KEY QUESTIONS for testing in the discipline
Guidelines for preparing for entrance computer testing
By ENGINEERING GRAPHICS
(discipline)
for specialties:
1-36 01 01 “Mechanical Engineering Technology”
1-36 01 03 “Technological equipment for machine-building production”
1-53 01 01 “Automation of technological processes and production”
1-74 06 01 “Technical support of agricultural production processes”
1st year, 1-2 semester
(course number, semester number)
FZO and
3rd year 1-2 semester TNF
(name of faculty)
EOP -1 COURSE -1 semester FZO = EOP -3 COURSE 1 semester FNO
IST-1 COURSE – 1st semester = IST-3 course TNF
Baranovichi 2012
INTRODUCTION
THEMATIC PLAN.
| No. | Name of section, topic | |
| Section I “Descriptive geometry and basics of geometric construction.” | ||
| 1. | Topic 1.1. Introduction to the subject of descriptive geometry and the formation of projection drawing | |
| 2. | ||
| 3. | ||
| 4. | Topic 1.4. The relative position of a straight line and a plane, two planes | |
| 5. | Topic 1.5. Transformation of a drawing by replacing projection planes, rotation and plane-parallel movement | |
| 6. | Topic 1.6. Surfaces - formation, image in the drawing, sections by planes | |
| 7. | Topic 1.7. Surface Intersection | |
| Section II “Projection drawing” | ||
| 8. | Topic 2.1. General rules for drawing up drawings, review of ESKD standards | |
| 9. | Topic 2.2. Geometric constructions | |
| 10. | Topic 2.3. Basic rules for making drawings | |
| 11. | Topic 2.4. Drawing dimensions (GOST 2.307-68) | |
| 12. | Topic 2.5. Axonometric projections with an axonometric section (GOST 2.317-69) |
Section I “Descriptive Geometry”
Topic 1.1. Introduction to the subject of descriptive geometry and the formation of projection drawing
Descriptive geometry is the basis of engineering education; subject of descriptive geometry;
projection method; central and parallel projection and their properties; rectangular (orthogonal) projection;
Monge method (historical background); a point in a system of two and three projection planes; orthogonal projections of a point and a rectangular coordinate system (Descartes coordinate system).
Topic 1.2. Projections of a straight line segment, the position of the line relative to the projection planes, the relative position of two lines
position of the line relative to the projection planes (lines of general and particular positions and their projections); point on a line;
relative position of lines: image of a drawing of parallel, intersecting and crossing lines; competing points on crossing lines (rule of competing points when determining the visibility of points).
Topic 1.3. Projections of a plane, position of a plane relative to projection planes, characteristic lines of a plane, projection of a right angle
defining a plane in a drawing in various ways; traces of plane; a point and a straight line in a plane (construction of their missing projections); plane level lines;
the position of the plane relative to the projection planes (general and particular planes);
collective property of projecting planes;
projections of flat figures; right angle projection theorem.
Topic 1.4. The relative position of a straight line and a plane, two planes
parallelism of a straight line and a plane, two planes;
the intersection of a line and a plane, two planes when one of the intersecting elements occupies a projecting position, and algorithms for constructing projections of the point of intersection of a line and a plane.
Topic 1.5. Transformation of a drawing by replacing projection planes, rotation And plane-parallel movement
purpose and methods of transformation;
method of replacing projection planes (replacing one and two projection planes; four main problems of drawing transformation, solved by the method of replacing projection planes);
rotation method (rotation around projecting lines - axis of rotation, center of rotation, radius of rotation, plane of rotation);
plane-parallel movement.
Topic 1.6. Surfaces - formation, image in the drawing, sections by planes
General information about faceted and curved surfaces;
education, forming, guiding; specifying and depicting the surface in the drawing;
surface projections (special cases):
polyhedra (oblique and regular straight lines - prism and pyramid), their sections by projecting planes;
surfaces of revolution: generatrix and axis of rotation of the surface, outline of the surface; characteristic lines on the surface of rotation (parallels, equator, throat, lines of meridional sections); examples of surfaces of revolution (straight cylinder, cone, sphere, torus); characteristic lines of sections of surfaces of revolution (cylinder, cone, sphere); projections of surfaces of revolution with cuts by projecting planes;
helical surfaces (straight and oblique helicoids, a point on the surface of the helicoid, a section of the helicoid by a projecting plane);
tangent lines and planes (general algorithm for constructing tangent planes to curved surfaces);
intersection of a general line with polyhedra and surfaces of revolution;
Topic 1.7. Surface Intersection
concept of line of intersection; general algorithm for constructing an intersection line;
four general cases of intersection of surfaces (using particular examples, when one or both surfaces are projecting);
constructing a line of intersection of surfaces using the method of auxiliary cutting planes;
coaxial surfaces; constructing a line of intersection of surfaces using the method of auxiliary secant concentric and eccentric spheres;
theorem on the intersection of second-order surfaces; Monge's theorem; the nature of the change in the line of intersection of the surfaces of 2 cylinders depending on the ratio of their diameters;
Section II “Projection drawing”
Topic 2.1. General rules for drawing up drawings, review of ESKD standards
Basic information about the uniform rules for the execution and execution of drawings and other technical documents in accordance with the ESKD as a set of state standards; purpose and dissemination of standards, their composition, classification and designation (GOST 2.001-70);
formats (GOST 2.301-68) and design of drawing sheets; main inscriptions (GOST
2.104-68) and filling out their columns; scales (GOST 2.302-68); lines (GOST 2.303-68); drawing fonts (GOST 2.304-81); drawing dimensions (GOST 2.307-68).
