Constructing 3 projections from 2 given. Creation of the third projection of a part from two data

A complete technical drawing contains at least three projections. However, knowledge to imagine an object in two projections is required from both the technologist and the skilled worker. As a result, in examination tickets in technical universities and colleges, problems are continuously encountered for constructing a third type for two given ones. In order to safely complete a similar task, you need to know the conventions used in technical drawing.

You will need

- paper;
- 2 projections of the part;
- drawing tools.

Instructions

1. The theses of the construction of the third type are identical for classical drawing, sketching and building a drawing in one of the computer programs prepared for this. First of all, analyze the given projections. See which types are given to you. When it comes to 3 views, this is a general projection, a top view and a left view. Determine what exactly is given to you. This can be done according to the location of the drawings. The left view is located on the right side of the general, and the top view is below it.

2. Establish a projection link with one of the predefined views. This can be done by extending the horizontal lines limiting the silhouette of the object to the right, when it is required to build a view from the left. For a top view, continue down the vertical lines. In any case, one of the parameters of the part will appear mechanically in your drawing.

3. Find the 2nd parameter on the existing projections, limiting the silhouettes of the part. When building a view on the left, you will find this size in the top view. When establishing a projection connection with the main view, the height of the part appeared in your drawing. This means that the width should be taken from the top view. When constructing a top view, the 2nd dimension is taken from the side projection. Draw the silhouettes of your subject in the third projection.

4. See if the part has protrusions, voids, holes. All this is noted on the general projection, which, by definition, should give the most accurate representation of the subject. Correctly, as in defining the general silhouette of a part in the third projection, establish a projection relationship between different elements. Find the rest of the parameters (for example, the distance from the center of the hole to the edge of the part, the depth of the protrusion, etc.) in the side or top view. Build the necessary items by looking at the measurements you find.

5. In order to check how correctly you coped with the task, try to draw a part in one of the axonometric projections. See how reasonably the elements of the third type you have drawn are located on the volumetric projection. It may be hefty that you will have to make some adjustments to the drawing. Drawing in perspective can help check your construction.

One of the most interesting tasks of descriptive geometry is the construction of the third of the kind for given 2. It requires a thoughtful approach and minute measurement of distances, therefore it is not invariably given the first time. Nevertheless, if you scrupulously follow the recommended sequence of actions, building the 3rd kind is absolutely permissible, even without spatial imagination.

You will need

- paper;
- pencil;
- ruler or compasses.

Instructions

1. First of all, try on the two available of the kind m determine the shape of the individual parts of the depicted object. If a triangle is shown in the top view, then it can be a triangular prism, a cone of revolution, a triangular or quadrangular pyramid. The shape of a quadrangle can be taken by a cylinder, quadrangular or triangular prism, or other objects. A circular image can represent a ball, cone, cylinder, or other surfaces of revolution. Either way, try to represent the general form of the object in the aggregate.

2. Draw the boundaries of the planes for the comfort of transferring the lines. Start transferring with the most comfortable and intelligible item. Take every point that you correctly "see" on both of the kind x and transfer it to the 3rd view. To do this, lower the perpendicular to the boundaries of the planes and continue it on the next plane. Please note that when going from of the kind on the left in a top view (or opposite), you need to use a compass or measure the distance with a ruler. So in place of your third of the kind two straight lines will intersect. This will be the projection of the selected point onto the 3rd view. In the same way, it is allowed to transfer as many points as desired, until the general appearance of the part becomes intelligible to you.

3. Check the correctness of the construction. To do this, measure the dimensions of those parts of the part that are fully reflected (say, a standing cylinder will be of the same "height" in the left and front views). In order to realize if you have not forgotten anything, try to look at the front view from the position of the observer from above and recalculate (though approximately) how many boundaries of holes and surfaces should be visible. All straight lines, every point must be reflected on all of the kind NS. If the part is symmetrical, remember to notice the axis of symmetry and check that both parts are equal.

4. Delete all construction lines, check that all visible lines are marked with a dashed line.

In order to depict this or that object, first, its individual elements are depicted in the form of the simplest figures, and after that their projection is performed. The construction of a projection is quite often used in descriptive geometry.

You will need

- pencil;
- compasses;
- ruler;
- reference book "Descriptive Geometry";
- elastic.

Instructions

1. Carefully read the data of the task: for example, the general projection F2 is given. The point F belonging to it is located on the lateral surface of the cylinder of revolution. It is required to construct 3 projections of point F. Imagine mentally how all this should look, and then proceed to build the image on paper.

2. A cylinder of revolution can be represented as a rotating rectangle, one of the sides of which is taken as the axis of revolution. The second side of the rectangle - opposite to the axis of rotation - forms the lateral surface of the cylinder. The other two sides represent the bottom and top of the cylinder.

3. Due to the fact that the surface of the cylinder of revolution when constructing the given projections is performed in the form of a horizontally projection surface, the projection of the point F1 must certainly coincide with the point P.

