Descriptive Geometry and Engineering Drawing
画法几何及工程制图
1
Chapter 1 Basic Drawing Knowledge
第一章
制图基本知识
§1–1 Basic Stipulation for Technical Drawing GB
技术制图国家标准的基本规定
§1–2 Dimensioning
尺寸注法
§1–3 Geometry Drawing
几何作图
§1–4 Size Analyzing, Dimensioning and Drawing Steps in
Planar Drawing
平面图形的尺寸分析、尺寸注法与画图步骤
2
§1–1 Basic Stipulation for Technical Drawing GB
技术制图国家标准的基本规定
The mechanical drawing GB of our country was decreed by state
Scientific and Technical Committee in 1959.And it had been three
times revised in 1970 and 1974 and 1984.
我国的国家标准《机械制图》是1959年由国家科学技术
委员会颁布的，并于1970年、1974年及1984年作了三次修订。
Our country has revised and supplemented the GB and made it
overall equate or equivalent to the ISO standard.
我国对现行的标准进行了修订和增补，全面等同或等效
采用了ISO标准。
This section mostly introduce the bottommost several term
standards for drawing.
本节主要介绍制图中最基本的几项标准。
3
1. The size and format of drawing
图纸幅面和格式
1)Size of drawing
图纸幅面(GB／T14689—1993)
While protracting the engineering drawing,we shall precedent
adopt the basic size which stated in Tab.1-1 .Necessarily,
allowing to attach lengthen size.
绘制工程图样时，应优先采用表1-l所规定的基本幅
面，必要时，也允许选用加长幅面。
The lengthen size must increase according to the short-side
that succeed integral multiple (To inquire the concrete
specification in relevant standard).
加长幅面的尺寸按基本幅面的短边成整数倍增加
(具体规格可查问相关标准)。
4
Tab.1-1 The basic size
表1-1 基本幅面
841
A4×4
mm
A1
A0
630
A4×3
420
A3
A2
A3×3 A3×4
210
A4
0
297
594
891
1189
Fig.1-1 The relation of drawing size
图1-1 图纸幅面尺寸关系
5
2) The format of drawing boundary
图框格式(GB／T14689—1993)
On the drawing, the drawing boundary must be drawn by heavy line.
The format can be broke into two types which include the nonbinding edge and binding edge, but the only one type the identical
product.
在图纸上必须用粗实线画出图框，其格式分为不留装订边
和留有装订边两种，但同一产品的图样只能采用同一种格式。
As non-binding edge type is shown in Fig.1-2, and binding edge
type is shown in Fig.1-3.
不留装订边的图纸，其图框格式如图1-2所示。留有装
订边的图纸，其图框格式如图1-3所示。
The value of a and b and c in drawing boundary size for basic size
can be referred in Tab.1-1. The drawing boundary size for lengthen
size must be attached to the large one number of the basic size.
基本幅面的图框尺寸a、e、c如表1-1规定，加长幅面的图
框尺寸按所选的基本幅面大一号的图框尺寸确定。
6
(a)
(b)
Fig. 1-2 Non-binding edge type for drawing boundary
图1-2 不留装订边的图框格式
7
（a）
（b）
Fig.1-3 Binding edge type for drawing boundary
图1-3 留有装订边的图框格式
8
3) Title strip (GB／T 10609.1—1989)
标题栏(GB／T 10609.1—1989)
According to the GB provision, the title strip must be shown on
every engineering drawing.
国家标准规定，每张工程图样上均应画出标题栏。
The content,format and size of every part for the title strip can refer
the Fig. 1-4.
标题栏的内容、标题栏的格式和各部分尺寸可参照图1-4所
示。
The location of the title strip,generally be put on the lower right corner
of the drawing.The letter heading of the title strip must accord with the
heading of the seeing drawing,which can refer the Fig.1-2 and Fig.1-3.
标题栏一般置于图纸的右下角，标题栏中的文字方向与看图
方向一致，如图1-2和图1-3所示。
9
180
16
12
16
subarea
number
标记 处数 分区
File No.
Date
Sign
更改文件号 签名
签名 年月日 标准化 签名 年月日
Design
Sign
审核
Assessor
工艺
Technics
12
12
16
Sign
批准
12
Standardization
Drawing’s name
阶段标记
Date
Authorize
12
单位名称
12
年月日
设计
Date
12
6.5
重量
比例
10
Tag
材料
4×6.5（=26）
Unit title
Weight
Scale
（9） 9
8×7（=56）
7
Material
共 张
16
第
Summed
张
单位名称
Serial number
图样代号
No.
