between straight line a and plane G.
5. Projections of points, lines, degenerate projections of planes and cylindrical surfaces are denoted by the same letters or numbers as the points, lines and
A1, B1,. ... ... ; a1, b1,. ... ... ; G1, F1,. ... ... - horizontal projections; A2, B2,. ... ... ; a2, b2,. ... ... ; G2, F2,. ... ... - frontal projections;
A3, B3,. ... ... ; a3, b3,. ... ... ; G3, F3,. ... ... - profile projections;
Aa, Ba,. ... ... ; aa, ba,. ... ... ; Ga, Fa,. ... ... - axonometric projections. 6. The following symbols are also used:
- belonging of a point (element of a set) to a geometric figure (set): А m, В Ф;
- belonging (inclusion) of a geometric figure (subset) to a given figure (set): m Г; t;
- union of sets: [AB] [BC] - broken line ABC; - intersection of sets: a G, F;
= - coincidence, operation result, assignment: A1 = B1, A = m G; |
||
- congruence: [AB] [CD]; |
||
- similarity: ABC |
||
| | - parallelism: a | | m, m | | G; |
||
- perpendicularity: m k, t Г; |
||
- - designation of crossing lines: a - b; |
||
- display, transformation: a a1, a1 a1; |
||
- logical consequence: m | | n |
m1 | | n1, m2 | | n2; |
|
Right angle (90 °).
If the symbols are crossed out with a slash, then this means the presence of a particle
And l - point A does not belong to line l; a / || b - straight lines a, b are not parallel.
Brief glossary of terms
Identity is a relationship between objects regarded as "the same"; the "limiting" case of the relation of equality.
Cyclic surfaces- surfaces formed by the movement of a circle of constant or variable radius.
Concentric spheres- spheres of different radii drawn from one center. Positional tasks- tasks in which it is required to establish a mutual position
and the mutual belonging of the considered geometric images.
Metric problems- tasks for determining the lengths of lines, sizes, angles, areas, volumes, etc.
Educational module 1
Topic 1. Graphic display of technical forms
Purpose: To study the method of graphical transmission of technical information. Objectives: - To study the method of image formation in technology.
- Master the techniques of obtaining reversible images - drawings.
1.1. Subject "Engineering Graphics", history of origin and development
The world around us is infinitely diverse and limitless. It is known that reality in human consciousness is formed in the form of mental images. These images can be operated in the imagination, transforming them into new, more complex or simple ones, you can reproduce images and their elements through music, plastic or using images on a sheet of paper, canvas, on a computer screen, etc.
Human-made images surround us everywhere: at work, at home, on vacation, in public places. If we consider them as materialized mental images, then they are an excellent means of communication between people. Therefore, a person's mastery of the technology of creating, recognizing and applied use of images is very important for the development of a personality, the disclosure of its potential.
Most often, people use graphic images made on a display screen or on paper to convey information.
“Graphics” is a general term that indicates a visual representation, an image of reality, most often, through contour lines, strokes, dots without the use of paints. The term “Graphics” comes from the Greek word “grafikos”, which has an older etymological root “gerph”, which means “to engrave, scratch”. Graphics are inherent in many areas of human activity. On the one hand, it is artistic creativity (engraving, lithography, easel graphics, illustrative graphics, etc.), on the other, technical creativity (engineering graphics, cartography, computer graphics, etc.). The connecting areas of knowledge that are based on the application of graphics are architecture, design, technical aesthetics, etc.
Various types of graphics are united by the commonality of functional processes, such as the obligatory abstraction of the considered real or artificial spatial relations and forms, their self-construction into a mental geometric image and its visualization.
Thus, graphics are a multifunctional system of human activity, which includes:
1. Perception of spatial relationships and forms (real or artificial).
2. Abstraction and self-construction of mental geometric images.
3. Communicative, cognitive visualization of the integral structure (gestalt) of the mental image.
The theoretical foundation of graphics is geometry, human physiology and psychology, and other sciences.
