Lesson topic: Analysis of the geometric shape of an object.
Lesson objectives:
- Master practical skills in analyzing the geometric shapes of objects based on their characteristic features.
- Learn to identify the simplest geometric bodies in real details.
Lesson objectives:
- Educational –
- start forming new concepts geometric body, geometric shape analysis;
- Continue to develop students’ ability to draw drawings of parts.
- Educational –
- cultivate the need to work and achieve the best results in studies.
- Developmental –
- continue the formation of logical thinking techniques (comparison, analysis, synthesis).
Equipment:
- for the teacher - three-dimensional wooden models of geometric bodies: cube, prism, pyramid, ball, cylinder, cone; table with a visual representation of the “support” part. Photo of the Nevyansk Tower.
- for students - handouts in the form of task cards containing visual images of geometric bodies; parts consisting of geometric bodies.
Lesson structure:
- Organizational part of the lesson 1–2 min.
- Updating knowledge 3–5 min.
- Learning new material 10 min.
- Reading drawings (oral work) 5 min.
- Individual graphic work 10 min.
- Summarizing what has been learned 5 min.
- Homework 3 min.
DURING THE CLASSES
Announce the topic and goals of the lesson.
– I want to start the lesson with information that, at first glance, has nothing to do with drawing. In order for the churches not to get lost in space and to be clearly visible from afar, it was necessary to find an expressive silhouette for them. The search for it led the architects to a compositional solution for churches with a tiered top made of a series of decreasing octagons.
The prototype of ancient bell towers was a military-defensive watchtower, which was built according to the traditional scheme - an eight on a four.
The leading role in the architectural appearance of the Ural city of Nevyansk, located in our region, is played by the famous “leaning” tower<Annex 1
>. It was built in 1725 and can be seen from any street in the city. It is believed that it was originally a watchtower. The height of the tower is 57.5 meters. The tower consists of four parts: a “quadrangle”, which occupies half the height. On the quadrangle, one on top of the other, there are three “octagons”. The tower is crowned with a “tent”. In drawing language, a tower is a combination of geometric bodies. But we must find out which ones by the end of the lesson.
(Write the topic of the lesson in your notebook)
Geometric body- this is a closed part of space, limited by flat and curved surfaces.
The shape of each body has its own characteristic features.
On your desks you have cards describing these geometric bodies. Let's get to know them better.<Appendix 2
>
(The teacher shows a model of a geometric body, one of the students reads out the definition and essential features of the body from the card)
- Ex. 4 from the workbook<Appendix 3 >. Using these geometric bodies, write and draw household items that have the shape of the indicated geometric bodies and their combinations.
In engineering, the shape of a part is often compared with simpler shapes - geometric bodies, and also the shapes of geometric bodies are used to describe the shape of more complex parts.
Any simple form technical details can be represented as geometric body shape(for example, the shape of a technical part “axle” can be represented as a cylinder shape - see Figure 73 in the textbook), and shape of a complex product- How combination of shapes of geometric bodies(for example, the “fork” part - see Fig. 73 in the textbook, ..., the tower, which we talked about at the beginning of the lesson). The considered approach to the study of parts is based on an analysis of its geometric shape.
Geometric shape analysis of an object is a mental dissection of an object into its constituent geometric bodies. (Write in notebook)
Let's consider how the geometric shape of an object is analyzed using a visual image of the part. We mentally divide the part into simple geometric bodies, name them and tell how they are located relative to each other in space.
For example, the “Support” part (poster on the board) consists of a rectangular parallelepiped (1) with five through cylindrical holes. In the center of the upper face of the rectangular parallelepiped there is a quadrangular prism (2) with a through cylindrical hole, the axis and diameter of which coincide with the axis and diameter of the hole of the part (1). The parallelepipeds are connected to each other by two stiffening ribs (3) in the shape of triangular prisms, which ensures their stable fastening.
By using the method of dividing a part into simple geometric bodies, you can learn to quickly, correctly read drawings and execute them competently.
Exercise: use a visual image of the part to analyze its shape (visual image of the part - poster on the board).
Answer: at the base of the part there is a rectangular parallelepiped with a through cylindrical hole in the center. Two more rectangular parallelepipeds are adjacent to it at the ends. One has a through cylindrical hole, the other has a rectangular cutout.
- Ex. 6 from the workbook<Appendix 4 >. Mentally divide these objects into geometric bodies and write down their names.
Names of elements of geometric bodies. Base, faces, edges, vertex, generatrix (the teacher shows models of geometric bodies, see the picture in the textbook).
- Ex. 7 from the workbook<Appendix 5 >. List and write down the names of the geometric bodies that make up the shape of the part.
- Now let's go back to the beginning of the lesson. As noted by the study, the Nevyansk Tower “is related to the tiered towers and bell towers of Ancient Rus', but is distinguished by its emphasized severity.” I'll remind you of her (read information from the board). <Appendix 6 >
– Let’s get acquainted with the definitions of “quadruple”, “octagon”, “tent” - I gave several children the task of finding the meanings of these words in dictionaries. (read out, post on the board)
So how can you now, having become familiar with geometric bodies, analyze the geometric shape of the Nevyansk Tower?
