Drawing of the third projection based on two given ones. Construction of the third type from two data

A point in space is determined by any two of its projections. If it is necessary to construct a third projection based on two given ones, it is necessary to use the correspondence of segments of projection communication lines obtained when determining the distances from a point to the projection plane (see Fig. 2.27 and Fig. 2.28).

Examples of solving problems in the first octant

Given A 1; A 2	Build A 3


Given A 2; A 3	Build A 1


Given A 1; A 3	Build A 2

Let's consider the algorithm for constructing point A (Table 2.5)

Table 2.5

Algorithm for constructing point A
By given coordinates A ( x = 5, y = 20, z = -9)

In the following chapters we will consider images: straight lines and planes only in the first quarter. Although all the methods considered can be applied in any quarter.

Conclusions

Thus, based on the theory of G. Monge, it is possible to transform the spatial image of an image (point) into a planar one.

This theory is based on the following provisions:

1. The entire space is divided into 4 quarters using two mutually perpendicular planes p 1 and p 2, or into 8 octants by adding a third mutually perpendicular plane p 3.

2. The image of a spatial image on these planes is obtained using a rectangular (orthogonal) projection.

3. To convert a spatial image into a planar one, it is assumed that the plane p 2 is stationary, and the plane p 1 rotates around the axis x so that the positive half-plane p 1 is combined with the negative half-plane p 2, the negative part p 1 - with the positive part p 2.

4. Plane p 3 rotates around the axis z(line of intersection of planes) until aligned with plane p 2 (see Fig. 2.31).

The images obtained on the planes p 1, p 2 and p 3 by rectangular projection of images are called projections.

Planes p 1, p 2 and p 3, together with the projections depicted on them, form a planar complex drawing or diagram.

Lines connecting the projections of the image to the axes x, y, z, are called projection communication lines.

For more precise definition images in space, a system of three mutually perpendicular planes p 1, p 2, p 3 can be used.

Depending on the conditions of the problem, you can choose either the p 1, p 2 or p 1, p 2, p 3 system for the image.

The system of planes p 1 , p 2 , p 3 can be connected to the Cartesian coordinate system, which makes it possible to define objects not only graphically or (verbally), but also analytically (using numbers).

This method of depicting images, in particular points, makes it possible to solve such positional problems as:

location of the point relative to the projection planes ( general position, belonging to the plane, axis);
position of the point in the quarters (in which quarter the point is located);
position of the points relative to each other (higher, lower, closer, further relative to the projection planes and the viewer);
position of the point’s projections relative to the projection planes (equidistance, closer, further).

Metric tasks:

equidistance of the projection from the projection planes;
ratio of projection distance from projection planes (2–3 times, more, less);
determining the distance of a point from the projection planes (when introducing a coordinate system).

Self-Reflection Questions

1. The intersection line of which planes is the axis z?

2. The intersection line of which planes is the axis y?

3. How is the line of projection connection between the frontal and profile projection of a point located? Show me.

4. What coordinates determine the position of the projection of a point: horizontal, frontal, profile?

5. In which quarter is point F (10; –40; –20) located? From which projection plane is point F farthest away?

6. The distance from which projection to which axis determines the distance of a point from the plane p 1? What coordinate of the point is this distance?

You will need

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

Instructions

Sources:

projection construction

Projection is strongly associated with the exact sciences - geometry and drawing. However, this does not prevent it from occurring all the time in seemingly non-scientific and everyday things: the shadow of an object that falls on a flat surface in sunlight, sleepers railway, any map and any drawing is already nothing else? like a projection. Of course, creating maps and drawings requires an in-depth study of the subject, but the simplest projections can be created independently, armed only with a ruler and a pencil.

You will need

* pencil;
* ruler;
* sheet of paper.

