How to correctly draw a circle in perspective, draw an ellipse. How to correctly draw a circle in perspective, draw an ellipse How to draw an oval knowing the radius of the circle

Sequence of constructions (Fig. 2.17)

1). Asked big AB and small CD oval axis (Fig. 2.17a);

2).Let's connect the dots A And WITH. On this line we plot a point M: SM=AO-OS=SK(Fig.2.17b);

3).Segment AM divide in half, and from the middle of this segment we restore the perpendicular until it intersects with the axes of the oval at the points O 1 And O 4(Fig. 2.17c);

4).Construct points symmetrical to the points O 1 And O 4, we get O 2 And O 3(Fig. 2.17d);

5).Draw the lines of centers O 1 O 3, O 1 O 4, O 2 O 3, O 2 O 4(Fig. 2.17d);

6).From the center O 4 draw an arc with radius R 1 =O 4 C until it intersects with the center lines О 4 О 1 And O 4 O 2 at points 1 and 2. Similarly, we find points 3 and 4 (Fig. 2.17e);

7). We draw the closing arcs of the oval from the centers O 1 And O 2 radius R 2 =O 1 A(Fig. 2.17g).

8) Construction results - Fig. 2.17z.

Execution of drawings of parts with mates

The construction of a drawing of such a part (Fig. 2.18) should begin with an analysis of the geometric elements that make up the image of the part and determination of its overall dimensions. Then you should think about what geometric constructions need to be made in the drawing. The image scale is selected according to the overall dimensions of the part. It is recommended to carry out the construction in the following sequence (Fig. 2.19):

1).Draw axial and center lines (Fig. 2.19a);

2).Draw circles whose centers are located at the intersection of the center lines (Fig. 2.19b);

3).Perform conjugations indicating the auxiliary constructions necessary to determine the centers and conjugation points:

a) between circles Ø32, construct an external joint with a radius R24 similar to the constructions in Fig. 2.13;

b) between circles Ø32 and Ø44, construct an internal joint with a radius of R76 similar to the constructions in Fig. 2.13;

c) carry out constructions to draw a tangent to circles Ø32 and Ø44, construct a tangent similar to the constructions in Fig. 2.16. The constructions are shown in Fig. 2.19 in, city

4).Draw dimension lines and enter size numbers.

ATTENTION!



Auxiliary constructions must be left on the drawing.

Slope

Slope is the tangent of the angle of inclination of one straight line to another (Fig. 2.20).

Let's take an arbitrary scale segment ( A). Let's construct a right triangle

i = tg α = =15:75=20%

In the drawing, the slope is specified either as a percentage (Fig. 2.21) or as a ratio of numbers (Fig. 2.22). A slope of 1:5 means that for every five units of length we have one unit of height. Those. straight line AC has a slope to BC of 20% or 1:5.

In the drawings, slopes are indicated with a special sign, see GOST 2.304-81. The acute angle of the slope sign should be directed towards the decrease in height, one side of the angle is parallel to the shelf of the leader line.

Fig.2.21 Fig.2.22

The slope is used, for example, in the production of shaped steel: channels, I-beams, T-sections, etc.

Let's consider an example of constructing the slope of the inner face of the lower flange of a channel (Fig. 2.23).

1. Using these dimensions, we find point A through which the given slope will pass (Fig. 2.24).

3. On the free field of the drawing, we build a slope of 10% (1:10 = 10:100) and through point A we draw a straight line parallel to the slope line.

Select a scale segment of any size.

3. An arc of radius 3 is the junction between the slope line and the vertical straight line. We build according to the rules for constructing connections between straight lines (Fig. 2.26).

Fig.2.26 Fig.2.27

4. An arc with a radius of 8 is the junction between the slope line and the vertical line of the rack (Fig. 2.27).

5. Similarly, we build the upper flange of the channel.

6. Since the height of the channel post is very large compared to the length of the shelf, and the post has a constant cross-section, a gap can be made, as shown in Figure 2.28.