Topic 2.2. Geometric Constructions
The order of constructing parallel and mutually perpendicular lines; dividing a line segment; constructing angles and dividing them ; construction of flat polygonal figures; determining the center of a circular arc; dividing a circle into equal parts; construction of regular polygons inscribed and circumscribed in a circle; conjugations: rules for performing conjugations of various geometric elements, most often found in the outlines of images of objects in drawings (two intersecting lines; two circles or arcs of a tangent line; two circles - internal and external tangency; a tangent to two circles; a circle with a straight line);
construction of slope and taper; designation of slopes and tapers;
construction of tangent lines to a circle, ovals, spiral and pattern curves (ellipse, parabola, hyperbola, involute, cycloid, etc.).
Topic 2.3. Basic rules for making drawings
Images - views, sections, sections (GOST 2.305-68):
basic provisions and definitions; species names; additional and local species and their location, designation and inscription of species; the ratio of the sizes of arrows indicating the direction of view when designating a view; types of cuts - horizontal, vertical (frontal and profile); designation and inscription of sections, their location; local incisions; connecting part of the view with part of the section, dividing them with a line; conventions and simplifications in images; sections taken out and superimposed, their location and designation; complex cuts (broken and stepped); application procedure, execution rules, designation of cutting planes in the drawing.
Designations of graphic materials and rules for their application on drawings (GOST 2.306-68):
shading of sections (graphic designation of materials, including non-metallic, opaque and translucent).
Topic 2.4. Applying dimensions(GOST 2.307-68)
general provisions; general requirements for applying dimensions; applying linear dimensions; drawing the size of the diameter of the surfaces of rotation; drawing the dimensions of the radii of circular arcs; drawing angular dimensions; drawing the dimensions of a prismatic surface, the base of which is a square; applying chamfer dimensions to prismatic surfaces; features of applying hole sizes (measuring the location of holes); basic concepts about bases in mechanical engineering and drawing dimensions from bases.
Topic 2.5. Axonometric projections with axonometric section(GOST 2.317-69)
rectangular (isometric and dimetric) and oblique projections (frontal and horizontal isometric and frontal dimetric); position of the axonometric axes, reduced distortion coefficients along the axes; image of circles, position of the axes of the ellipses, dimensions of the major and minor axes of the ellipses; applying shading on an axonometric section.
Topic 1. General informationThe main element in solving graphic problems in engineering graphics isdrawing .
Below the drawing imply a graphic representation of objects or their parts. Drawings are carried out in strict accordance with the rules of projection in compliance with established requirements and conventions. Moreover, the rules for depicting objects or their components in drawings remain the same in all industries and construction.
The image of an object in the drawing must be such that it can be used to establish its shape as a whole, the shape of its individual surfaces, the combination and relative position of its individual surfaces. In other words, the image of an object must give a complete picture of its shape, structure, dimensions, as well as the material from which the object is made, and in some cases include information about the methods of manufacturing the object. A characteristic of the size of the object in the drawing and its parts is their dimensions, which are plotted on the drawing. Objects in drawings are usually depicted on a given scale.
Images of objects on the drawing must be placed so that its field is evenly filled. The number of images in the drawing must be sufficient to obtain a complete and unambiguous idea of it. At the same time, the drawing should contain only the required number of images, it should be minimal, that is, the drawing should be concise and contain a minimum amount of graphic images and text sufficient for free reading of the drawing, as well as its production and control.
Fig 1.1.1
The visible contours of objects and their edges in the drawings are made with a solid thick main line. The necessary invisible parts of the object are made using dashed lines. If the depicted object has constant or regularly changing cross sections, is made in the required scale and does not fit on the drawing field of a given format, it can be shown with gaps.
The rules for constructing images on drawings and designing drawings are given and regulated by a set of standards of the “Unified System of Design Documentation” (ESKD).
The image in the drawings can be made in various ways. For example, using rectangular (orthogonal) projection, axonometric projections, linear perspective. When making mechanical engineering drawings in engineering graphics, the drawings are made using the rectangular projection method. The rules for depicting objects, in this case products, structures or corresponding components, in drawings are established by GOST 2.305-68.
When constructing images of objects using the rectangular projection method, the object is placed between the observer and the corresponding projection plane. The main projection planes are taken to be the six faces of the cube, inside of which the depicted object is located (Fig. 1.1.1, a). Faces 1, 2 and 3 correspond to the frontal, horizontal and profile planes of projections. The faces of the cube with the images obtained on them are combined with the plane of the drawing (Fig. 1.1.1, b). In this case, face 6 can be placed next to face 4.
The image on the frontal plane of projections (on face 1) is considered the main one. The object is positioned relative to the frontal plane of projections so that the image gives the most complete idea of the shape and size of the object and carries the most information about it. This image is called the main image. Depending on their content, images of objects are divided into types, sections, sections.
Topic 2. Constructing views in a drawing
The image of the visible part of the surface of an object facing the observer is called the view.
According to the content and nature of implementation, types are divided into basic, additional and local.
GOST 2.305-68 establishes the following name for the main views obtained on the main projection planes (see Fig. 1.1.1):
1 - front view (main view); 2 - top view; 3 - left view; 4 - right view; 5 - bottom view; 6 - rear view. In practice, three types are more widely used: front view, top view and left view.
The main views are usually located in a projection relationship with each other. In this case, there is no need to write the name of the views on the drawing.
If any view is displaced relative to the main image, its projection connection with the main view is broken, then an inscription of type “A” is made above this view (Fig. 1.2.1).