50
Phase sign
Fig.1-4 The format of title strip
图1-4 标题栏格式
10
20
16
18
10
10
Among the school’s drawing exercise, for brevity, suggesting to
adopt the simplified title strip that showed in the Fig.1-5.
在制图作业中，为了简便，建议采用图1-5所示简化标题
栏。
14
7
25
Number
Name
Quantity
Material
Remark
8
45
序号
名称
数量
材料
备注
Serial number图号
6 6
34
6
Drawing’s name 图名
制图
校对
审核
12
比例 重量
数量
Scale Weight Quantity
Mapper
Corrector
Assessor
20
45
6 6
14
Unit title单位名称
15
15
45
130
Fig.1-5 The format of simplified title strip
图1-5 简化标题栏格式
11
2. Scale (GB／T 14690—1993)
比例(GB／T 14690—1993)
The ratio between graphic linear dimension of drawing and the
homologous linear dimension of the practicality is called scale.
图样中图形与其实物相应要素的线性尺寸之比称为比例。
The scale include: scale of original cost, scale of magnification &
shrink.
比例分为：原值比例、放大比例和缩小比例。
While protracting a drawing, select the respond scale value from
Tab.1-2, necessarily, allowing to select the scale value from Tab.1-3.
绘制图样时，应由表1-2中规定的比例系列中选取适当的
绘图比例；必要时，也允许选用表1-3中比例系列中的比例。
12
Tab.1-2 The preferred value of scale series
表1-2 优先选用的比例系列
Pour: n is positive integer
注：n为正整数
Tab.1-3 The allowing value of scale series
表1-3 允许选用的比例系列
Pour: n is positive integer
注：n为正整数
13
While protract the drawing, the scale shall be selected by the effective
demand, but the dimensioning must be filled in with the true size. As
showing in Fig.1-6.
在绘制图样时，应根据实际需要选择比例，但标注尺寸时，
必须按机件的真实尺寸填写，如图1-6所示。
(a)1:2
(b)1:1
(c)2:1
Fig.1-6 The non-relevance between dimension and drawing scale
图1-6 尺寸数字与画图比例无关
14
The every parts of a assembly must be drawn with the identical
scale,and must be filled in the title strip.
绘制同一机件的各个视图应采用相同的比例，并在标题拦
的比例一栏中填写。
If some of the parts had been drawn with different scale, it must be
given addition label as shown in Fig.1-7.
当某个视图需要采用不同的比例时，必须另行标注，如
图1-7所示。
Fig.1-7 Give addition label to views with different scales
图1-7 不同比例的视图应加标注
15
3. Font (GB／T 14691—1993)
字体(GB／T 14691—1993)
Beside using the graphic to express the partial on the drawing, there
also were necessary number and words to explanation the size and
specification and so on.
在图样上除了要用图形来表达零件的结构形状外，还必须
用数字及文字来说明它的大小和技术要求等其他内容。
The written form of Chinese, letter and number on the
technology drawing and technological document can be refer
the unify provision in the GB.
国家标准对技术图样和技术文件中书写的汉字、字母
和数字的书写形式都作了统一规定。
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1) Basic Stipulation
基本规定
(1)The written form of Chinese, letter and number on the technology
drawing and technological document must obey: typeface skill
whole, stroke clarity, interval uniformity, arrange tidiness.
图样和技术文件中书写的汉字、数字和字母都必须做
到：字体工整、笔画清楚、间隔均匀、排列整齐。
(2)The nominal size series for of the font height (with h
express)：1.8，2.5，3.5，5，7，10，14，20mm. Font
height representative typeface.
字体高度(用h表示)的公称尺寸系列为：1.8，2.5，
3.5，5，7，10，14，20mm。字体高度代表字体的号数。
17
(3)The Chinese must written in long imitation song-dynasty, and
must use the simplified character which published and
popularized by state. The length of Chinese must not less than
3.5mm.
汉字应写成长仿宋体，并应采用国家正式公布推行的简
化字。汉字的高度不应小于3.5mm。
(4)Both letter and number have two types include A and B.
But there were only one type on a drawing.
字母和数字分为A型和B型两种。在一张图上只能
采用同一种字体。
(5)The letter and number on the drawing could be written in
italic and lifting. The heading of italic must list to starboard
and the horizontal reference was 75°.