7. We put down the dimensions. We save all constructions in the drawing.

2.9. Taper

Taper is the ratio of the difference in diameters of two cross sections of a truncated cone to the length between them (Fig. 2.29).

In the drawing, taper is most often expressed as percentages or ratios. The taper sign with an acute angle is directed towards the smaller diameter. The taper is placed either on the shelf of the leader line (Fig. 2.30) or above the center line (Fig. 2.31).

If the drawing indicates taper, then the dimensions on the rod and in the hole are set differently, based on the cone manufacturing technology, since normal taper is established on computer-controlled machines. Therefore, the normal taper must be indicated, and the “extra” size removed.

On a conical rod, the larger of the two diameters is indicated, since to manufacture the part you need to take a workpiece of a larger diameter. The small diameter is not indicated (Fig. 2.31).

In a hole of two diameters, the smaller one is indicated, since to obtain a taper you must first drill a hole with a diameter equal to the small diameter, and then bore the tapered hole (Fig. 2.32).

General purpose tapers are standardized. Their meaning can be found in GOST 8593-81.

In the task you need to construct a taper according to the dimensions and instead of a letter n enter the numerical value obtained by calculating using the formula in Fig. 2.29. Enter dimensions (Fig. 2.33)

Control questions

1. Formulate the concept of “conjugation”.

2. What pairing is called external, internal and mixed?

3. How are junction points determined?

4. What is called a slope and how to determine the magnitude of the slope?

5. What is called taper?

Applying dimensions

(GOST 2.307-68)

The basis for determining the size of the depicted product and its elements are the dimensional numbers printed on the drawing.

The rules for drawing dimensions on drawings and other technical documents for products from all branches of industry and construction are established by GOST 2.307 - 68. Dimensions are a very important part of the drawing. An omission or error in at least one of the dimensions makes the drawing unusable.

Therefore, dimensioning is one of the most critical stages in the preparation of a drawing.

When completing the first training drawings, the student needs to know the basic rules for drawing dimensions on the drawings.

Oval is a closed convex plane curve. The simplest example of an oval is a circle. Drawing a circle is not difficult, but you can construct an oval using a compass and ruler.

You will need

  • – compass;
  • - ruler;
  • - pencil.

Instructions

1. Let us know the width of the oval, i.e. its horizontal axis. Let us construct a segment AB different from the horizontal axis. Let's divide this segment into three equal parts by points C and D.

2. From points C and D as centers we construct circles with a radius equal to the distance between points C and D. We denote the intersection points of the circles with the letters E and F.

3. Let's unite points C and F, D and F, C and E, D and E. These lines intersect the circles at four points. Let's call these points G, H, I, J respectively.

4. Note that the distances EI, EJ, FG, FH are equal. Let's denote this distance as R. From point E as the center, draw an arc of radius R, connecting points I and J. Let's connect points G and H with an arc of radius R centered at point F. Thus, the oval can be considered constructed.

5. Let the length and width of the oval be known now, i.e. both axes of symmetry. Let's draw two perpendicular lines. Let these lines intersect at point O. On the horizontal line, plot a segment AB with the center at point O, equal to the length of the oval. On a vertical line we plot a segment CD with a center at point O, equal to the width of the oval.

6. Let's unite the straight points C and B. From point O as the center, draw an arc of radius OB connecting straight lines AB and CD. Let's call the point of intersection with the straight line CD point E.

7. From point C we draw an arc of radius CE so that it intersects the segment CB. Let's denote the intersection point by point F. Let's denote the distance FB by Z. From points F and B as from centers we'll draw two intersecting arcs of radius Z.

8. We connect the points of intersection of 2 arcs of a straight line and call the points of intersection of this line with the axes of symmetry points G and H. Let's put the point G* symmetrically to the point G tangent to the point O. And put the point H* symmetrically to the point H tangent to the point O.

9. We connect points H and G*, H* and G*, H* and G with straight lines. Let us denote the distance HC as R, and the distance GB as R*.