Answer: the tower consists of four parts - a regular quadrangular prism and three octagonal prisms, standing on top of each other. The tower is crowned by an octagonal pyramid.
– What other geometric bodies did you meet today? (Ball, cube, cone, cylinder)
– Why do we need to analyze the geometric shape of an object? ( To read and execute quickly and correctly).
Homework: in the textbook §10, pp. 58 – 61. Come up with and create a visual representation of a toy, the shape of which consists of simple geometric bodies (show example). If it is difficult to complete the drawing, you can sculpt a toy from plasticine.
Literature:
- Textbook for grades 7-8 of general education institutions “Drawing”, authors: A.D. Botvinnikov, V.N. Vinogradov, I.S. Vyshnepolsky.
- Workbook No. 3 on drawing for grade 7, authors: N.G. Preobrazhenskaya, T.V. Kuchukova, I.A. Belyaeva.
Municipal educational institution "Secondary school No. 35"
Analysis of the geometric shape of an object
(multimedia lesson)
9th grade
Prepared by: Salmina Natalya Anatolyevna
2005 – 06 academic year
Topic: Analysis of the geometric shape of an object
Goals : recall geometric bodies, give the concept of analyzing the shape of an object; teach students to find simple geometric bodies in any technical detail, read and construct their drawings; develop spatial concepts and thinking; cultivate a sense of time and responsibility in the team.
Lesson type: lesson of learning new material.
Methods:quiz, conversation, reading and completing drawings, exercises, working with a textbook.
Material support:models of geometric bodies, formation of geometric bodies, technical details.
DURING THE CLASSES.
- Organizational part.
- Message of the topic, lesson objectives
Lesson topic: “Analysis geometric shape of an object." We must remember the basic geometric bodies, learn how to construct their projections, and use this information when reading the drawing. (slide number 1)
- Learning new material.
- Conducting a quiz "Remember geometric bodies».
Teacher: Before considering a new topic, we organize a quiz “Remember geometric bodies” between three teams (rows).
Task – remember geometric bodies.I will lean on. guys, based on your knowledge from the course in geometry, drawing technology. The team that gives the most correct answers will win. Ready?.
I'm starting a quiz.
Question to team 1:What is this geometric body called? (Cube demonstration). Conclusion. (slide number 2)
Question 11 to the team: Name this geometric body. (Demonstration of a hexagonal prism). Conclusion. (slide number 3)
Question 111 to the team:What is the name of this geometric body? (Demonstration of a quadrangular pyramid.) Conclusion. (slide number 4)
Question to team 1:What geometric body is formed by rotating a rectangle? Conclusion. (slide number 5)
Question 11 to the team: What geometric body is formed when a triangle rotates? Conclusion. (slide number 6)
Question 111 to the team:What geometric body is formed when a trapezoid rotates? Conclusion. (slide number 7)
Question for everyone: Shown are ski poles with points in the form of a cone, a prism and a pyramid. Their frontal projections are the same, but their horizontal ones?
1 team – 1 pic.
2nd team – 2nd pic.
3rd team – 3rd pic.
Conclusions. (slide number 8)
All teams coped with the quiz questions and showed good knowledge of geometric bodies.
- Conversations about the analysis of the geometric shape of objects.
The names of geometric bodies were originally the names of specific objects that have a shape more or less close to the shape of a given body. So the word " cylinder" meant roller, roller, the word "cone" - pine cone, the word "prism" - sawn (meaning a sawn log), “ pyramid " comes from the word " purees with ", which the Greeks called the Egyptian pyramids. Some scientists suggest that the shape of the pyramid, in turn, was suggested to the Egyptians by the promising convergence of the sun's rays. This light effect can sometimes be observed when the sun appears through a break in the clouds. The ball is bounded by a surface called sphere, from the Greek word"sfeira" - ball. (slide no. 9-10)
Man studied the shape of objects in the process of his practical activities.
Take a closer look at geometric bodies; the shape of each body has its own characteristic features, by which we distinguish a cylinder from a cone, and a cone from a pyramid. We are speaking " cube "and everyone imagines its shape. We say " ball “, and again we have a very specific image.
Let's consider some features of geometric bodies.
Geometric bodies are divided intobodies of revolution and polyhedra
What bodies of rotation do you know? Conclusion.
Cylinder, cone and truncated conehave the following elements:
axis of rotation, base, generatrix, cylinder - cylindrical surface, cone - conical surface, cone also has an apex. (slide no. 11-12)
Ball - axis of rotation, center, equator, meridian. (slide number 13)
What geometric solids from polyhedra do you know? Conclusion.
Parallelepiped : rectangular, cube has vertices, face, edge. (slide No. 14
Prism : base, top, edge, face. (slide number 15)
Pyramid, truncated pyramid-vertex, edge, face. (slide number 16)
What elements are common to these geometric bodies? Conclusion.
And so, we have discussed with you the elements of geometric bodies by which we distinguish them from each other.