Instructions

The first method of constructing a projection is by central projection and is especially suitable for depicting objects on a plane when it is necessary to reduce or increase their actual size (Fig. a). The central design algorithm is as follows: we denote the design plane (P") and the design center (S). To project ABC into the plane P", we draw through the center point S and points A, B and C AS, SV and SC. Their intersection with the plane P" forms points A", B" and C", when connected by straight lines we obtain 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 P plane are not, but parallel to the designated design direction (S). Nuance: the design direction cannot be parallel to the P plane. When connecting 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 easily be a step in the descriptive.

Video on the topic

One of the most fascinating tasks in descriptive geometry is the construction of the third kind given two. It requires a thoughtful approach and pedantic measurement of distances, so it is not always given the first time. However, if you carefully follow the recommended sequence of actions, it is quite possible to construct the third view, even without spatial imagination.

You will need

- a sheet of paper;
- pencil;
- ruler or compass.

Instructions

First of all, try the two available kind m determine the shape individual parts of the depicted object. If the top view shows a triangle, then it can be a prism, cone of rotation, triangular or. The shape of a quadrangle can be taken by a cylinder, or a triangular prism or other objects. An image in the shape of a circle can represent a ball, cone, cylinder, or other surface of revolution. Either way, try to imagine the overall shape of the object as a whole.

Draw the boundaries of the planes for ease of transferring lines. Start with the most convenient and understandable element. Take any point that you definitely "see" on both kind x and move it to the third view. To do this, lower the perpendicular to the boundaries of the planes and continue it on the next plane. Please note that when switching from kind on the left in the top view (or vice versa), you must use a compass or measure the distance using a ruler. So in place of your third kind two lines intersect. This will be the projection of the selected point onto the third view. In the same way, you can do as many points as you like until it becomes clear to you general view details.

Check the correctness of the construction. To do this, measure the dimensions of those parts of the part that are completely (for example, a standing cylinder will be the same “height” in the left view and the front view). In order to make sure that you don’t mind, try from the position of an observer from above and count (at least approximately) how many boundaries of holes and surfaces should be visible. Every straight line, every point must have a reflection on everyone kind X. If the part is symmetrical, do not forget to mark the axis of symmetry and check the equality of both parts.

Delete all auxiliary lines, check that all invisible lines are marked with a dotted line.

To depict a particular object, first depict it individual elements in the form of simple figures, and then their projection is performed. The construction of projection is quite often used in descriptive geometry.

You will need

- pencil;
- compass;
- ruler;
- reference book “Descriptive Geometry”;
- rubber.

Instructions

Carefully read the conditions of the task: for example, the frontal projection F2 is given. The point F belonging to it is located on the side of the cylinder. It requires the construction of three projections F. Mentally imagine how it all should look, then start building the image.

A cylinder of rotation can be represented in the form of a rotating rectangle, one of the sides of which is taken as the axis of rotation. The second rectangle - opposite to the axis of rotation - lateral surface cylinder. The rest represent the bottom and top of the cylinder.

Due to the fact that the surface of the cylinder of rotation when constructing given projections is made in the form of a horizontally projecting surface, the projection of point F1 must necessarily coincide with point P.

Draw the projection of point F2: since F is on the front surface of the cylinder of rotation, point F2 will be point F1 projected onto the lower base.

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

Video on the topic

Please note

When constructing image projections, follow the basic rules used in descriptive geometry. Otherwise, projections will not be possible.

Useful advice

To construct an isometric image, use the top base of the rotation cylinder. To do this, first construct an ellipse (it will be located in the x"O"y plane). After that, draw tangent lines and the lower half-ellipse. Then draw a coordinate polyline and use it to construct a projection of point F, that is, point F."

Sources:

Construction of projections of points belonging to a cylinder and a cone
how to construct a cylinder projection

Horizontal lines - isohypses (lines of equal heights) - lines that connect points on the earth's surface that have the same height marks. The construction of contour lines is used to compile topographic and geographical maps. Contour lines are constructed based on measurements with theodolites. The places where the cutting planes exit outward are projected onto horizontal plane.

