When studying drawing and engineering graphics everyone surely faces need of creation of details for an isometric projection. To draw an isometry of any subject, it is necessary to understand its basic principles.

## It is required to you

- — leaf of a Whatman paper;
- — pencil;
- — ruler;
- — compasses;
- — protractor.

## Instruction

1. Construct by means of a line and a protractor or compasses and a line of an axis of coordinates for a rectangular (otrogonalny) isometric projection. In this kind of an axonometrical projection all three axes — OX, OY, OZ — form among themselves corners in 120 °, at the same time the axis of OZ has vertical focus.

2. For simplicity you draw an isometric projection without distortions on axes as it is accepted to equate isometric coefficient of distortion to unit. By the way, the word "isometric" in translation from Greekmeansof "equal size". Actually at display of a three-dimensional object to the plane the relation of length of any projected piece parallel to a coordinate axis, to the valid length of this piece equally for all three axes 0.82. Therefore the linear sizes of a subject in an isometry (at the accepted distortion coefficient) increase by 1.22 times. At the same time the image remains correct.

3. Begin to project a subject on the axonometrical plane from its top side. Measure on OZ axis from the center of crossing of axes of coordinates detail height. Carry out by thin lines of axis X and Y through this point. From the same point postpone a half of a piece of length of a detail on one axis (for example, on axis Y). Carry out through the found point a piece of the necessary size (detail width) parallel to other axis (OX).

4. Now along other axis (OX) postpone a half of width. Through this point carry out a piece of the necessary size (detail length) parallel to the first axis (OY). Two nacherchenny pieces have to be crossed. Complete the rest of the top side.

5. If in this side there is a round opening, draw it. In an isometry the circle is represented in the form of an ellipse because we look at it at an angle. Calculate the sizes of axes of this ellipse proceeding from diameter of a circle. They are equal: a = 1.22D and b = 0.71D. If the circle is located on the horizontal plane, an axis and an ellipse always horizontal, axis b — vertical. At the same time the distance between ellipse points on an axis of X or Y is always equal to diameter of a circle of D.

6. Draw the vertical edges equal to detail height from three corners of the top side. Connect edges through their lower points.

7. If the figure has a rectangular opening, draw it. Postpone from the center of an edge of the top side vertical (parallel to axis Z) a piece of the necessary length. Through the received point draw a piece of the required size parallel to the top side, so and axis X. From extreme points of this piece draw vertical edges of the necessary size. Connect their lower points. Carry out an internal edge of an opening which has to be parallel to axis Y from the lower right point of the drawn rhombus.