Depending on the base, the prism and pyramid may be different. If the base is a hexagon, then the prism and pyramid are called hexagonal; if a triangle, then a triangular prism or pyramid.
Question: Take a closer look at the objects around us. What can you notice? (Students' answers)
Generalization. That's right, objects have the shape of geometric bodies or represent a combination of them.
Parallelepiped, prisms – residential multi-storey building, village house;
Ball - ball;
Cylinder – drum;
Cone - fire bucket;
Truncated cone – flower pot, bucket; (slide number 17)
The shape of machine parts and mechanisms is also based on geometric bodies.
Take a look at the table. (slide number 18)
Various details are shown here. Some of them are of the simplest form.
Question: What shape are the axle and roller? What is the shape of the gasket?
(Students' answers).
Generalization. About such parts as the axle and roller, we will say that they are cylindrical, and about the gasket - it is prismatic.
Other parts have a more complex shape; they are a collection of geometric bodies. For example: a roller is formed by adding another smaller cylinder to a cylinder. And the bushing is cylindrical, from which another cylinder of smaller diameter has been removed.
It is more difficult to understand the shape of a more complex part, such as a fork, from a drawing.
Question: How can it be easier to determine the shape of objects from a drawing? (Students' answers).
Generalization. To do this, a complex-shaped part is mentally dissected into its individual constituent parts, which have the shape of various geometric bodies.
Definition: the mental division of an object into its constituent geometric bodies is calledanalysis of geometric shape.(slide number 19)
An image of the support is given. What is its shape? (slide number 20)
It is composed of a rectangular parallelepiped, two half-cylinders and a truncated cone. The part has a cylindrical through hole. After such “dismemberment” the shape of the part is easier to determine.
3.Primary consolidation: oral questioning.
Questions and tasks for consolidation:
Figure 1 (slide no. 21)
- What geometric bodies are depicted?
- Is there any rotation in the image of the body?
If there are, name them.
- Which geometric body is closest to us?
- Which geometric bodies touch each other?
Figure 2 (slide no. 22)
- What geometric bodies does this composition consist of?
- Determine the top view of this composition.
IV. Consolidation of the studied material.(slide number 23)
Practical exercise
Task: using a visual image of the part, draw it in the required number of views.
V. Homework(slide number 24)
VI. Final part.(slide number 25)
Let's summarize the lesson by filling in the empty columns of the text with the necessary words and terms.
- Every detail can be mentally ________________
for individual _____________
- This process is called ___________________
- Only two geometric bodies differ in identical projections: __________________ and ____________________
Analysis of the geometric shape of objects. Bodies of rotation. Group of geometric bodies
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Equipment for the student: |
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Accessories, textbook “Drawing”, ed. A. D. Botvinnikova §10, 11, 16, colored pencils. |
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Rules for making drawings of geometric bodies. Sequence of reading a group of geometric bodies. |
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Fixing the material
Working with cards
Fixing the material
Using colored pencils, complete the task on the card.
Geometric shape analysis -
Drawing of a part according to these two types
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Equipment for the student: |
tools, |
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f A4, tools |
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Analyze drawings, give an accurate verbal description of the object depicted in the drawing. |
Obtaining axonometric projections of plane figures
Homework:
Repeat paragraph 7-7.2; complete the construction of table 1.
Equipment for students:
textbook "Drawing" ed. Botvinnikova A.D., workbook, drawing accessories.
Square in dimetric projection
Exercise:
Construct a square in isometric projection
Triangle in dimetry Triangle in isometry
Hexagon in dimetry and isometry
Exercise:
Construct a hexagon in isometric projection
Exercise:
Axonometric projections volumetric bodies
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Equipment for the student: |
Textbook "Drawing" ed. A.D. Botvinnikova, notebook, instruments. |
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Accessories, textbook “Drawing”, ed. A. D. Botvinnikova page 49 table No. 2, §7-8. |
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Rules for constructing axonometric projections. |
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Methods for constructing a volumetric part in isometry. |
Construct images in axonometry starting from flat figures lying at the base of the part. Learn to analyze the resulting images.
Review task:
Construct a geometric figure on a horizontal projection plane.
Amount (increasing)
Clipping
Reinforcement task
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Equipment for the student: |
Axonometric projection of a part with cylindrical elements |
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Textbook "Drawing" ed. A. D. Botvinnikova, accessories, notebook. |
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Accessories, textbook “Drawing”, ed. A. D. Botvinnikova § 7-8. |
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Rules for constructing a part with a curved surface. |
The general concept of “axonometry of a part”.
Analyze the shape of the part and the resulting image.
Ellipse –
Oval -Algorithm for constructing an oval
1. Let's construct an isometric projection of a square - a rhombus
ABCD2. Let us denote the points of intersection of the circle and the square 1 2 3 43. From the top of the rhombus (4 D2. Let us denote the points of intersection of the circle and the square 1 2 3 4) draw a straight line to the point(3). We get the segment.
4, which will be equal to the arc radius3 R4 .
