Projecting a presentation for a lesson on the topic. Drawing lesson "rectangular projection onto three mutually perpendicular projection planes" Presentation projection

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Slide captions:

Projection types of projection, projection onto one projection plane

Projection is the process of constructing an image of an object on a plane. The resulting image is called a projection of the object. The word projection comes from the Latin projection - throwing forward. In this case, we look (take a glance) and display what we see on the plane of the sheet. PROJECTION

PROJECTION OF POINT a A H Projection plane (H) Projecting ray (Aa) Projected point (A) Projection of point A on the plane (a)

PROJECTION Projection is the process of constructing a projection of an object. Projection plane – the plane on which the projection is obtained. The projecting ray is a straight line with the help of which the projection of vertices, faces, and edges is constructed.

TYPES OF PROJECTION

CENTRAL PROJECTION If the projecting rays emanate from one point, then such a projection is called central. The point from which the projection emerges is the center of projection. EXAMPLE: photographs and film footage, shadows cast from an object by the rays of an electric light bulb.

PARALLEL PROJECTION If the projecting rays are parallel to each other, then such projection is called parallel. An example of a parallel projection can be considered the sun's shadows of objects, as well as streams of rain.

PARALLEL PROJECTION Oblique projection - the projecting rays are parallel and fall on the projection plane at an acute angle. Rectangular projection - the projecting rays are parallel and fall on the projection plane at an angle of 90 degrees.

PROJECTION ON ONE PLANE OF PROJECTIONS The plane located in front of the viewer is called frontal, and is designated by the letter V. The object is placed in front of the plane so that its two surfaces are parallel to this plane and are projected without distortion.

DETAIL DRAWING Based on the resulting projection, we can judge the height, length and diameter of the hole. What is the thickness of the object? s6

What kind of “projection” did the water jets give in each case? Bucket in the shower Bucket in the heavy rain

CONSISTENCY EXERCISE No. New concepts Definition 1 Image on a plane. 2 The plane on which the projection is obtained. 3 A straight line with which an object is projected onto a plane. 4 Projection in which the projecting rays come out from one point. 5 Projection in which the projecting rays are parallel to each other. 6 Projection, in which the projecting rays fall on the projection plane at right angles. 7 Projection in which the projecting rays do not fall on the projection plane at right angles. Projection beam, central projection, projection, oblique projection, plane projection, parallel projection, rectangular projection. Projection. Projection plane. Projection beam. Central projection. Parallel projection. Rectangular projection. Oblique projection.

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The straight line is perpendicular to the frontal plane of projections P2 and parallel to P1 and P3. The frontal projection A2 B2 degenerates into a point. On P1 and P3 the straight line is projected in natural size. Projection A1 B1 is perpendicular to the x coordinate axis Spatial picture Complex drawing A B x Frontally projecting straight line (P2) P 1

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x Spatial picture Complex drawing A B Horizontally projecting straight line (P1) The straight line is perpendicular to P1, therefore its horizontal projection A1 B1 degenerates into a point. With respect to P2 and P3, the straight line is parallel and is depicted in full size on these projection planes. Projection A2 B2 is perpendicular to the coordinate axis x P 2 1 P 1

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All points of straight line AB are equidistant from the profile plane of projections P3 and have the same coordinate x (x = const). Horizontal A1 B1 and frontal A2 B2 straight line projections are perpendicular to the x axis. Profile projection A3 B3, angles and have natural size on P3 Spatial picture Complex drawing z O x y1 y3 B A p Level lines: profile straight line (p P3) B 3 z y

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Spatial picture Complex drawing x B f Straight lines: frontal (f P2) A All points of straight line AB are equidistant from the frontal plane of projections P2 and have the same coordinate y (y= const). The horizontal projection of the front A1 B1 is parallel to the x axis. Frontal projection of the front A2 B2, angles and are depicted in natural size on P2 y=const y=const

