Construction of the 3rd type based on two given ones. Construction of the third type from two data

Constructing the third projection of a part using two data

First you need to find out the shape of the individual parts of the object; To do this, you need to simultaneously consider both given images. It is useful to keep in mind which surfaces correspond to the most common images: circle, triangle, hexagon, etc. In the shape of a triangle in the top view (Fig. 41) the following can be depicted: triangular prism 1, triangular 2 and quadrangular 3 pyramids, cone of rotation 4, truncated prism 5.

The shape of a quadrangle (square) can be seen in the top view (Fig. 41): cylinder 6, triangular prism 8, quadrangular prisms 7 and 10, as well as other objects limited by planes or cylindrical surfaces 9.

The shape of a circle can be seen from above: a ball, a cone, a cylinder and other surfaces of rotation. The top view of a regular hexagon shape is a regular hexagonal prism.

Having determined the shape of individual parts of the surface of an object, you need to mentally imagine their image on the left and the entire object as a whole.

To construct the third type from two data, use various ways: construction using general dimensions; using an auxiliary line; using a compass; using straight lines drawn at an angle of 45°, etc.

Let's look at some of them.

Construction using an auxiliary line(Fig. 42). In order to transfer the width of a part from the top view to the left view, it is convenient to use the auxiliary straight line. It is more convenient to draw this straight line to the right of the top view at an angle of 45° to the horizontal direction.

To build the third projection A 3 peaks A, let's draw through its frontal projection A 2 horizontal line 1. The desired projection will be located on it A 3. After this, through horizontal projection A 1 draw a horizontal line 2 until it intersects with the auxiliary line at the point A 0 . Through the point A 0 draw vertical line 3 until it intersects line 1 at the desired point A 3 .

Profile projections of the remaining vertices of the object are constructed similarly.

After the auxiliary straight line has been drawn at an angle of 45°, it is also convenient to construct the third projection using a crossbar and a triangle (Fig. 80b). First through the frontal projection A 2 draw a horizontal line. Draw a horizontal line through the projection A 1 there is no need, it is enough to apply a crossbar and make a horizontal notch at the point A 0 on the auxiliary line. After this, moving the rod down a little, we apply the square with one leg to the rod so that the second leg passes through the point A 0, and mark the position of the profile projection A 3 .

Construction using baselines. To construct the third type, it is necessary to determine which lines of the drawing should be taken as the basic ones for measuring the dimensions of the images of the object. Such lines are usually taken to be axial lines (projections of the planes of symmetry of an object) and projections of the planes of the bases of the object.

Let us use an example (Fig. 43) to construct a view on the left using two given projections of an object.

By comparing both images, we establish that the surface of the object includes the surfaces of: regular hexagonal 1 and quadrangular 2 prisms, two cylinders 3 and 4 and truncated cone 5. The object has a frontal plane of symmetry F, which is convenient to take as the basis for measuring the width of individual parts of an object when constructing its view on the left. The heights of individual sections of an object are measured from the lower base of the object and are controlled by horizontal communication lines.

The shape of many objects is complicated by various cuts, cuts, and intersections of component surfaces. Then you first need to determine the shape of the intersection lines, construct them at individual points, entering the designations of the projections of the points, which after completing the constructions can be removed from the drawing.

In Fig. 44 there is a left view of an object, the surface of which is formed by the surface of a vertical cylinder of rotation with T-shaped cutout in its upper part and a cylindrical hole occupying a front-projecting position. The plane of the lower base and the frontal plane of symmetry F are taken as the base planes. Image T-shaped cutout in the left view is constructed using dots A,IN,WITH,D And E contour of the cutout, and the line of intersection of cylindrical surfaces - using points TO,L,M and symmetrical to them. When constructing the third type, the symmetry of the object relative to the plane is taken into account F.

2.6. Control questions

1. Which image is taken as the main one in the drawing?

2. How is the object positioned relative to the frontal plane of projection?

3. How are images divided in the drawing depending on their content?

4. What are the rationales for choosing the number of images?

5. What image is called a view?

6. How are the main views located in the projection relationship in the drawing and what are their names?

7. What types are designated and how are they labeled?

8. What is the size of the letter used to designate the species?

9. What are the ratios of the sizes of the arrows indicating the direction of view?

10.Which species are called additional and which are called local?