4. Draw the projection of point F2: since F is on the common surface of the cylinder of revolution, point F2 will be projected onto the lower base by point F1.

5. Build the third projection of point F using the ordinate: set F3 on it (this projection point will be located to the right of the z3 axis).

Related Videos

Note!
When constructing image projections, follow the basic rules used in descriptive geometry. Otherwise, the projection will fail.

Helpful advice
To create an isometric view, use the top base of the cylinder of rotation. To do this, first draw an ellipse (it will be placed in the x'O'y 'plane). Later on, draw tangent lines and a lower semi-ellipse. After that, draw a coordinate polyline and, with its support, build a projection of point F, that is, point F '.

There are not so many people in our time who have never in their life had the opportunity to draw or draw something on paper. The knowledge to execute a primitive drawing of some structure is sometimes very useful. It is permissible to spend a lot of time explaining "on the fingers" how this or that thing was done, while it happens that one is pleased with one glance at its drawing, in order to realize it without any words.

You will need

- Whatman sheet;
- drawing accessories;
- drawing board.

Instructions

1. Select the sheet format on which the drawing will be executed - in accordance with GOST 9327-60. The format should be such that it was allowed to place the main views details in the appropriate scale, as well as all the necessary cuts and sections. For simple parts, choose the A4 format (210x297 mm) or A3 (297x420 mm). The 1st can be located with its long side only vertically, the 2nd - vertically and horizontally.

2. Draw a drawing frame, departing from the left edge of the sheet 20 mm, from the rest 3 - 5 mm. Draw a title block - a table in which all data about details and drawing. Its dimensions are determined by GOST 2.108-68. The width of the bar label is constant - 185 mm, the height varies from 15 to 55 mm, depending on the purpose of the drawing and the type of institution for which it is performed.

3. Select the scale of the main image. The permissible scales are determined by GOST 2.302-68. They should be preferred so that all the main elements are perfectly visible on the drawing. details... If, at the same time, some places are not clearly visible, it is allowed to transfer them in a separate view, showing them with the desired magnification.

4. Select the main image details... It should represent such a direction of gaze at the detail (direction of projection), from which its structure is revealed especially fully. In most cases, the main image is the location where the part is on the machine during the bar operation. Parts that have an axis of rotation are located on the main image, as usual, so that the axis has a horizontal position. The main image is located in the upper part of the drawing on the left (if there are three projections) or close to the center (in the absence of a side projection).

5. Determine the location of the remaining images (side view, top view, sections, cuts). Views details are formed by its projection onto three or two mutually perpendicular planes (Monge's method). In this case, the part should be located in such a way that many or all of its elements are projected without distortion. If any of these types is informationally redundant, do not perform it. The drawing should have only those images that are needed.

6. Select the cuts and sections that you want to execute. Their difference from each other lies in the fact that the section also shows what is behind the cutting plane, while the section displays only what is located in the plane itself. The cutting plane can be stepped and broken.

7. Start sketching at ease. When drawing lines, be guided by GOST 2.303-68, which defines views lines and their parameters. Place images at such a distance from each other so that there is enough space for sizing. If the planes of the sections pass along the monolith details, hatch the sections with lines going at an angle of 45 °. If, in this case, the hatching lines coincide with the main lines of the image, it is allowed to draw them at an angle of 30 ° or 60 °.

8. Draw dimension lines and add dimensions. In doing so, be guided by the following rules. The distance from the first dimension line to the silhouette of the image must be at least 10 mm, the distance between adjacent dimension lines must be at least 7 mm. The arrows must be about 5 mm long. Write the numbers in accordance with GOST 2.304-68, take their height equal to 3.5-5 mm. Place the numbers closer to the middle of the dimension line (but not on the image axis) with some offset relative to the numbers on the adjacent dimension lines.

Related Videos

Making an accurate drawing is time-consuming many times. Consequently, in the event of an urgent need to make some part, it is often not a drawing, but a sketch that is made. It is performed quite quickly and without the use of drawing tools. At the same time, there are a number of requirements that the sketch must meet.

You will need

- detail;
- paper;
- pencil;
- measuring instruments.

Instructions

1. The sketch must be accurate. According to it, the person who will make a copy of the part must get an idea of both the appearance of the product and its design features. Consequently, observe the subject before everyone else. Determine the relationship between the various parameters. See if there are holes, where they are, their size and the ratio of the diameter to the total size of the product.

2. Determine which view will be the main one and how accurate it is about the detail. The number of projections depends on this. There may be 2, 3 and more of them. How many projections you need depends on their location on the sheet. You need to proceed from how difficult the product will be.

3. Choose a scale. It should be such that the master could easily make out even the smallest details.

4. Start sketching with centerlines and centerlines. In the drawings, they are usually indicated by a dotted line with dots between strokes. These lines indicate the middle of the part, the center of the hole, etc. They remain in the working drawings.

