1.
Equilateral polygonEquilateral polygon
Slope and taperSlope and taper
Tangency principleTangency principle
Techniques for drawing 2D objectsTechniques for drawing 2D objects
ExerciseExercise
Geometric ConstructionGeometric Construction
2.
2
Equilateral polygonEquilateral polygon
1.1. Regular hexagons
2.2. Equilateral Polygon
1)1) Construct regular hexagon 40mm across corners.Construct regular hexagon 40mm across corners.
2)2) Construct regular hexagon 40mm across corners and the othConstruct regular hexagon 40mm across corners and the oth
1) Draw a regularregular pentagon given the distancepentagon given the distance
across flats.
2) Draw a regularregular polygonpolygon given the distancegiven the distance
across flats.
3.
3
∠ 1∶ n30°
∠ 1∶ 8
α
1∶ n
10
Slope and taperSlope and taper
1.1.SlopeSlope
H
L
5
80
100
O
TheThe slope symbolslope symbol::
SlopeSlope= tan= tanαα== HH / L/ L
When dimensioning, the oblique direction of the slope symbolWhen dimensioning, the oblique direction of the slope symbol
should be in accordance with the actual slope direction.should be in accordance with the actual slope direction.
ExampleExample: Drawing of slope(Drawing of slope(∠∠ 11∶∶88, upon, upon pointpoint OO 55mmmm && leftleft 100100mmmm).).
4.
4
R1
o
R1
Construct principle: The key in tangency principle is to find the centerConstruct principle: The key in tangency principle is to find the center
of the arc and the tangent position of the corresponding lines, line andof the arc and the tangent position of the corresponding lines, line and
arc, and arcs respectively.arc, and arcs respectively.
Tangency principleTangency principle
The so-called tangency principle is often used for smoothThe so-called tangency principle is often used for smooth
connection between lines and circles using arcs.connection between lines and circles using arcs.
R2
R1
o
R= R1 + R2
o
R2
R1
o
R= R1 − R2
o
Arc connection lines
External arc connection
Between two pieces of arcs
Internal arc connection
between two pieces of arcs
a
aa
aa
5.
5
Example:Example:
Example:Example:
Example:Example:
Tangency principleTangency principle
1.1.((Acute angleAcute angle)) 3.3.((Right angleRight angle))
1.1.((ExternallyExternally))
1.1.((ExternallyExternally)) 2.2. ((InternallyInternally))
11. A. Arc connection between two lines.rc connection between two lines.
2. Arc connection between two pieces of arcs.2. Arc connection between two pieces of arcs.
3. Arc connection between one line and another piece of arc.3. Arc connection between one line and another piece of arc.
2.2.((Obtuse angleObtuse angle))
There are three cases, i.e.There are three cases, i.e.
2.(2.(InternallyInternally))
6.
6
General drawing proceduresGeneral drawing procedures
Techniques for drawing 2D objectsTechniques for drawing 2D objects
1) Analyze dimensions and curve segments and plan for1) Analyze dimensions and curve segments and plan for
the drawing procedures.the drawing procedures.
2) Define the scale, select the size of drawing sheet, and fix2) Define the scale, select the size of drawing sheet, and fix
the drawing sheet on the drawing board.the drawing sheet on the drawing board.
3) Draw the border lines and produce the title box.3) Draw the border lines and produce the title box.
（（ 11 ）） PreparationPreparation
7.
7
22 ）） RequirementsRequirements
Use extra thin lines and the sketches should be accurate, clearUse extra thin lines and the sketches should be accurate, clear
and clean.and clean.
Techniques for drawing 2D objectsTechniques for drawing 2D objects
（（ 22 ）） Rough sketchesRough sketches
11 ）） Procedure for rough sketchesProcedure for rough sketches
First draw datum lines for drawing positioning, then draw allFirst draw datum lines for drawing positioning, then draw all
known curve segments, then intermediate segments, andknown curve segments, then intermediate segments, and
finally draw connection segments.finally draw connection segments.
8.
8
33 ）） RequirementsRequirements
Be consistent in drawing different types of curve segments.Be consistent in drawing different types of curve segments.
The drawing should be produced with smooth connection between elements with tidyThe drawing should be produced with smooth connection between elements with tidy
lettering and clean drawing.lettering and clean drawing.
Techniques for drawing 2D objectsTechniques for drawing 2D objects
（（ 33 ）） Finalizing the drawingFinalizing the drawing
11 ）） Before producing the final drawing, one should check the sketches carefully,Before producing the final drawing, one should check the sketches carefully,
correct all mistakes, and erase all unnecessary curve segmentscorrect all mistakes, and erase all unnecessary curve segments..
22 ）） The procedure is as followsThe procedure is as follows
①①First thick lines and then thin lines:First thick lines and then thin lines: One should first draw continuous thick lines,One should first draw continuous thick lines,
then draw dashed thin lines, long dashed dotted thin lines and continuous thin lines.then draw dashed thin lines, long dashed dotted thin lines and continuous thin lines.
②②First curved then straight: One should first produce curved segments and thenFirst curved then straight: One should first produce curved segments and then
straight lines.straight lines.