The most studied is the function of communicative, cognitive visualization - the technique of drawing, drawing, engraving, sketching, etc.
Based on the homology of the known types of graphics, the following classification is possible:
1. According to the belonging of the formed mental geometric image to a specific field of activity: engineering graphics, cartography, illustrative graphics, presentation graphics, construction graphics, business graphics, etc.
2. According to the degree of formalization of the mental geometric image: analog (drawing, photograph, etc.), analog-sign-symbolic, sign-symbolic.
3. By belonging to a specific technology of communicative, cognitive visualization: easel graphics, engraving, computer graphics, drawing, etc.
Engineering graphics is a complex academic discipline that forms the basis of engineering education and includes three main sections: "Descriptive geometry", "Technical drawing", "Computer graphics".
The study of engineering graphics provides the development of spatial-shaped engineering thinking and the acquisition of knowledge, skills and abilities to perform and read technical drawings and project documentation.
In the section "Descriptive geometry" methods of obtaining graphical models of space and algorithms for solving spatial problems are studied.
The section "Technical drawing" studies the general rules for the execution and reading of graphic information in accordance with existing standards.
In the section "Computer graphics" methods of automation of graphic work are considered.
The appearance of graphic images is closely related to the history of mankind. The oldest images are known - cave paintings, engraved on stone more than 20,000 years ago in the Stone Age. At that time, people believed in magic, believing that images can be used to influence the world around them. It was believed, for example, that it was necessary to hit a drawn animal with an arrow or a spear in order to ensure the success of the upcoming hunt.
The Bronze Age (about 4,000 BC) is characterized by the appearance of ornamentation in the form of wavy lines and other geometric shapes.
The first graphic signs - cuneiform - were invented by the inhabitants of Mesopotamia (present-day Iraq). Mathematical cuneiform texts on clay plates date back to the 2nd millennium BC. The inhabitants of Mesopotamia also succeeded in the construction business. The giant temple of the god Marduk in Babylon (6th century BC) could not have been erected without advances in construction graphics (images in the plan
– above). An integral part of the temple was ziggurat - quadrangular in plan and tapering upward stepped tower. This ziggurat belongs to one of the seven wonders of the world.
Stylized (simplified) forms were used to decorate the walls of buildings. The ancient Egyptians for graphic communication invented their own curly signs - hieroglyphs denoting whole concepts. For example, the movement was represented by a pair of legs. Simplified, cursive hierographic notation
– hieratic writing.
The walls and columns of buildings in Ancient Egypt (flourished in the 14th century BC) were decorated with reliefs and paintings, which are easy to recognize by the peculiar methods of depicting a person. Each part of the figure is presented in its turn so that it can be seen as fully as possible: the feet of a person's legs are in profile, and the eyes and shoulders are in full face.
Geometry and graphics since ancient times cannot exist without each other. Axioms and theorems of geometry help to abstract reality, and graphics artificially materialize idealistic images of the surrounding reality. The history of graphics is also the history of the development of geometry. The first guides to geometry that have come down to us are mathematical papyri created by the Egyptian priest Ahmes (about 2000 BC).
The most famous are the Rinda Papyrus (British Museum) and Moscow papyrus(Pushkin Museum in Moscow), which describe the solution of problems to determine the area of a triangle, rectangle, trapezoid and circle, as well as the volume of a parallelepiped and a cylinder.
Significant achievements in the development of geometry and graphics date back to the ancient period (6-16 centuries BC).
Thales of Miletus (625-547 BC) is supposed to have been the founder of geometry as a science. Pythagoras (570-500 BC) created the first geometric school, the doctrine of similarity and methods for constructing polyhedra. Aristotle (384-322 BC) introduced a description of an indefinite concept -
axioms and assertions-theorems. Archimedes (287-212 BC) developed methods for finding areas, surfaces and volumes of various figures and bodies. Hipparchus (180-125 BC) introduced a coordinate system to determine the position of a point on the earth's surface.
Summing up the development of geometry and its deductive construction was carried out by Euclid. His main work "Beginnings" contains the provisions of planimetry, stereometry.