5. When crossing a segmentAT 2AndACwe get a pointO1.
When crossing a line 2. Let us denote the points of intersection of the circle and the square 1 2 3 44 AndACwe get a pointO2.
6. From the received centersO1AndO2let's draw arcs(3). We get the segment1 , which will connect points 2 and 3, 4 and 1.
Consolidating new material
! work in the workbook
Make isometric projections of the circle parallel to the frontal and profile projection planes.
Drawing and visual representation of the part
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Equipment for the student: |
F A4, tools, textbook |
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§12, tracing paper |
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Analyze the shape of the part, build 3 types of parts and apply dimensions. |
Technical drawing
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Equipment for the student: |
Textbook "Drawing" ed. A. D. Botvinnikova§9, accessories, notebook. |
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Accessories, textbook “Drawing”, ed. A. D. Botvinnikova § 9 |
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Rules for making technical drawings and techniques for making parts. |
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Perform axonometric projections depicting flat figures. Perform technical drawing. |
Technical drawing –
Hatching methods:
Fixing the material
Complete a technical drawing of the part, two views of which are shown in Fig. 62
Projections of vertices, edges and faces of an object
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Equipment for the student: |
Textbook "Drawing" ed. A.D. Botvinnikova, accessories, notebook, colored pencils. |
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Accessories, textbook “Drawing”, ed. A. D. Botvinnikova §12, fA4, colored pencils. |
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Methods for selecting a point on a plane. Principles of constructing edges and faces. |
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Construct projections of points and faces. |
? Problem
What is a rib?
What is the top of an object?
What is the edge of an object?
Projection of a point
Practical work:
Label the projections
points on the part drawing, marked in the visual image.
Graphic work No. 9
Part sketch and technical drawing
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Equipment for the student: |
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Tools, graph paper, fA4, § 18 |
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What is a sketch? Sketch rules |
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Complete the sketch in the required number of types. |
Draw according to the sketch. What's called?
Fixing the material
sketch
Exercise tasks
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Equipment for the student: |
Applying dimensions taking into account the shape of the object |
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tools, textbook, notebook, tracing paper. |
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Rice. 113 (1, 2, 3, 5, 8, 9) |
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General rule for drawing dimensions in a drawing.
Repetition and consolidation of the material covered.
Practical work:
Oral exercise
Cutouts and slices on geometric bodies
Parts elements SLOT
- a groove in the form of a slot or groove on machine parts. For example, a slot in the head of a screw or screw into which the end of a screwdriver is inserted when screwing it in. GROOVE
- an oblong depression or hole on the surface of a part, limited on the sides by parallel planes. LYSKA
– a flat cut on one or both sides of cylindrical, conical or spherical sections of a part. The flats are designed to be grabbed with a wrench, etc.- this is an annular groove on the rod, technologically necessary for the exit of a threaded tool during the manufacture of a part or for other purposes.
KEYWAY GROOVE- a slot in the form of a groove, which serves to install a key, which transmits rotation from the shaft to the bushing and vice versa.
CENTER HOLE- an element of a part that serves to reduce its mass, supply lubricant to rubbing surfaces, connect parts, etc. The holes can be through or blind.
CHAMFER– turning a cylindrical edge of a part onto a truncated cone.
Exercise: Instead of numbers, write the names of the part elements
Exercise: Perform an axonometric projection of the part
Practical work No. 7
"Reading Blueprints"
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Equipment for the student: |
Textbook, notebook, sheet. |
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Graph paper, §17 |
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Learn the methods of constructing 3 types, analyze the geometric shape of an object, know the names of the elements of a part. |
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Analyze the drawing, determine dimensions, give an accurate verbal description |
Graphic dictation
“Drawing and technical drawing of a part based on a verbal description”
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Equipment for the student: |
Format (notebook), tools |
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Tools, graph paper. |
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Rules for sketching |
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Determine the necessary and sufficient number of types for a given part. Select the main view. Dimension. |
Option #1
Frame is a combination of two parallelepipeds, of which the smaller one is placed with a larger base in the center of the upper base of the other parallelepiped. A through stepped hole runs vertically through the centers of the parallelepipeds.
The total height of the part is 30 mm.
The height of the lower parallelepiped is 10 mm, length 70 mm, width 50 mm.
The second parallelepiped has a length of 50 mm and a width of 40 mm.
The diameter of the bottom step of the hole is 35 mm, height 10 mm; diameter of the second stage is 20 mm.
Note:
Option No. 2
Support is a rectangular parallelepiped, to the left (smallest) face of which is attached a half-cylinder, which has a common lower base with the parallelepiped. In the center of the upper (largest) face of the parallelepiped, along its long side, there is a prismatic groove. At the base of the part there is a through hole of a prismatic shape. Its axis coincides in the top view with the axis of the groove.
The height of the parallelepiped is 30 mm, length 65 mm, width 40 mm.
Half-cylinder height 15 mm, base (3). We get the segment 20 mm.
The width of the prismatic groove is 20 mm, the depth is 15 mm.
Hole width 10 mm, length 60 mm. The hole is located at a distance of 15 mm from the right edge of the support.