10. From point H as the center we draw an arc of radius R intersecting lines HG and HG*. From the point H* as the center we draw an arc of radius R intersecting the lines H*G* and H*G. From points G and G* as centers we draw arcs of radius R*, closing the resulting figure. The construction of the oval is completed.

Not everyone knows that an ellipse and an oval are different geometric shapes, even though they are similar in appearance. Unlike an oval, an ellipse has a regular shape, and it will not be possible to draw it using a compass alone.

You will need

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

Instructions

1. Take paper and pencil, draw two straight lines perpendicular to each other. Place a compass at the point where they intersect and draw two circles of different diameters. In this case, the smaller circle will have a diameter equal to the width, that is, the minor axis of the ellipse, and the huge circle will correspond to the length, that is, the major axis.

2. Divide the huge circle into twelve equal parts. Using straight lines that will pass through the center, connect the division points that are located in reverse. As a result, you will also divide the smaller circle into twelve equal segments.

3. Number it. Do this so that the highest point in the circle is called point 1. Then draw vertical lines down from the points on the large circle. In this case, skip points 1, 4, 7 and 10. From the points on the small circle corresponding to the points on the large circle, draw horizontal lines that will intersect with the verticals.

4. Connect the points with a smooth oblique where the verticals and horizontals intersect and points 1, 4, 7, 10 on the small circle. The result was a correctly constructed ellipse.

5. Try another method of constructing an ellipse. On paper, draw a rectangle with a height and width equal to the height and width of the ellipse. Draw two intersecting lines that will divide the rectangle into four parts.

6. Using a compass, draw a circle that intersects the long line in the middle. Place the rod of the compass in the center of the side of the rectangle. The radius of the circle should be equal to half the length of the side of the figure.

7. Mark the points where the circle intersects the vertical center line, stick two pins into them. Place a third pin at the end of the middle line and tie all three with linen thread.

8. Take out the third pin and put a pencil in its place. Draw a curve using thread tension. An ellipse will be obtained if all actions were performed correctly.

Video on the topic

Despite the fact that the ellipse and the oval are very similar in appearance, geometrically they are different figures. And if an oval can be drawn only with the help of a compass, then it is impossible to draw a true ellipse with the help of a compass. It turns out that we will consider two methods for constructing an ellipse on a plane.

Instructions

1. The first and most primitive method of drawing an ellipse: Draw two straight lines perpendicular to each other. From the point of their intersection with a compass, draw two circles of different sizes: the diameter of the smaller circle is equal to the given width of the ellipse or the minor axis, the diameter of the larger circle is equal to the length of the ellipse, the major axis.

2. Divide the huge circle into twelve equal parts. Connect the division points located opposite each other with straight lines passing through the center. The smaller circle will also be divided into 12 equal parts.

3. Number the points clockwise so that point 1 is the highest point on the circle.

4. From the division points on the larger circle, in addition to points 1, 4, 7 and 10, draw vertical lines downwards. From the corresponding points lying on the small circle, draw horizontal lines intersecting the vertical ones, i.e. the vertical line from point 2 of the larger circle must intersect with the horizontal line from point 2 of the small circle.

5. Combine with a smooth oblique the intersection points of the vertical and horizontal lines, as well as points 1, 4, 7 and 10 of the small circle. The ellipse is built.

6. For another method of drawing an ellipse, you will need a compass, 3 pins and strong linen thread. Draw a rectangle whose height and width are equal to the height and width of the ellipse. Using two intersecting lines, divide the rectangle into 4 equal parts.

7. Using a compass, draw a circle intersecting the long center line. To do this, the support rod of the compass must be installed in the center of one of the sides of the rectangle. The radius of the circle is determined by the length of the side of the rectangle, divided in half.

8. Mark the points where the circle intersects the vertical center line.

9. Insert two pins into these points. Insert the third pin into the end of the midline. Tie linen thread around all three pins.

10. Remove the third pin and use a pencil instead. Using even thread tension, outline the curve. If everything is done correctly, you should end up with an ellipse.