Fig 1.2.1
Fig 1.2.2
Fig 1.2.3
The direction of view should be indicated by an arrow, indicated by the same capital letter of the Russian alphabet as in the inscription above the view. The ratio of the sizes of the arrows indicating the direction of view should correspond to those shown in Fig. 1.2.2.
If the views are in projection connection with each other, but are separated by any images or are not located on the same sheet, then an “A” type inscription is also made above them. An additional view is obtained by projecting an object or part of it onto an additional projection plane that is not parallel to the main planes (Fig. 1.2.3). Such an image must be performed in the case when any part of the object is not depicted without distorting the shape or size on the main projection planes.
In this case, the additional projection plane can be located perpendicular to one of the main projection planes.
When an additional view is located in direct projection connection with the corresponding main view, it does not need to be designated (Fig. 1.2.3, a). In other cases, the additional view must be marked on the drawing with an inscription of type “A” (Fig. 1.2.3, b),
Fig 1.2.4
and the image associated with the additional view must have an arrow indicating the direction of view, with the corresponding letter designation.
The secondary view can be rotated while maintaining the same position as the item in the main image. In this case, you need to add a sign to the inscription (Fig. 1.2.3, c).
A local view is an image of a separate, limited area of the surface of an object (Fig. 1.2.4).
If a local view is located in direct projection connection with the corresponding images, then it is not designated. In other cases, local species are designated similarly to additional species; the local species may be limited by the cliff line (“B” in Fig. 1.2.4).
Topic 3. Construction of the third type of object based on two data
First of all, you need to find out the shape of individual parts of the surface of the depicted object. To do this, both given images must be viewed simultaneously. It is useful to keep in mind which surfaces correspond to the most common images: triangle, quadrilateral, circle, hexagon, etc.
In the top view, in the shape of a triangle, the following can be depicted (Fig. 1.3.1, a): triangular prism 1, triangular 2 and quadrangular 3 pyramids, cone of rotation 4.
Fig 1.3.1
An image in the form of a quadrangle (square) can be seen in the top view (Fig. 1.3.1, b): a cylinder of rotation 6, a triangular prism 8, quadrangular prisms 7 and 10, as well as other objects limited by planes or cylindrical surfaces 9.
The shape of a circle can be in the top view (Fig. 1.3.1, c): ball 11, cone 12 and cylinder 13 of rotation, other surfaces of rotation 14.
The top view in the shape of a regular hexagon has a regular hexagonal prism (Fig. 1.3.1, d), limiting the surfaces of nuts, bolts and other parts.
Having determined the shape of individual parts of the surface of an object, you need to mentally imagine their image on the left and the entire object as a whole.
To construct the third type, it is necessary to determine which lines of the drawing should be taken as the basic ones for reporting the dimensions of the image of the object. As such lines, axial lines are usually used (projections of the planes of symmetry of an object and projections of the planes of the bases of an object). Let's analyze the construction of the left view using an example (Fig. 1.3.2): using the data from the main view and the top view, construct a left view of the depicted object.
By comparing both images, we establish that the surface of the object includes the surfaces of: regular hexagonal 1 and quadrangular 2 prisms, two cylinders 3 and 4 of rotation and a truncated cone 5 of rotation. The object has a frontal plane of symmetry Ф, which is convenient to take as the basis for reporting the dimensions along the width of individual parts of the object when constructing its left view. The heights of individual sections of an object are measured from the lower base of the object and are controlled by horizontal communication lines.
Fig 1.3.2
Fig 1.3.3
The shape of many objects is complicated by various cuts, cuts, and intersections of surface components. Then you first need to determine the shape of the intersection lines, and you need to build them at individual points, introducing designations for the projections of points, which after completing the construction can be removed from the drawing.
In Fig. 1.3.3 shows a left view of an object, the surface of which is formed by the surface of a vertical cylinder of rotation, with a T-shaped cutout in its upper part and a cylindrical hole with a frontally projecting surface. The plane of the lower base and the frontal plane of symmetry F are taken as the base planes. The image of the L-shaped cutout in the view on the left is constructed using the cutout contour points A B, C, D and E, and the intersection line of the cylindrical surfaces is constructed using points K, L, M and them symmetrical. When constructing the third type, the symmetry of the object relative to the plane F was taken into account.
Topic 4. Making cuts in the drawing
The image of an object mentally dissected by one or more planes is called a cut. Mental dissection of an object relates only to this cut and does not entail changes in other images of the same object. The section shows what is obtained in the secant plane and what is located behind it.
Sections are used to depict the internal surfaces of an object in order to avoid a large number of dashed lines, which can overlap each other if the internal structure of the object is complex and make the drawing difficult to read.
To make a cut, you need to: mentally draw a secant plane in the right place on the object (Fig. 1.4.1, a); mentally discard part of the object located between the observer and the cutting plane (Fig. 1.4.1, b), project the remaining part of the object onto the corresponding projection plane, make the image either in place of the corresponding type, or in the free field of the drawing (Fig. 1.4.1 , V); shade a flat figure lying in a secant plane; if necessary, give a designation of the section.
Depending on the number of cutting planes, cuts are divided into simple - with one cutting plane, complex - with several cutting planes.
Fig 1.4.1
Depending on the position of the cutting plane relative to the horizontal projection plane, the sections are divided into:
horizontal - the cutting plane is parallel to the horizontal plane of projections;
vertical - the cutting plane is perpendicular to the horizontal plane of projections;
inclined - the secant plane makes an angle with the horizontal plane of projections that is different from a right angle.
A vertical section is called frontal if the cutting plane is parallel to the frontal plane of projections, and profile if the cutting plane is parallel to the profile plane of projections.