Note: When drawing dimensions, consider the part as a whole.
Option No. 3
Frame is a combination of a square prism and a truncated cone, which stands with its large base in the center of the upper base of the prism. A through stepped hole runs along the axis of the cone.
The total height of the part is 65 mm.
The height of the prism is 15 mm, the size of the sides of the base is 70x70 mm.
The height of the cone is 50 mm, the lower base is Ǿ 50 mm, the upper base is Ǿ 30 mm.
The diameter of the lower part of the hole is 25 mm, height 40 mm.
The diameter of the upper part of the hole is 15 mm.
Note: When drawing dimensions, consider the part as a whole.
Option No. 4
Sleeve is a combination of two cylinders with a stepped through hole that runs along the axis of the part.
The total height of the part is 60 mm.
The height of the lower cylinder is 15 mm, the base is Ǿ 70 mm.
The base of the second cylinder is Ǿ 45 mm.
Bottom hole Ǿ 50 mm, height 8 mm.
The upper part of the hole is Ǿ 30 mm.
Note: When drawing dimensions, consider the part as a whole.
Option No. 5
Base is a parallelepiped. In the center of the upper (largest) face of the parallelepiped, along its long side, there is a prismatic groove. There are two through cylindrical holes in the groove. The centers of the holes are spaced from the ends of the part at a distance of 25 mm.
The height of the parallelepiped is 30 mm, length 100 mm, width 50 mm.
Groove depth 15 mm, width 30 mm.
Hole diameters 20 mm.
Note: When drawing dimensions, consider the part as a whole.
Option No. 6
Frame It is a cube, along the vertical axis of which there is a through hole: semi-conical at the top, and then turning into a stepped cylindrical one.
Cube edge 60 mm.
The depth of the semi-conical hole is 35 mm, the upper base is 40 mm, the bottom is 20 mm.
The height of the bottom step of the hole is 20 mm, the base is 50 mm. The diameter of the middle part of the hole is 20 mm.
Note: When drawing dimensions, consider the part as a whole.
Option No. 7
Support is a combination of a parallelepiped and a truncated cone. The cone with its large base is placed in the center of the upper base of the parallelepiped. In the center of the smaller side faces of the parallelepiped there are two prismatic cutouts. A through hole of cylindrical shape Ǿ 15 mm is drilled along the axis of the cone.
The total height of the part is 60 mm.
The height of the parallelepiped is 15 mm, length 90 mm, width 55 mm.
The diameters of the cone bases are 40 mm (lower) and 30 mm (upper).
The length of the prismatic cutout is 20 mm, width 10 mm.
Note: When drawing dimensions, consider the part as a whole.
Option No. 8
Frame is a hollow rectangular parallelepiped. In the center of the upper and lower base of the body there are two conical tides. A through hole of cylindrical shape Ǿ 10 mm passes through the centers of the tides.
The total height of the part is 59 mm.
The height of the parallelepiped is 45 mm, length 90 mm, width 40 mm. The thickness of the walls of the parallelepiped is 10 mm.
The height of the cones is 7 mm, the base is Ǿ 30 mm and Ǿ 20 mm.
Note: When drawing dimensions, consider the part as a whole.
Option No. 9
Support is a combination of two cylinders with one common axis. A through hole runs along the axis: at the top it is prismatic in shape with a square base, and then cylindrical in shape.
The total height of the part is 50 mm.
The height of the lower cylinder is 10 mm, the base is Ǿ 70 mm. The diameter of the base of the second cylinder is 30 mm.
The height of the cylindrical hole is 25 mm, the base is Ǿ 24 mm.
The base side of the prismatic hole is 10 mm.
Note: When drawing dimensions, consider the part as a whole.
Test
Graphic work No. 11
“Drawing and visual representation of the part”
Using the axonometric projection, construct a drawing of the part in the required number of views on a scale of 1:1. Add dimensions.
Graphic work No. 10
“Sketch of a part with design elements”
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Equipment for the student: |
tools, textbook, graph paper |
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Tools, graph paper. |
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Sketch rules |
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Make a sketch and put the dimensions correctly |
Draw a drawing of a part from which parts have been removed according to the markings applied. The projection direction for constructing the main view is indicated by an arrow.
Graphic work No. 8
"Part drawingctransforming its form"
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Equipment for the student: |
tools, fA4, textbook |
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Tools, graph paper. |
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Execute drawing |
General concept of shape transformation. Relationship between drawing and markings
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Equipment for the student: |
Textbook, notebook, graph paper, accessories |
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Textbook fig. |
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151 (get to know each other), fA4 |
Analyze the form. Draw the drawing in orthogonal rectangular projection.
Graphic work
Making a drawing of an object in three views with transforming its shape (by removing part of the object)
Complete the technical drawing of the part, making, instead of the protrusions marked with arrows, notches of the same shape and size in the same place.
Logical thinking taskSubject
Logical thinking task"Design of drawings"
"Drawing tools and accessories"Crossword
"Projection"
1.The point from which the projecting rays emanate during central projection.
