summary of curved solids 曲曲曲曲面面面面立立立立体体体体概概概概...

Summary of Curved Solids

曲面立体概述Right Cylinder

圆柱体Cone 圆锥体圆锥体Sphere

圆球体圆球体Exercise Exercise

练习题练习题

Projection of Curved Solids 曲面立体的投影曲面立体的投影

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Right cylinder, , Cone 圆柱、圆锥圆柱、圆锥

Curved solids: When an element (a line or a curve) revolves around an Curved solids: When an element (a line or a curve) revolves around an axis, a revolution surface is produced. Curved solids that areaxis, a revolution surface is produced. Curved solids that are surrounded by revolution surfaces are called revolution.surrounded by revolution surfaces are called revolution. 曲面立体曲面立体 : : 一条母线（直线或曲线）绕一轴线回转而形成的曲一条母线（直线或曲线）绕一轴线回转而形成的曲面面 ,, 称为回转面称为回转面 ;; 由回转面所围成的立体，称为回转体。由回转面所围成的立体，称为回转体。

Sphere, Cirque 圆球、圆环圆球、圆环 Curved solids 曲面立体曲面立体 ::

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Summary of Curved Solids 曲面立体概述曲面立体概述

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1.1. Projection of a right cylinderProjection of a right cylinder 圆柱体的投影圆柱体的投影 Draw stepsDraw steps 画图步骤画图步骤：


Right Cylinder 圆柱体圆柱体

DrawDraw centerlines and centerlines and datum datum lines.lines.先画中心线和基准线；先画中心线和基准线；Add view of the upper or lower face. Add view of the upper or lower face. 再画反映顶或底面形状的视图；再画反映顶或底面形状的视图；Complete three views. Complete three views. 按三等规律画全三视图。按三等规律画全三视图。

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Limit elements are usually the boundary between visible and Limit elements are usually the boundary between visible and invisible regions of the correspondinginvisible regions of the corresponding projection direction.projection direction. 转向轮廓线通常是回转面上对某投射方向可见部分与转向轮廓线通常是回转面上对某投射方向可见部分与不可见部分的分界线。不可见部分的分界线。

MethodMethod ：：方法方法

It could be obtained on the circle following It could be obtained on the circle following the projection principle and accumulationthe projection principle and accumulation ．．利用有积聚性的圆投影求之。利用有积聚性的圆投影求之。

2.2.Getting points on the surface of a right cylinderGetting points on the surface of a right cylinder 圆柱体表面取点圆柱体表面取点

Distinguish:Distinguish: 判别判别

LabelLabel ：：标注标注

All invisible points are written in bracketsAll invisible points are written in brackets..

对不可见的点加括号以示区别。对不可见的点加括号以示区别。


Example1. Draw Example1. Draw a right cylindera right cylinder and get points on the surface. and get points on the surface. 画圆柱及表面上点的三视图

Right Cylinder 圆柱体圆柱体

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1. 1. Projection of a coneProjection of a cone 圆锥体的投影圆锥体的投影Draw stepsDraw steps 画图步骤画图步骤：


Cone 圆锥体圆锥体

DrawDraw centrelines and centrelines and datum datum lines.lines.先画中心线和基准线；先画中心线和基准线；Add view of the lower face. Add view of the lower face. 再画反映底面形状的视图；再画反映底面形状的视图；Complete three views. Complete three views. 按三等规律画全三视图。按三等规律画全三视图。

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Element methodElement method 辅助素线法

2.2.Getting points on the surface of a coneGetting points on the surface of a cone 圆锥体表面取点圆锥体表面取点

Circle methodCircle method 辅助纬圆法


Example2. Draw a cone and get points on the surface.Example2. Draw a cone and get points on the surface. 画圆锥及表面上点的三视图

Cone 圆锥体圆锥体

Limit elements are usually the boundary between visible Limit elements are usually the boundary between visible and invisible regions of the correspondingand invisible regions of the corresponding projection direction.projection direction. 转向轮廓线通常是回转面上对某投射方向可见部分与转向轮廓线通常是回转面上对某投射方向可见部分与不可见部分的分界线。不可见部分的分界线。 All invisible points are written in bracketsAll invisible points are written in brackets..


Method:Method: 方法方法


Label:Label:标注标注

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Sphere Sphere 圆球圆球体体1.1. Projection of Projection of sphere sphere 圆球体的投影圆球体的投影

Draw stepsDraw steps 画图步骤画图步骤： Draw centerlines and symmetry lines.Draw centerlines and symmetry lines.先画出各视图的回转轴线和对称中心线；先画出各视图的回转轴线和对称中心线；

Complete three limit elements of Complete three limit elements of sphere.sphere.再画三个处于转向轮廓线位置的素线圆投影。再画三个处于转向轮廓线位置的素线圆投影。


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2.2.Getting points on the surface Getting points on the surface of a sphere of a sphere 　　　　　　　　圆球体表面取点圆球体表面取点


Example3. Draw a sphere and get points on the surface.Example3. Draw a sphere and get points on the surface. 画圆球及表面上点的三视图

SphereSphere 圆球体圆球体

Circle methodCircle method 辅助纬圆法

Limit elements are usually the boundary between visible Limit elements are usually the boundary between visible and invisible regions of the correspondingand invisible regions of the corresponding projection direction.projection direction. 转向轮廓线通常是回转面上对某投射方向可见部分转向轮廓线通常是回转面上对某投射方向可见部分与不可见部分的分界线。与不可见部分的分界线。

All invisible points are written in bracketsAll invisible points are written in brackets..


