Instruction

1

May need to create a axonometric projection of some body of rotation.

First we need to relate the body with some rectangular coordinate system, in this case, as one of the axes for the convenience of the account should take the axis of body rotation.

First we need to relate the body with some rectangular coordinate system, in this case, as one of the axes for the convenience of the account should take the axis of body rotation.

2

Then the drawn second orthogonal projection of the object.

3

Now you need to build the axonometric axis, to position them so you need to ensure the visibility of the larger surface of the object, to simplify the build, you can take the coordinate axis of the rectangular isometric projection, in this case, the coefficients of distortion on the axes can be considered equal to 1.

4

Elements of the figure are projected along the axonometric axes in the ratio 1:1.

For clarity of presentation axonometric projection, is the cut nearest his quarters, with subsequent hatching.

For clarity of presentation axonometric projection, is the cut nearest his quarters, with subsequent hatching.

# Advice 2: How to build perspective

Axonometric projection is very important in Sciences such as drawing and geometry. It is a very clear three-dimensional image of the object. How to build

**perspective**?Instruction

1

Let your task is to build the axonometric projection of a given body of rotation. First and foremost, you need to relate this body with any rectangular coordinate system. As the body of rotation, in this case, for ease of account one of the axes of the coordinate system has to align with the axis of body rotation.

2

Now we need to draw a second orthogonal projection of the body, as shown in the figure.

3

Then you must go to the construction of the axonometric axes. Keep in mind that they need to have on the sheet, to the greater part of the surface of the object was ensured visibility. In order to simplify the task of building it is best to take the coordinate axis used in rectangular isometric projection shown in the figure. With this choice, the coefficients of the distortion for each of the axes become equal to one. If you're doing standard axonometric axes in which adjacent axes form an angle of 120 degrees, the distortion coefficient is equal to 0.82. This will create additional complexity in the image of the object.

4

All elements of a given shape needs to be projected in the ratio of one-to-one along the axonometric axes. To ensure that the image was more clear, in the nearest quarter of the part is cut, with subsequent hatching. The line of hatch according to the rules applied in parallel, any conditional diagonals of a square lying in the considered coordinate plane. Side of this square must be parallel to the axonometric axes. In one part of different cross sections it is necessary to stroke with an inclination in different directions.

Useful advice

The construction of the axonometric projection of objects in many textbooks on technical drawing it is recommended to start with building their bases, then the bases are gradually added perspective of other elements: edges, faces, vertices, and bases.

# Advice 3: How to build the axonometric projection

Axonometric projection of parts of machines are often used in the design documentation in order to demonstrate the design features of the part (subassembly), to see how it looks the item (node) in space. Depending on the angle at which are located the axes, axonometric projections are divided into rectangular and oblique-angled.

You will need

- Program for drawing, pencil, paper, eraser, protractor.

Instruction

1

A rectangular projection. Isometric projection. When you build a rectangular isometric projection take into account the distortion ratio in the X, Y, Z, equal to 0.82, while the circumference parallel to the planes of projection are projected on the axonometric plane of projections in the form of ellipses, the major axis of which is equal to d and with a minor axis of 0.58 d, where d is the diameter of the original circle. For ease of calculation isometric

**projection**are performed without distortion of the axes (distortion factor equal to 1). In this case, the projected circle will have the form of ellipses with the major axis, equal to 1.22 d, and the minor axis equal to d of 0.71.2

Dieticheskaya projection. When building rectangular dimetrically projection takes into account the distortion factor along the axes X and Z, equal to 0.94, and the Y – axis is 0.47. In practice dieticheskoe

**projection**simplistically perform without distortion in X and Z and the distortion factor along the Y-axis = 0,5. A circle parallel to the frontal plane of projection is projected onto her in the form of an ellipse with the major axis equal to 1.06 d and the minor axis, is equal to 0,95 d, where d is the diameter of the original circle. Circle, parallel to the other two axonometric planes are projected onto them in the form of ellipses with the axes, respectively, equal to 1.06 d and 0.35 d.3

Oblique projection. Frontal isometric projection. When building a front isometric view standard the optimum angle of the axis Y to the horizontal of 45 degrees. Allowed tilt angles of the Y-axis to the horizontal - 30 degrees and 60 degrees. The distortion ratio in the X, Y, and Z equal to 1. Circumference 1, located parallel to the frontal plane of projection is projected onto it without distortion. Circles parallel to the horizontal and profile planes of projections, made in the form of ellipses 2 and 3 with the major axis equal to 1.3 d and a minor axis equal to 0,54 d, where d is the diameter of the original circle.

