Lecture10 Projection of Solids

7/31/2019 Lecture10 Projection of Solids

1/40

ME 111: Engineering Dra

Lecture 10

29.08.2011

Projection of Solids

Indian Institute of Technology GuwahGuwahati 781039


2/40

SolidsA 3-D object having length, breadth and thicknes

by surfaces which may be either plane or curved

of the two.

Classified under two main headings

Polyhedron

Solids of revolution

Regular polyhedron solid bounded only by pla(faces). Its faces are formed by regular polygons

all dihedral angles are equal to one another.

Other polyhedra when faces of a polyhedron equal identical faces, they may be classified into

pyramids.


3/40

Five regular polyhedra

Tetrahedronfour equal

e uilateral trian ular faces

Cube/hexahedronsixequal square faces

Octaequila

Dodecahedrontwelve equalregular pentagonal faces

Icosahedrontwenty equaequilateral triangular faces


4/40

Prism a polyhedron formed by two equregular polygon, end faces connected bywhich are either rectangles or parallelogr

Different types of prisms


5/40

Pyramids a polyhedron formed by a planeits base and a number of triangles as its smeeting at a point, called vertex or apex.

Axis the imaginary line connecting the apecenter of the base.

Inclined/slant faces inclined triangular sid

the apex and the base corners.

Right pyramid when the axis of the pyramperpendicular to its base.

Oblique pyramid when the axis of the pyrainclined to its base.


6/40

Square pyramidTriangular pyramid Rectan

Pentagonal pyramid Hexagonal pyramid Obli


7/40

Solids of revolution when some of the plane revolved about one of their sides solids of revolutio

Cylinder when a rectangle

Sphis revolved about one of its sides,the other parallel side generates acylinder.

revolved about one of its sides,the hypotenuse of the righttriangle generates a cone.

is revdiame

Oblique cylinder when a parallelogram isrevolved about one of its

sides, the other parallel sidegenerates a cylinder.

O


8/40


9/40

Visibility when drawing the orthographic views o

object, it will be required to show some of the hidden

as invisible and are shown on the orthographic view

Rules of visibility

All outlines of every view are visible the outline

the views are shown by full lines.


10/40

In the top view, the highest portions of the objec

Frustum of a pentagonal py

face ABCDE is the highest,visible in the top view.

In the top view, edges ab, bcare shown as full lines.pentagonal faces A1B1C1D

,

The slant edges AA1, BB1EE1 are invisible in the top vare shown as lines of dashe

The line connecting a visibinvisible point is shownline of dashes unless they


11/40

In the front view - the front faces of the objecIn the front vie

ABB1A1 and B

front faces, hen

In the front view

b, c and a1, b1,

the observer. H

view, the lines

c c 1 are s own

The corners d,

invisible in the f

lines, ee1, dd

hence shown a

The top rear e

and dc coinci

front visible edge

Object


12/40

In the side view - the face lying on that side

As sheen

view, the c

and e1, a1side and

the left vie

aa1 an

shown as

edges d

coincide w

edges ee

respective


13/40

Projections of solids placed in differe

The solids may be placed on HP in various positions

(1) The way the axis of the solid is held with respec

both -

Perpendicular to HP or VP

Parallel to either HP or VP and incline

Inclined to both HP and VP


14/40

Axis of the solid perpendicular t

A solid when placed on HP with its axis perpendicula

will have its base on HP. This is the simplest positio

solid can be placed.

When the solid is placed with the base on HP pos

top view, the base will be projected in its true sha

Hence, when the base of the solid is on HP, the top v

first and then the front view and the side views are pr


15/40

Only one position in which a cylinder or a cone ma

with its base on HP.


16/40

Four positions of a prism placed with its


17/40

Four positions of a triangular pyram

placed with its base on HP


18/40

Axis of the solid perpendicular t

When a solid is placed with its axis perpendicbase of the solid will always be perpendiculparallel to VP.

Hence in the front view, base will be projshape

Therefore, when the axis of the solid is perpenthe front view is drawn first and then the top aare drawn from it.


19/40

When a cylinder rests on HP with

its axis perpendicular to VP, one ofits generators will be on HP.

When a cone rests on HP wperpendicular to VP, one ofthe circumference of the ba

HP.


20/40

Prism placed with their axis perpendicular to VP in thre

positions.


21/40

Pyramid placed with their axis perpendicular to Vdifferent positions.


22/40

Axis of the solid inclined to HP and para

When a solid is placed onHP with its axis inclined to

HP, the elemental portionof the solid that lies on

HP depends upon thetype of the solid.

When a p

HP with its

it, then itone of itson one o

HP.

When a pyramid is placed onaxis inclined to HP, then wone of its base edges on HPbase corners on HP or one

edges on HP or one of itfaces on HP or an apex on H


23/40

Case 1. When the solid lies with an e

base on HPIf the solid is required to be placed

edge of the base on HP, then init

solid has to be placed with its base

suc a an e ge o e

perpendicular to VP, i.e., to XY line in

preferably to lie on the right side.