③③Draw parallel lines from top downwards, then vertical lines from left to right, andDraw parallel lines from top downwards, then vertical lines from left to right, and
finally inclined lines.finally inclined lines.
④④Dimension.Dimension.
⑤⑤Check and fill in the title box.Check and fill in the title box.
9.
9
ExerciseExercise
Mark the following drawing onMark the following drawing on A4A4 sheet , scalesheet , scale 2:12:1;;
continues thick linecontinues thick line 0.80.8mm; dimension sizemm; dimension size 3.53.5..
TitleblockTitleblock
11.
11
d
6
1 4
2 3
5
Regular hexagons
1.1.To divide the circumcircle.To divide the circumcircle.
2.2.Join these points to formJoin these points to form
the hexagon.the hexagon.
1) Construct regular hexagon 40mm across corners.1) Construct regular hexagon 40mm across corners.
StepsSteps
12.
12
2) Construct regular hexagon 40mm across corners and theConstruct regular hexagon 40mm across corners and the
other across flats.other across flats.
Regular hexagons
Step off the radius round it to give sixStep off the radius round it to give six
equally spaced points,Join these pointsequally spaced points,Join these points
to form the hexagon.to form the hexagon.
dd
RR
RR
60°60°
(1)(1) (2)(2)
dd
Draw tangents to this circle with a 60° setDraw tangents to this circle with a 60° set
square to produce the hexagon.square to produce the hexagon.
13.
13
0 A
1
1.To divide the circumcircle.To divide the circumcircle.
5
BC
2
34
Equilateral Polygon
1) Draw a regularregular pentagon given the distance across flats.
2.To find the C point.To find the C point.
3.Step off the radius round.Step off the radius round.
4.Join these points to form theJoin these points to form the
pentagon.pentagon.
StepsSteps
14.
14
4040
P Q
1
2
3
4
5
6
A
F
E
D
C
B
G
Equilateral Polygon
2) Draw a regularregular polygonpolygon given the distance
across flats.
StepsSteps
1.To divide the circumcircle.To divide the circumcircle.
2.To find the PTo find the P 、、 Q point.Q point.
3.Step off the radius round.Step off the radius round.
4.Join these points to form theJoin these points to form the
regular polygon.regular polygon.
15.
15
< 90°
RR
RR
0
1.1. To draw an arc of given radius RTo draw an arc of given radius R=10mm to touch twoto touch two
straight lines.straight lines.( <90°).
Tangency principleTangency principle
StepsSteps ：：
R
1. Find the center O of a circle.
2. Find the tangent point.
3. Draw the connection arc.
16.
16
> 90°
RR
RR
0
22.. To draw an arc of given radius RTo draw an arc of given radius R=10mm to touch two straight lines.to touch two straight lines.(>>90°).
Tangency principleTangency principle
StepsSteps
R
1. Find the center O of a circle.
2. Find the tangent point.
3. Draw the connection arc.
17.
17
R
01
RR
90°
0
33.. To draw an arc of given radius RTo draw an arc of given radius R=10mm to touch twoto touch two
straight lines.straight lines.(==90°).
Tangency principleTangency principle
StepsSteps
R
1. Find the center O of a circle.
2. Find the tangent point.
3. Draw the connection arc.
18.
18
1. Find the center O of a circle.
R1+ R
R2+ R
2. Find the tangent point.
O1
O2
0
R
1. To draw an arc externally of a given radius R =251. To draw an arc externally of a given radius R =25mmmm to touch two circleto touch two circle
of radii Rof radii R11 =20=20mmmm and Rand R22 =10=10mmmm..
Tangency principleTangency principle
RR1
RR2
3. Draw the connection arc.
StepsSteps
19.
19
0 外
R外
R −R1
R −R2
RR1
RR2
O1
O2
0
点 鼠 左 示后面内容请 击 标 键显点 鼠 左 示后面内容请 击 标 键显
2. To draw an arc internally of a given radius R =452. To draw an arc internally of a given radius R =45mmmm toto
touch two circle of radii Rtouch two circle of radii R11 =20=20mmmm and Rand R22 =10=10mmmm..
R
Tangency principleTangency principle
1. Find the center O of a circle.
2. Find the tangent point.
3. Draw the connection arc.
StepsSteps
20.
20
RR
R1+ R
0
O1
3. To draw an arc externally of a given radius R=253. To draw an arc externally of a given radius R=25mmmm to touch a givento touch a given
straight line and a circles of radii Rstraight line and a circles of radii R11=20=20mmmm..
Tangency principleTangency principle
RR1
1. Find the center O of a circle.
2. Find the tangent point.
3. Draw the connection arc.
StepsSteps
R
21.
21
RR
R1− R
O1 0
Tangency principleTangency principle
4. To draw an arc internally of a given radius R=204. To draw an arc internally of a given radius R=20mmmm toto
touch a given straight line and a circles of radii Rtouch a given straight line and a circles of radii R11=40=40mmmm..
RR1
StepsSteps
1. Find the center O of a circle.
2. Find the tangent point.
3. Draw the connection arc.
R
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