2008秋季第10讲平面立体课件 机械制图 北京航空航天大学出版社

s

s
⑵
棱锥的三视图Three views of the pyramid
a a c a(c) c b
三棱锥处于图示位置时，其底 面ABC是水平面，在俯视图上反映 实形。侧棱面SAC为侧垂面，另两 个侧棱面为一般位置平面。Triangular
Pyramid be located as right figure. Its bottom is horizontal plane and shows true shape in the Top view. Side SAC is W-perpendicular plane and the other two sides are oblique planes.
正六棱柱
Right hexagonal prism
消隐后效果 After hidding the invisible edges
5.4 平面与平面立体相交（切割型平面立体）
Intersection of a plane and a polyhedra (Cut-like polydedra)
截切： 用一个平面与立体相交，截去立体的一部分。
Front view( Main view)-Frontal projection Top view-Horizontal projection Left view-Profile projection
Three projections and Three views
高
主视图 —— 体的正面投影 俯视图 —— 体的水平投影 左视图 —— 体的侧面投影
s b
⑶
在棱锥面上取点

Locate points on the faces of the pyramid
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s
同样采用平面上取点法。
The same method as the locating points on the plane
k n ( n ) a a b c ac (c b ) a c s k n
⑶ 棱柱面上取点Locate points on the faces of prism
由于棱柱的表面都是平面， 所以在棱柱的表面上取点与在 a 平面上取点的方法相同。 (b )

a

All the faces of the prism are planes on which locating points can be the same way as locating points on plane.
俯视左视宽相等且对应
Top and Left views are equal in width
长对正 高平齐 宽相等
宽
3.三视图之间的方位对应关系
Corresponding orientations of three views
上Top
左Left 右Right 后Back
上Top
前Front
下Bottom 后Back
Cutting : Cut down part of a object with a plane
截平面 Cutting plane — 用以截切物体的平面
Plane used to cut the object。
截交线Line of section — 截平面与物体表面的交线。
Intersection line of cutting plane and the surfaces of object.
基本几何体
Basic Solid
平面体
Plane solid
棱柱 Prism 棱锥 Pyramid 圆柱 Cylinder
回转体 空间形体
Solids Revolved solid
圆锥 Cone
圆球 Sphere
堆垒型 Piled-like 组合体
Complex
切割型 Cut-like 相贯型 Penetrated-liDrawing of the cut-like polyhedra
关键是正确地画出截交线的投影。
The key is the section.
⒈ 求截交线的两种方法Two ways：
★ 求各棱线与截平面的交点→棱线法。
Find the intersection points of the edges and the cutting plane->edge method
Projections of solid are Combination of the projections of all the surfaces by which that solid is constructed.
一、体的投影
Projections of Solid
V
二、三面投影与三视图 1.视图的概念 Views
☆ 截平面与体的相对位置
The position of the cutting plane toward the object
确定截交 线的形状
Determine the shape of the section
☆ 截平面与投影面的相对位置
The position of the cutting plane toward the projection plane
★ 求各棱面与截平面的交线→棱面法。
Find the intersection line of the faces and the cutting plane->face method
⒉ 求截交线的步骤Steps： ★ 空间及投影分析Analysis of the spatial object and projections

k
b
平面基本体
Plane Basic Solids
棱柱 Prism 正棱柱 Right prism 斜棱柱 Oblique prism
棱锥 Pyramid 正棱锥 Right pyramid 斜棱锥 Oblique pyramid 正四棱锥
Right square pyramid
棱台
Frustum ( Truncated Pyramid )
例1：求四棱锥被截切后的俯视图和左视图。
Complete the top view and left view of the truncated square pyramid.
2.棱锥Pyramid
⑴ 棱锥的组成 Construct of Pyramid 由一个底面和几个侧棱面 组成。侧棱线交于一点——锥 顶。 A pyramid has a polygon for a base
and triangular lateral faces intersecting at a common point called the Vertex
长
宽
2.三视图之间的度量对应关系
主视俯视长相等且对正
Front and Top views are equal in length Corresponding relations of three views
三等关系
Tri-equality
主视左视高相等且平齐
Front and Left views are equal in height
截断面Section — 因截平面的截切，在物体上形成的平面。
The face produced by the cutting
讨论的问题：截交线的分析和作图 。
Problems to be solved: lines of section
一、平面立体截切的基本形式
The usual ways by which the polyhedra be cut
截交线的性质Characteristics of the
section ：
截交线是一个由直线组成的封闭的平面多边形，其形状 取决于平面体的形状及截平面对平面体的截切位置。
Section is a closed , planar polygon bounded by lines. The shape of section is determined by the shape of the object and the position of the cutting plane.

b
b
点的可见性规定：
Regulation about the visibility of point
a
若点所在的平面的投影可见，点的投影也可见；若平 面的投影积聚成直线，点的投影也可见。
Point is visible if the plane that contains the point is visible; Point is regarded as visible if the plane containing the point is concentrated to line.
第五章
Chapter 5
平面立体
Polyhedra (Plane Solid)
平面立体：全部由平面多边形围成的立体
Polyhedra: Solids bounded by plane surfaces . The surfaces are called faces.
5.1 空间形体的分类 Classification of Solids
截交线的每条边是截平面与棱面的交线。
The edges of section are the intersection of the cutting plane and faces of the object.
求截交线的实质是求两平面的交线
Determining the section means finding the intersection of two planes