you need

- - pencil;
- - line;
- - compasses;
- - meter;
- - triangle.

Guide

1

basis of these laws is the method of projections.

In the space are plane P ', the point S - projection center and an arbitrary point A (Figure 1).If through the points S and A draw a line to the intersection with the plane P ', you get the point A'.It is the projection of A in the space of projections on a plane P '.Direct SA called projecting beam.Drawing, built with the help of design, it is a projection.

In the space are plane P ', the point S - projection center and an arbitrary point A (Figure 1).If through the points S and A draw a line to the intersection with the plane P ', you get the point A'.It is the projection of A in the space of projections on a plane P '.Direct SA called projecting beam.Drawing, built with the help of design, it is a projection.

2

If projecting rays are perpendicular to the plane of projection, such projections are called rectangular.

When determining the position of a point in space at one of its projection plane of projection insufficient.The
refore introduced an additional second plane.The most suitable is an arrangement of projection planes, wherein one of them is vertical, and the other - the horizontal.

When determining the position of a point in space at one of its projection plane of projection insufficient.The

3

projection plane arranged horizontally is called the horizontal plane of projection, and is denoted P₁.

vertical plane situated in front of the observer, called the frontal plane of projection and is designated P₂.The plane perpendicular to the plane P₁ P₂ (figure 2).Direct mutual intersection of the two planes of projection is called the axis of projections x₁₂.

vertical plane situated in front of the observer, called the frontal plane of projection and is designated P₂.The plane perpendicular to the plane P₁ P₂ (figure 2).Direct mutual intersection of the two planes of projection is called the axis of projections x₁₂.

4

Assuming that the plane of the drawing coincides with the frontal plane of projection, the H plane P₁ is perpendicular to the plane of the drawing.

5

planes P₁ and P₂ should simultaneously coincide with the plane of the drawing.For this plane P₁ is rotated around the axis x₁₂ to align with the plane P₂ (figure 3).

6

the drawing are denoted by the plane P₂ and P₁ and carried out only horizontal line - axis projection x₁₂ (Figure 4).

7

Point A is located in the planes P₁ and P₂ (figure 5).To construct the projections of A held projecting rays AA₂ perpendicular P₂ and AA₁ - perpendicular to the plane P₁.A₂ - front view of a point A and A₁ - horizontal projection of point A in space.

8

rectangular projection of two mutually perpendicular planes projections called orthogonal projections.

AA₁ - the distance from point A to the plane P₁;AA₁ = A₂A₁₂.

AA₂ - the distance from point A to the plane P₂;AA₂ = A₁A₁₂.

AA₁ - the distance from point A to the plane P₁;AA₁ = A₂A₁₂.

AA₂ - the distance from point A to the plane P₂;AA₂ = A₁A₁₂.

9

drawing, which shows the projection of the point, combined with a plane called the complex drawing (course).In the drawing a horizontal and integrated front projection located at one point of the vertical link A₂A₁ perpendicular to the coordinate axis x₁₂.

10

example.Build an integrated drawing point A remote from the plane P₁ 30 mm, and the plane P₂ - 20 mm (Figure 6).

11

Spend axis x₁₂.Perpendicular to the axis line build vertical ties.From coordinate axis set aside a segment equal to 30 mm, - get a front projection of A₂.Similarly A₁₂A₁ lay off of 20 mm - get a horizontal projection of a point A₁

imaging is the desired complex drawing and defines the position of the point A in space.

imaging is the desired complex drawing and defines the position of the point A in space.