图样上的字母和数字可写成斜体和直体。斜体字
的字头向右倾斜，与水平基准成75°。
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2) Font sample
字体示例
(1) Sample of long imitation
song-dynasty Chinese
长仿宋体汉字示例
(2) Sample of Latin letter
拉丁字母示例
The capitalization and italic of A Font
A型字体大写斜体
The lower case and italic of A Font
A型字体小写斜体
19
(3)Demonstration of
Arabic numerals
阿拉伯数字示例
Italic
斜体
Lifting
直体
A Font
A型字体
Italic
斜体
(4)Demonstration of
Roman numerals
罗马数字示例
Lifting
直体
A Font
A型字体
20
3) Stipulation of integrated application
综合应用的规定
(1)The digital and letter that were used to as indices, fraction, limit
deviation, footnote and so on, generally adopt the smallness one
number font. Sample:
用作指数、分数、极限偏差、脚注等的数字和字母，一
般应采用小一号的字体。示例：
21
(2)The numeric character, physical quantity sign, unit of measure sign
and another sign, code name which on the drawing, should respond
the national relate statute and standard provision.
图样中的数字符号、物理量符号、计量单位符号以及其他
符号、代号，应分别符合国家的有关法令和标准的规定。
Sample:
示例：
(3)The sample of another application
其他应用示例
22
4. Drawing string (GB／T17450-1998，GB／T4457．4-2M2)
图线(GB／T17450—1998，GB／T4457．4—2M2)
1) The type and dimension of drawing string
线型及图线尺寸
Among the GB of technical drawing,there were 15 basic types of
string,the codes of the types were No.01~No.15.
国家标准《技术制图》中，规定了15种基本线型，线型
的代码为No.01~No.15。
Among this, there were 9 typical string for mechanical
drawing as shown in Tab.1-4.
其中机械制图中常用的图线有9种，见表1-4。
23
Tab.1-4 Typical string for mechanical drawing
表1-4 机械制图中常用图线
24
（续表01 Add watch 01）
25
（续表02 Add watch 02）
26
（续表03 Add watch 03）
27
The width of string on the mechanical drawing must select
from the number series.
机械制图中的图线宽度应根据图样类型和尺寸大小
在下列数系中选择。
The common radio of the number series was 1:1.4：0 .25mm，
0.35mm，0.5mm，0.7mm，1mm，1.4mm，2mm.
该数系的公比约为1:1.4：0 .25mm，0.35mm, 0.5mm，
0.7mm，1mm，1.4mm，2mm。
28
The beam ratio between wide string and thin string was 2:1.
机械图样中粗线与细线的宽度比为2 :1。
The width and group of drawing string refer the Tab1-5,among them
precedent to select 0.5 and 0.7.
图线宽度及组别见表1-5，其中0.5和0.7组别为优先采用的
图线组别。
Tab.1-5 The width and group of drawing string
表1-5 图线宽度和图线组别
Group of drawing string
线型组别
mm
0.25
0.35
0.5
0.7
1
1.4
2
01.2；02.2；
04.2
0.25
0.35
0.5
0.7
1
1.4
2
01.1；02.1；
04.1；05.1
0.13
0.18
0.25
0.35
0.5
0.7
1
Linetype width
线型宽度
29
The string element of drawing string(the independent and
discontinue string, such as point, length different drawn and
interval)should conform the provision that shown in Tab.1-6.
图线中线素(线型中不连续线的独立部分，如点，长
度不同的画和间隔)的长度宜符合表1-6的规定。
Tab.1-6 Length of string element
表1-6 线素的长度
String element
线素
Line type
线型No.
Length
长度
String element
线素
Line type
线型No.
Length
长度
Point
点
04，05
≤0.5d
Draw
画
02
12d
Short interval
短间隔
02，04，05
3d
Long draw
长画
04，05
24d
Pour: d is the line width
注：d为图线宽度
30
2) The application and brushwork of drawing string
图线的应用与画法
The application and demonstration of conventional string for
mechanical drawing can refer Tab.1-4 and Fig.1-8.
机械制图中常用图线的应用及其示例见表1-4和图1-8。
While drawing,the fellow rules must be observed:
绘图时应遵守以下几点：
(1)In a identical drawing, the width of uniformity solid should
substantial agreement. The length and interval of imaginary string,
stipple string, two-dot chain string should severalty approximately
equality.
同一图样中，同类固线的宽度应基本一致。虚线、点画
线、双点画线的线段长度和间隔应各自大致相等。
(2)Unless otherwise prescribed, the minimum clearance of twain
parallel should not less then 0.7mm.
除非另有规定,两条平行线的最小间隙不得小于0.7mm。
31
Fig.1-8 The application demonstration of drawing string
图1-8 图线的应用示例
32
(3)If the solid string,imaginary string, stipple string and two-dot
chain string had each intersect, they must intersect at the
lineation.
