You will need

- pencil;
- - the range;
- a pair of compasses;
- - a triangle.

Instruction

1

When designing on a plane axonometric projections N’ natural coordinate system Oxyz will axonometric coordinate system O ' x'y'z’, and the projection of any point of the axonometric projection or axonometric view A’ (figure 1). If you move from plot the horizontal projection of point A₁ of the new system, it will be so-called secondary projection and the point will have the axonometric coordinates.

2

The ratio of the axonometric coordinate is called the natural rates of distortion on the axes. They are designated u, v, w, and the magnitude of the angles between the axonometric axes respectively, α, β, and γ.

There are different types of perspective. In an engineering drawing often used rectangular and axonometric. Depending on the values of the distortion u, v, w rectangular axonometric view is divided into types:

- isometric – indicators of distortions in all three axes are equal u=v=w.

the diameter of the indicators of distortion are equal in two axes u=w≠v.

Typically, the metrics of distortion u, v, w have fractional values, but to simplify the build using the given values. For example, in the isometric view given coordinates equal natural.

There are different types of perspective. In an engineering drawing often used rectangular and axonometric. Depending on the values of the distortion u, v, w rectangular axonometric view is divided into types:

- isometric – indicators of distortions in all three axes are equal u=v=w.

the diameter of the indicators of distortion are equal in two axes u=w≠v.

Typically, the metrics of distortion u, v, w have fractional values, but to simplify the build using the given values. For example, in the isometric view given coordinates equal natural.

3

Example. To build a rectangular isometric projection of the prism (figure 2).

Complex drawing of a prism is specified in the system of axes xyz, the origin point O.

Complex drawing of a prism is specified in the system of axes xyz, the origin point O.

4

Construct axonometric axis O x'y'z’. The angles between the axes α, β, γ is equal to 120⁰ (figure 3).

5

In the axonometric axes build a secondary projection of the prism. Let the origin point O’ and the axis z’ passes through the major axis of the prism z. All sizes with comprehensive drawing, move on the axis x O y’ unchanged because the coefficients of distortion on the axes equal to 1.

From the point O’ put cut and О₁1₁ О₁4₁ axis x’. Mark the points 1’ and O’, and y’ put cut OA. Get the point O’, A’.

From the point O’ put cut and О₁1₁ О₁4₁ axis x’. Mark the points 1’ and O’, and y’ put cut OA. Get the point O’, A’.

6

On the plot cut 6₁5₁ parallel to the axis x₁, hence, the segment 6’5’ guide parallel to the axis x’. Put it distance А₁6₁ and А₁5₁. Mark the resulting point 6’, 5’, and similarly to construct symmetric points on the 2’, 3’.

7

Determine the position of the points 7’ and 8’, putting aside the size 7₁А₁. Thus, in axonometric projection is constructed of a secondary projection of the base of the prism– 1’,2’,...8’. From each point draw straight, parallel to the axis Z’. On these lines set the height of each point with the frontal projection of the prism on the plot.

From point 1’ put cut 1₂9₂, and from the points 2’ and 6’ – cut 2₂10₂. From the rest of the points 3’, 4’, etc. set aside marked with the height h. Combining all constructed points will get a perspective of the prism.

From point 1’ put cut 1₂9₂, and from the points 2’ and 6’ – cut 2₂10₂. From the rest of the points 3’, 4’, etc. set aside marked with the height h. Combining all constructed points will get a perspective of the prism.

# 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 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.