Complex cuts can be stepped if the cutting planes are parallel to each other, and broken if the cutting planes intersect with each other.
The cuts are called longitudinal if the cutting planes are directed along the length or height of the object, or transverse if the cutting planes are directed perpendicular to the length or height of the object.
Local cuts serve to reveal the internal structure of an object in a separate limited place. The local section is highlighted in the view by a solid wavy thin line.
The rules provide for the designation of cuts.
Fig 1.4.2
Fig 1.4.3
The position of the cutting plane is indicated by an open section line. The starting and ending strokes of the section line should not intersect the contour of the corresponding image. Arrows should be placed on the initial and final strokes indicating the direction of view (Fig. 1.4.2). Arrows should be applied at a distance of 2...3 mm from the outer end of the stroke. In case of a complex section, strokes of an open section line are also drawn at the bends of the section line.
Near the arrows indicating the direction of view from the outside of the angle formed by the arrow and the stroke of the section line, capital letters of the Russian alphabet are written on a horizontal line (Fig. 1.4.2). Letter designations are assigned in alphabetical order without repetitions and without omissions, with the exception of the letters I, O, X, b, ы, b.
The cut itself must be marked with an inscription like “A - A” (always two letters, separated by a dash).
If the secant plane coincides with the plane of symmetry of the object, and the section is made in place of the corresponding view in the projection connection and is not divided by any other image, then for horizontal, vertical and profile sections it is not necessary to mark the position of the secant plane and the section does not need to be accompanied by an inscription. In Fig. 1.4.1 the frontal section is not marked.
Simple oblique cuts and complex cuts are always designated.
Let's look at typical examples of constructing and designating sections in drawings.
In Fig. 1.4.3 a horizontal section “A - A” was made in place of the top view. A flat figure lying in a secant plane - a section figure - is shaded, and the visible surfaces
Fig 1.4.4
Fig 1.4.5
located under the cutting plane, are limited by contour lines and are not shaded.
In Fig. 1.4.4 a profile section is made in place of the view on the left in projection connection with the main view. The cutting plane is a profile plane of symmetry of the object, so the cut is not indicated.
In Fig. 1.4.5 a vertical section “A - A” is made, obtained by a cutting plane that is not parallel to either the frontal or profile projection planes. Such sections can be built in accordance with the direction indicated by the arrows (Fig. 1.4.5), or placed in any convenient place in the drawing, as well as rotated to the position corresponding to the one accepted for this item in the main image. In this case, the sign O is added to the cut designation.
The oblique section is made in Fig. 1.4.6.
Fig 1.4.6
It can be drawn in a projection connection in accordance with the direction indicated by the arrows (Fig. 1.4.6, a), or placed anywhere in the drawing (Fig. 1.4.6, b).
In the same figure, in the main view, a local section is made showing through cylindrical holes at the base of the part.
Fig 1.4.7
Fig 1.4.8
In Fig. 1.4.7, in place of the main view, a complex frontal stepped section is drawn, made by three frontal parallel planes. When making a step cut, all parallel cutting planes are mentally combined into one, i.e., a complex cut is designed as a simple one. On a complex section, the transition from one cutting plane to another is not reflected.
When constructing broken sections (Fig. 1.4.8), one secant plane is placed parallel to any main projection plane, and the second secant plane is rotated until it aligns with the first.
Fig 1.4.9
Fig 1.4.10
Together with the secant plane, the section figure located in it is rotated and the cut is made in the rotated position of the section figure.
The connection of part of the view with part of the section in one image of the object according to GOST 2.305-68 is allowed. In this case, the boundary between the view and the section is a solid wavy line or a thin line with a break (Fig. 1.4.9).
If half of the view and half of the section are connected, each of which is a symmetrical figure, then the line dividing them is the axis of symmetry. In Fig. 1.4.10 there are four images of the part, and on each of them half of the view is connected with half of the corresponding section. In the main view and the left view, the section is placed to the right of the vertical axis of symmetry, and in the top and bottom views - to the right of the vertical or below the horizontal axis of symmetry.
Fig 1.4.11
Fig 1.4.12
If the contour line of an object coincides with the axis of symmetry (Fig. 1.4.11), then the boundary between the view and the section is indicated by a wavy line, which is drawn so as to preserve the image of the edge.
Hatching of a sectional figure included in the section must be carried out in accordance with GOST 2.306-68. Non-ferrous, ferrous metals and their alloys are indicated in cross-section by hatching with solid thin lines of thickness from S/3 to S/2, which are drawn parallel to each other at an angle of 45° to the lines of the drawing frame (Fig. 1.4.12, a). Hatch lines can be drawn slanted to the left or to the right, but in the same direction on all images of the same part. If the hatch lines are drawn at an angle of 45° to the lines of the drawing frame, then the hatch lines can be placed at an angle of 30° or 60° (Fig. 1.4.12, b). The distance between parallel hatching lines is chosen in the range from 1 to 10 mm, depending on the hatching area and the need to diversify the hatching.
Non-metallic materials (plastics, rubber, etc.) are indicated by shading with intersecting mutually perpendicular lines (checkered shading), inclined at an angle of 45° to the frame lines (Fig. 1.4.12, c).
Let's look at an example. Having completed the frontal section, we will connect half of the profile section with half of the left view of the object specified in Fig. 1.4.13, a.
Analyzing this image of the object, we come to the conclusion that the object is a cylinder with two through prismatic horizontal and two vertical internal holes,
Fig 1.4.13
of which one has the surface of a regular hexagonal prism, and the second has a cylindrical surface. The lower prismatic hole intersects the surface of the outer and inner cylinder, and the upper tetrahedral prismatic hole intersects the outer surface of the cylinder and the inner surface of the hexagonal prismatic hole.
