Methods of the image and their practical application are studied by descriptive geometry. Any subject has three dimensions. For the image of its spatial form on the plane it is necessary to know laws of transition from three-dimensional representation to two-dimensional, i.e. to be able to read the drawing.
It is required to you
- - pencil;
- - ruler;
- - compasses;
- - measuring instrument;
- - triangle.
Instruction
1. The basis of these laws is formed by a method of projections. In space are plane P’, S point – the center of projections and any point And (figure 1). If through points of S and A to draw a straight line before crossing with plane P’, the point will turn out And’. It is a projection of a point And in space on the plane of projections P’. The straight line of SA is called the projecting beam. The drawing constructed by means of design is projective.
2. If the projecting beams are perpendicular to the plane of projections, such projections are called rectangular. When determining position of a point in space on its projection of one plane of projections it is not enough. Therefore the second plane is entered in addition. The most acceptable is such arrangement of the planes of projections at which one of them is vertical, and another – is horizontal.
3. The plane of projections located horizontally is called the horizontal plane of projections and is designated P ₁. The vertical plane located before the observer is called the frontal plane of projections and is designated P ₂. Plane P ₂ is perpendicular to plane P ₁ (figure 2). The straight line of mutual crossing of two planes of projections is called an axis of projections x ₁₂.
4. If to assume that the plane of the drawing coincides with the frontal plane of projections, then the horizontal plane of projections P ₁ will be perpendicular to the drawing plane.
5. Planes P ₁ and P ₂ have to coincide with the drawing plane at the same time. For this purpose plane P ₁ rotate around axis x ₁₂ before combination with plane P ₂ (figure 3).
6. On the drawing planes P ₂ and P ₁ are not designated, and only the horizontal straight line – an axis of projections x ₁₂ is drawn (figure 4).
7. The point And is located in the system of planes P ₁ and P ₂ (figure 5). For creation of projections of a point And the projecting AA beams ₂ perpendicularly P ₂ and AA ₁ – perpendicular to plane P ₁ are carried out. And ₂ – a frontal projection of a point And, and And ₁ – a horizontal projection of a point And in space.
8. Rectangular projections of a point to two mutually perpendicular planes of projections are called orthogonal projections.AA ₁ – distance from a point And to plane P ₁; AA ₁ = AA ₁₂. AA ₂ – distance from a point And to plane P ₂; AA ₂ = AA ₁₂.
9. The drawing on which the point projections combined with one plane are presented is called the complex drawing (epyury). On the complex drawing the horizontal and frontal projections of one point are located on the AA vertical communication line ₁, perpendicular to an axis of projections x ₁₂.
10. Example. To construct the complex drawing of a point And, remote from plane P ₁ on 30 mm, and from plane P ₂ – on 20 mm (figure 6).
11. Carry out axis x ₁₂. Perpendicularly to an axis build the line of vertical communication. From an axis of projections postpone the piece equal to 30 mm, – receive a frontal projection of a point And ₂. Similarly postpone a piece And ₁₂ And ₁, equal 20 mm, – receive a horizontal projection of a point the APostroennyy image is the required complex drawing and defines the provision of a point And in space.