11. When is an additional species not designated?

12. Which image is called a section?

13. How do you indicate the position of the cutting plane when making cuts?

14. What inscription marks the incision?

15. What is the size of the letters along the section line and in the inscription marking the section?

16. How are cuts divided depending on the position of the cutting plane?

17. When is a vertical section called frontal, when is it called profile?

18. Where can horizontal, frontal and profile cuts be located and when are they not indicated?

19. How are cuts classified depending on the number of cutting planes?

20. How to draw a section line in a complex section?

21. What cuts are called step cuts? How are they drawn and designated?

22. What cuts are called broken? How are they drawn and designated?

23. What section is called local and how does it stand out in the view?

24. What serves as the dividing line when connecting half of the view and the section?

25. What serves as a dividing line if, when connecting half of the view and the section, the contour line coincides with the axis of symmetry?

26. How is a stiffener shown in section if the cutting plane is directed along its long side?

27. How is the contour of a group hole identified in a circular flange if it does not fall into the plane of a given section?

28. Which image is called a section?

29. How are sections that are not part of the section classified?

30. Which sections are preferred?

31. Which line represents the contour of the extended section and which line represents the contour of the superimposed section?

32. Which sections are not marked or labeled?

33. When making a section, how do you indicate the position of the cutting plane?

34. What inscription accompanies the section?

35. How is the rendered section placed on the drawing field?

36. What is the accepted symbol for depicting a section along the axis of a surface of rotation that bounds a hole or recess?

38. How are various sections shaded in a part drawing?

39. List the methods for constructing the third type of part using two data.

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 deep learning object, but the simplest projections can be constructed independently, armed only with a ruler and pencil.

You will need

  • * pencil;
  • * ruler;
  • * 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.

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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

  • - paper;
  • - pencil;
  • - ruler or compass.

Instructions

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 prism, cone of revolution, 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. Anyway, try to imagine general shape the subject 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 form 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, its individual elements are first 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

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 is opposite the axis of rotation - the side surface of the 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).

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note

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

Helpful 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

Horizontals - 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. Contour 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, universal symbols are used, which are contour (scale), non-scale and explanatory. In addition, there are additional elements accompanying 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. To graphically plot the horizontal line 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 a straight line connecting two given points using 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, today they are used to construct contour lines. computer programs, such as "Archicad" and "Architerra".

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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

  • - 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. Endpoints designate, for example, 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

Having completed the layout of the drawing and completed two specified projections of the part, they proceed to the next stage of work - constructing the third projection of the part.

Two specified projections can be: frontal and horizontal, frontal and profile. In both cases, the construction is performed in the same way.

In Fig. Figure 2 shows the construction of a profile projection based on given frontal and horizontal projections.

The construction was made using the rectangular (orthogonal) projection method, i.e. all three images (projections) were constructed without violating the projection connection, but the coordinate axes and projection connection lines are absent in the drawing. To ensure that the projection connection is not disrupted when constructing images, it is necessary to apply a crossbar or triangle in the direction of the corresponding projection connection simultaneously to two projections on which this moment carry out construction.

According to two given projections, in in this case frontal and horizontal, a profile is constructed by transferring dimensions in height from the frontal projection, and in width - from the horizontal projection. To do this, first determine the location of the profile dimensional rectangle, draw the axis of symmetry and carry out the construction in the following order. Size A from frontal projection (part height) and size G from the horizontal projection (width of the part) is used when constructing an overall rectangle. The base of the model is a parallelepiped with a width G (already built) and height V , which is built on a profile projection, taken from the frontal one. To do this, to the front projection in height V apply a crossbar, and draw a thin horizontal line on the profile within the overall rectangle. The lower base of the model on the profile projection is built.

On the base of the model there is a quadrangular prism with two inclined faces. Its upper base is located at a height A from the lower base of the part and is already constructed as the height of the overall rectangle. It remains to construct the width of the upper and lower bases. They are the same size and equal in size d , which is taken on a horizontal projection. To do this, measure half the distance on a horizontal projection d and lay it down on the profile projection in both directions from the axis of symmetry. Two vertical lines are drawn through the constructed points, limiting the image of this prism. The prism standing on the base of the part is built.

The part has two slots: left and right. On the frontal projection they are depicted by lines of an invisible contour, and on the horizontal projection by a line of a visible contour. To construct them on a horizontal projection, half the distance is measured from the center line e and, accordingly, are laid on the lower base of the profile projection. Two thin lines are drawn upward from the constructed points, parallel to the axis of symmetry. They will limit the distance along the width of the slot. Its height (distance b ) are built according to the frontal projection, for which to the highest point of the distance b apply a gauge and at this height, on the profile projection, draw a thin horizontal line limiting the slot at the top.