实线、虚线、点画线、双点画线互相相交时，应在画
线处相交。
(4)While drawing the axis string, center of symmetry string, towdot chain string and two-dot chain string as interrupt
department, all of them should go beyond contour 3 to 5 mm.
绘制轴线、对称中心线、双点画线及作为中断处的双
点画线，均应超出轮廓线3~ 5mm。
33
(5)If the broken arc and imaginary string tangency each other, the
imaginary string should draw to point of contact and the broken
arc should leaf clearance. Refer Fig.1-9.
当虚线圆弧和虚线直线相切时，虚线直线应画到切点，
虚线圆弧则留有间隙，如图1-9所示。
Fig.1-9 The brushwork of imaginary string
图1-9 虚线的画法
34
(6)If the graphic was too small,there were difficulty to draw stipple
string and two-dot chain string,the fine string could substitute
them. As show in fig.1-10.
当图形较小，绘制点画线或双点画线有困难时，可用细
实线代替。如图1-10.
The fine string could substitute
short stipple string
Stipple string must
intersect at the lineation.
点画线较短时用细实线代替
The stipple string should go beyond
contour 3 to 5 mm.
圆心应是画线相交
超出图形线约3~5mm
Fig.1-10 Brushwork of stipple string
图1-10 点画线的画法
35
§1–2
Dimensioning (GB／T4458.4-2003)
尺寸注法(GB／T4458.4-2003)
In the engineering drawing, the graphic only used to express the
structure shape. To express the size of them, you must superscript
the size on the drawing.
在工程图样中，图形只能表达机件的结构形状，若要表达
它的大小，则必须在图形上标注尺寸。
Therefore, the drawing and the size of them become the main base
to manufacture the machine piece.
因此，图形及图形上的尺寸就成为加工制造机件的主要依
据。
36
While dimensioning the drawing, the fellow rules must be obey:
exactness, integrity, clearness, reason.
尺寸标注要求做到：正确、完整、清晰、合理。
The exactness means the dimension must concern the GB.
所谓正确，即尺寸标注要符合有关国家标准的要求；
The integrity means the dimension must written uniform full, and
not much, not a little and not repeat.
所谓完整，即尺寸注写必须齐全，要求做到不多、不少、
不重复；
The clearness means the dimension layout distinctness, law,
and facilitate see the drawing.
所谓清晰，即尺寸布局明显、有规律，便于看图；
The reason means the dimension as well as guarantee design
requirement and consider the convenience of process and measure.
所谓合理，即所注尺寸既要保证设计要求，同时又要考
虑加工和测量时的方便。
37
1. Basic rule
基本规则
(1)The real size of the mechanical component must accord to
dimension which dimensioned on the drawing and it has no
relation to the size of drawing and the accuracy of the graphic.
机件的真实大小应以图样上所注的尺寸数值为依据，
与图形的大小及绘图的准确度无关。
(2) If the unit of the drawing dimension is mm, the code or title
for the unit of measure is not necessarily labeled. But if
adopt the other unit, the code or title of the unit must be
labeled.
图中的尺寸，以mm为单位时，不需标注计量单位
的代号或名称。若采用其他单位，则必须注明相应的计
量单位代号或名称。
38
(3)The dimension that dimensioned on the drawing is the last
finish size,if not the additional explanation is necessary.
图样中所标注的尺寸，为该图样所示机件的最后完
工尺寸，否则应另加说明。
(4) Every dimension of the mechanical component is labeled
only once generally, and the dimension should be labeled at
the most vivid drawing to reflect the structure.
机件的每一尺寸，一般只标注一次，并应标注在反
映该结构最清晰的图形上。
39
2. Composing of the dimension
尺寸的构成
The rounded size is
generally composed by size
borderline, dimension line
and dimension figure. As
show in Fig.1-11.
每个完整的尺寸，一
般应由尺寸界线、尺寸线
和尺寸数字组成。如图111所示。
Fig. 1-11 Element of size
图1-11 尺寸要素
40
1) Borderline of size
尺寸界线
The size borderline must be drawn in fine line,and it should be
draw from the graphic contour line,ax or center of the symmetry
string.Refer the Fig.1-11.
尺寸界线用细实线绘制，并应由图形的轮廓线、轴线或
对称中心线处引出，如图1-11所示。
You also can use the contour line, ax or the center of symmetry
string as the size borderline.
也可利用轮廓线、轴线或对称中心线作为尺寸界线。
41
The size borderline generally plumb with
the dimension string, if necessarily it may
incline. To dimension at the lubricity
transition department, the contour string
must be prolonged by the fine string, and
the size borderline is be educed from the
point of intersection.