5. Draw the outer silhouettes of the part. They are indicated by a thick permanent line. Be diligent to convey the aspect ratio correctly. Apply the inner (visible) outlines.

6. Make cuts. This is done in the same way as in any other drawing. The solid surface is shaded with oblique lines, the voids remain unfilled.

7. Draw dimension lines. From the points, the distance between which you want to mark, there are parallel vertical or horizontal strokes. Draw a straight line between them with arrows at the ends.

8. Measure the part. Specify the length, width, hole diameters and other dimensions required for accurate work. Write the dimensions on the sketch. If necessary, apply signs indicating the methods and qualities of processing different surfaces of the product.

9. The final stage of the work is filling the stamp. Fill in the product data. In technical universities and design organizations there are standards for filling stamps. If you make a sketch for yourself, then it is allowed to primitively indicate what kind of part it is, the material from which it is made. The person who will make the part should see all other data in your sketch.

Related Videos

The drawing serves so that the one who will grind a part or build a house can get the most accurate idea of the appearance of the object, its structure, the ratio of parts, and surface treatment methods. One projection for this, as usual, is unsatisfactory. In educational drawings, three types are usually performed - main, left and top. For objects with difficult shapes, right and back views are also used.

You will need

- detail;
- measuring instruments;
- drawing tools;
- a computer with AutoCAD.

Instructions

1. The sequence of execution of the drawing on a sheet of whatman paper and in AutoCAD is approximately identical. Take a look at the detail first. Determine which perspective will give the most accurate idea of the form and functional features. This projection will become its main view.

2. See if your part looks identical when you look at it from the right and left. Not only the number of projections depends on this, but also their location on the sheet. The left view is located to the right of the main one, and the right view is, respectively, to the left. At the same time, in a flat projection, they will look as if they are at ease in front of the eyes of the observer, that is, without perspective control.

3. Drawing methods are identical for all projections. Place the object in your mind in the system of planes onto which you will project it. Analyze the shape of the object. See if it is permissible to divide it into more primitive parts. Answer the question, in the shape of which body it is allowed to completely inscribe your object entirely or any of its fragments. Imagine what the individual parts look like in orthographic projection. The plane onto which the object is projected when building a left view is on the right side of the object itself.

4. Measure the part. Remove the basic parameters, set the ratio between the whole object and its individual parts. Select a scale and draw a basic view.

5. Select a construction method. There are two of them. To complete the drawing, using the removal technique, first apply the general silhouettes of the object, to the one that you are looking at from the left or right. After that, little by little begin to delete volumes, tracing notches, silhouettes of holes, etc. When accepting an increment, one element is first drawn, and then the rest are slowly added to it. The choice of method depends primarily on the difficulty of the projection. If the detail, when looking at it from the left or right, is a clearly expressed geometric figure with a small number of deviations from the severe shape, it is more comfortable to use the removal technique. If there are a lot of fragments, and the part itself cannot be inscribed into any figure, it is better to stepwise attach the elements to each other. The difficulty of the projections of the same part can be different, therefore, it is allowed to change the methods.

6. Either way, start building the side view with the bottom and top lines. They must be on the same tier as the corresponding lines of the main species. This will provide a projection link. Later, apply general silhouettes of the part or its first fragment. Observe the size ratio.

7. Having drawn the general silhouettes of the side view, add centerlines, hatching, etc. to it. Dimension. The projection does not need to be signed invariably. If all views of the part are located on one sheet, then only the rear view is signed. The location of the rest of the projections is determined by the standards. If the drawing is made on several sheets and one or both side views are not on the sheet on which the main one, they need to be signed.

Related Videos

Helpful advice
When building a side view in AutoCAD or another drawing program, it is not strictly necessary to combine the upper and lower lines of the main and side views at the first stage. The drawing is allowed to be performed in fragments, and the tiers can be combined when you start preparing it for printing.

You will need

- a set of drawing pencils of different hardness;
- ruler;
- square;
- compasses;
- eraser.

Instructions

Sources:

building a projection

Projection is strongly associated with the exact sciences - geometry and drafting. However, this does not prevent her from meeting all the time in far, it would seem, not scientific and ordinary things: the shadow of an object that falls on a flat surface in sunlight, railway sleepers, any map and any drawing are nothing else? as a projection. Of course, creating maps and drawings requires a deep study of the subject, but the simplest projections can be built independently, armed only with a ruler and a pencil.

You will need

* pencil;
* ruler;
* paper.

Instructions

The first method of constructing a projection is by central projection and is especially suitable for images on the plane of objects, when it is necessary to reduce or increase their actual size (Fig. A). The central design algorithm is as follows: we designate the design plane (P ") and the design center (S). To design ABC in the P" plane, draw AS, SB and SC through the center point S and points A, B and C. Their intersection with the plane P "forms points A", B "and C", when connected by straight lines, we get the central projection ABC.

The second method differs from the one described above only in that the straight lines, with the help of which the vertices of the triangle ABC are projected into the plane P ", are not, but parallel to the designated direction of projection (S). Nuance: the direction of projection cannot be parallel to the plane P". When connecting the projection points A "B" C "we get a parallel projection.

