To quickly and most clearly convey the shape of an object, technical drawings are used.
Technical drawing is an image made by eye and by hand according to the rules of axonometry.
When performing technical drawings, the axes must be placed at the same angles as for axonometric projections, and the dimensions of objects must be laid out along the axes.
The choice of axonometric projection on the basis of which the technical drawing will be made depends on the shape of the part.
The frontal dimetric projection is convenient for depicting parts whose curvilinear outlines are located in a plane parallel to the xOz plane (see Fig. 92 and 93). Isometric projections are preferable when depicting parts whose curved elements are located in different planes.
It is convenient to perform technical drawings on lined paper. In Fig. 103 shows ways to make it easier to work with a pencil by hand.
An angle of 45 is easy to construct by dividing the right angle in half (Fig. 103, a). To construct an angle of 30, you need to divide the right angle into three equal parts (Fig. 103, b).
A regular hexagon can be drawn in isometry (Fig. 103, c) if a segment equal to 4i is plotted on the axis located at an angle of 30°, and 3.5a on the vertical axis. This is how we obtain the points that define the vertices of a hexagon whose side is 2a.
To describe a circle, you first need to apply four strokes on the center lines, and then four more between them (Fig. 103, d).
It is not difficult to construct an oval by inscribing it into a rhombus. To do this, strokes are applied inside the rhombus to mark the line of the oval (Fig. 103, e), and then the oval is outlined.
To give technical drawings volume, shading is applied to them (Fig. 104). In this case, it is assumed that the light falls on the object from the top left. Illuminated surfaces are not shaded. Hatching is applied to shaded surfaces, which is more frequent the darker the surface.
You can apply shading not to the entire surface, but only in places that emphasize the shape of the object (Fig. 105).
To identify the internal outlines of objects on axonometric projections and technical drawings, sections are used (Fig. 106, a), which are made with planes parallel to the planes of the projections. The hatching lines of the sections are drawn as shown in Fig. 106, b, i.e. parallel to the diagonal of the projections of squares built on the x and z axes, x and y, y and z
When applying dimensions, extension lines are drawn parallel to the axonometric axes, and dimension lines are parallel to the measured segment (Fig. 106, a and Fig. 87, d).
Answer the questions
1. What is the difference between a technical drawing and an axonometric projection?
2. How are the axes positioned when performing technical drawings?
3. What are the rules for shading technical drawings in order to reveal the volume of an object?
4. How are extension and dimension lines placed when drawing dimensions on axonometric projections?
Assignments for §15 and Chapter III
Exercise 47
Construct by hand on checkered paper: a) angles of 45 and 30°; b) the axis of the frontal dimetric projection (see Fig. 85, c); c) axes of isometric projection (see Fig. 85, c); d) circle with a diameter of 30 mm; e) three ovals, depicting a circle with a diameter of 40 mm in an isometric projection (place one oval perpendicular to the x-axis, the other - to the y-axis, the third - to the z-axis). Complete technical drawings of the parts shown in Fig. 107: for the examples in Fig. 107, a and b - based on the frontal dimetric projection, for examples in Fig. 107, c - E - based on isometric projection. Determine the dimensions by the number of cells, assuming that the side of the cell is 5 mm. Shade the surface of the parts.
Exercise 48
Take the “Construction of Visual Images” filmstrip from the school’s film library and repeat the material on the topic.
Hints for exercises for Chapter III
To § 12.
1 - projection object; 2 - projecting rays; 3 - projection plane; 4 - projection.
For exercise 40
The sequence of performing the exercise is shown in Fig. 275.
For exercise 41
It is advisable to follow the correct isometric projection sequence triangular prism, shown in Fig. 276.
When designing machine parts, it is often necessary to quickly draw visual images of the parts in order to more easily imagine their shape. The process of making such images is called technical drawing. Typically, technical drawing is done in a rectangular isometric projection.
The drawing of a part (Fig. 18, a) begins with the construction of its overall outline - a “cell”, drawn by hand with thin lines. Then the part is mentally dissected into separate geometric elements, gradually sketching all parts of the part.
Rice. 18. Construction of a technical drawing
Technical drawings of an object are more visual if they are covered with strokes (Fig. 18, b). When applying strokes, consider that the rays of light fall on the object from the right and above or from the left and above.
Illuminated surfaces are shaded with thin lines at a great distance from each other, and dark surfaces are shaded with thicker lines, placing them more often (Fig. 19).
Rice. 19. Applying light and shadow
1.5. Making simple cuts
For an idea of internal form of the object in the drawing, invisible contour lines are used. This makes the drawing difficult to read and can lead to errors. The use of conventional images - sections - simplifies the reading and construction of the drawing. A cut is an image of an object obtained by mentally dissecting it with one or more cutting planes. In this case, the part of the object located between the observer and the cutting plane is mentally removed, and what is obtained in the cutting plane and what is located behind it is depicted on the projection plane.