24/40

When the solid lies with an edge of base o

When a pehas to be

edge of bathat the bainclined tothe prism isbase on HPthe base p

right side.

In this positiotop and frontdrawn with th(c1)(d1) perp

line in the topfront view, thappears as a


25/40

Since the prism has to lie with anedge of the base on HP, the frontview of the prism is tilted on the

edge c1(d1) such that the axis isinclined at to HP.

Redraw the first front view in thetilted position.

Whenever the inclination of axis with HP is given, first the base is

rawn a - n e ron v ew,otherwise improper selection of theposition of the axis may result inthe base edge c1(d1) lying aboveor below the XY line.

The second top view is projectedby drawing the vertical projectorsfrom the corners of the secondfront view and the horizontalprojectors from the first top view.


26/40

Top and the front views of a hexagonal pyramid when it of its base edges with its axis or the base inclined to HP


27/40

Case.2 : When the solid lies on one of of the base on HP

When a solid lies on one of its corners of the base on

edges of the base containing the corner on which it lies m

inclinations or different inclination with HP.

Corner of the base on HP with two base ed es contaon which it rests make equal inclinations with HP

Initially the solid should be placed with its base on H

imaginary line connecting the center of the base

corners is parallel to VP, i.e. to XY line in the top view,

lie on the right side.


28/40

For example, when ahexagonal prism has tobe placed with a corner

of the base on HP suchthat the base or theaxis is inclined to HP,then initially the the prismis placed with its base onHP such that animaginary lineconnecting the centerof the base and acorner is parallel to VPand it lies on the rightside.

In this position, the firstset of top and front viewsare drawn the line(o1)(d1) is parallel to theXY line in the top view.


29/40

Since the prism has to lieon one of its corners ofthe base on HP, the front

view of the prism is tiltedon the corner d1 suchthat the axis is inclined at to HP.

Redraw the front view inthe tilted position. The

(90- ) in the front view.

The second top view isprojected by drawing thevertical projectors fromthe corners of the second

front view and horizontalprojectors from the firsttop view.


30/40

Case.2 for Pyramid: The top and front views of the prests on HP on one of its base corners such thaedges containing the corner on which it rest

inclinations with HP.


31/40

Case-3 When a pyramid lies on one of its triangu

HPIf a pyramid has to beplaced on one of its

triangular faces onHP, then initially letthe pyramid beplaced with its baseon HP.

In the first front view,

line, i.e., oc(d)represents atriangular face.

Redraw the front viewsuch that the

triangular faceoc(d) lies on HP.

Project the top view inthis position.


32/40

CASE-4: When a pyramid lies on one of its slant

When a pyramid lies with one of its slant edges on H

triangular faces containing the slant edge on which ieither equal inclinations or different inclinations with


33/40

Methods of drawing the projections of sol

Two methods

1. Change of position method - the solids are place

simple position and then tilted successively in two o

to obtain the final osition.

SOLID WITH AXIS INCLINED TO BOTH THE

2. Auxiliary plane method (Change of reference-lin

the solids are placed initially in the simple position a

two auxiliary planes are setup to obtain the views in

position.


34/40

Problem.1 A cube of 30 mm side rests with one of its edgeone of the square faces containing that edge is inclined the edge on which it rests being inclined to 600 to VP. Dprojections.


35/40

Problem2. Draw the top and front views of a rectangulaof base 40x 50 mm and height 70 mm when it lies ontriangular faces on HP. The longer edge of the base of tlying on HP is inclined at 600 to VP in the top view wit

pyramid being nearer to VP.


36/40

Problem-3: A Hexagonal Pyramid, base 25 mm si

mm long, has one of its slant edges on the gro

containing that edge and the axis is perpendicular

inclined at 45

0

to VP. Draw the projections whnearer to the VP than the base.

Draw the TV of the pyramid

with a side of base parallel to

XY. The slant edges AO and DO

.FV also.

Tilt the FV so that do is in XY.

Project the second TV.

Draw a new reference line X1Y1making 45o angle with o1p1 (the

top view of the axis) and project

the final FV.


37/40

Problems on cones

Problem4. A cone of base 80 mm diameter and height 10

one of its generators on HP and the axis appears to be

at an angle of 400 in the top view. Draw its top and fron


38/40

Problem5.

A cone of base 60 mm diameter and the axis 80 mm long lies inclined at 450 and 300 to HP and VP, respectively. Draw theviews of the cone.


39/40

SOLID WITH AXIS INCLINED TO BOTH THE

If the axis of a solid is inclined to both the RPs thensolved in three stages.

Example: A triangular pyramid of edge of base s mmaxis h mm is resting on a side of base on the HP.pyramid is inclined at to the HP and to theprojections.


40/40

Documents

Lecture10 Projection of Solids