Despite its simplicity, the skill of constructing such simple projections helps to develop spatial thinking and can safely step in descriptive.

Related Videos

Sources:

horizontal is like in 2019

When creating an architectural project or developing an interior design, it is very important to imagine how the object will look in space. Axonometric projection can be used, but it is good for small objects or details. The advantage of frontal perspective is that it gives an idea not only of the appearance of the object, but allows you to visually represent the ratio of sizes depending on the distance.

You will need

- paper;
- pencil;
- ruler.

Instructions

The principles of building a frontal perspective are the same for a Whatman sheet and a graphic editor. So do it on a sheet. If the object is small, A4 format will suffice. For a frontal perspective or interior, take a sheet. Lay it horizontally.

For a technical drawing or drawing, select a scale. Take some clearly distinguishable parameter as a reference - for example, buildings or the width of a room. Draw on the sheet an arbitrary segment corresponding to this line, and calculate the ratio.

This will also become the base of the picture plane, so place it at the bottom of the sheet. Designate the end points, for example, as A and B. For a picture, you do not need to measure anything with a ruler, but determine the ratio of the parts of the object. The sheet must be larger than the plane of the sky so that

13.1. A method of constructing images based on an analysis of the shape of an object. As you already know, most objects can be thought of as a combination of geometric bodies. Therefore, in order to read and execute drawings, you need to know how these geometric bodies are depicted.

Now that you know how such geometric bodies are depicted in a drawing, and have learned how vertices, edges and faces are projected, it will be easier for you to read the drawings of objects.

Rice. 100. Projections of a part

Figure 100 shows part of the machine - counterweight. Let's analyze its shape. What geometric bodies you know can be divided into? To answer this question, let us recall the characteristic features inherent in their images of geometric bodies.

In Figure 101, and one of them is conditionally highlighted in brown. What geometric body has such projections?

Projections in the form of rectangles are typical for a parallelepiped. Three projections and a visual image of the parallelepiped, highlighted in figure 101, i in brown, are given in figure 101, b.

In Figure 101, conventionally in gray, another geometric body is highlighted. What geometric body has such projections?

You met with such projections when considering images of a triangular prism. Three projections and a visual image of the prism highlighted in gray in Figure 101, c, are given in Figure 101, d. Thus, the counterweight consists of a rectangular parallelepiped and a triangular prism.

But the part that is inside the brown dashed lines and the circle in Figure 101, e has been removed from the parallelepiped. What geometric body has such projections?

You met with projections in the form of a circle and two rectangles when considering images of a cylinder. Consequently, the counterweight contains a cylinder-shaped hole, three projections and a visual representation of which are given in Figure 101, f.

Analysis of the shape of an object is necessary not only when reading, but when performing drawings. So, having determined the shape of which geometric bodies the parts of the counterweight shown in Figure 100 have, it is possible to establish an expedient sequence for constructing its drawing.

For example, a counterweight drawing is built like this:
1) in all views, a parallelepiped is drawn, which is the base of the counterweight;
2) a triangular prism is added to the parallelepiped;
3) draw an element in the form of a cylinder. In the top and left views, it is shown with dashed lines, since hole-I is not invisible.

Rice. 101. Analysis of the shape of the part

30. Draw a part called a bushing from the description. It consists of a truncated cone and a regular quadrangular prism. The diameter of one base of the cone is 30 mm, the other is 50 mm, the height of the truncated cone is 50 mm. The prism is attached to the larger base of the cone, which is located in the middle of its base, measuring 50 x 50 mm. Prism height 10 mm. A through cylindrical hole 0 20 mm is drilled along the axis of the bushing. The hub axis is perpendicular to the profile plane of the projections.

13.2. The sequence of constructing views in the drawing of the part.
Consider an example of building types of parts - supports (Fig. 102).

Rice. 102. Visual representation of the support

Before proceeding with the construction of images, it is necessary to clearly imagine the general initial geometric shape of the de-gali (whether it will be a cube, cylinder, parallelepiped, etc.). This shape must be kept in mind when constructing views.

The general shape of the object shown in Figure 102 is a rectangular parallelepiped. It has rectangular cutouts and a triangular prism cutout. We begin to depict the part with its general shape - a parallelepiped (Fig. 103. a).
Having projected the parallelepiped on the plane V, H, W, we get rectangles on all three projection planes. The frontal plane of the projections will reflect the height and length of the part, that is, dimensions 30 and 34. On the horizontal plane of the projections, the width and length of the part, that is, dimensions 26 and 34. On the profile plane, the width and height, that is, the dimensions 26 and 30.

Each dimension of the part is shown twice without distortion: w, cat - on the frontal and profile planes, length on the frontal and horizontal planes, width - on the horizontal and profile planes of the projections. However, the same dimension cannot be applied to the drawing twice.