Video on the topic

The designer is repeatedly faced with the need to build arc given curvature. Parts of buildings, spans of bridges, and fragments of parts in mechanical engineering can have this shape. The thesis of building an arch in any type of design is no different from what a schoolchild has to do in a drawing or geometry lesson.

You will need

  • - paper;
  • - ruler;
  • – protractor
  • – compass;
  • – computer with AutoCAD program.

Instructions

1. In order to build arc with the help of ordinary drawing tools, you need to know 2 parameters: the radius of the circle and the angle of the sector. They are either specified in the conditions of the problem, or they need to be calculated based on other data.

2. Place a dot on the sheet. Designate it as O. Draw a straight line from this point and plot the length of the radius on it.

3. Align the zero division of the protractor with point O and set aside this angle. Draw a straight line through this new point with the beginning at point O and plot the length of the radius on it.

4. Spread the legs of the compass to the size of the radius. Place the needle at point O. Connect the ends of the radii with an arc using a compass pencil.

5. The AutoCAD program allows you to build arc according to several parameters. Open the program. In the top menu you will find the main tab, and in it the “Drawing” panel. The program will offer several types of lines. Select the Arc option. You can also do it through the command line. Enter the command _arc there and press enter.

6. You will see a list of parameters according to which you can build arc. There are quite a lot of options: three points, the center, the beginning and the end. Allowed to build arc by origin, center, chord length or internal angle. An option is offered for two extreme points and a radius, for a central and final or starting point and an internal corner, etc. Choose the appropriate option depending on what you are famous for.

7. Whatever you prefer, the program will prompt you to enter the necessary parameters. If you are building arc using any three points, you can indicate their location with cursor support. It is also possible to indicate the coordinates of any point.

8. If among the parameters by which you build arc, you have a corner, you will have to call the context menu a 2nd time. First, mark the points specified in the conditions with a cursor or with coordinate support, then call up the menu and enter the angle size.

9. The algorithm for constructing an arc using two points and a chord length is exactly the same as using two points and an angle. True, in this case it should be borne in mind that the chord subtends 2 arcs of one circle. If you are building a smaller arc, enter the correct value, large - negative.

Video on the topic

An oval is a geometric figure that is used to display individual parts of interior items, draw animals and much more. Many people are interested in how to draw an oval correctly by hand.

How to draw an oval yourself correctly

In order for the drawing to turn out beautiful and harmonious, it is necessary to correctly and accurately draw all its elements. However, not everyone knows how to make an ellipse by hand correctly and beautifully.

To make an ellipse, you need to take:

  • album sheet;
  • ruler;
  • pencil;
  • eraser.

Initially, you need to draw a rhombus in the middle of the sheet, all sides of which will be equal, and the opposite sides will be parallel. The rhombus should be such that an oval of the required size fits well into it. Then you need to fit an oval into the resulting diamond. After this, the diamond must be erased with a pencil.

Draw an oval evenly and beautifully

To look great, you need to know how to draw an oval with a compass in a few minutes. To make an ellipse using a compass, you need to take:

  • album sheet;
  • pencil;
  • compass;
  • thread;
  • pins.

To draw an ellipse beautifully, you must initially draw two straight lines that will be perpendicular. Place the point of the compass at the intersection of the two lines and then draw a circle.

The diameter of such a circle will correspond to the width of the ellipse. Then, leaving the compass in the same place, you need to draw a slightly larger circle to get the length of the ellipse. Then you need to connect the two circles, erasing the extra lines. Thus, you will get a beautiful and even oval, from which you can then draw various animals and birds. Knowing how to draw an oval by hand, you can make very beautiful and original drawings without much difficulty.

How to Draw a Guinea Pig Based on an Oval

Drawings of animals and birds drawn from simple geometric shapes look very interesting. Many are interested in coming out of the oval with their children.

Using an oval you can quickly and beautifully draw a guinea pig. To make a drawing, you need to draw two ovals in a horizontal position, one of which will be slightly smaller than the other.