4

Horizontal isometric projection. Horizontal isometric projection of the part (node) is based on the axonometric axes are located as shown in Fig. 7. You can change the angle between the Y axis and the horizontal is 45 degrees and 60 degrees, to keep the same 90 degree angle between axes Y and X. the distortion Ratio in the X, Y, Z equal to 1. A circle lying in a plane parallel to the horizontal plane of projection is projected in the form of a circle 2 without distortion. Circle, parallel, frontal and profile planes of projections have the form of ellipses 1 and 3. The dimensions of the axes of the ellipses associated with the initial diameter d of a circle the following relationship:

1 ellipse – major axis equal to 1.37 d, the minor axis is 0, 37d; 3 ellipse – major axis equal to 1.22 d, the minor axis – 0.71 d.

1 ellipse – major axis equal to 1.37 d, the minor axis is 0, 37d; 3 ellipse – major axis equal to 1.22 d, the minor axis – 0.71 d.

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Dieticheskaya front projection. Dieticheskaya oblique frontal projection of the part (node) is based on the axonometric axes similar to the axes of the frontal isometric projection, but differ from it the distortion factor along the Y-axis, which is equal to 0.5. The X-and Z-distortion factor equal to 1. It is also possible to change the angle of the Y-axis to the horizontal up to 30 degrees and 60 degrees. A circle lying in a plane parallel to a frontal axonometric plane of projections), is projected to it without distortion. The circumference parallel to the planes of projection horizontal and profile, are plotted in the form of ellipses 2 and 3. The sizes of the ellipses of the size of the circle diameter d are expressed by the relationship:

the major axis of ellipses 2 and 3 is equal to 1.07 d; minor axis of ellipses 2 and 3 is equal to 0.33 d.

the major axis of ellipses 2 and 3 is equal to 1.07 d; minor axis of ellipses 2 and 3 is equal to 0.33 d.

Note

Axonometric projection (from al-Greek. ἄξων axis, and ancient Greek. μετρέω "measure") is a method of image геометричеук4уеских items in the drawing using parallel projections.

Useful advice

The plane on which the projection is made is called an axonometric or an art. Axonometric projection is called rectangular, if a parallel projection projecting perpendicular to the picture plane ( =90 ) and oblique, if the rays make with the picture plane, the angle 0<

# Advice 4: How to draw axonometric

How to portray three-dimensional body on the plane of the paper? For this purpose, methods of perspective (from the Greek words "axis" — axon and "measure" — metreo) or projection. The easiest way to show this principle in the case of Cuba.

You will need

- - a sheet of paper,
- pencil,
- - line
- - protractor.

Instruction

1

The axonometric view can be made in a rectangular projection, and oblique. First, build the cube in a rectangular isometric projection, i.e. the projection occurs perpendicular to the plane of projection and the scale on each axis the same. Usually, for simplicity, the distortion factor is accepted equal 1.

Draw three axes. To do this with a ruler and pencil draw a vertical line from about the middle of the sheet up. Using the protractor from this line put angle of 120 degrees to both sides and make the appropriate line. Turned axis in space. Now on these axes put the same segments. From the points draw lines parallel to a coordinate axis. For this purpose again it is necessary from each point to postpone for 120 degrees in both directions. And on each beam with a ruler put a cut of the same magnitude as before. Now, connect the resulting points in parallel lines. Get the rectangular cube in isometric projection. It still bears the name orthogonal.

Draw three axes. To do this with a ruler and pencil draw a vertical line from about the middle of the sheet up. Using the protractor from this line put angle of 120 degrees to both sides and make the appropriate line. Turned axis in space. Now on these axes put the same segments. From the points draw lines parallel to a coordinate axis. For this purpose again it is necessary from each point to postpone for 120 degrees in both directions. And on each beam with a ruler put a cut of the same magnitude as before. Now, connect the resulting points in parallel lines. Get the rectangular cube in isometric projection. It still bears the name orthogonal.