尺寸界线一般应与尺寸线垂直，
必要时才允许倾斜；在光滑过渡处标
注尺寸时，必须用细实线将轮廓线延
长，从它们的交点处引出尺寸界线。
如图1-12。
Fig.1-12 The brushwork of size
borderline and dimension line
图1-12 尺寸界线与尺寸线的画法
42
2) Dimension line
尺寸线
The dimension line must be drawn with the fine line,and there are
two types for the terminal:arrowhead and bias, as show in the
Fig.1-13 and Fig.1-14.
尺寸线用细实线绘制，其终端有两种形式：箭头和斜线，
如图1-13和1-14所示。
The width of broad real
line is d.
d为粗实线的宽度
The height of dimension figure is h.
h为尺寸数字的高度
Fig.1-13 Brushwork of arrowhead
图1-13 箭头画法
Fig.1-14 The bias substitute the arrowhead
图1-14 斜线代替箭头
43
While to dimension the diameter of circle or the radius of arc, the
terminal of the dimension line only use the arrowhead type. As
show in Fig.1-15a, b, c, d.
标注圆的直径、圆弧的半径尺寸时，尺寸线终端只能采用
箭头形式，如图1-15a、b、c、d所示。
If the radius of the arc is too big, or the center of the arc can’t
draw on the drawing, the dimension line can draw act on the
Fig.1-15e.
当圆弧的半径过大或在图纸范围内无法标注其圆心位置
时，尺寸线可按图1-15e的形式标注。
If the center of circle is not necessarily labeled, refer the Fig.1-15f
to dimension.
若不需要标注其圆心位置时，则可按图1-15f的形式标注
尺寸线。
44
(a)
(d)
(b)
(e)
(c)
(f)
Fig.1-15 Dimension of arc
图1-15 圆弧尺寸
45
The dimension line cannot be substituted by other drawing,
generally it cannot be drawn on the position of the other drawing
string or drawn on their production. As show on Fig.1-16.
尺寸线不能用其他图线代替，一般也不得与其他图线重合
或画在其延长线上(图1-16)。
Right
正确
Wrong
错误
Fig.1-16 The correct errors contrast of dimension
图1-16 尺寸标注正误对比
46
While drawing the symmetry machine piece,only to draw the moiety
or some greater than half of it.The dimension line should summary
exceed the center of symmetry string or the fracture line.
对称机件的图形只画其一半或略大于一半的，尺寸线应略
超过对称中心线或断裂线。
The only one arrowhead is drawn on one end. As show on the
Fig.1-17,Fig.1-18.
此时仅在尺寸线的一端画出箭头，如图1-17、图1-18所示。
Fig.1-17 The rupture brushwork of
symmetric graphic dimension
图1-17 对称图形断裂画法的尺寸
Fig.1-18 The dimension of
symmetric graphic
图1-18 对称图形的尺寸
47
While the terminal of dimension use the
arrowhead type, if the place is insufficient, you
can use the dot or bias to substitute the
arrowhead . As show in Fig.1-19.
当尺寸线终端采用箭头形式时，在位置
不够的情况下，允许用圆点或斜线代替箭头，
如图1-19所示。
Fig.1-19 The dot
substitute the arrowhead
图1-19 圆点代替箭头
3) Dimension figure
尺寸数字
The position of dimension
figure for linear dimension
refer the Fig.1-20.
线性尺寸的尺寸数字的
注写位置如图1-20所示。
Fig.1-20 Dimension figure(one)
图1-20 尺寸数字(一)
48
The heading of dimension figure for linear dimension refer the
Fig.1-21 and Fig.1-22.
线性尺寸尺寸数字的方向，应按图1-21和1-22所示形式填
写。
Avoid dimensioning at this area.
避免在此范围内标注尺寸
Fig.1-21 Dimension figure(two)
图1-21 尺寸数字(二)
Fig.1-22 Dimension figure(three)
图1-22 尺寸数字(三)
49
Any drawing string are not allow to pass the dimension.
尺寸数字不允许被任何图线所通过。
If inevitability, the drawing string must be broken. As show in the
Fig.1-23 and Fig.1-24.
当不可避免时，必须把图线断开，如图1-23、图1-24所示。
Fig.1-23 Dimension figure(four)
图1-23 尺寸数字(四)
Fig.1-24 Dimension figure(five)
图1-24 尺寸数字(五)
50
3. The all kinds of dimension
各类尺寸注法
1) Linear dimension
线性尺寸
While dimensioning,the dimension line must parallel with the line
segment that labeled.
标注线性尺寸时，尺寸线必须与所标注的线段平行。
The size borderline generally plumb with the dimension line (if
necessary, allow to incline), and it should go beyond the
dimension line 2~3mm.