One oval should intersect with another, and then the outer corners formed when the two shapes intersect should be closed with lines. This will create the neck of the animal. In the center of a small oval you need to draw a point, from which you will then get an eye.

After this, you need to draw small ears at the top of the small oval. When everything is ready, you should draw the guinea pig's paws. It is worth considering that the front legs should be slightly shorter than the hind legs and almost invisible.

When everything is completely drawn, the extra lines can be erased, and then you need to color the guinea pig, making the animal spotted.

Knowing how to draw an oval, you can make very beautiful drawings of animals and birds based on this geometric figure.

How to draw or draw an oval?

For an artist, the ability to draw an oval beautifully and correctly is extremely important. When planning to write this article, I first read on the Internet what they say about drawing ovals, so as not to repeat myself.

By the way, let's not confuse an oval with an ellipse. They are similar, but they are not the same thing. We will look at the ellipse in the topic “perspective of a circle.”

But about the oval I will say this: the methods of drawing an oval are varied and complex. And it is also important for what purpose we need to draw an oval.

If an oval template is required for design work, then I do it in this cunning way. I trace a round object twice with a pencil and connect these circles by hand with arcs.

You can use a compass, but I always take the opportunity to develop my eye.

If the hand is as true as an Indian's, then the figure is quite satisfactory.

It’s another matter if an oval is needed for a drawing. For example, you painted a “turtle” coloring book and want to draw the same one according to the example. And not with the help of tracing paper or transferring through window glass, but just by drawing (drawing) a beautiful, even oval.

Children of any age tend to draw an oval in one fell swoop - crookedly and tilted to the right. But the outline of such a complex figure is a serious geometric construction.

Let's draw a vertical axis and a horizontal one perpendicular to it.

If we draw using a ruler, then we check with a square whether the angles are really right. If we draw by hand, then we need to rotate the picture to evaluate it from different points of view. From the point of intersection of the axes, we measure segments of equal length in both directions horizontally - the width of the oval and vertically - the height of the oval. First, slowly and very beautifully draw the first curved line limiting one of the four sectors. Here you have to rely on your sense of harmony. We draw the next line symmetrically, again carefully monitoring the accuracy of the dimensions. Having decided on the sketch of the oval, we erase the extra lines and outline the one we need:

Here, comrades, there are many pitfalls: usually children are in a hurry. Or, busy drawing out details, they do not see the whole. As in the case of the very strong temptation to draw either a rhombus or a rectangle with rounded corners.

So I repeat again: drawing or drawing an oval is not so easy

How to draw an ellipse using a compass?
Let's look at how to build an ellipse not by hand or by eye, but if necessary, for example, constructing an ellipse larger than 50 mm. In this case, a special technique for constructing an ellipse is used.
Let's consider one of the construction methods.
Let's draw an ellipse, which is an isometric representation of a circle. To do this, we will sequentially perform the following steps.

  1. We draw with a diameter of 30 mm. In isometric form, this circle has the appearance of an ellipse with axes of 21.3 mm and 36.6 mm.
  1. From the center of the future ellipse we will draw 2 auxiliary circles, which will have diameters equal to the minor and major axis of the ellipse. Next, we draw several rays from the center that must intersect both circles. For clarity, let's consider only one quarter. The number of constructed auxiliary rays is selected depending on the required construction accuracy and the size of the ellipse. We use 3 beams (this number of beams is suitable for ellipses with a major axis of 60 - 120 mm).

  1. Next you need to get additional points of the ellipse. For this purpose, the following must be done with each ray: through the point of intersection of the ray with the small circle, draw a horizontal line towards the large circle, and through the point of intersection of the ray with the large circle, lower the perpendicular to the drawn horizontal line. As a result, we get point 2, point 3 and point 4. Point 1 and point 5 will also belong to the ellipse.

  1. We draw a curve through the resulting 5 points. Please note that the ellipse curve is strictly perpendicular to the axes.

  1. It is necessary to complete the remaining 3 quarters of the ellipse. To do this, you can perform similar actions, but it is easier and faster to reflect points 2, 3 and 4 relative to the axes.


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