First, we will perform all constructions with thin lines. Since the main view and the top view are symmetrical, the axes of symmetry are plotted on them.

Now we will show the cutouts on the projections of the parallelepiped (Fig. 103, b). It is more expedient to show them first in the main view. To do this, set aside 12 mm to the left and right of the axis of symmetry and draw vertical lines through the points obtained. Then, at a distance of 14 mm from the upper edge of the part, draw segments of horizontal lines.

Rice. 103. The sequence of construction of views of the part

Let's construct projections of these cutouts in other views. This can be done using communication lines. After that, in the top and left views, you need to show the lines that limit the projection of the cutouts.

In conclusion, the images are outlined with the lines established by the standard, and dimensions are applied (Fig. 103, c).

1. Name the sequence of actions that make up the process of constructing types of an object.
2. For what purpose are projection communication lines used?

13.3. Creates cutouts on geometric bodies. On
Figure 104 shows images of geometric bodies, the shape of which is complicated by various kinds of notches.

Details of this shape are widespread in technology. To draw or read their drawing, you need to imagine the shape of the workpiece from which the part is obtained, and the shape of the cutout. Let's look at some examples.

Rice. 104. Geometric Solids Containing Cutouts

Rice. 105. Analysis of the shape of the gasket

Example 1. Figure 105 shows a drawing of the gasket. What shape does the removed part have? What was the shape of the blank?
After analyzing the drawing of the gasket, we can conclude that it was the result of removing the fourth part of the cylinder from the rectangular parallelepiped (workpiece).

Rice. 106. Creation of projections of a part with a cutout

Example 2. In Figure 106, a drawing of the plug is given. What is the shape of its preparation? What resulted in the shape of the part?

After analyzing the drawing, you can come to the conclusion that the part is made from a cylindrical blank. A cut was made in it, the shape of which is clear from Figure 106, b.

How do you create a projection of the cutout in the left view?

First, a rectangle is drawn - a view of the cylinder on the left, which is the original shape of the part. Then, constructing a projection of the cutout "Its dimensions are known, therefore, the points a", b "and a, b, which determine the projection of the cutout, can be considered as given.

The construction of profile projections a ", b" of these points is shown by communication lines with arrows (Fig. 106, c).

Once you've established the shape of the cutout, it's easy to decide which lines in the left view should be outlined with solid thick main lines, which with dashed lines, and which should be removed altogether.

Rice. 107. Exercise tasks

31. Consider the images in Figure 107 and determine what shape parts are removed from the blanks to obtain parts. Complete the technical drawings for these parts.
32. Construct the missing projections of points, lines and cutouts given by the teacher in the drawings you made earlier.

13.4. Construction of the third type.
We will sometimes have to perform tasks in which it is necessary to build a third one based on the two available types.

Rice. 108. Drawing of a bar with a cut

In Figure 108, you can see an image of a bar with a cutout. Two views are given: front and top. You want to build a left view. To do this, you must first imagine the shape of the depicted part. Comparing the views in the drawing, we conclude that the bar has the shape of a parallelepiped measuring 10 x 35 x 20 mm. A rectangular cutout is made in the parallelepiped, its size is 12 x 12 x 10 mm.

The view to the left, as you know, is placed at the same height as the main view to the right of it. We draw one horizontal line at the level of the lower base of the parallelepiped, and the other at the level of the upper base (Fig. 109, a). These lines limit the height of the left view. Draw a vertical line anywhere between them. It will be the projection of the back face of the bar onto the profile plane of the projections. From it to the right we set aside a segment equal to 20 mm, that is, we limit the width of the bar, and draw another vertical line - the projection of the front face (Fig. 109.6).

Let us now show the cutout in the detail in the left view. To do this, set aside to the left of the right vertical line, which is the projection of the front face of the bar, a segment of 12 mm and draw another vertical line (Fig. 109, c). After that, we delete all auxiliary construction lines and outline the drawing (Fig. 109, d).

Rice. 109. Construction of the third projection

The third projection can be built based on the analysis of the geometric shape of the object. Let's see how this is done. Figure 110, a, shows two projections of the part. We need to build a third.

Rice. 10. Construction of the third projection from two data

Judging by these projections, the part is composed of a hexagonal prism, a parallelepiped and a cylinder. Mentally combining them into a single whole, we represent the shape of the part (Fig. 110, c).

We draw an auxiliary line in the drawing at an angle of 45 ° and proceed to the construction of the third projection. You know what the third projections of a hexagonal prism, parallelepiped and cylinder look like. We draw successively the third projection of each of these bodies, using communication lines and axes of symmetry (Fig. 110, b).

Note that in many cases it is not necessary to build a third projection on the drawing, since the rational execution of images involves the construction of only the necessary (minimum) number of views, sufficient to reveal the shape of the object. In this case, the construction of the third projection of the subject is only an educational task.

1. You have familiarized yourself with different ways of constructing the third projection of an object. How do they differ from each other?
2. What is the purpose of using the constant line? How is it done?