Instructions

The level surface for measuring horizontal lines in Russia is considered to be the zero of the Kronstadt water gauge. It is from this that the contour lines are counted, which makes it possible to connect with each other separate plans and maps drawn up by various organizations. Horizontal lines determine not only the earth's topography, but also the topography of water basins. Isobaths (water contours) connect points of equal depth.

To indicate the relief, general symbols are used, which are contour (scale), non-scale and explanatory. In addition, there are also additional elements, related conventional signs. They include all kinds of inscriptions, rivers, and color schemes for the cards.

There are two ways to construct a horizontal line on a plan between two points: graphical and analytical. For graphic construction horizontally on the plan, take graph paper.

Draw several horizontal parallel lines at equal distances on the paper. The number of lines is determined by the number of required sections between two points. The distance between the lines is assumed to be equal to the specified distance between the horizontal lines.

Draw two vertical parallel lines at a distance equal to the distance between the given points. Mark these points on them, taking into account their height (altitude). Connect the dots with a slanted line. The points where the line intersects the horizontal lines are the points where the cutting planes exit outward.

Transfer the segments obtained as a result of intersection to horizontal straight line connecting two given points, by the orthogonal projection method. Connect the resulting points with a smooth line.

To construct contours analytical method use formulas derived from signs. In addition to these methods, computer programs such as Archicad and Architera are also used today to construct contour lines.

Video on the topic

Sources:

the 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. You can use axonometric projection, but it is good for small objects or details. The advantage of frontal perspective is that it gives an idea not only of appearance object, but allows you to visually imagine the ratio of sizes depending on the distance.

You will need

- a sheet of paper;
- pencil;
- ruler.

Instructions

The principles of constructing a frontal perspective are the same for a piece of Whatman paper and a graphic editor. So do it on a sheet of paper. If the item is small, A4 format will be sufficient. For frontal perspective or interior, take a sheet. Lay it horizontally.

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

This one will 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 don’t need to measure anything with a ruler, but determine the ratio of the parts of the object. The sheet must be larger than the picture plane in order to

A complete technical drawing contains at least three views. However, the knowledge to imagine an object from two projections is required from both the technologist and the skilled worker. It is therefore in exam papers In technical universities and colleges, problems involving the construction of the third type from two given ones are constantly encountered. In order to successfully complete a similar task, you need to know symbols, adopted in technical drawing.

You will need

- a sheet of paper;
— 2 projections of the part;
- drawing tools.

Instructions

1. The principles for constructing the third type are identical for classical drawing, drawing up a sketch and constructing a drawing in one of the pre-prepared computer programs. Analyze the given projections before everyone else. Look at exactly what types you are given. When we're talking about about 3 views, then this is the general projection, the top view and the 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 with right side from the general, and the view from above is below it.

2. Establish a projection connection with one of the specified types. This can be done by extending the horizontal lines that limit the silhouette of the object to the right when it is necessary to construct a view from the left. If we are talking about a top view, continue the vertical lines down. In any case, one of the part parameters will appear mechanically in your drawing.

3. Find the 2nd parameter on existing projections that limits the silhouettes of the part. When constructing a view on the left given size you will find 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 you need to take the width from the top view. When constructing a top view, the 2nd dimension is taken from the lateral projection. Mark the silhouettes of your subject in the third projection.

4. See if the part has protrusions, voids, or holes. This is all noted on the general projection, which, by definition, should give the most accurate idea of the subject. It is true that in the same way as when determining the overall silhouette of a part in the third projection, establish a projection relationship between different elements. The remaining parameters (say, the distance from the center of the hole to the edge of the part, the depth of the protrusion, etc.) can be found in the side or top view. Construct the necessary elements by considering the measurements you have discovered.

5. To check how well you have completed the task, try drawing a part in one of the axonometric projections. See how intelligently the elements of the third type you have drawn are located on the volumetric projection. It may be that some adjustments will have to be made to the drawing. A drawing taking into account perspective can also help you check your construction.

