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Divide a Circle Into 3 Equal Parts and 6 Equal Parts

+ In case of insufficient space, the number is drawn on the extension of the dimension line and is usually written on the right side of this line (figure 1.26).

+ The direction of the long dimension numbers is placed in the inclined direction of the dimension line.

+ The direction of the angle size digits is recorded as shown in Figure 1.27


Ø350

Ø280

Ø240

Ø200

Figure 1.25

6

Ø8

15 12





Figure 1.26 Figure 1.27 . Dimensional number direction

1.7.2.4. Letters and symbols

R15

R10

The symbols accompanying the size numbers are as follows:

- Radius

- Square edge

- Diameter

R

Figure 1.28

Figure 1.29

Figure 1.30

- Slope

Figure 1.31

- Cone


Figure 1.32

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Ø20


Ø30 Ø50












Figure 1.28


Figure 1.29

40




1:5


1:5


1:5








Figure 1.30




Figure 1.31



Figure 1.32


The edges of the corresponding slope symbol are parallel to the slope line.

The tip of the cone symbol points towards the recorded cone tip.

- Before the dimensions of the radius or diameter of the sphere, write the word "sphere" (Figure 1.33).

sentence Ø 24

Figure 1.33

REVIEW QUESTIONS


1. Explain the significance of applying National Standards and International Standards in technical drawings.

2. List some standards for drawing presentation.

3. How are the main paper sizes created?

4. What is the drawing title block used for and where is it located on the drawing?

5. What is scale? Does the size shown on the drawing depend on the size of the figure?

6. State the meaning of some types of drawing lines. What are their shapes and sizes?

7. What units are used for the length dimensions on the drawing? How are those units written?

8. What elements are needed to record dimensions on a drawing?

9. What is the direction of the long and angular dimensions of the digits?

10. When recording dimensions, what signs and symbols are commonly used?

Chapter 2 GEOMETRIC DRAWING

Machine parts have different shapes, however, they have a certain geometric shape, usually consisting of straight lines, circular arcs, and other curves. In the drawing process, we often encounter some problems with drawing tools. Drawing with drawing tools is called geometric drawing.

In engineering, when constructing figures, in addition to rulers and compasses, other tools are also used such as T-rulers, squares, protractors, etc.

Geometric drawing is also applied to marking work in the fields of forging, welding, cold working, turning, modeling, etc.

2.1. Basic modeling

2.1.1. Constructing parallel lines

Given a line a and a point C outside line a. Through C draw line b parallel to line a.

2.1.1.1. Construction using ruler and compass (figure 2.1)

- On line a, take an arbitrary point B as the center, draw a circular arc with radius equal to segment CB, this circular arc intersects line a at point A.

- Draw a circular arc with center C, radius CB and a circular arc with center B, radius CA, these two arcs intersect at D.

C

b

D

A

a

B

CA

- Connect CD, that is line b parallel to line a.


CB

Figure 2.1. Constructing parallel lines using compass

2.1.1.2. Constructing figures using a ruler and a square

Apply the property of equal corresponding angles of parallel lines by using a square to slide on a ruler (or 2 squares to slide on each other) to construct parallel lines. The construction is as follows (Figure 2.2):

- Place one edge of the square along the given line a and press the edge of the ruler against another edge of the square.

- Then slide the square along the edge of the ruler to the position where the edge of the square passes through point C.

- Draw a straight line along the edge of the square passing through point C, we get that straight line.

a

C

Figure 2.2. Constructing parallel lines using a ruler and a square.

R

1

R

1

R

2.1.2. Constructing perpendicular lines


2.1.2.1. Construction with ruler and compass (figure 2.3)

The construction is as follows:

- Take point C as the center, draw an arc with a radius greater than the distance from point C to line a, this arc intersects line a at two points A and B.

- Take A and B as the center, respectively.

arc has radius larger than AB . Two

2

This arc intersects at point D.

- Connecting C and D, CD is a line perpendicular to line a.

If C lies on line a, the drawing is similar to the above.

2.1.2.2. Construction with ruler and square

Use two right-angled edges of the square to draw, as follows (Figure 2.4):

- Place one right-angled edge of the square along the given line a and press the edge of the ruler against the hypotenuse of the square.

- Slide the square to the position so that the edge

the other side of the square of the square passes through point C.

Given a line a and a point C outside line a. Draw a line through point C perpendicular to line a.

C


AB a


D

Figure 2.3. Constructing a perpendicular line using a ruler and compass

C


a


Figure 2.4. Constructing a perpendicular line using a ruler and a square.

- Draw a straight line through C along the right angle side of the square.