2. What is obtained as a result of modeling.
3. Cube face.
4. The image obtained during projection.
5. In this axonometric projection, the axes are located at an angle of 120° to each other.
6. In Greek, this word means “double dimension.”
7. Side view of a person or object.
8. Curve, isometric projection of a circle.
9. The image on the profile projection plane is a view...Rebus on the topic
"View"
Logical thinking taskRebus
"Drawing tools and accessories""Developments of geometric bodies"
"Axonometry"
Vertically:
Translated from French as “front view”.
The concept in drawing on which the projection of a point or object is obtained.
The boundary between the halves of a symmetrical part in the drawing.
Geometric body.
Translated from Latin, “throw, throw forward.”
The boundary between the halves of a symmetrical part in the drawing.
The science of graphic images.
Unit of measurement.
Translated from Greek “double dimension”.
Translated from French as “side view”.
In the drawing, “she” can be thick, thin, wavy, etc.
Working programmFrom "____" _________ 2014 Working program By drawing Grades 8 and 9 Modified based on the program... separate A4 sheets, exercises in notebooks.) 1. Sketch of the part with the required cut...
The development of the lesson is recommended for teaching a lesson in 8th grade “Analysis of the geometric shape of an object” with a presentation attached to the lesson. Study and initial awareness of new educational material, understanding of connections and relationships in the objects of study. Formation and development of skills: remember geometric bodies, learn to find simple geometric bodies, read and draw drawings.
Download:
Preview:
Drawing lesson in 8th grade.
Subject : "Analysis of the geometric shape of an object"
Bagomolova Lidiya Serafimovna teacher of fine arts and drawing,
GBOU Secondary School No. 416, Peterhof
year 2014
Lesson topic : Analysis of the geometric shape of an object.
1. Didactic rationale for the lesson
Lesson Objectives : study and initial awareness of new educational material. Understanding connections and relationships in objects of study.
- Educational goals:
To promote the formation and development of skills and abilities: remember geometric bodies, give the concept of analyzing the shape of an object, teach students to find simple geometric bodies in any technical detail.
- Developmental goals:
Teach students to confidently distinguish models of geometric bodies and name them correctly.
Promote the development of students' speech.
Help develop spatial thinking.
To promote the formation and development of students’ cognitive interest in the subject.
Continue developing logical thinking techniques (comparison, analysis, synthesis).
Equipment:
For the teacher: three-dimensional models of geometric bodies: cube, prism, pyramid, ball, cylinder, cone; technical means: computer with MS Windows operating system, multimedia projector, screen. Presentation for the lesson.
For students: handouts in the form of cards - tasks containing visual images of geometric bodies; parts consisting of geometric bodies.
Lesson structure:
- Organizational part of the lesson 1 min.
- Updating knowledge 3 min.
- Learning new material 23 min.
- Generalization and consolidation of the studied material 12 min.
- Summing up 3 min.
- Homework 3 min.
During the classes
- Organizational moment - checking presence. Reflection-
Teacher:
Creating a problem situation: Please look at the drawing of the part, (slide) can you determine the shape of the part?
Students: Hard enough.
The topic of our lesson will help us with this. Write down the topic of today's lesson in your notebook (slide) “Analysis of the geometric shape of an object.” Read the topic again and try to determine the objectives of the lesson: What do you want to learn about? What questions have arisen?
Students: 1. What is analysis of the geometric shape of an object?
2. Why is it needed?
3. What geometric shapes exist?
Today in the lesson we must learn to analyze the geometric shape of objects, and for this we need the ability to listen, analyze, and be able to highlight the most important and essential.
It will help to reveal the topic of our lesson - the plan of our work. (slide-3)
We will consider the following questions:
- The concept of the shapes of geometric bodies.
- Geometric bodies are the basis of the shape of parts.
- What is the easiest way to determine the shape of an object?
I suggest you remember what geometric bodies are familiar to you from the subject “geometry”, and from our previous topics, when we built axonometric projections of flat figures and flat-sided objects?
Students: cylinder, cube, parallelepiped, etc.
Teacher: What is a geometric body? A geometric body is a closed part of space, limited by flat and curved surfaces.
All geometric bodies can be divided into two groups: Polyhedra - which have flat faces, and bodies of rotation, which have curved surfaces (slide) (write in a notebook).
Each geometric body has its own characteristics (slide)
By these characteristics we distinguish a ball from a cube, etc. You are already familiar with most of these bodies. We say "cube" and everyone imagines its shape. We say “ball” and again the image of a certain geometric body appears in our minds. Let's get to know them better. (slides)
Now let's check how well you can imagine images of geometric bodies. There are cards on your tables. Assignment: Write down in your notebook in one column the numbers of images of faceted geometric bodies and their names, and in the other column - bodies of revolution. (slide)
Let's check how the guys coped with the task.
(If necessary, everyone together corrects errors in the answers)
Faceted geometric bodies include: 1. hexagonal prism, 2. hexagonal pyramid, 3. parallelepiped, 4. cube, 5. hexagonal truncated pyramid, 6. hexagonal prism, 7. hexagonal truncated prism.