33. In the drawing of the part (Fig. 111, a), the left view is not a child - it does not show images of a semicircular cutout and a rectangular hole. As instructed by the teacher, redraw or transfer the drawing to the tracing paper and supplement it with the missing lines. What lines (solid main lines or dashed lines) do you use for this purpose? Draw the missing lines also in Figures 111, b, c, d

34. Redraw or transfer onto tracing paper the data in Figure 112 projections and build profile projections of the parts.
35. Redraw or transfer onto tracing paper the projections indicated to you in Figure 113 or 114 by the teacher. Place the missing projections in place of the question marks. Complete the technical drawings of the parts.

Building views begins with a mental choice of the position of the part in front of the projection planes. Then choose the number of types necessary and sufficient to identify the shape of the part, as well as the method of their construction.

The choice of the position of the part in the system of projection planes depends on its working position, manufacturing method in production, and shape. For example, if a part is made on a lathe, then its axis of rotation should be horizontal in the drawing.

Drawing views can be performed in various ways. Let's take a look at some of them.

Construction of views based on the sequential drawing of geometric bodies that make up the shape of an object. In order to complete the drawing in this way, it is necessary to mentally divide the part into its constituent simple geometric bodies, finding out how they are located relative to each other. Then you need to select the main view of the part and the number of images that make it possible to understand its shape and sequentially depict one geometric body after another until the shape of the object is fully displayed. It is necessary to observe the dimensions of the form and correctly orient its elements relative to each other (Table 8).

The construction of views based on the element-by-element drawing of geometric bodies that make up the shape of an object is carried out using the methods of removal and increment.

When drawing a geometric body using the removal technique in the drawing, the shape of the workpiece is successively changed by removing volumes similar to the techniques of its processing by turning, drilling, milling, etc.

When drawing a geometric body using the increment technique, the volumes of the product elements complement each other, as it were, increment.

8. Element-wise drawing of geometric bodies that make up the shape of an object

Construction of views using a constant direct drawing (external coordination method). A constant straight line of a drawing is a line that is drawn from the center of coordinates (point O) down to the right at an angle of 45 ° (Fig. 86).

The object is mentally placed in a system of projection planes. The axes of the projection planes are taken as the coordinate axes. The projection communication between the top view and the left view is carried out using projection communication lines, which are drawn up to the intersection with a constant straight line of the drawing and are built at an angle of 90 ° to each other.

The constant straight line of the drawing, as a rule, is used in those cases when it is necessary to construct a third type of part from two given views (see Fig. 86). Having re-drawn two types of parts, they build a constant straight line of the drawing and draw lines of projection communication parallel to the OX axis until they intersect with the constant straight line of the drawing, and then parallel to the OZ axis.

The considered construction method is called the external coordination method, since the object is fixed in space relative to the axes of the projection planes, which are located outside the depicted object.

(If the projection axes are not shown in the drawing and it is necessary to perform a third view of the part, then you can build a constant line of the drawing anywhere on the right side of the top view.)

Building views using internal object coordination. Internal coordination consists in the mental introduction of additional coordinate axes tied to the projected object.

Rice. 86. Construction of the third projection on two given using a constant straight drawing

Rice. 87. Building views by means of internal coordination of an object

Three typical projections - general, profile and horizontal - contain the necessary and content information about the external appearance and internal structure of parts that have one axis of symmetry. If a part has a difficult configuration or many internal cavities with a curved surface, additional cuts and projections may be needed.

You will need

- a set of drawing pencils of various hardness;
- ruler;
- square;
- compasses;
- eraser.

Instructions

1. The projection relationship between the elements of the part is maintained at any distance between the images of 3 views of this part in the drawing. Due to this connection, it is allowed to build a third missing one on two projections. Let you be given a front view of a part (general projection) and a side view (profile projection). This assumption is possible for any 2 projections, the tea part can be rotated as desired.

2. Draw a thin vertical line between the general and profile projections. Extend this line down to the tier of the desired location of the third projection. Draw a thin horizontal line under these two projections at an arbitrary distance. The third projection will be built below the horizontal line below the general projection. Auxiliary vertical and horizontal lines are used to build the third projection of the part.

3. Construct projections of all vertices of the 2 available views of the part onto a construction contour. In other words, drop the perpendiculars to the construction contour from all vertices on the general and profile projections. Extend the perpediculars drawn from the points of the common surface below the auxiliary horizontal line to the desired location for the third projection. You now have the width of the not yet drawn third projection. It is not necessary to continue perpendiculars drawn from the points of the profile projection beyond the horizontal.

4. Place the needle of the compass at the intersection of the auxiliary vertical and horizontal lines. Set the compass pencil to the point of intersection of the auxiliary contour and the perpendicular dropped from the point of the profile projection. With the resulting radius, mark down on the auxiliary vertical. In the same way, with the support of a compass, transfer the projections of all vertices of the profile projection from the auxiliary horizontal to the auxiliary vertical.