5 slide

All points of straight line AB are equidistant from the horizontal projection plane P1 and have the same applicate z= const. The frontal projection of the horizontal A2 B2 is parallel to the x axis. Horizontal projection of the horizontal line A1 B1, corners and are depicted in full size on P1 Spatial picture Complex drawing x h B A Straight lines: horizontal (h P1) z=const

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In the drawing, the projections of a segment of a straight line in general position have distorted metric characteristics; none of its projections are parallel to the coordinate axes or perpendicular to them. The straight line in general position is inclined to all planes of the projections. The straight line in general position k

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For a straight line in a particular position, the natural values ​​of any of its characteristics are determined in a complex drawing. The level line is projected without distortion onto the projection plane to which it is parallel. One of the projections of the projecting line degenerates into a point. The line of particular position is parallel or perpendicular to one of the projection planes. The line parallel to one of the projection planes is called the level line: Horizontal level line (horizontal) h P1 Frontal level line (frontal) f P2 Profile line p P3 A straight line perpendicular to one of the projection planes is called a projecting straight line: Horizontally projecting straight line P1 Frontally projecting straight line P2 Profile projecting straight line P3 Direct lines of particular position

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Metric characteristics of the segment: current – natural size of the segment; – angle of inclination of the segment to the plane P1; – angle of inclination of the segment to the plane P2; – angle of inclination of the segment to the plane P3 B A Position of the straight line relative to the projection planes N.V. A 2 B 1 B 2 A 1 B 3 A 3 z y

Slide 9

To construct a profile projection of a straight line on an axisless drawing, draw the drawing constant k at an angle of 45. With its help, along communication lines, a profile projection of straight line A3 B3 is obtained, the position of which is determined by the differences in coordinates z and y k 45 An axle-free drawing is a drawing in which there are no projection axes. An axle-free drawing 45 z B 1

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Projections of line m pass through pairs of corresponding projections of points: horizontal projection of line m1 – through A1 and B1; frontal projection of straight line m2 – through A2 and B2 x Spatial picture Complex drawing Line projections x O A B m

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The position of line m in space is determined by two arbitrary points A and B lying on this line. This is the most convenient way to define a straight line. A straight line m is considered given if projections of its two points A and B are constructed on a complex drawing. Spatial picture Projections of the straight line O A B m

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Slide 13

Metric problems Task 1. Determine the distance from point A to straight line l by changing the projection planes P4 P1 P4 l 2. P5 P4 P5 l AK - the required distance. With the second transformation, we introduce a new projection plane P5 perpendicular to straight line l so that the straight line takes the projecting position. On P5 we determine the natural value A5 K5 of the perpendicular AK P1 P2 x l2 A1 l1 A2 P4 P5 x2 l4 P1 P4 x1 K1 K2

Slide 14

Metric problems Task 1. Determine the distance from point A to straight line l by changing the projection planes. The required distance is a perpendicular. Let us introduce a new projection plane P4 parallel to straight line l so that the straight line occupies a particular position of the level. According to the theorem on the projection of right angles, the projection of the required distance A4K4 l4 is determined on the projection plane P4 P4 P1 P4 l P1 P2 x l2 A1 l1 A2 l4 P1 P4 x1

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The relative position of two lines. Intersecting lines do not intersect and are not parallel to each other. Projections of intersecting lines can be parallel, because the lines m and n lie in parallel planes. Projections of intersecting lines may have an intersection, because lines m and n are not parallel to each other. 1 and 2 – competing points belonging to different lines m n m1 n1 m2 n2 x m 1 m n x n 1 2

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The relative position of two lines. Parallel lines do not have common points. Projections of parallel lines do not intersect. Projections of lines of the same name are parallel or coincide if the parallel lines lie in the projecting plane n m x n 1 m n m1 n1 m2 n2 m 1 n 1 m 2 n 2 m 2 n 2 m 1

Slide 17

The relative position of two lines Intersecting lines have one common point B A D C K x C 2 AB CD = K(K1, K2) A1 B1 C1 D1 = K1 A2 B2 C2 D2 = K2 The intersection point K of lines AB and CD is projected into the intersection points of the corresponding projections straight lines: on P1 - this is point K1; on P2 - point K2. The intersection points K1 and K2 of the same line projections lie on the same connection line B 1 A 1 A 2 B 2 D 1 D 2 C 2 C 1 A 1 A 2 B 2 B 1 D 2 C 1 D 1