The frontal section of an object (Fig. 1.4.13, b) is made by the frontal plane of symmetry of the object and is drawn in place of the main view, and the profile section is made by the profile plane of symmetry of the object, so neither one nor the other needs to be designated. The left view and the profile section are symmetrical figures; their halves could be delimited by an axis of symmetry, if not for the image of the edge of the hexagonal hole coinciding with the axial line. Therefore, we separate the part of the view to the left of the profile section with a wavy line, depicting most of the section.
Topic 5. Making sections in the drawing
The image of a figure obtained by mental dissection by one or more planes, provided that only what is included in the cutting plane is shown in the drawing, is called a section. A section differs from a section in that it depicts only what directly falls into the cutting plane (Fig. 1.5.1, a). A section, like a cut, is a conventional image, since the cross-section figure does not exist separately from the object: it is mentally torn off and depicted on the free field of the drawing. Sections are part of the section and exist as independent images.
Sections that are not part of the section are divided into extended (Fig. 1.5.1, b) and superimposed (Fig. 1.5.2, a). Preference should be given to extended sections, which can be placed in the section between parts of the same image (Fig. 1.5.2, b).
According to the shape of the sections, they are divided into symmetrical (Fig. 1.5.2, a, b) and asymmetrical (Fig. 1.5.1, b).
Fig 1.5.1
Fig 1.5.2
Fig 1.5.3
Fig 1.5.4
The contour of the extended section is drawn with solid main lines, and the superimposed one with solid thin lines, and the contour of the main image at the location of the superimposed section is not interrupted.
The designation of sections in the general case is similar to the designation of sections, i.e. the position of the cutting plane is displayed by section lines on which arrows are drawn, giving the direction of view and denoted by the same capital letters of the Russian alphabet. In this case, an inscription of the type “A - A” is made above the section (see Fig. 1.5.2, b).
For asymmetrical superimposed sections or those made in a gap in the main image, a section line with arrows is drawn, but not marked with letters (Fig. 1.5.3, a, b). Superimposed symmetrical section (see Fig. 1.5.2, a), symmetrical section made in the break of the main image (see Fig. 1.5.2, b), extended symmetrical section made along the trace of the cutting plane (see Fig. 1.5 .1, a), are drawn up without drawing a section line.
Fig 1.5.5
If the secant plane passes through the axis of the surface of rotation that bounds the hole or recess, then the contour of the hole or recess is drawn completely (Fig. 1.5.4, a).
If the cutting plane passes through a through non-circular hole and the section turns out to consist of separate independent parts, then cuts should be used (Fig. 1.5.4, b).
Oblique sections are obtained from the intersection of an object with an inclined plane that makes an angle different from a straight line with the horizontal plane of projections. In the drawing, inclined sections are made according to the type of extended sections. An inclined section of an object must be constructed as a set of inclined sections of its constituent geometric bodies. The construction of inclined sections is based on the method of replacing projection planes.
When drawing an inclined section, you need to determine which surfaces bounding the object are cut by the cutting plane, and which lines are obtained from the intersection of these surfaces with this cutting plane. In Fig. 1.5.5 an inclined section “A - A” was constructed. The cutting plane intersects the base of the object along a trapezoid, the inner and outer cylindrical surfaces - along ellipses, the centers of which lie on the main vertical axis of the object. Reading the shape of an inclined section is made easier by plotting the horizontal projection of the inclined section as an overlay section.
Topic 7. Conventions and simplifications when depicting an object
When making various images of an object, GOST 2.305-68 recommends the use of certain conventions and simplifications, which, while maintaining clarity and clarity of the image, reduce the amount of graphic work.
If the view, section or section are symmetrical figures, then you can draw only half of the image or slightly more than half of the image, limiting it with a wavy line (Fig. 1.7.1).
It is allowed to simplify the depiction of cut lines and transition lines; instead of pattern curves, draw circular arcs and straight lines (Fig. 1.7.2, a), and show a smooth transition from one surface to another conditionally (Fig. 1.7.2, b) or not show it at all (Fig. 1.7.2, c ).
Elements such as spokes, thin walls, stiffeners are shown unshaded in section if the cutting plane is directed along the axis or long side of such an element (Fig. 1.7.4). If there is a hole or recess in such elements, then a local incision is made (Fig. 1.7.5, a).
Holes located on the round flange and not falling into the secant plane are shown in section as if they were in the secant plane (Fig. 1.7.5, b).
Fig 1.7.4
Fig 1.7.5
To reduce the number of images, it is allowed to depict the part of the object located between the observer and the cutting plane with a thick dash-dotted line (Fig. 1.7.6). The rules for depicting objects are set out in more detail in GOST 2.305-68.
Fig 1.7.6
Topic 8. Constructing a visual image of an object
To construct a visual image of an object, we will use axonometric projections. It can be done according to its complex drawing. Using, fig. 1.3.3, let’s construct a standard rectangular isometry of the object depicted on it. Let's use the given distortion coefficients. Let us accept the location of the origin of coordinates (point O) - in the center of the lower base of the object (Fig. 1.8.1). Having drawn the isometric axes and set the image scale (MA 1.22:1), we mark the centers of the circles of the upper and lower bases of the cylinder, as well as the circles limiting the T-shaped cutout. We draw ellipses that are isometry of circles. Then we draw lines parallel to the coordinate axes that limit the cutout in the cylinder. Isometry of the line of intersection of a through cylindrical hole,
Fig 1.8.1
Fig 1.8.2
the axis of which is parallel to the Oy axis with the surface of the main cylinder, we build by individual points, using the same points (K, L, M and symmetrical to them) as when constructing the view on the left. Then we remove the auxiliary lines and finally outline the image, taking into account the visibility of individual parts of the object.