MethodMethod ：：方法方法


LabelLabel ：：标注标注

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Exercise. Complete each drawing by adding the missing detail.Exercise. Complete each drawing by adding the missing detail. 补全回转体及其表面上各点的补全回转体及其表面上各点的 HH 、、 WW 面投影。面投影。

a'

c'

（（ 11 ）） Draw a cone and get points on surface.Draw a cone and get points on surface.

画圆锥及各点的三投影画圆锥及各点的三投影

b'

（（ 22 ）） Draw a sphere and get points on surface.Draw a sphere and get points on surface.

画圆球及各点的三投影画圆球及各点的三投影

c'

b'

(a' )

a

c"

(a")b"

cba

a"

(b)

(b")

c

c"

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11

b

c

a

C

S

B A

1. Draw 1. Draw a right cylindera right cylinder and get points on the surface. and get points on the surface. 画圆柱体及表面上各点的三视图。画圆柱体及表面上各点的三视图。

StepsSteps 作图步骤：作图步骤：11 ）） Draw centerlines.Draw centerlines. 画各视图的轴线画各视图的轴线; ; 22 ）） DrawDraw thethe accumulation view.accumulation view. 画有积聚性的俯视图画有积聚性的俯视图 ;;33 ）） DrawDraw thethe limit elements.limit elements. 画主视图轮廓素线画主视图轮廓素线 ;;44 ）） Draw all views of Draw all views of cylinder.cylinder. 根据投影规律求圆柱第三投根据投影规律求圆柱第三投影影 ;;55 ）） Draw all views of pointsDraw all views of points. . 由圆柱积聚性投影求各点的三投影由圆柱积聚性投影求各点的三投影。。

请请点点击击鼠鼠标标左左键键显显示示后后面面内内容容

c"c"a"a"

(b"b"))

a'((c'c'))

b'b'

12

S

A

BC

K

k a

1

b

2. Draw a cone and get points on the surface.2. Draw a cone and get points on the surface. 画圆锥体及其表面上各点的三视图。画圆锥体及其表面上各点的三视图。

Steps Steps 作图步骤：11 ）） Draw centerlines. Draw centerlines. 画各视图的轴线画各视图的轴线 ;;

22 ）） DrawDraw thethe top view.top view. 画俯视图的底圆轮廓画俯视图的底圆轮廓 ;;

33 ）） DrawDraw thethe limit elements.limit elements. 画主视图轮廓线画主视图轮廓线;;44 ）） Draw all views of Draw all views of cone.cone. 求圆锥的第三投影求圆锥的第三投影 ;;

55 ）） Draw all views of Draw all views of AA.. 求求 AA 点三投影点三投影 (( 辅助素线辅助素线法法 ););66 ）） Draw all views of Draw all views of BB.. 根据根据 BB 点的特殊位置求其三投点的特殊位置求其三投影影 ;;7)7) Draw all views of Draw all views of CC.. 求求 CC 点的三投影点的三投影 (( 辅助纬圆法辅助纬圆法 ))。。请点击鼠标左键显示后面内容请点击鼠标左键显示后面内容

b"

(a")a'

(c') c"

c

1′

PP''

PP

k"k'

b'

13

D

C B

A S

c

a

3. Draw a sphere and get points on the surface.3. Draw a sphere and get points on the surface. 画圆球体及其表面上各点的三视图。画圆球体及其表面上各点的三视图。

StepsSteps 作图步骤作图步骤：11 ）） Draw centerlines. Draw centerlines. 画各视图的轴线画各视图的轴线 ;;22 ）） DrawDraw thethe limit elements.limit elements. 画处于轮廓位置的素线圆投影画处于轮廓位置的素线圆投影 ;;33 ）） Draw all views of Draw all views of AA.. 根据根据 AA 点的特殊位置求其三投点的特殊位置求其三投影影 ;;44 ）） Draw all views of Draw all views of BB、、 CC.. 根据根据 BB..CC 点的特殊位置求其三投影点的特殊位置求其三投影;;55 ）） Draw all views ofDraw all views of DD.. 求求 DD 点的三投影点的三投影 (( 用辅助平面法用辅助平面法 ))。。


a"a"a'a'

((c"c"))c'c'

d"d'd'

b"b"((b'b'))

b

(d)

PP''

PP

14

在图片上点击鼠标左键可以“暂停”或再次“播放”在图片上点击鼠标左键可以“暂停”或再次“播放”

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在图片上点击鼠标左键可以“暂停”或再次“播放”在图片上点击鼠标左键可以“暂停”或再次“播放”

summary of curved solids 曲曲曲曲 面面面面 立立立立 体体体体 概概概概...

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summary of curved solids 曲曲曲曲面面面面立立立立体体体体概概概概...