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Determination of the natural size of a segment and its angles of inclination to the projection planes Diagram: Г2 Г2 To transfer the straight line to a horizontal position, the frontal projection of the straight line (A2 В2 А2 В2) is placed parallel to the x-axis. New projections of points A1 and B1 are located on the corresponding traces of the frontal planes of the level Ф(Ф1) and Ф(Ф1). On P1 we have n.v. line segment and angle

Slide 19

Determination of the natural size of the segment and its angles of inclination to the projection planes x Scheme: D2 The horizontal projection of the straight line (A1 B1 A1 B1) is placed parallel to the x axis. The frontal projection (determining the NV of the segment and angle) is set by new projections of points A2 and B2, located on the corresponding traces of the horizontal planes of the level Г(Г2) and Г(Г2)

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Determination of the natural size of a segment and its angles of inclination to the projection planes. This segment AB occupies a general position; we transform it into a frontal line of the level by moving the ends of the segment along the horizontal planes of the level according to the diagram

21 slides

Determination of the natural size of a segment and its angles of inclination to the projection planes Scheme: To determine the angle, the straight line AB must be rotated around the i-axis P2 to a horizontal position. The axis passes through point A, which is stationary. Point B2 rotates along a circular arc with the center at point i2 to position B2 A2 of the x axis. On P1, the angle and segment AB are not distorted

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Determination of the natural size of a segment and its angles of inclination to the projection planes Scheme: To simplify, the horizontally projecting axis of rotation l is drawn through point B, which remains stationary. Point A1 describes an arc of a circle with center at point l1 so that B1 A1 x axis. Then straight line AB will take the position of the front. On P2, the angle and segment AB are not distorted

Slide 23

Determination of the natural size of the segment and its angles of inclination to the projection planes x A1 B1 A2 B2 P2 P1 x1 P4 P1 A4 B4 The x2 axis of the new projection plane P5 will be drawn parallel to the frontal projection of the segment A2 B2. This transformation stores the y-coordinates of the points. On P5, the natural size of the segment and its angle of inclination to the projection plane are determined P2 x2 P2 P5 A5 B5 Scheme:

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Definition of present day segment and its angles of inclination to the projection planes (method of replacing projection planes) The x1 axis of the new projection plane P4 will be drawn parallel to the horizontal projection of the segment A1 B1. This transformation preserves the z-coordinates of the points. On P4, the natural size of the segment and its angle of inclination to the projection plane are determined P1 x1 P4 P1 A4 B4 Scheme.

Sections: Technology

Goals and objectives of the lesson:

educational: show students how to use the rectangular projection method when making a drawing;

The need to use three projection planes;

Create conditions for the formation of skills to project an object onto three projection planes;

developing: develop spatial concepts, spatial thinking, cognitive interest and creative abilities of students;

educating: responsible attitude towards drawing, to cultivate a culture of graphic work.

Methods and techniques of teaching: explanation, conversation, problem situations, research, exercises, frontal work with the class, creative work.

Material support: computers, presentation “Rectangular projection”, tasks, exercises, exercise cards, presentation for self-test.

Lesson type: lesson to consolidate knowledge.

Vocabulary work: horizontal plane, projection, projection, profile, research, project.

During the classes

I. Organizational part.

State the topic and purpose of the lesson.

Let's carry out lesson-competition, for each task you will receive a certain number of points. Depending on the points scored, a grade for the lesson will be assigned.

II. Repetition of projection and its types.

Projection is the mental process of constructing images of objects on a plane.

Repetition is carried out using presentation.

1. Students are asked problematic situation . (Presentation 1)

Analyze the geometric shape of the part on the front projection and find this part among the visual images.

From this situation it is concluded that all 6 parts have the same frontal projection. This means that one projection does not always give a complete picture of the shape and design of the part.