To construct an axonometric image of an object, taking into account the section, we will use the conditions of the problem, the solution of which is shown in Fig. 1.4.13, a. In a given drawing, to construct a visual image, we mark the position of the projections of the coordinate axes and on soy Oz we mark the centers 1,2,..., 7 of the object figures located in the horizontal planes G1", T"2, ..., G7", this is the top and the lower base of the object, the base of the internal holes. To convey the internal shapes of the object, we will cut out 1/4 of the object using coordinate planes xOz and yOz.
Fig 1.8.3
The flat figures obtained in this case are already constructed on a complex drawing, since they are halves of a frontal and profile section of objects (Fig. 1.4.13, b).
We begin constructing a visual image by drawing the dimetric axes and indicating the scale MA 1.06: 1. On the z axis we mark the position of centers 1, 2,..., 7 (Fig. 1.8.2, a); We take the distances between them from the main type of object. We draw the dimetric axes through the marked points. Then we construct cross-sectional figures in dimetry, first in the xOz plane, and then in the yOz plane. We take the dimensions of the coordinate segments from the complex drawing (Fig. 1.4.13); At the same time, we reduce the dimensions along the y-axis by half. We hatch the sections. The angle of inclination of the hatching lines in axonometry is determined by the diagonals of parallelograms constructed on the axonometric axes, taking into account the distortion coefficients. In Fig. 1.8.3, a shows an example of choosing the direction of hatching in isometry, and in Fig. 1.8.3, b - in dimetry. Next, we construct ellipses - the dimetry of circles located in horizontal planes (see Fig. 1.8.2, b). We draw contour lines of the outer cylinder, internal vertical holes, and build the base of these holes (Fig. 1.8.2, c); we draw visible lines of intersection of horizontal holes with the outer and inner surfaces.
Then we remove the auxiliary construction lines, check the correctness of the drawing and outline the drawing with lines of the required thickness (Fig. 1.8.2, d).
INTRODUCTION 6
^ SECTION 1. DESIGN OF DRAWINGS 6
1.1. Types of products and their structure 6
1.2. Types and completeness of design documents 7
1.3. Stages of development of design documentation 9
1.4. Title blocks 10
1.5. Formats 11
1.6. Scale 11
1.7. Drawing lines 12
1.8. Drawing fonts 13
1.9. Hatching 14
^ SECTION 2. IMAGES 15
2.1. Types 15
2.2. Sections 17
2.3. Designation of sections 18
2.4. Making sections 19
2.5. Cuts 19
2.6. Designation of simple cuts 21
2.7. Making simple cuts 21
2.8. Making difficult cuts 21
^ SECTION 3. CONVENTIONAL GRAPHIC IMAGES IN THE DRAWINGS 23
3.1. Conventions and simplifications when performing images 23
3.2. Selecting the required number of images 24
3.3. Arrangement of images on the drawing field 25
3.4. Image on the drawing of intersection and transition lines 26
3.5. Constructing intersection and transition lines 27
^ SECTION 4. DIMENSIONING 28
4.1. Main types of machining of parts 28
4.2. Brief information about bases in mechanical engineering 29
4.3. Dimensioning system 29
4.4. Dimensioning methods 31
4.5. Shaft drawing 31
4.6. Structural elements of parts 32
4.7. Threaded grooves 35
4.8. Foundry bases, machining bases 36
4.9. Dimensions on casting drawings 37
^ SECTION 5. AXONOMETRIC PROJECTIONS 37
5.1. Types of axonometric projections 37
5.2. Axonometric projections of flat figures 41
5.3. Axonometric projections of 3-dimensional bodies 44
^ SECTION 6. THREADS, THREADED PRODUCTS AND CONNECTIONS 47
6.1. Geometric shape and basic thread parameters 47
6.2. Thread assignments and standards 50
6.3. Thread image 51
6.4. Thread designation 53
6.5. Image of threaded products and connections 54
6.6. Designation of standard threaded products 60
^ SECTION 7. DETACHABLE CONNECTIONS 62
7.1. Fixed connectors 62
7.2. Bolt connection 62
7.3. Pin connection 63
7.4. Screw connection 64
7.5. Pipe connection 65
7.6. Movable detachable joints 65
7.7. Key connections 66
7.8. Spline connections 66
^ SECTION 8. PERMANENT CONNECTIONS, GEARS 67
8.1. Illustrations and symbols of welds 67
8.2. Gear and worm gears 69
8.3. Conventional images of gear wheels 73
8.4. Spur Gear Drawing 74
^ SECTION 9. SURFACE ROUGHNESS 75
9.1. Standardization of surface roughness 75
9.2. Surface roughness parameters 76
9.3. Selecting surface roughness parameters 77
9.4. Example of roughness standardization 77
9.5. Signs for indicating roughness 79
9.6. Rules for designating roughness 80
^ SECTION 10. SKETCHES 84
10.1. Sketch of the detail. Sketch requirements 84
10.2. Sequence of sketches 85
10.3. General requirements for stocking sizes 87
10.4. Techniques for measuring parts 88
10.5. Surface roughness and its designation 89
10.6. Materials in mechanical engineering 92
^ SECTION 11. ASSEMBLY DRAWING 101
11.1. Definition of assembly drawing 101
11.2. Requirements for assembly drawing 102
11.3. Sequence of assembly drawing 102
11.4. Applying item numbers 104
11.5. Assembly drawing specification 105
11.6. Conventions and simplifications in assembly drawings 107
^ SECTION 12. DETAILING DRAWINGS 108
12.1. Reading a general arrangement drawing 108
12.2. Making detail drawings 109
12.3. Reading the drawing “Pressure valve” 110
12.4. Sequence of execution of the housing drawing 112
DEPARTMENT OF MECHANICS AND GRAPHICS
L.A. Kozlova
ENGINEERING GRAPHICS
Tutorial
MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION
FEDERAL STATE BUDGET EDUCATIONAL INSTITUTION
"TOMSK STATE UNIVERSITY OF CONTROL SYSTEMS AND RADIO ELECTRONICS"
DEPARTMENT OF MECHANICS AND GRAPHICS
L.A. Kozlova
ENGINEERING GRAPHICS
Tutorial
The textbook is intended for students of all specialties,
studying the course
"Engineering Computer Graphics".