2.1.3. Divide a line segment equally

R

R

2.1.3.1. Divide a line segment in half


- Construction using ruler and compass: to divide a given line segment AB in half, we use a ruler and compass to draw the perpendicular bisector of that line segment. Construction is as shown in Figure 2.5.


I

AB


Figure 2.5. Divide a line segment in half using a ruler and compass.

- How to construct using a ruler and a square: use a square to construct an isosceles triangle, taking segment AB as the base. Then construct the height of that isosceles triangle. The construction is as shown in Figure 2.6.

A

B

A

C

B

Figure 2.6. Dividing a line segment in half using a ruler and a square.

2.1.3.1. Divide a line segment into equal parts


How to draw as follows (Figure 2.7)

- Through A (or B) draw any ray Ax (should draw angle xAB as an acute angle).

- Place n equal segments on ray Ax. The division points are: 1', 2',.., n'.

Divide line segment AB into n equal parts.

x

n '

3'

2'

1'


A 1 2 3 B

Figure 2.7. Divide a line segment into equal parts

- Connect n' with B.

- Through 1', 2',.., (n-1)' draw lines parallel to n'B. The intersection points 1, 2 ,...n on AB divide AB into n equal parts.

2.1.4. Drawing slope and taper

2.1.4.1. Slope

The slope between line AB and line AC is the tangent of angle BCA (Figure 2.8).

i = b = AB tg

a AC

For example :

Through point C, draw a straight line with slope i = 1:5 compared to line AB (Figure 2.9).

There will be two cases:

the length of that angle.

B

S


AaC

Figure 2.8. Slope

So drawing the slope is drawing the angle according to

b

* Case 1 : Point C lies on AB. How to draw:

- From C, place five equal segments on AB at will.

- From D draw a straight line AB

- Set DE = 1/5 CD

- Connect E with C to get CE with slope to AB is i = 1:5.

* Case 2 : Point C is outside AB. How to draw:

- From C, lower line AB at D

- From D, place five equal segments on AB and CD.

- Connect C with E to get CE, a line with a slope of 1:5 to AB.


E


AC 1 2 3 4 DB

1:5

1:5C

AE 4 3 2 1 DB

a)

b)

Figure 2.9. How to draw slope

2.1.4.2. Cone

L

H

The taper is the ratio of the difference K

D

d

2

diameter of two perpendicular sections of a circular cone of revolution with the distance between the two sections (figure 2.10)

D d

K= = 2tg

L


Figure 2.10 . Taper

In the machine manufacturing industry, common taper degrees for conical joints are specified in TCVN 135 - 63 as follows:

1 : 200 ; 1 : 100 ; 1 : 50 ; 1 : 30 ; 1 : 20 ; 1 : 15 ; 1 : 12 ; 1 : 10 ; 1 : 8 ; 1 : 7 ; 1 :

5; 1: 3; or according to 2α there are: 30 0 ; 45 0 ; 60 0 ; 75 0 ; 90 0 ; 120 0 .

Drawing the taper of a cone means drawing the two outermost generators of the cone with a slope of K/2 with respect to the cone axis.

For example:

Draw a cone shaft K = 1:5 with diameter D = 20 mm and length L = 35 cm. The drawing is as follows (Figure 2.11):

- Drawing the taper K = 1:5 means we draw the slope equal to 1:10 of the two generator lines with respect to the axis.

- From A and B, construct a slope with the axis equal to 1:10. To do so, set CA = CB = 10 mm.

- Set CD to 100 mm.

- Connect D with A and B, we get angle ADB = 2 and taper K = 1:5.

1:5

C

D

A

35

20

A




Figure 2.11. How to draw taper

2.1.4.3. How to record slope and taper dimensions

According to TCVN 5705 - 1993, it is stipulated that before the dimension number indicating slope or taper, the slope or taper symbol is written (according to the convention in section 1.1.7). The top of the symbols must point towards the corner vertex of the shape (figure 2.10).

- The slope dimensions are written on the line parallel to the bottom of the slope.

- The taper dimension is written above the axis of the cone or on a line parallel to the axis of the cone.

2.2. Divide the circle equally

2.2.1. Divide the circle into 3 and 6 equal parts

The radius of a circle is equal to the length of the side of the inscribed regular hexagon, so we can deduce how to divide the circle into 3 or 6 equal parts using a ruler and compass (Figure 2.12).

2.2.2. Divide the circle into 4 and 8 equal parts

Two perpendicular diameters divide the circle into 4 equal parts. To divide the circle into 8 equal parts, we divide the 4 right angles in half by drawing the angle bisectors of those right angles (Figure 2.13).

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