What is the way out of this situation? (Look at the part from the other side).

2. There was a need to use another projection plane. (Horizontal projection).

3. The need for a third projection arises when two projections are not enough to determine the shape of an object.

Sizing:

• on the frontal projection – length and height;
• on a horizontal projection – lenght and width;
• on profile projection – width and height.
  

Conclusion: this means that in order to learn how to make drawings, you need to be able to project objects onto a plane.

Exercise 1

Fill in the missing words in the definition text.

1. There are _______________ and ______________ projection.

2. If ______________ rays come out from one point, projection is called ______________.

3. If ______________ rays are directed parallel, projection is called _____________.

4. If ______________ rays are directed parallel to each other and at an angle of 90 ° to the projection plane, then the projection is called ______________.
5. A natural image of an object on a projection plane is obtained only with ______________ projection.

6. The projections are located relative to each other______________________________.

7. The founder of the rectangular projection method is _______________

Task 2. Research project

Match the main types indicated by numbers with the parts indicated by letters and write the answer in your notebook.

Fig.4

Task 3

An exercise to review knowledge of geometric bodies.

Using the verbal description, find a visual image of the part.

Description text.

The base of the part has the shape of a rectangular parallelepiped, the smaller faces of which have grooves in the shape of a regular quadrangular prism. In the center of the upper face of the parallelepiped there is a truncated cone, along the axis of which there is a through cylindrical hole.

Rice. 5

Answer: part No. 3 (1 point)

Task 4

Find the correspondence between the technical drawings of the parts and their frontal projections (the direction of projection is marked with an arrow). Based on the scattered images of the drawing, make a drawing of each part, consisting of three images. Write your answer in the table (Fig. 129).

Rice. 6

III. Practical work.

Task No. 1. Research project

Find the frontal and horizontal projections for this visual image. Write the answer in your notebook.

Assessment of work in the lesson. Self-test. (Presentation 2)

The points for grading the first part of the work are written on the board:

23-26 points “5”

19-22 points “4”

15 -18 points “3”

Task No. 2. Creative work and verification of its implementation
(creative project)

Draw the frontal projection into your workbook.
Draw a horizontal projection, changing the shape of the part in order to reduce its mass.
If necessary, make changes to the front projection.
To check the completion of the task, call one or two students to the board to explain their solution to the problem.

(10 points)

IV. Summing up the lesson.

1. Assessment of work in the lesson. (Checking the practical part of the work)

V. Homework assignment.

1. Research project.

Work according to the table: determine which drawing, designated by a number, corresponds to the drawing, designated by a letter.

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Slide captions:

RECTANGULAR PROJECTION

RECTANGULAR PROJECTION V The vertical plane of projections (V), located in front of the viewer, is called frontal. To construct a projection of an object, we draw projecting rays perpendicular to the plane V through the vertices and points of the holes of the object

FRONTAL PROJECTION V S 6 Based on the resulting projection, we can judge two dimensions of an object - height and width. So that such an image can be used to judge the shape of a flat part, it is supplemented with an indication of the thickness (S) of the part

Analyze the geometric shape of the part on the front projection and find this part among the visual images.

A drawing presented in three projections or views gives the most complete idea of ​​the shape and design of an object and is called a COMPLEX DRAWING Frontal Front view Profile Left view Horizontal Top view

X One projection does not always determine the geometric shape of an object. In this case, it is possible to construct two rectangular projections of an object onto two mutually perpendicular planes: frontal (V) and horizontal (H). The line of intersection of the planes (X) is called the axis of projections

RECTANGULAR PROJECTION V H The constructed projections turned out to be located in space in different planes (vertical and horizontal). To obtain a drawing of an object, both planes are combined into one

RECTANGULAR PROJECTION V H

RECTANGULAR PROJECTION V H

Analyze the geometric shape of the part on the frontal and horizontal projections and find this part among the visual images.