One of the most interesting problems in descriptive geometry is the construction of the third kind for given 2. It requires a thoughtful approach and meticulous measurement of distances, and therefore is not always given the first time. However, if you scrupulously follow the recommended sequence of actions, it is absolutely possible to build the 3rd type, even without spatial imagination.

You will need

- a sheet of paper;
- pencil;
- ruler or compass.

Instructions

1. First of all, try the two available kind m determine the shape of individual parts of the depicted object. If the top view shows a triangle, then it can be a triangular prism, a cone of rotation, a triangular or quadrangular pyramid. The shape of a quadrangle can be taken by a cylinder, a quadrangular or triangular prism, or other objects. An image in the shape of a circle can represent a ball, cone, cylinder, or other surface of rotation. One way or the other, try to imagine the overall shape of the object in its entirety.

2. Draw the boundaries of the planes for the comfort of transferring lines. Start transferring with the most comfortable and intelligible element. Take any point that you correctly “see” on both kind x and move 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 switching from kind on the left in the top view (or opposite), you need to use a compass or measure the distance using a ruler. So in place of your third kind two lines intersect. This will be the projection of the selected point onto the 3rd view. In the same way, you can transfer as many points as desired until you understand the overall appearance of the part.

3. Check the correctness of the construction. To do this, measure the dimensions of those parts of the part that are completely reflected (say, a standing cylinder will be the same “height” in the left view and the front view). In order to realize whether you have forgotten anything, try to look at the front view from the position of an observer from above and count (albeit approximately) how many boundaries of holes and surfaces should be visible. Every straight line, every point must have a reflection on everyone kind X. If the part is symmetrical, do not forget to mark the axis of symmetry and check the equality of both parts.

4. Remove all auxiliary lines, check that all noticeable lines are marked with a dotted line.

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

You will need

- pencil;
- compass;
- ruler;
— reference book “Descriptive Geometry”;
- rubber.

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 side surface of the rotation cylinder. It requires the construction of 3 projections of point F. Mentally imagine how all this should look, then proceed to construct the image on paper.

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

3. Due to the fact that the surface of the cylinder of rotation when constructing given projections is made in the form of a horizontally projecting surface, the projection of point F1 must necessarily coincide with point P.

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

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

Video on the topic

Pay attention!
When constructing image projections, follow the basic rules used in descriptive geometry. Otherwise, it will not be possible to execute the projections.

Useful advice
To construct an isometric image, use the upper base of the rotation cylinder. To do this, first construct an ellipse (it will be placed in the x’O’y’ plane). Later, draw tangent lines and a lower half-ellipse. After this, draw a coordinate polyline and, with its support, construct a projection of point F, that is, point F’.

There are not many people these days who have never in their lives had the opportunity to draw or draw something on paper. The knowledge to execute a primitive drawing of some design is sometimes very useful. You can spend a lot of time explaining “on your fingers” how this or that thing is made, while it is enough to just look at its drawing in order to realize it without any words.

You will need

– sheet of whatman paper;
– drawing accessories;
- drawing board.

Instructions

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

2. Draw a frame for the drawing, departing from the left edge of the sheet 20 mm, from the rest 3 - 5 mm. Draw the main inscription - a table in which all data about details and drawing. Its dimensions are determined by GOST 2.108-68. The width of the core inscription 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 being made.

3. Select the scale of the main image. Acceptable scales are determined by GOST 2.302-68. They should be preferred so that all the main elements are clearly visible in the drawing details. If some places are not clearly visible, they can be moved a separate species, shown at the required magnification.

4. Select main image details. It should represent the direction of view of the part (projection direction), from which its design is revealed especially fully. In most cases, the main image is the location in which the part is on the machine during execution rod operation. Parts that have an axis of rotation are located on the main image, as usual, so that the axis is horizontal. The main image is located at the top of the drawing on the left (if there are three projections) or close to the center (if there is no side projection).