To geometric bodies of rotation. 1. cylinder, 2. cone, 3. frustum. 4. ball, 5. Thor.
Take a close look at the objects around us.
They also take the form of geometric solids or a combination thereof. I name bodies, and you give examples of objects:
Ball-pyramid - prism-cone-cylinder-torus.
In engineering, the shape of a part is often compared with simpler shapes - geometric bodies, and also the shapes of geometric bodies are used to describe the shape of more complex parts (slide).
Any simple shape of a technical part can be represented as the shape of a geometric body (for example, the shape of a technical part “axle” can be represented as a cylinder shape - (slide), and the shape of a complex product can be represented as a combination of shapes of geometric bodies (for example, a part “fork”)
The considered approach to the study of parts is based on an analysis of its geometric shape.
Analysis of the geometric shape of an object is the mental division of an object into its constituent geometric bodies. (write in notebook) (slide).
Let's consider how the geometric shape of an object is analyzed using a visual image of the part. We mentally divide the part into simple geometric bodies, name them and tell how they are located relative to each other in space (slide).
An image of the part is given. What is its shape? It is composed of a rectangular parallelepiped, two half-cylinders and a truncated cone located on top. The part has a cylindrical hole.
By using the method of dividing a part into simple geometric bodies, you can learn to quickly, correctly read drawings and execute them competently.
Task: analyze the shape of the part you looked at at the beginning of the lesson (slide).
The “Support” part consists of a rectangular parallelepiped with five through cylindrical holes. In the center of the upper face of the rectangular parallelepiped there is a quadrangular prism with a through cylindrical hole, the axis and diameter of which coincide with the axis and diameter of the hole of the part. The parallelepipeds are connected to each other by two stiffening ribs in the shape of triangular prisms, which ensures their stable fastening.
Topic of lesson 1. Analysis of the geometric shape of an object. 1 hour
Lesson topic 2 . Projections of elements of geometric bodies. Practical work1 hour
Lesson type: learning new material taking into account previously acquired knowledge.
Target : introduce students to graphic culture and
mastering graphic methods of transmitting information;
repeat the names of geometric bodies;
learn to analyze the shape of an object, find simple geometric bodies
in any detail;
develop logical thinking andspatial imagination.
Lesson plan:
Organizational part – 3 min.
Theoretical part: - 10 min.
Repetition of basic geometric bodies and their elements
Analysis of the geometric shape of an object
Reading blueprints
3. Practical part: - 20 min
4. Final work: - 7 min.
5. Lesson summary: 5 min
- Grading
- Reflection
6. Homework
During the classes
Organizing time
Greeting, checking readiness for the lesson. 3 min
setting a learning taskslide 1
II
. Theoretical part
The shape of each geometric body has its own characteristic features. By these characteristics we distinguish a cylinder from a cone, and a cone from a pyramid. We say “cube” and everyone imagines its shape. We say “ball”, and again the shape of a certain geometric body appears in our consciousness.
It is very important in the process of graphic thinking to be able to determine the geometric shape of the depicted object as a whole and each of its elements separately.Each form has its own abilities.
To do this, you need to firmly know by what projections the main geometric bodies are depicted in the drawing; then, by comparing the projections of the same object depicted in the drawing, you can imagine its shape.
Slide 2 Before considering the projections of geometric bodies, let us recall the geometric bodies known to you.
Question: Why did I divide the bodies into groups? What can you say about each group?
regrouped view
slide 3
(Students' response).
On the left are the bodies of rotation obtained by the generatrix by rotating around its axis.
on the right are polyhedra; all these bodies have a face, a vertex, an edge.
So, let's conclude thatgeometric bodies are divided into two groups :
located on the leftbodies of rotation ,
on right - polyhedra.
- independent work of students in workbooks.
Slide 4 . Assignment for students: Write down the name of each geometric figure and its corresponding number.
Parallelepiped 2, 3
Cube 4
Cylinder 1, 10
Cone 5, 7
Truncated cone 14
Prism 11 (4, 2, 3,)
Pyramid 6
Truncated pyramid 13
Thor 9, 12
Ball 8
After filling out the table, the result is checked bySlide 5
Students compare the result with the work in their notebook.
Assignment for students: Determine the surfaces of which geometric bodies form
slide 6 detail data form
(Students' response).
--- Cone, two cylinders of different diameters having a common horizontal axis
--- The base of the object is a parallelepiped, on the upper face there is a cylinder with a vertical axis and two blue cubes located on the edge of the upper face.
--- The object consists of geometric bodies: a yellow torus, a cylinder, a gray cone, all located in a common horizontal axis.
--- This body consists of two truncated cones with the intersection of vertices in their formation.
--- The object consists of three cylinders of different diameters with a common horizontal axis.
--- The sixth body has a vertical axis to accommodate three cylinders of different diameters.
--- The base of the object is a parallelepiped, on the top face there is a smaller parallelepiped, and two red identical tetrahedrons are attached to the end face.
--- The object is formed by cubes and two tetrahedral pyramids, having a common base with the side faces of the cube.