In the teachings of Plato (428-348 BC), descriptions of polyhedra played an important role. The tetrahedron symbolized fire, the cube-earth, the octahedron-air, the icosahedron-water, and the dodecahedron-the universe.
V Greek period Simon of Cleonia introduced profile drawing using perspective. Based on the works of Simon, Agafarch wrote a book about his graphic techniques, which helped Anaxagoras (500-428 BC) and Democritus (460-370 BC) develop the theory of geometric constructions in perspective ... The new drawing method was used by Apollodorus in architectural projects. Many of the techniques of modern computer graphics have their roots in ancient Greek graphic works.
V Roman era famous scientistPapp (250 BC), who discovered the general theorem on the volume of bodies of revolution. The achievements of the Romans in the field of engineering structures (bridges, roads, multi-storey buildings, etc.) are significant.
The next stage in the development of geometry and graphics is associated with the opening of universities and the growth of European cities. During this time, graphics were given considerable attention in the university teaching of painting and engineering. In 1450. typography with movable letters was invented.
V 1516 centuries the advancement of public knowledge about graphic images was promoted byLeonardo da Vinci(1452-1519), recognized artist and engineer. In 1525 he published a book on geometric constructions. Leonardo owns the term "golden ratio".
Albrecht Durer (1471-1528), German artist, mathematician laid the foundations of orthogonal design, deduced the mathematical rules of perspective constructions.
V 17th century French scientists P. Ferma and R. Descartes laid the foundations of analytic geometry,
while J. Desargues and B. Pascal developed the principles of projective geometry.
The most important prerequisites for understanding the world around us were the works of the Italian scientist G. Galileo (1564-1642), the German scientist I. Kepler (1571-1630) and the Polish astronomer N. Copernicus.
V 1569 great cartographer G. Mercator published a map of the world on 18 sheets, where for the first time cylindrical projection and drawings were used to solve navigation problems.
English mathematician, artist B. Taylor (1685-1731) in 1715 published the work “ Principles of Linear Perspective”.
In the period 1754-69. the origin of descriptive geometry was influenced by the works of the French engineer Frezier, who used orthogonal projections onto mutually perpendicular planes.
The missing link to the graphic image system was added by the French engineer G. Montge (1746-1818), when he complexly linked two orthogonal projections of a three-dimensional body on one plane.
Being an outstanding geometer, an excellent graphic artist, G. Monge created a classic work on descriptive geometry "Geometriе descriptive".
Since 1795 Descriptive geometry became an academic discipline in France, and then within 50 years it spread to the following countries: Russia - 1811, USA - 1817, Spain - 1819, Germany - 1828, Italy - 1838, Belgium - 1840, Sweden - 1842, Egypt - 1845, Norway - 1845, Britain - 1851.
On the territory of Russia, since ancient times, graphic images have been used in the construction business, in the production of handwritten and printed books, etc.
In 1570 developed “ Drawing "of Moscow Russia... Cartographic and drawing works were successfully continued by Semyon Remizov. In 1707 produced "Drawing book of cities and lands of Siberia".
Drawing business became widespread under Peter I. The Moscow drawing school was created. A drawing manual is published "Compass and ruler techniques" (1725).
In the second half of the 18th century, the development of the economy contributed to the cultural and technical rise of the country. The study of drawings, projects completed during this period, allowed us to assert that design methods and techniques for performing graphic images have reached a high level in Russia. I.I.Polzunov (1728-1766) created a drawing of the world's first factory steam engine. In the drawing of a steam power plant (1763), the author uses sections to reveal the features of his invention. The drawings of the bridge made by the Russian inventor I.P. Kulibin (1735-1818) have survived.
Russian architects were proficient in projection methods: V.I.Bazhenov (1737-1799),
A.N. Voronikhin (1760-1814), M.F. Kazakov (1738-1812). According to their designs, monuments of classical Russian architecture were created: "Pashkov's House", Kazan Cathedral, Petrovsky Palace.