5. Determine the location of the remaining images (side view, top view, sections, sections). Species details are formed by projecting it onto three or two mutually perpendicular planes (Monge’s method). In this case, the part must be positioned 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 to be made. Their difference from each other is that the section also shows what is located behind the cutting plane, while the section displays only what is located in the plane itself. The cutting plane can be stepped or broken.

7. Feel free to start drawing. When drawing lines, follow GOST 2.303-68, which defines species lines and their parameters. Place the images at such a distance from each other that there is enough space for setting dimensions. If the cutting planes pass along the monolith details, hatch the sections with lines running at an angle of 45°. If the hatch lines coincide with the main lines of the image, you can draw them at an angle of 30° or 60°.

8. Draw dimension lines and mark down dimensions. In doing so, be guided 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 numbers in accordance with GOST 2.304-68, take their height to be 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 placed on adjacent dimension lines.

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Carrying out an accurate drawing repeatedly requires a large investment of time. Consequently, in case of an urgent need to manufacture some part, it is often not a drawing that is made, but a sketch. 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;
- a sheet of 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. Therefore, first of all, carefully examine the object. Determine the relationship between various parameters. See if there are holes, where they are located, their size and the ratio of the diameter to the overall size of the product.

2. Determine which view will be the main one and how accurate an idea it gives of the part. The number of projections depends on this. There may be 2, 3 or more. Their location on the sheet depends on how many projections you need. You need to proceed from how difficult the product will be.

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

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

5. Draw the external silhouettes of the part. They are indicated by a thick, constant line. Try to convey the size ratio correctly. Draw internal (visible) outlines.

6. Make the cuts. This is done correctly 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. Parallel vertical or horizontal strokes extend from the points the distance between which you want to indicate. Draw a straight line between them with arrows at the ends.

8. Measure the part. Specify the length, width, hole diameters and other dimensions needed to perform the job accurately. 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 work is filling out the stamp. Enter product information into it. In technical universities and design organization There are standards for filling out stamps. If you are making a sketch for yourself, then you can simply 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.

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The drawing serves so that those who will grind a part or build a house can get the most accurate idea of the appearance of the object, its structure, the relationship of parts, and methods of surface treatment. One projection for this, as usual, is unsatisfactory. In training drawings there are usually three views - main, left and top. For objects of difficult shape, views from the right and from behind are also used.

You will need

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

Instructions

1. The sequence of drawing on a sheet of Whatman paper and in the AutoCAD program is approximately identical. First of all, look at the detail. Determine which angle will give the most accurate idea of the shape and functional features. This projection will become its main view.

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

3. The methods for constructing a drawing are identical for all projections. Mentally position the object in the system of planes on which you will project it. Analyze the shape of the object. See if it can be divided into more primitive parts. Answer the question into the shape of which body your entire object or any fragment of it can be completely inscribed. Imagine what the individual parts look like in orthogonal projection. The plane on which the object is projected when constructing a left view is located on the right side of the object itself.

4. Measure the part. Remove the basic parameters, establish the relationship between the whole object and its individual parts. Select a scale and draw the main 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 on the one that you are looking at from the left or right. After this, gradually begin to remove volumes, drawing recesses, silhouettes of holes, etc. When taking 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 a detail, when viewed from the left or right, is clearly expressed geometric figure With a small number of deviations from the severe form, it is more comfortable to use the removal technique. If there are a lot of fragments, but the part itself cannot fit into any shape, it is better to attach the elements to each other step by step. The difficulty of projections of the same part can be different, and therefore the methods can be changed.

6. In any case, start building the side view from the bottom and top lines. They must be on the same tier as the corresponding lines of the main view. This will provide projection communication. After this, apply the general silhouettes of the part or its first fragment. Maintain size ratio.

7. Having drawn the general silhouettes of the side view, apply axial lines, shading, etc. on it. Add dimensions. Signing a projection is not always required. If all views of a part are located on one sheet, then only the rear view is signed. The location of the remaining projections is determined by the standards. If the drawing is made on several sheets and one or both side views are not on the same sheet as the main one, they need to be signed.