ANNOTATION
The manual contains the theoretical foundations of descriptive geometry and engineering graphics, examples of solving geometric problems and constructing graphic projections. The textbook is intended for all specialists
benefits of students studying the course “Engineering Graphics”
Introduction…………………………………………………………………………………… 5
1 Fundamentals of descriptive geometry…………………………………………. 7
1.1 Symbolism……………………………………………………….......... 7
1.2 Central projection…………………………………………………….. . 8
1.3 Parallel projection………………………………………… 9
1.4 Rectangular (orthogonal) projection…………………… 10
1.5 Projecting a point……………………………………………………………... 12
1.6 Projection of straight lines in general position………………………...... 15
1.7 Division of a segment in a given ratio……………………………… 16
1.8 Traces of a straight line………………………………………………………... 16
1.9 Right triangle method…………………………………. 17
1.10 Projection of private lines……………………….. 18
1.11 The relative position of a point and a line……………………………........ 20
1.12 Mutual position of lines………………………………………….. 20
1.13 Determining the visibility of a faceted body…………………………….. 25
1.14 Flatness……………………………………………………………… 25
1.15 A point and a straight line in a plane………………………………………….. 28
1.16 The relative position of a straight line and a plane, planes……………. 34
1.17 Methods for converting a complex drawing…………………… 45
1.17 Polyhedra………………………………………………………50
1.18 Bodies of rotation………………………………………………………. 53
2 Basic rules for drawing up drawings………………………………… 60
2.1 Unified system of design documentation. ESKD standards. 60
2.2 Formats…………………………………………………………………………………60
2.3 Scale………………………………………………………………………………… 61
2.4 Lines………………………………………………………………………………… 63
2.5 Drawing fonts…………………………………………………… 64
2.6 Images on technical drawings……………………………… 66
2.7 Graphic designation of materials in sections………………….. 78
2.8 Applying dimensions……………………………………………………………... 81
2.9 Visual axonometric images……………………….. 92 3 Detailing………………………………………………………………………………… 97
3.1 Contents and scope of work……………………………………………………… 98
3.2 Reading the assembly drawing………………………………………………………. 97
H.3 Example of reading a drawing…………………………………………….. .99
3.4 Parts drawings………………………………………………………. 103
3.5 Selection and application of dimensions……………………………………………………………. 111
3.6 Filling out the title block……………………………………118
3.7 Determining the dimensions of a part from its image using a scale graph……………………………………………………….
4 Connections………………………………………………………………………………… 119
4.1 Threads…………………………………………………………………………………. 120
4.1 Threaded connections…………………………………………………………………… 123
4.2 Calculation of a screw connection………………………………………………………....... 123
Introduction
IN The number of disciplines that form the basis of engineering education includes “Engineering Graphics”.
Engineering graphics is the conventional name of an academic discipline that includes the basics of descriptive geometry and the basics of a special type of technical drawing.
Descriptive geometry is a science that studies the patterns of depicting spatial forms on a plane and solving spatial problems using protection-graphic methods.
Historically, image methods arose in the primitive world.
IN At the beginning of development, a drawing appeared, then a letter - writing. Milestones in the development of graphics: rock painting, the creation of great artists of the era of objection.
However, the formation of a scientific theory of image began in the 17th century, when the doctrine of optics arose. In 1636, geometer Girard Disargues gave a coherent theory of images in perspective.
IN the further development of the drawing was played by the French mathematician and engineer Gaspard Monge(1746-1818). The merit of G. Monge is that he summarized the available data on the construction of a flat drawing and created an independent scientific discipline called “Descriptive Geometry” (1798). G. Monge said: descriptive geometry has the following goal: in a drawing that has two dimensions, accurately depict bodies of three dimensions. From this point of view, this geometry should be necessary both for the engineer drawing up the project and for the one who is assigned to work on these projects.
Metric (measuring) geometry, created, as is known, by the works of Euclid, Archimedes and other mathematicians of antiquity, grew out of the needs of land surveying and navigation.
Descriptive geometry received a comprehensive and deep scientific and theoretical justification only after the birth of geometry on the pseudosphere. It was created by the great Russian geometer Lobachevsky (1793-1856).
IN In Russia, descriptive geometry began to be studied in 1810 at the Institute of the Corps of Railway Engineers in St. Petersburg.
Descriptive geometry is a branch of geometry that studies spatial forms by their projections on a plane. Its main elements are:
1. Create an image method
2. Development of methods for solving positional and metric problems using their images.
Descriptive geometry is a link between mathematics, technical drawing and other subjects. Makes it possible to construct geometric shapes on a plane and to represent the shape of a product using a flat image.