A simple cut is a cut made using a single cutting plane. The most commonly used are vertical (frontal and profile) and horizontal cuts.
In Fig. 20 two vertical sections are made: frontal (A-A) and profile (B-B), the cutting planes of which do not coincide with the symmetry planes of the part as a whole (in this case there are none at all). Therefore, the position of the cutting planes is indicated in the drawing, and the corresponding sections are accompanied by inscriptions.
The position of the cutting plane is indicated by a section line made by an open line. The strokes of an open section line should not intersect the outline of the image. On the strokes of the section line, arrows are placed perpendicular to them, indicating the direction of view. Arrows are applied at a distance of 2-3 mm from the outer end of the stroke of the section line.
Near each arrow, from the side of the outer end of the stroke of the section line protruding 2-3 mm beyond them, the same capital letter of the Russian alphabet is applied.
The inscription above the section, underlined by a solid thin line, contains two letters that indicate the cutting plane, written through a dash.
Rice. 20. Vertical cuts
In Fig. Figure 21 shows the formation of a horizontal section: the part is cut by plane A, parallel to the horizontal plane of projections, and the resulting horizontal section is located at the location of the top view.
Rice. 21. Horizontal section
In one image it is allowed to combine part of the view and part of the section. Hidden contour lines on connecting parts of a view and section are usually not shown.
If the view and the section located in its place are symmetrical figures, then you can connect half the view and half the section, separating them with a thin dash-dotted line, which is the axis of symmetry (Fig. 22).
Rice. 22. Connection of half view and section
Hatching in drawings (Fig. 252, a), in contrast to shading in rectangular projections, is usually applied in different directions. The line separating one hatched plane from another is drawn as the main line. In Fig. 252, b shows a hollow brick in a rectangular dimetric projection. The figure shows that thin ribs in axonometric projections are cut and shaded on a common base.
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Long solid pieces should not be cut all the way through. A local cut is made for the part where there is a recess (Fig. 252, c). If necessary, long parts are drawn with a gap (Fig. 253, a). The break lines are drawn slightly wavy, two to three times thinner than the main lines. For orientation, the size of the full length of the part is applied. A break in a tree is shown in the form of zigzag lines (Fig. 253, b).
Technical drawings, as a rule, are not intended for the manufacture of parts based on them, so dimensions are usually not applied to them. If dimensions must be applied, then this is done in accordance with GOST 2.317-69 and 2.307-68 (Fig. 254, a). In Fig. 254, b and c shows the application of vertical dimensions for the pyramid and cone (dimensions 25 and 36). In Fig. 254, g shows the correct application of the cylinder diameter size in parallel coordinate axis. The dimension shown along the major axis of the ellipse is crossed out as incorrectly plotted.
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It is especially important to mark the axes of the holes in the drawings (Fig. 254, a); in this case, the major axis of the ellipse should not be drawn. In the case of very small holes, only the main axis can be drawn - the geometric axis of the surface of revolution (the hole on the right side of the cube).
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Invisible contour lines are applied in drawings only if they add additional clarity to the image.
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The main way to convey relief should be considered the application of shadow strokes: straight lines for polyhedra, cylinders and cones, and curves for other bodies of revolution. Along with this, scribbling with a grid and short strokes is sometimes used. Screening with a mesh is shown in Fig. 255, a and b, and in short strokes - in Fig. 255, c and d. From an examination of the last drawings it is clear that the clarity of the image is achieved not by a large number of shadow strokes, but by their correct location on the surface of the part.
When making axonometric drawings and ink drawings, shading with dots is sometimes used, approaching shading (Fig. 256, a and b), thickened shadow lines (Fig. 256, c and d).
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Technical drawing in design practice has great importance, being the primary form of the image. An engineer or designer, when starting to create a project, most often begins his work with the construction of a technical drawing, because it is completed much faster than a drawing and is more visual, i.e., with a drawing that has a high execution technique and helps to create a drawing , make a project.
A technical drawing is a drawing made by eye, by hand, without the use of measuring and drawing tools. Technical drawing is performed according to the laws of axonometric projections of descriptive geometry. Technical drawing is designed to quickly create a visual representation of a part or structure.
Depending on the nature of the object and the task posed in a particular project, a technical drawing can be performed either in a central projection (in perspective) or according to the rules of parallel projections (in axonometry).
A technical drawing can be linear (without chiaroscuro) or three-dimensional with the rendering of chiaroscuro and color.
To give the drawing greater clarity and expressiveness in technical drawing, conventional means of conveying volume with
using shading - chiaroscuro. Chiaroscuro called the distribution of light on the surfaces of an object. Chiaroscuro plays main role when perceiving the volume of an object. The illumination of an object depends on the angle of inclination of the light rays. When light rays fall on an object perpendicularly, the illumination reaches its greatest intensity, so that part of the surface that is located closer to the light source will be lighter, and that further away will be darker.