5. Restore the perpendiculars to the vertical construction line from the projections of the vertices of the profile projection of the part transferred to it. Extend the resulting perpendiculars until they intersect with the more closely constructed lines of the third projection.

6. Finish drawing the third projection of the part. Draw a core line around the silhouette of the part and all visible parts of the projection. Use the dashed line to fill in the visible parts of the part. The locations of the circles on the executable third projection are indicated by the squares obtained by intersecting the perpendiculars to the auxiliary lines. Write circles in these squares.

7. To conclude the work, draw dimension lines and add dimensions.

Projection is strongly associated with the exact sciences - geometry and drawing. However, this does not prevent her from meeting all the time in the distance, seemingly not scientific and ordinary things: the shadow of an object that falls on a flat surface in clear light, railway sleepers, any map and any drawing more closely is nothing else? as a projection. Finally, the creation of maps and drawings requires a deep understanding of the subject, but the simplest projections can be built on their own, armed only with a ruler and a pencil.

You will need

* pencil;
* ruler;
* paper.

Instructions

1. The 1st method of constructing a projection is called central projection and is extremely suitable for images on the plane of objects, when it is necessary to reduce or increase their actual size (Fig. A). The central projection algorithm is as follows: we denote the projection plane (P ') and the projection center (S). In order to project the triangle ABC into the plane P ', draw straight lines AS, SB and SC through the center point S and points A, B and C. Their intersection with the plane P 'forms points A', B 'and C', when connected by straight lines we get the central projection of the triangle ABC.

2. The second method differs from the one described above only in that the straight lines, with the help of which the vertices of the ABC triangle are projected into the plane P ', do not intersect, but are parallel to the indicated direction of projection (S). Nuance: the design direction cannot be parallel to the P 'plane. By connecting the ABC projection points, we get a parallel projection. Despite the simplicity, the skill of constructing such primitive projections wonderfully helps to develop spatial thinking and can be bravely considered the first step in descriptive geometry.

Related Videos

You will need

- paper;
- pencil;
- ruler or compasses.

Instructions

4. Delete all construction lines, check that all visible lines are marked with a dashed line.

You will need

- pencil;
- compasses;
- ruler;
- reference book "Descriptive Geometry";
- elastic.

Instructions

4. Draw the projection of point F2: since F is on the common surface of the cylinder of revolution, point F2 will be projected onto the lower base by point F1.

5. Build the third projection of point F using the ordinate: set F3 on it (this projection point will be located to the right of the z3 axis).

Related Videos

Note!
When constructing image projections, follow the basic rules used in descriptive geometry. Otherwise, the projection will fail.

Helpful advice
To create an isometric view, use the top base of the cylinder of rotation. To do this, first draw an ellipse (it will be placed in the x'O'y 'plane). Later on, draw tangent lines and a lower semi-ellipse. After that, draw a coordinate polyline and, with its help, construct a projection of point F, that is, point F '.

Contours - isohypses (lines of identical heights) - lines that connect points on the earth's surface that have identical elevations. The construction of contour lines is used to draw up topographic and geographical maps. Contours are constructed based on measurements by theodolites. The exit points of the secant planes outward are projected on horizontal plane.

Instructions

1. In our country, there are different scales for constructing sections between horizontals. In some cases, for a more accurate presentation of difficult terrain, horizontal lines with an arbitrary section are used. On maps, horizontal lines are drawn with red-chestnut or red ink.

2. The zero of the Kronstadt tide stock is considered to be a level surface for measuring contours in Russia. It is from it that the contours are counted, which makes it possible to combine individual plans and maps drawn up by different organizations. The contours determine not only the earth's relief, but also the relief of water basins. Isobaths (water contours) connect points with identical depths.

3. To designate the relief on the maps, general conventional symbols are used, which are contour (scale), off-scale and explanatory. In addition, there are additional elements accompanying conventional signs. These include all kinds of inscriptions, names of rivers, cities, color design of maps.

4. For the preparation of construction drawings and plans, there are special symbols provided for by the current SNiPs.

5. It is allowed to build a horizontal line on the plan between two points by two methods: graphical and analytical. For graphic construction of the horizontal on the plan, take graph paper.

6. Draw several horizontal, parallel lines at an equal distance on the paper. The number of lines is determined by the number of required sections between two points. The distance between the lines is taken equal to the specified distance between the contours.

7. Draw two vertical, parallel lines at a distance equal to the distance between the given points. Sweep these points on them, considering their height (altitude). Join the points with a slanted line. The intersection points of the horizontal straight lines are the points where the cutting planes go out.

8. Transfer the segments resulting from the intersection to horizontal a straight line connecting two specified points in an orthogonal projection manner. Combine the resulting points with a smooth line.

9. To construct contours in an analytical way, they use formulas derived from the similarity signs of triangles. In addition to these methods, computer programs such as "Archikad" and "Architerra" are also used today to build contours.