2

To get a rectangular diametrical projection, and save the sizes in any two axes, and the remaining is distorted in a desired or arbitrary degree. In fact, the cube turns into a parallelepiped.

In addition there are rectangular oblique projection, in which projection occurs at any angle to the plane in addition to direct. Distinguish frontal isometric projection, front demetrescu and horizontal isometric projection.

In addition there are rectangular oblique projection, in which projection occurs at any angle to the plane in addition to direct. Distinguish frontal isometric projection, front demetrescu and horizontal isometric projection.

3

In order to build a front oblique projection, put the following angles between the axes: horizontal and vertical — 90 degrees, and the third axis tilt relative to the vertical to 135 degrees. In addition, allowed other deviations 120 or 150 degrees. After that, build a projection similar to the previous case, but only in the frontal projection will maintain the aspect ratio. For horizontal projection, the proportion will keep in the horizontal plane.

Note

During isometric projections is difficult to assess the depth and height of the graphic.

Useful advice

Axonometric view is most often used in an engineering drawing and CAD and in computer games for creating three-dimensional objects and panoramas.

# Advice 5: How to build isometric projection

All objects of reality exist in three-dimensional space. In the drawings they have to portray in a two dimensional coordinate system, and it does not give the viewer an adequate understanding of how the object looks in reality. Therefore, technical drawing, apply the projection, allowing to transfer the amount. One of them is called isometric.

You will need

- paper;
- - drawing utensils.

Instruction

1

Construction of isometric projections start with the arrangement of the axles. One of them is always vertical, and in the drawings it is usually designated as the Z axis, the Initial point is denoted as O. we Continue the axis OZ down.

2

The remaining two axes can be defined in two ways, depending on what drawing tools you have. If you have a protractor, set aside from the axis OZ in both sides of the angles equal to 120º. Swipe X and y axes.

3

If you have only a compass, draw a circle of arbitrary radius with center at point O. let's Continue the axis OZ until its second intersection with the circle and a dot, for example, 1. Spread the legs of the compasses at a distance equal to the radius. Draw a arc with center at point 1. Mark the point of intersection with the circle. They also indicate the directions of the axes X and Y. the left side of the Z-axis moves the X axis to the right - Y.

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*Construct an isometric*

**projection**of a plane figure. The coefficients of distortion in isometric along all axes are accepted 1. To construct a square of side a, put it away from point O of the axes X and Y and make the serifs. Swipe through the resulting points straight lines parallel to both these axes. Square in this projection looks like a parallelogram with angles of 120º and 60º.

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*To build the triangle, it is necessary to continue the X-axis so that a new part of the beam is located between the axes Z m Y. Divide the side triangle in half and mark the resulting dimension from the point On the X-axis in both directions. On the Y-axis put the height of the triangle. Connect the ends of the segment located on the X-axis, with the resulting point on the y-axis.*

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*In a similar way is constructed in an isometric projection and a trapezoid. On the X-axis in one and the other side of the point About set aside half of the base of this geometric figure, and the Y - axis height. Using the tick marks on the Y-axis guide line parallel to the X-axis, and mark on it in both directions half of the second founding. Connect the resulting points with ticks on the x-axis.*

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*A circle in isometric view looks like an ellipse. It can be constructed as the coefficient of distortion, and without. In the first case, the large diameter is equal to the diameter of the circle, and the small amount of 0.58 from him. When you build without accounting for this factor axis of the ellipse will be equal to, respectively, 1.22 and 0.71 diameter of the original circle.*

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Flat figures can be located in space both horizontally and vertically. As a basis we can take any axis, principles of construction remain the same as in the first case.

Useful advice

Dimensional object of complex shape, analyze and mentally divide it into more simple, is better every way to present a close to form geometric shapes. It may be necessary to postpone the dimensions are not on the axes, and parallel to them lines. The distance between these lines depend on the shape of the part. For example, one of the axes to postpone the distance from the edge to a recess or protrusion and draw a line parallel to the other two axes. Isometric projection of a fragment in this case is based not on the main grid, and additional.