尺寸界线一般应与尺寸线垂直(必要时才允许倾斜)，并
应超出尺寸线2~3mm。
2) The dimension of circle ,arc and sphere
圆、圆弧及球面尺寸
51
The dimension of radius must be labeled on the arc projection of
the drawing,and the dimension line must pass the center of the
circle.As show in the Fig.1-15.
半径尺寸必须标注在投影为圆弧的图样上，且要求尺寸线
必须通过圆心，如图1-15所示。
The labeling dimension of the spherical diameter or radius,as show
in Fig.1-25.
球面的直径或半径的标注，如图1-25所示。
(b)
(a)
Fig.1-25 Dimension of the sphere
图1-25 标注球面尺寸
(c)
52
3) Dimension of angle
角度尺寸
While dimension the angle,the size borderline must go beside the
radial direction.
标注角度尺寸时的尺寸界线应沿径向引出。
The number of the angle must write in horizontal direction, and
the unit must be there for the angle size, refer Fig.1-26.
角度的数字，一律写成水平方向，角度尺寸必须注明单
位。如图1-26所示。
Fig.1-26 Figure of angle
图1-26 角度数字
53
4) The dimension of arc and chord
弧长及弦长尺寸
As show in Fig.1-27, Fig.1-28, Fig.1-29.
如图1-27、1-28、1-29所示。
Fig.1-27 Dimension of chord
图1-27 弦长尺寸
Fig.1-28 Dimension of arc(one)
图1-28 弧长尺寸(一)
Fig.1-29 Dimension of arc(two)
图1-29 弧长尺寸(二)
54
5) The label of square structure
正方形结构的标注
As show in Fig.1-30.
如图1-30所示
Fig.1-30 Sign of square
图1-30 正方形符号
55
6)The dimension of strait
position
位置窄小的尺寸标注
If the dimension is
small,the arrowhead or
dimension figure could
dispose on the outside of
the size borderline,as
show in Fig.1-31.
当要标注的尺寸小，
箭头或尺寸数字可以布
置在尺寸界线外面，如
图1-31所示。
Fig.1-31 The dimension of strait position
图1-31 位置窄小的尺寸注法
56
7)The dimension symbolic of thickness
厚度符号的标注
As show in Fig.1-32.
如图1-32所示。
8) The sign and abbreviation
符号和缩写词
Fig.1-32 Thickness symbolic
图1-32 厚度符号
While dimensioning, the sign and abbreviation should be used
precedent.
标注尺寸时，应尽可能使用符号和缩写词。
57
§1-3 Geometry Drawing
几何作图
The outline of mechanical component are mainly composed by
line,circle,arc and other plane curve.So grip the construct means of
some geometry are one of the important foundation.
机件的轮廓形状基本上是由直线、圆、圆弧及其他平面
曲线所组成的，所以掌握几何图形的作图方法是正确绘制机
械图样的重要基础之一。
58
1. Regular polygon
正多边形
Take the regular pentagon as a example. To draw the regular
pentagon base on the circum circle of it,refer the fellow construct
steps and means(as show in Fig.1-48):
以正五边形为例 。已知正五边形外接圆，作正五边形。
其作图步骤及方法如下（图1-48）：
1) Equation the radius 0A of circle, you can get point B.
己知圆的半径0A，等分0A，得点B;
2) Draw circle use the point B as center and the B1as the
length value,the circle deliver the OA to point C.
以点B为圆心，B1之长为半径画弧，交OA于C点；
59
3)The side length of regular pentagon equal C1,use the value to
equate the circle,the point 2,3,4,5 and so on will be get.
C1即为正五边形的边长，用它等分圆周，依次得2、
3、4、5等各点；
4) To connect all points, you will get the regular pentagon
that inscribe the known circle.
连接各点即得与己知圆内接的正五边形。
2. Ellipse
椭圆
To introduce two means that the most used:four heart circle method
(approximation brushwork) and concentric method (precision
brushwork)
介绍二种最常用的方法：四心圆法(近似画法)和同心圆法
(精确画法)。
60
1) Four heart circle method
四心圆法
If know the long axis and short axis of the elliptical, you may use
four heart circle method to draw the elliptical fellow the steps that
refer Fig.1-50.
已知椭圆的长轴、短轴，用四心圆法作椭圆的步骤见图150。
Fig.1-50 Drawing the ellipse by the four heart circle method
图1-50 用四心圆法画椭圆
61
2) Concentric circle method
同心圆法
If know the long axis and short axis of the elliptical,you may use
concentric circle method to draw the elliptical fellow the steps that
refer Fig.1-51.