The image of the visible part of the surface of an object facing the observer is called the view.

GOST 2.305-68 establishes the following name for the main views obtained on the main projection planes (see Fig. 1.1.1): 7 - front view (main view); 2 - top view; 3 - left view; 4 - right view; 5 - bottom view; b - rear view. In practice, three types are more widely used: front view, top view and left view.

The main views are usually located in a projection relationship with each other. In this case, there is no need to write the name of the types on the drawing.

If any view is displaced relative to the main image, its projection connection with the main view is broken, then an inscription of type “A” is made above this view (Fig. 1.2.1).

The direction of view should be indicated by an arrow, indicated by the same capital letter of the Russian alphabet as in the inscription above the view. The ratio of the sizes of the arrows indicating the direction of view should correspond to those shown in Fig. 1.2.2.

If the views are in projection connection with each other, but are separated by any images or are not located on the same sheet, then an “A” type inscription is also made above them. An additional view is obtained by projecting an object or part of it onto an additional projection plane that is not parallel to the main planes (Fig. 1.2.3). Such an image must be performed in the case when any part of the object is not depicted without distorting the shape or size on the main projection planes.

In this case, the additional projection plane can be located perpendicular to one of the main projection planes.

When an additional view is located in direct projection connection with the corresponding main view, it does not need to be designated (Fig. 1.2.3, a). In other cases, the additional view must be marked on the drawing with an inscription of type “A” (Fig. 1.2.3, b),

and the image associated with the additional view must have an arrow indicating the direction of view, with the corresponding letter designation.

The secondary view can be rotated while maintaining the same position as the item in the main image. In this case, you need to add a sign to the inscription (Fig. 1.2.3, c).

A local view is an image of a separate, limited area of ​​the surface of an object (Fig. 1.2.4).

If a local view is located in direct projection connection with the corresponding images, then it is not designated. In other cases, local species are designated similarly to additional species; the local species may be limited by the cliff line (“B” in Fig. 1.2.4).

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Topic 3. Construction of the third type of object based on two data

First of all, you need to find out the shape of individual parts of the surface of the depicted object. To do this, both given images must be viewed simultaneously. It is useful to keep in mind which surfaces correspond to the most common images: triangle, quadrilateral, circle, hexagon, etc.

In the top view, in the shape of a triangle, the following can be depicted (Fig. 1.3.1, a): triangular prism 1, triangular 2 and quadrangular 3 pyramids, cone of rotation 4.

An image in the form of a quadrangle (square) can be seen in the top view (Fig. 1.3.1, b): a cylinder of rotation 6, a triangular prism 8, quadrangular prisms 7 and 10, as well as other objects limited by planes or cylindrical surfaces 9.

The shape of a circle can be in the top view (Fig. 1.3.1, c): ball 11, cone 12 and cylinder 13 of rotation, other surfaces of rotation 14.

The top view in the shape of a regular hexagon has a regular hexagonal prism (Fig. 1.3.1, d), limiting the surfaces of nuts, bolts and other parts.

Having determined the shape of individual parts of the surface of an object, you need to mentally imagine their image on the left and the entire object as a whole.

To construct the third type, it is necessary to determine which lines of the drawing should be taken as the basic ones for reporting the dimensions of the image of the object. As such lines, axial lines are usually used (projections of the planes of symmetry of an object and projections of the planes of the bases of an object). Let's analyze the construction of the left view using an example (Fig. 1.3.2): using the data from the main view and the top view, construct a left view of the depicted object.

By comparing both images, we establish that the surface of the object includes the surfaces of: regular hexagonal 1 and quadrangular 2 prisms, two cylinders 3 and 4 of rotation and a truncated cone 5 of rotation. The object has a frontal plane of symmetry Ф, which is convenient to take as the basis for reporting the dimensions along the width of individual parts of the object when constructing its left view. The heights of individual sections of an object are measured from the lower base of the object and are controlled by horizontal communication lines.

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, entering designations for the projections of points, which after completing the construction can be removed from the drawing.

In Fig. 1.3.3 shows a left view of an object, the surface of which is formed by the surface of a vertical cylinder of rotation, with a T-shaped cutout in its upper part and a cylindrical hole with a frontally projecting surface. The plane of the lower base and the frontal plane of symmetry F are taken as the base planes. The image of the L-shaped cutout in the view on the left is constructed using the cutout contour points A B, C, D and E, and the intersection line of the cylindrical surfaces is constructed using points K, L, M and them symmetrical. When constructing the third type, the symmetry of the object relative to the plane F was taken into account.

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