Determine which part this drawing corresponds to

RECTANGULAR PROJECTION V H W In order to reveal the shape of an object, two projections are not always enough. In this case, you need to build another plane. The third projection plane is called the profile plane, and the projection obtained on it is called the profile projection of the object. It is designated by the letter W

To obtain a drawing of an object, the W plane is rotated 90 0 to the right, and the H plane is rotated 90 0 down

RECTANGULAR PROJECTION H W V

RECTANGULAR PROJECTION H W V

RECTANGULAR PROJECTION The resulting drawing contains three rectangular projections of the object: frontal, horizontal and profile. Projection axes and projecting rays are not shown in the drawing

RECTANGULAR PROJECTION 76 78 18 30 58 60 F 30 26 18 Chertil Petrov V. Checked School No. 1274 class. 9 B steel 1:1 Stand In the drawing, the projections are placed in a projection connection. A drawing consisting of several rectangular projections is called a drawing in the system of rectangular projections

TASK No. 3 The arrows show the projection directions. The projection of the part is indicated by numbers. a) which projection (indicated by a number) corresponds to each direction of projection (indicated by a letter) b) name projections 1,2,3.

Three details are given, different in shape, which are projected onto two projection planes in exactly the same way. In this case, the profile projection of the part makes it possible to accurately determine the shape of each of them.

QUESTIONS FOR CHECKING Is one projection of an object always sufficient in a drawing? What are projection planes called? How are they designated? What are the names of the projections obtained by projecting an object onto three projection planes? How are these planes located relative to each other?

TYPES OF PROJECTION

Presentation on drafting

Understanding Projection .

• Images of objects in drawings, in accordance with the rules of the state standard, are performed using the method (method) of rectangular projection. Projection is the process of constructing a projection of an object. How are projections made? Consider this example.
• Let us take an arbitrary point A and some plane H in space (Fig. 37). Let us draw a straight line through point A so that it intersects the plane H at some point a. Then point a will be the projection of point A. The plane on which the projection is obtained is called the projection plane. The straight line Aa is called the projecting ray. With its help, point A is projected onto plane H. Using this method, projections of all points of any spatial figure can be constructed.

Rice. 37. Obtaining projections of a point

Rice. 38. Projection of a figure

• In the future, we will denote points taken on an object by capital letters, and their projections by lowercase letters. The projection of point A onto a given plane will be point 0 as a result of the intersection of the projecting ray Aa with the projection plane. The projections of points B and C will be points b and c. By connecting points a, b and with line segments on the plane, we obtain figure abc, which will be the projection of the given figure ABC.
• An idea of ​​projection can be obtained by looking at the shadows of objects. Let's take, for example, a wire model of a prism (Fig. 39). Let this model, when illuminated by sunlight, cast a shadow on the wall. The shadow thus obtained can be taken as the projection of a given object.

Rice. 39. Getting the model's shadow

Center and parallel projection

• If the projecting rays, with the help of which the projection of an object is constructed, come from one point, the projection is called central (Fig. 40). The point from which the rays originate is called the center of projection. The resulting projection is called central .

Rice. 40. Central projection

• The central projection is often called perspective. Examples of central projection are photographs and film frames, shadows cast from an object by the rays of an electric light bulb, etc. Central projections are used in drawing from life.
• If the projecting rays are parallel to each other (Fig. 41), then the projection is called parallel. and the resulting projection is parallel. An example of parallel projection can be considered the solar shadows of objects (Fig. 39).

• It is easier to construct an image of an object in a parallel projection than in a central one. In drawing, such projections are used to construct drawings and visual images.
• With parallel projection, all rays fall on the projection plane at the same angle. If it is any acute angle, as in Figure 41, then the projection is called oblique .

Rice. 41. Oblique projection

• In the case when the projecting rays are perpendicular to the projection plane (Fig. 42), i.e., they make an angle of 90° with it, projection is called rectangular. The resulting projection is called rectangular.

Rice. 42. Rectangular projection

• What is projection? Give examples of projections.
• How to construct a projection of a point on a plane? projection of the figure?
• What projection is called central, parallel, rectangular, oblique?
• What projection method is used when constructing a drawing and why?