The history of descriptive geometry in Russia is inextricably linked with the activities of the Institute of the Corps of Railway Engineers, founded in St. Petersburg in 1809. The first professor of descriptive geometry was the French engineer C. Potier. The Institute has trained a lot of qualified teachers, of whom, first of all, Yakov Alexandrovich Sevastyanov(1796-1846). In 1821, Sevastyanov Ya.A. publishes the first Russian textbook “ Foundations of descriptive geometry”.
V 1855 The works of a professor at the Institute of the Corps of Railway Engineers are published A.H. Reder, dedicated to the method of projections with numerical marks and axonometric projections.
Professors N.I. Makarov (1824-1904) and V.I. Kurdyumov (1853-1904) had a significant influence on the development of methods of teaching descriptive geometry in Russia. Reading lectures, V. I. Kurdyumov pointed out that “if a drawing is a language of technology, equally understandable to all peoples, then descriptive geometry serves as the grammar of this language, since it teaches us to read strangers correctly.
and to express our own thoughts, using only lines and dots as words, as elements of any image ”.
V works of the academician ES Fedorova “New geometry as the basis of drawing” (1907), “Simple and
precise representation of points - a space of four dimensions on a plane by means of vectors ”(1909) the possibilities of using the projected properties of figures in crystallography are shown and methods of plane images of four-dimensional systems are developed.
Professor A.K. Vlasov (1868-1922) initiated the application of projective geometry to the theory of axonometry and nomography.
Kurdyumov's student, Professor N.A. Rynin (1877-1942), successfully found applications of graphic constructions to solving engineering problems in construction, aviation, mechanics, shipbuilding, and film perspective.
Professor N.I. Mertsalov (1866-1948) - the founder of the theory of spatial mechanisms - used the projection method to study spatial gearing.
The theory of perspective and the theory of shadows as applied to architectural and construction design was developed by Professor A.I. Dobryakov (1865-1947).
Professor of Moscow University N.A. Glagolev (1888-1945) wrote the first course in descriptive geometry entirely on a projective basis. In 1924 he made a theoretical basis for the main theorem on axonometry. N.A. Glagolev used projective methods when constructing nomograms, which are used in various fields of technology.
The improvement of the teaching of descriptive geometry in universities was facilitated by the scientific and methodological work of Professor N.F. Chetverukhin (1881-1974) and his students. Chetverukhin's works are known in the theory of positional and metric completeness of images, in the development of parametric methods for constructing projection drawings.
The activity of Professor I.I.Kotov (1909-1976) was aimed at creating algorithms and geometric models of design processes, including models of wireframe surfaces, problems of reproducing surfaces and their images using a computer.
1.2. Display Objects
and main content of graphic information
All objects of space surrounding a person are characterized by such common features as shape, color, size, position... Each object can be represented as a set of points, each of which has no magnitude, but occupies a certain place in space. Fix the point, i.e. its position in space can be determined, for example, using the x, y, z coordinate system.
A point is the simplest of the figures, which has no size, no shape, but a position, it is a 0-dimensional object.
Line - the trajectory of a moving point, has a length, shape (straight line, curve) and position relative to the selected coordinate system. Line - 1-dimensional display object (has a length).
More complex objects are displayed in the form flat and volumetric figures... So, for a flat figure, graphic information contains a characteristic of the shape - rectangular, round or otherwise; two main dimensions - length and width and position relative to the selected coordinate system. Therefore, a flat figure is a 2-dimensional display object. The volumetric figure (body) has three dimensions - length, width, height- 3-dimensional object of space.
That. four types of objects in space are considered (Fig. 1.1 - 1.4): point, lines, flat and volumetric figures, through the graphic display of which information about the shape, dimensions (except for the point) and position relative to the selected coordinate system is transmitted.
1.3. Projection method. Projection apparatus
V the basis for constructing images of an object in space on a plane is the method of projections. Projection is the construction of an image of an object on a plane (Fig. 1.5) using projection rays emanating from one point (center).