Video on the topic

Useful advice
When constructing a side view in AutoCAD or another drawing program, it is not strictly necessary to combine the top and bottom lines of the main and side views at the first stage. You can execute the drawing in fragments, and combine the tiers when you start preparing it for printing.

13.1. A method for constructing images based on analysis of the shape of an object. As you already know, most objects can be represented as a combination of geometric bodies. Therefore, to read and complete 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 drawings of objects.

Rice. 100. Part projections

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

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

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

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

You encountered 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 located inside the brown dashed lines and circle in Figure 101, d. has been removed from the parallelepiped. What geometric body has such projections?

You encountered projections in the form of a circle and two rectangles when considering images of a cylinder. Consequently, the counterweight contains a hole in the shape of a cylinder, three projections and a visual image of which are given in Figure 101, e.

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

For example, a counterweight drawing is built like this:
1) on 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. Part shape analysis

30. Draw the description of a part called a bushing. 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 more reason cone, which is located in the middle of its base measuring 50 x 50 mm. The height of the prism is 10 mm. A through cylindrical hole 0 20 mm is drilled along the axis of the bushing. The axis of the bushing is perpendicular to the profile plane of projections.

13.2. The sequence of constructing views on a part drawing.
Let's consider an example of constructing views of a part - support (Fig. 102).

Rice. 102. Visual representation of the support

Before you start constructing images, you need to clearly imagine the general initial geometric shape of the de-gali (whether it will be a cube, cylinder, parallelepiped, etc.). This form 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 cutout in the form of a triangular prism. Let's start depicting the detail with it general form- parallelepiped (Fig. 103.a).
By projecting the parallelepiped onto the planes V, H, W, we obtain rectangles on all three projection planes. On the frontal plane of projections the height and length of the part will be reflected, i.e. dimensions 30 and 34. On the horizontal plane of projections - the width and length of the part, i.e. dimensions 26 and 34. On the profile plane - width and height, i.e. dimensions 26 and 30.

Each dimension of the part is shown without distortion twice: length - on the frontal and profile planes, length - on the frontal and horizontal planes, width - on the horizontal and profile planes of projections. However, you cannot put the same dimension on the drawing more than once.

All constructions will be done first with thin lines. Since the main view and the top view are symmetrical, axes of symmetry are marked on them.

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

Rice. 103. Sequence of constructing part views

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

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

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

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

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

Rice. 104. Geometric bodies containing cutouts

Rice. 105. Gasket shape analysis

Example 1. Figure 105 shows a drawing of the gasket. What shape does the removed part have? What was the shape of the workpiece?
Having analyzed the drawing of the gasket, we can come to the conclusion that it was obtained as a result of removing the fourth part of the cylinder from a rectangular parallelepiped (blank).

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

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

After analyzing the drawing, we can come to the conclusion that the part is made from a cylindrical blank. There is a cutout in it, the shape of which is clear from Figure 106, b.

How to construct a projection of the cutout in the view on the left?

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, points a, b, and a, b, which define the projections of the cutout, can be considered as given.

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

Having established the shape of the cutout, it is easy to decide which lines in the left view should be outlined with solid thick main lines, which with dashed lines, and which to delete altogether.

Rice. 107. Exercise tasks

31. Look at the images in Figure 107 and determine what shape the parts are removed from the blanks to obtain parts. Make technical drawings of these parts.
32. Construct the missing projections of the points, lines and cuts given by the teacher on the drawings you completed earlier.

13.4. Construction of the third type.
Sometimes we will have to complete tasks in which it is necessary to construct a third using two existing types.

Rice. 108. Drawing of a block with a cutout

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

The view on the left, as we 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 view on the left. Draw a vertical line anywhere between them. It will be the projection of the back face of the block onto the profile projection plane. From it to the right we will set aside a segment equal to 20 mm, i.e. we will limit the width of the bar, and we will draw another vertical line - the projection of the front face (Fig. 109.6).