已知椭圆的长轴、短轴，用同心圆法作椭圆的步骤见图151。
Fig.1-51 Drawing the ellipse by the concentric circle method
图1-51 用同心圆法画桶圆
62
3. Pitch and taper
斜度与锥度
1) Pitch
斜度
C
H
Pitch =
H
 1: n
L
A
L
B
Fig.1-52 pitch
图1-52 斜度
Use tangent of the twain lines or inter planar included angle to
express the pitch.
斜度的大小以两直线或平面间夹角的正切来表示。
The form to express it is simplicity fraction 1:n.As show in
Fig.1-52.
以简单分数1:n的形式来表示。如图1-52所示。
63
Drawing the pitch that pass a contact point,the fellow means and
steps will be used,refer Fig.1-53.
过已切点作斜度的方法及步骤如图1-53所示。
The method to label pitch refer Fig.1-54a.
标注斜度的方法如图1-54a所示。
1:5
1:8
(a)
(b)
Fig.1-53 Brushwork of pitch
图1-53 斜度的画法
Fig.1-54 Dimension of pitch and taper
图1-54 斜度与锥度的标注
64
Use the fine line to protract the sign of pitch, the width of the line is
1／10h.As show in Fig.1-55a.
斜度的符号用细实线绘制，线宽为1／10h。如图1-55a。
Notice that the lopsidedness of the pitch symbolic must respond
with the line or the oblique direction of plane.
应当注意，斜度符号的倾斜边方向应与直线或平面倾斜
的方向一致。
（a）H is equal to font height.
h=字体高度
（b）H is equal to font height.
h=字体高度
Fig.1-55 The brushwork of pitch symbol and taper symbol
图1-55 斜度符号与锥度符号的画法
65
2) Taper
锥度
Use the ratio of bottom circle
diameter and the height as the
taper for the just conic.
将正圆锥的底圆直径与
圆锥高度之比称为锥度。
If it is truncated cone,the taper
equate the ratio of the twain
bottom circles diameter
difference and the height,as
show in Fig.1-56.
若是圆台，其锥度为两
底圆直径之差与圆台高度之
比，如图1-56所示。
Taper =
D
Dd

 1: n
L
l
Fig.1-56 Taper
图1-56 锥度
Usually to write the taper in the
form of 1:n.
通常把锥度写成1 :n的形式。
66
To draw the taper that pass a know point,the means and steps refer
the Fig.1-57.
过已知点作锥度的方法及步骤如图1-57所示。
Known point
已知端点
Fig.1-57 The brushwork of taper
图1-57 锥度的画法
67
Refer the Fig.1-54b to dimension the taper in the mechanical
drawing.The brushwork of taper symbol refer the Fig.1-55b.
锥度在机械图样中的标注方法如图1-54b所示，锥度符号的
画法如图1-55b所示。
4. Arc joint
圆弧连接
While draw the drawing, frequently met the instance to draw a
string (line or arc) that glossily transition to other line (line or arc).
在绘制图样时，常常会遇到由一条线(直线或圆弧)光滑地
过渡到另一条线(直线或圆弧)的情况。
The glossily transition is called arc joint. As show in Fig.1-58.
这种光滑地过渡，称为圆弧连接。如图1-58所示。
68
Linked point
Linked point
Linked point
Linked arc’s center
Linked point
Fig.1-58 The plane figure of pitman
图1-58 连杆的平面图形
69
At the practical drawing,the radius of joint arc usually is known,the
key is determine the center of joint arc and the conjunction.
在实际作图中，通常连接弧的半径为已知，关键是要求出
连接弧圆心及连接点。
1) The connective basic geometry theory of arc
圆弧连接的基本几何原理
Central track
圆心轨迹
(1) The joint of arc and known line
圆弧与已知直线连接
As shown in Fig.1-59.
如图1-59所示。
Linked point
连接点
Fig.1-59 Joint of arc and known line
图1-59 圆弧与己知直线连接
70
(2) The joint of arc and known arc
圆弧与已知圆弧连接
As shown in Fig.1-60.
如图1-60所示。
Linked point
连接点
Linked point
连接点
Central track
圆心轨迹
Central track
圆心轨迹
（a）Exterior contact
（b）Inscribe
外切
内切
Fig.1-60 Joint of arc and known arc
图1-60 圆弧与已知圆弧连接
71
2) Some ordinary brushwork of joint for arc
几种常见圆弧连接画法
(1) Use the arc to join two deliver lines(As shown in Fig.1-61).