When studying a course in descriptive geometry, students, along with mastering theoretical principles, acquire the skills of accurate graphical solution of spatial problems of a metric and positional nature. The ability to find a shorter way to solve a graphical problem forms the general engineering culture of a young specialist.
Studying descriptive geometry allows you to:
1. Learn to make drawings, i.e. study ways of graphically depicting existing and created objects.
3. Acquire skills in solving spatial problems on a projection drawing.
4. Develop spatial and logical thinking.
Engineering graphics is the foundation on which all technical projects of science and technology will be based in the future, and which enables the student, and then the engineer, to carry out design work and study technical literature rich in drawings.
You can read or draw up drawings only if you know the techniques and rules for drawing them up. One category of rules is based on strictly defined depiction techniques that have the force of methods, the other category is based on numerous, often unrelated conventions adopted when drawing up drawings and stipulated by GOSTs.
GOSTs are state all-Union standards, the complex of which constitutes the Unified System of Design Documents adopted in Russia. The main purpose of ESKD standards is to establish uniform rules for the implementation, execution and circulation of design documentation at all Russian enterprises.
The theoretical basis of drawing is descriptive geometry. The main goal of descriptive geometry is the ability to depict all possible combinations of geometric shapes on a plane, as well as the ability to carry out research and their measurements, allowing for the transformation of images. Images constructed according to the rules of descriptive geometry allow you to mentally imagine the shape of objects and their relative position in space, determine their sizes, and explore the geometric properties inherent in the depicted object. The study of descriptive geometry contributes to the development of spatial imagination, which is necessary for an engineer to deeply understand a technical drawing and to be able to create new technical objects. Without such an understanding of the drawing, no creativity is conceivable. In any field of technology, in the multifaceted engineering activity of man, drawings are the only and irreplaceable means of expressing technical ideas.
Descriptive geometry is one of the disciplines that forms the basis of engineering education.
Thus, the subject “Engineering Graphics” consists of two parts:
1. Considerations of the basics of projecting geometric images in the course of descriptive geometry and
2. Studying the laws and rules for making drawings in a technical drawing course.
1. BASICS OF DESCRIPTION GEOMETRY
1.1 Symbolism
match | tangents |
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belong, are e- |
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perpendicular | crossing |
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congruent | intersection of many |
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parallel | |||||||||
are displayed | right angle |
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negation of sign | includes, contains |
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A, B, C, D... - points | Planes |
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Point projections | Traces of planes |
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The basis of descriptive geometry is the method of projections.
The rules for constructing images set out in descriptive geometry are based on the method of projections. Any regular image of objects on a plane (for example, a sheet of paper, a monitor tap) is a projection of it onto this plane.
We call a correct image constructed in accordance with the laws of geometric optics that apply in the real world. Thus, projections are: technical drawing, photograph, technical drawing, shadow falling from an object, image on the retina, etc. There are images made in deviation from these laws. These, for example, are drawings of primitive people, children's drawings, paintings by artists of various non-realistic movements, etc. Such images are not projections and geometric research methods cannot be applied to them.
The Latin base of the word projection means "throwing forward."
Descriptive geometry considers several types of projection. The main ones are central and parallel projection.
1.2 Center projection
To obtain central projections, it is necessary to specify the projection plane H and the projection center S.
The center of the projections acts as a point light source, emitting projection rays. The points of intersection of the projecting rays with the projection plane H are called projections (Fig. 1.1). Projections do not work when the center of projection lies in a given plane or the projection rays are parallel to the plane of projections.
Center projection properties:
1. Each point in space is projected onto a given projection plane into a single projection.
2. At the same time, each point on the projection plane can be a projection of many points if they are on the same projection ray
3. A straight line that does not pass through the center of projection is projected as a straight line (the projecting straight line is a point).
4. A flat (two-dimensional) figure that does not belong to the projecting plane is projected as a two-dimensional figure (figures belonging to the projecting plane are projected along with it as a straight line).
5. A three-dimensional figure appears two-dimensional.
The eye and camera are examples of this image system. One central projection of a point does not make it possible to judge the position of the Point itself in space, and therefore in technical drawing this projection
almost never used. To determine the position of a point using this method, it is necessary to have two central projections of it, obtained from two different centers (Fig. 1.2). Central projections are used to depict objects in perspective. Images in central projections are visual, but inconvenient for technical drawing.
1.3 Parallel projection
Parallel projection is a special case of central projection, when the center of projection is moved to an improper point, i.e. to infinity. With this position of the center of projections, all projecting lines will be parallel to each other (Fig. 1.3). Due to the parallelism of the projecting lines, the method under consideration is called parallel, and the projections obtained using it are called parallel projections. The parallel projection apparatus is completely determined by the position of the projection plane (H) and the projection direction.
Parallel projection properties:
1. With parallel projection, all the properties of the central projection are preserved, and new ones arise:
2. To determine the position of a point in space, it is necessary to have two parallel projections of it, obtained with two different projection directions (Fig. 1.4).
3. Parallel projections of mutually parallel lines are parallel, and the ratio of the lengths of segments of such lines is equal to the ratio of the lengths of their projections.
4. If the length of a straight segment is divided by a point in in any relation, then the length of the projection of the segment is divided by the projection of this point in the same relation (Figure 1.15).
5. A flat figure parallel to the plane of projections is projected by parallel projection onto this plane into the same figure.
Parallel projection, like central projection, with one projection center, also does not ensure the reversibility of the drawing.
Using the techniques of parallel projection of a point and a line, you can build parallel projections of a surface and a body.