Related Videos

When creating an architectural plan or developing an interior design, the main thing is to imagine how the object will look in space. It is allowed to use axonometric projection, but it is excellent for small objects or details. The prevalence of general perspective is that it gives an idea not only of the external appearance of the object, but allows you to visually represent the ratio of sizes depending on the distance.

You will need

- paper;
- pencil;
- ruler.

Instructions

1. The theses for building a general perspective are identical for a Whatman sheet and a graphic editor. Consequentially execute it on the sheet. If the object is small, A4 size will be enough. For a general perspective of the building or interior, take a larger sheet. Lay it horizontally.

2. For a technical drawing or a drawing, select a scale. Take some clearly distinguishable parameter as a standard - say, the length of a building or the width of a room. Draw on the sheet an arbitrary segment corresponding to this line, and calculate the ratio.

3. This one will become the base of the picture plane, so place it at the bottom of the sheet. Designate the final points, say, as A and B. For the picture, you do not need to measure anything with a ruler, but determine the ratio of the parts of the object. The sheet must be larger than the plane of the picture, so that on the horizon line it was allowed to place two more points needed for construction. Divide this line into equal segments and mark them, say, with numbers.

4. Determine the 2nd parameter of the picture plane. This could be, say, the height of the room. If you are going to build a frontal perspective buildings, capturing a piece of the surrounding space, the height of the picture plane can be arbitrary. From points A and B, draw perpendiculars up to the height of the plane of the sky and connect their ends with a straight line.

5. Choose a location for the skyline. It should be slightly above the center of the picture plane. When building a general perspective of the interior of a traditional room in a modern house, say, the horizon line should be approximately 1.5-2 m high. If the ceilings are high, then the horizon line may be higher.

6. Mark the vanishing point on the horizon. Designate it, say, as P. Up from it, draw a perpendicular to the horizon line. Measure or roughly estimate the diagonal of the picture plane. Multiply this parameter by 2. Set this distance from point P along the perpendicular. Designate the new point as S.

7. From line SP at points S, set aside 2 angles of 45? and continue the rays until they intersect with the horizon line. Place points C and D. These are called distance points. Knowing their location and vanishing point, it is allowed to build a grid of general perspective.

8. Determine where the observer will be in relation to what is depicted on the picture plane. Better to place it somewhere on the edge. Merge this point with point P. Project the second distance point to the base of the picture plane. Combine the projection and the observer's point with P.

9. To determine the location of the transverse grid lines, combine one of the distance points with the points on the base of the plane of the sky, which you designated with numbers. Merge the second detachment point with the diagonal end of the base. The points of intersection of this line with segments D1, D2, etc. will give you the likelihood of determining the ratio of sizes as they move away from the observer.

10. If the plane of the object is directly in front of the viewer, it will turn out in the drawing exactly the same as in nature. Draw planes at an angle along the grid lines. All lines must converge at point P. The viewer sees them correctly at the same angle as in nature. Moreover, their sizes are also limited by the grid lines, which makes it possible to observe the ratio.

Related Videos

A pyramid is called a spatial geometric figure, one of the faces of which is the base and can have the shape of any polygon, and the rest - the lateral ones - are invariably triangles. All lateral surfaces of the pyramid converge at one common vertex opposite to the base. For a complete representation in the drawing of the features of this figure, its horizontal and general projections are absolutely sufficient.

Instructions

1. Start projecting a pyramid with a positive triangular base with a horizontal projection of that base. First, draw a horizontal line equal to the length of the base edge at the given scale. Designate its extreme left point with one, and the right one with three. After that, set aside the length of the segment on the compass and the intersection of the auxiliary circles drawn from points 1 and 2, designate it with the number 3. Combine point 3 with the edges of the segment - now the drawing contains the lines of all 3 edges of the base, and the construction of its horizontal projection can be considered complete.

2. On a horizontal projection, notice the top of the pyramid - it will coincide with the intersection of 2 auxiliary segments drawn between the vertices of the triangle and the midpoints of the opposite sides. Designate the projection of the vertex with the letter S and combine it with the corners of the base triangle - these are the horizontal projections of the edges of the side faces. This completes the horizontal projection drawing.

3. Start drawing the general projection by constructing line 1'-2 ', parallel to line 1-2 - this will be the general projection of the base. After that, draw a vertical connection line from the horizontal projection of the top of the pyramid S and set aside from its intersection with the 1′-2 ′ segment the distance equal to the specified height of the figure on the same scale. At this distance, put a point S '- this is the general projection of the vertex.

4. Draw a vertical connection line from point 3 of the horizontal projection and mark its intersection with the segment 1′-2 ′ - this is the general projection of the third corner of the base, designate it 3 ′. Then draw the projections of the lateral edges by joining points 1 ′, 2 ′ and 3 ′ with point S ’. The general projection drawing will also be completed on this.

5. The sequence of operations for pyramids with bases of other shapes will be the same - start with a horizontal projection, then build a frontal projection along the lines of communication.

Related Videos