In technical drawing, it is conventionally accepted that the light source is located at the top left and behind the painter.
Chiaroscuro consists of the following elements: own shadow, falling shadow, reflex, halftone, light and highlight.
Own shadow - a shadow located on the unlit part of an object.
Falling shadow - a shadow cast by an object on any surface. Since the technical drawing is mainly of a conventional, applied nature, falling shadows are not shown on it.
Reflex - reflected light on the surface of an object in its unlit part. It is slightly lighter in tone than the shadow. With the help of a reflex, the effect of convexity and stereoscopicity of the pattern is created.
Semitone - a dimly lit place on the surface of an object. Halftones make a gradual, smooth transition from shadow to light so that the drawing does not turn out to be too contrasting. Halftone “sculpts” volumetric form subject.
Light - illuminated part of the surface of an object.
Blik - the lightest spot on an object. In technical drawing, highlights are shown mainly on surfaces of revolution.
Shadows in a technical drawing are depicted using shading, shading or shading (intersecting shading)
ALGORITHM FOR CONSTRUCTING A TECHNICAL DRAWING OF A PART
When starting to perform a technical drawing, it is necessary to first study the depicted object and mentally break it down into its constituent elementary geometric bodies. Next, you should determine the basic proportions of the object: the ratio of height, width and length, as well as the proportions of its individual parts. Then the appropriate type of axonometry is selected and axonometric axes are constructed.
Technical drawing begins with general outlines object, and then move on to depicting its individual parts. Dimensions are not indicated on the technical drawing, since, as a rule, parts are not manufactured from drawings.
Invisible contour lines are usually not drawn in a technical drawing; Hatching in a technical drawing, in contrast to a drawing, is performed with straight or curved lines, solid or intermittent, of the same or different thickness, as well as by applying shadows.
A technical drawing is a visual image that has the basic properties of axonometric projections or a perspective drawing, made without the use of drawing tools, on a visual scale, in compliance with proportions and possible shading of the form.
A technical drawing can be performed using the central projection method, and thereby obtain a perspective image of the object, or the parallel projection method (axonometric projections), constructing a visual image without perspective distortions.
Technical drawing can be performed without revealing volume by shading, with shading of volume, as well as conveying the color and material of the depicted object.
In technical drawings, it is allowed to reveal the volume of objects using the techniques of shading (parallel strokes), scribbling (strokes applied in the form of a grid) and dot shading.
The most commonly used technique for identifying the volume of objects is shaking.
It is generally accepted that light rays fall on an object from the top left. Illuminated surfaces are not shaded, while shaded surfaces are covered with shading (dots). When shading shaded areas, strokes (dots) are applied with the smallest distance between them, which makes it possible to obtain denser shading (dot shading) and thereby show shadows on objects. Table 1 shows examples of shape detection geometric bodies and details using shattering techniques.
Rice. 1. Technical drawings revealing volume by shading (a), scribbling (b) and dot shading (e)
Table 1. Shading the shape using shading techniques
Technical drawings are not metrically defined images unless they are marked with dimensions.
An example of constructing a technical drawing in a rectangular isometric projection (isometry) with a distortion coefficient along all axes equal to 1. When the true dimensions of the part are plotted along the axes, the drawing turns out to be 1.22 times larger than the real part.
Methods for constructing an isometric projection of a part:
1. The method of constructing an isometric projection of a part from a form-generating face is used for parts whose shape has a flat face, called a form-generating face; The width (thickness) of the part is the same throughout; there are no grooves, holes or other elements on the side surfaces.
The sequence of constructing an isometric projection is as follows:
· construction of isometric projection axes;
· construction of an isometric projection of the formative face;
· construction of projections of other faces by depicting the edges of the model; outline of the isometric projection (Fig. 1).
Rice. 1. Construction of an isometric projection of the part, starting from the formative face
2. The method of constructing an isometric projection based on the sequential removal of volumes is used in cases where the displayed form is obtained as a result of removing any volumes from the original form (Fig. 2).
3. The method of constructing an isometric projection based on sequential increment (adding) of volumes is used to create an isometric image of a part, the shape of which is obtained from several volumes connected in a certain way to each other (Fig. 3).
4. Combined method of constructing an isometric projection. An isometric projection of a part whose shape is obtained as a result of a combination in various ways shaping is performed using a combined construction method (Fig. 4).
An axonometric projection of a part can be performed with an image (Fig. 5, a) and without an image (Fig. 5, b) of invisible parts of the form.
Rice. 2. Construction of an isometric projection of a part based on sequential removal of volumes
Rice. 3. Construction of an isometric projection of a part based on sequential increments of volumes
