Axonometry or axonometric projection is a parallel projection onto one plane of any geometric element and the coordinate axes to which this geometric element belongs. On a complex drawing (diagram) in orthogonal projections, the position of a point, line, surface relative to the projection planes is displayed. The distance of these geometric elements from the projection planes are their natural coordinates.

## It is necessary

- - pencil;
- - ruler;
- - compasses;
- - triangle.

## Instructions

### Step 1

When projecting axonometric projections P 'of the natural coordinate system Oxyz onto the plane, the axonometric coordinate system O'x'y'z' will be obtained, and the projection of any point will be an axonometric projection or axonometry A '(Figure 1). If you transfer from the diagram the horizontal projection of the point A эп to the new system, this will be the so-called secondary projection and the point will have axonometric coordinates.

### Step 2

The ratio of axonometric coordinates to natural coordinates is called the distortion indicators along the axes. They are denoted by u, v, w, and the angles between the axonometric axes are respectively α, β and γ.

There are different types of axonometry. In mechanical engineering, rectangular axonometry is often used. Depending on the magnitude of the distortion indicators u, v, w, rectangular axonometry is divided into types:

- isometry - distortion indices along all three axes are equal to each other u = v = w.

- dimetry - distortion indices are equal along two axes u = w ≠ v.

Typically, the distortion indicators u, v, w have fractional values, but to simplify the constructions, their reduced values are used. For example, in isometry, the given coordinates are equal to natural ones.

### Step 3

Example. Construct a rectangular isometric projection of the prism (Figure 2).

The complex drawing of the prism is specified in the xyz axis system, the origin is the point O.

### Step 4

Plot axonometric axes O'x'y'z '. The angles between the axes α, β, γ are equal to 120⁰ (Figure 3).

### Step 5

In axonometric axes, construct a secondary projection of the prism. Let the origin point O 'and the z-axis pass through the main z-axis of the prism. Transfer all dimensions from the complex drawing to the x'O'y 'axis without changes, since the distortion coefficients along the axes are equal to 1.

From point O ’mark the segment O₁1₁ and O₁4₁ along the x’ axis. Mark points 1 'and O', and along the y-axis mark the line segment О₁А₁. Get points O ', A'.

### Step 6

On the diagram, the segment 6₁5₁ is parallel to the x₁ axis, which means that the segment 6'5 'is drawn parallel to the x x axis. Set aside the distance А₁6₁ and А₁5₁ on it. Mark the obtained points 6 ', 5' and similarly construct the points 2 ', 3' symmetrical to them.

### Step 7

Determine the position of points 7 'and 8', setting aside the dimensions 7 'A'. Thus, in the axonometric projection, a secondary projection of the base of the prism is built - 1 ', 2', … 8 '. Draw straight lines from each point parallel to the Z 'axis. On these lines, plot the height of each point from the frontal projection of the prism on the plot.

From point 1 'set aside line segment 1₂9₂, and from points 2' and 6 '- line segment 2₂10₂. From other points 3 ', 4', etc. set aside the marked height h. Having connected all the constructed points, you will receive an axonometry of this prism.