Let us now show in the view on the left the cutout in the part. To do this, put a 12 mm segment to the left of the right vertical line, which is the projection of the front edge of the block, and draw another vertical line (Fig. 109, c). After this, 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 constructed based on an analysis of the geometric shape of the object. Let's look at how this is done. Figure 110a shows two projections of the part. We need to build a third one.

Rice. 10. Construction of the third projection based on 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, let’s imagine the shape of the part (Fig. 110, c).

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

Please note that in many cases there is no need to construct a third projection in the drawing, since rational execution of images involves constructing only the necessary (minimum) number of views sufficient to identify the shape of the object. In this case, the construction of the third projection of the object is only an educational task.

1. Have you read the in different ways constructing a third projection of the object. How are they different from each other?
2. What is the purpose of using a constant line? How is it carried out?

33. In the drawing of the part (Fig. 111, a) the view on the left is not drawn - it does not show images of a semicircular cutout and a rectangular hole. As instructed by the teacher, redraw or transfer the drawing onto tracing paper and complete it with the missing lines. What lines (solid main or dashed) 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 of the projection and construct profile projections of the parts.
35. Redraw or transfer onto tracing paper the projections indicated to you in Figure 113 or 114 by your teacher. Construct the missing projections in place of the question marks. Perform technical drawings of parts.

Date____

Grade: 9 ""

Topic: Construction of the third type of object based on two data

Goal: to teach how to construct the third type of object based on two data

Tasks:

Consolidate knowledge about the types in the drawing;

Develop spatial understanding and thinking, the ability to analyze the geometric shape of an object and skills in working with drawing tools;

To educate: hard work, accuracy, creative attitude to work, independence

Lesson type: combined

Lesson methods: explanatory - illustrative, practical

Form of organization: collective, individual

Lesson progress

Org moment

Repetition

2 . Test

Message new

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, a triangular prism, triangular and quadrangular pyramid, cone of rotation, etc.

Let's analyze the construction of the left view based on the data from the main view and the top view

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. a left view of an object is constructed, 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 were taken as the base planes. The image of the L-shaped cutout in the view on the left was constructed using the cutout contour points A B, C, D and E, and the intersection line of the cylindrical surfaces was 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.

Consolidation

Work using cards (build a third type based on two given ones)

Bottom line

Construction of the third type by measurement.

Opens (Fig.9) (technical drawing closed.

If the part is not very complex and for some reason it is impossible to make a projection connection with the top view, the third view is plotted using a ruler. If the part is simple and you can visualize it in your mind, there is no need to create a technical drawing.

Question: Who will build the top view of this part?

The student is called at will and builds a left view of part 9 on the IAD.

A technical drawing of the part is opened for verification.

Summary: This method cannot always be applied. For example, if there was no projection relationship between the front view and the top view, would we be able to construct the cut line? No. Therefore, I still recommend that you adhere to the projection connection in all three views.

4.Now let's return to our original task. In the lessons we will use the “constant line” method to construct a drawing.

You have images of two types of parts printed on paper on your table.

Task 1: Glue the first task into your notebook so that there is space left for constructing the third type. Place the notebook horizontally. Draw a constant straight line. Build a third view.

Students work in a notebook.

The one who completed the task first completes it on the IAD.

There are several solutions to this problem.

Question: Who will find another solution?

Students take turns coming to the board and offering

your decisions. Are opening (Fig. 6, 5, 4, 3, 2)

5. Exercises for the eyes.

To give our eyes a rest, let’s do some gymnastics for them.

Hold a pencil at arm's length in front of you. Without taking your eyes off it, bring it to the bridge of your nose, move it straight away from you (several times), then at arm's length, following the pencil, move it to the right - to the left.

6. Task2:We pasted the second task into the notebook. We built a third type based on two types of parts.

Opens(Fig. 10) Technical drawing closed.

The first one to complete it in a notebook draws it on the board.