CONCLUSION: Each item under consideration was divided into
the simplest geometric bodies.
Next task: determine the surfaces of which geometric bodies
They form the shape of these objects.
There is an oral frontal survey of students.
slide 7 exercise: Find among the models marked with numbers models of parts made up of the same geometric bodies as the models marked with letters. Here students group the parts. The rest write down the results of their work in a notebook.
More correct answers: A- 7 B- 1, 5, 12 C- 8 D- 4 D- 6 E- 9 F- 3
CONCLUSION: To make it easier to understand the shape of an object from a drawing, a complex part is mentally dissected into its individual constituent parts, which have the shape of various geometric bodies. This is called analyzing the geometric shape of an object. Students write the definition in their notebooks.
Now let's take a closer look at the objects around us. They have a shape
geometric bodies we considered earlier or represent a combination of them.
The shape of machine parts is also based on geometric bodies.
- Name objects that have the shape of any geometric bodies or their combinations.(For example, a chair is several quadrangular prisms connected together, a reel is cylinders plus truncated cones, a pencil is a hexagonal prism, etc.)
slide 8.
Various details are shown here, some of which are simple in shape.
Question: What geometric shape do the parts have?
(Students' response).
We say about parts such as a gasket that they are prismatic or prismatic, and about parts such as a roller that they are cylindrical.
Gasket – parallelepiped or tetrahedral prism
Roller - cylinder
Ring – cylinder with cylindrical hole
Roller – two cylinders of different diameters located with a horizontal axis
Stand – two truncated hexagonal pyramids with a through hexagonal hole
(
Students' answer).
CONCLUSION:These parts are a collection of geometric bodies. For example, a roller is formed by adding another cylinder to a cylinder. Similarly, a stand part is formed from two identical polyhedra. A ring, for example, is formed by removing another, smaller in diameter, from one cylinder.
Question: How can you understand the shape of a more complex part from a visual image, for example a support?
(
Student answers)
Mentally ungroup the part, i.e., trace the formation of the part from simple geometric bodies.slide 9
(
Student answers)
The base is a tetrahedral prism, two halves of one cylinder. Two truncated cones with a common base of smaller diameter and a cylindrical through hole having a common vertical axis with two truncated cones and a tetrahedral prism.
Question: So how do you determine the geometric shape of a complex part?
(
Student answers)
To do this, a complex-shaped part is mentally dissected into its individual constituent parts, which have the shape of various geometric bodies.
This is the analysis of the geometric shape of an object.
Primary consolidation of knowledge.
Slide 10. Z assignment: read the drawing and find the corresponding one
visual representation of the detail.
Part No. 1 two cylinders of different diameters with a horizontal axis
Part No. 2 with horizontal axis of parts Cone, two cylinders of different diameters
It is also important to learn to imagine invisible
surfaces and elements of an object.
Slide 11. Correct answer.
Part No. 3 with a common horizontal axis of a cylinder with a cylindrical through hole and a truncated cone with a through cone-shaped hole
Part No. 4 has a common horizontal axis of a cylinder and a truncated cone with a common end-to-end cylindrical hole
III . Practical part
Slide 12
Exercise: perform an analysis of the geometric shape of an object based on the image of the part:
dismember into geometric bodies; name them and tell how they are located relative to each other in space
Fig.1"Support" SL No. 12
Answer: The “Support” part consists of a rectangular parallelepiped (1) with five through cylindrical holes. In the center of the upper face of the rectangular parallelepiped there is a quadrangular prism (2) with a through cylindrical hole, the axis and diameter of which coincide with the axis and diameter of the hole of the part (1). The parallelepipeds are connected to each other by two stiffening ribs (3) having form
Triangular prisms, which ensures stable fastening of the prism (2).
rice. 2 "Stem" SL No. 12
Answer: three stepped cylinders of different diameters with a horizontal axis of location; the cylinder of the largest diameter has cut off vertical opposite edges; in the cylinder of medium diameter, on the end side there is a horizontal through hole of a prismatic shape; they are connected to each other by a small cylinder.
Slide 13
Using the drawing of the part, analyze its shape.
Answer additional questions:
- What do the thin intersecting lines on the projection of the product mean?
- Which element (part) of the product does the 2x45 entry refer to?
- What are the overall dimensions of the part?
- What does the square sign mean?
Answers to additional questions:
What do the thin intersecting lines on the product projection mean?
(flat edge)
Which element (part) of the product does the entry 2x45 refer to?
(chamfer height 2mm angle 45)
What are the overall dimensions of the part? (40 mm by 66 mm)
What does the square sign mean?
(parallelepiped shape, square base with sides 40 mm)
IV . Final work.
Slide 14 Determine the surfaces of which geometric bodies
form the shape of these objects?
V. Summing up the lesson
Reflection.
What new things have you learned?
Where can this knowledge and skills be applied?
What did you like about the lesson?
VI
. Homework
Using the drawing, draw a frontal projection and construct a profile projection of a group of geometric bodies. Complete a technical drawing of it.
D/z. handouts in the form of cards.