用圆弧连接两相交直线(图1-61)。
(a) Use the arc to join two (b) Seek the centre of a
deliver lines
circle
圆弧连接两相交直线
(c) Seek the linked points (d) Link the arc
求连接点
连接圆弧
求圆心
Fig.1-61 Arc join two known deliver lines
图1-61 用圆弧连接相交两已知直线
72
(2) Use arc join a known line and a known arc(As show in Fig.1-62.)
用圆弧连接一已知直线与一己知圆弧(图1-62)。
(a) Use arc join a
known line and a
known arc
(b) Seek the centre
of a circle
(c) Seek the linked points
求连接点
求圆心
(d) Link the arc
连接圆弧
用圆弧连接已知
直线和已知圆弧
Fig.1-62 Use arc to joint a known line a known arc
图1-62 用圆弧连接已知直线及已知圆狐
73
(3) Use the arc to join two known arcs.
用圆弧连接两已知圆弧。
a. Use arc to exterior contact two know arcs (As shown in Fig.1-63)
圆弧与两已知圆弧外切(图1-63）
Fig.1-63 Arc exterior contact two know arcs
图1-63 圆弧与两l知圆弧外接
74
b. A arc inscribes a known arc and exterior contacts other a known
arc (As show in Fig.1-64).
圆弧与一已知圆弧内切，外切于另一已知圆弧(图1-64)。
Fig.1-64 A arc inscribes a known arc and exterior contacts other a known arc
图1-64 圆弧与两已知圆弧内外接
75
§1-4 Size Analyzing, Dimensioning and Drawing Steps
in Planar Drawing
平面图形的尺寸分析、尺寸注法与画图步骤
1. Size Analyzing for Planar Drawing
平面图形的尺寸分析
Divide the planar drawing acting on the function in two types:
figuration size and orient size.
平面图形上的尺寸按其作用可分为定形尺寸和定位尽寸两类。
The figuration size is the size that can be used to ascertain the shape
of geometric element on the plane drawing.
将确定平面图形上几何元素形状大小的尺寸称为定形尺寸。
The orient size is the size that can be used to ascertain the position of
geometric element on the plane drawing. (As show in Fig.1-65).
将确定几何元素位置的尺寸称为定位尺寸。如图1-65所示。
76
The orient size must have a
origination point and the
origination point is called size
base.
标注定位尺寸时，必须有
个起点，这个起点称为尽寸基
准。
Fig.1-65 The size of plane drawing
图1-65 平面图形的尺寸
The length and width of a plane drawing at least have a size base.
平面图形长和宽每个方向至少应有一个尺寸基准。
The center of symmetry string, ax of circle or arc as well as the
bottom string of graphic and the brow string and so on can also be
used to be the size base .(As show in Fig.1-65)
用来作基准的可以是对称中心线、圆或圆弧的中心线以
及图形的底线及边线等。如图1-65。
77
There are some ordinary samples about how to dimension the
graphics in Fig.1-66.
图1-66列举了一些常见图形的尺寸注法。
Fig.1-66 The dimension for ordinary plane drawing
图1-66 常见平面图形的尺寸标注
78
2. The line segment analyses for plane drawing
平面图形的线段分析
1) Classify the line segment
线段的分类
Divide the line segment into
three types:known line
segment,midline segment and
stub line, base on whether the
size of line segment is
complete know or not.
按线段的尺寸是否完全
给出将其分为已知线段、中
间线段和连接线段三类。
Fig.1-67 The line segment analyses for plane
drawing
图1-67 平面图形的线段分析
79
2) Brushwork of the plane drawing
平面图形的画法
While drawing a plane drawing,all size on the drawing should be
analyzed first,to distinguish all the property of line segment and arc.
画平面图形时，应当先分析图形中的全部尺寸，分清各线
段和圆弧的性质。
Then draw the known line segment or arc, draw the midline segment,
and draw the stub line last.
在画中间圆弧和连接圆弧时，一定要找出圆心和连接点
(切点)。
While drawing the middle arc and the joint arc, the center of circle
and the conjunction point( point of contact) must be found out.
然后先画已知线段（圆弧），再画中间线段，最后画连接
线段。
80
Refer the Fig.1-67 to explain the draw steps for plane
drawing(Fig.1-68).
以图1-67所示的平面图形为例，说明其绘图步骤(图1-68)。
（b）Draw the known line
（a）Draw the base line
画出已知线
画图形的基准线
（c）Draw the midline segment
画中间线段
（d） Draw the linked
line
画出连接线段
81
（e）Label dimension
标注尺寸
（f）Widen the drawing
加深图线
Fig.1-68 The draw steps for plane drawing
图1-68 平面图形的作图步骤
82
83