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ME 111: Engineering Dra
Lecture 10
29.08.2011
Projection of Solids
Indian Institute of Technology GuwahGuwahati 781039
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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.
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Five regular polyhedra
Tetrahedronfour equal
e uilateral trian ular faces
Cube/hexahedronsixequal square faces
Octaequila
Dodecahedrontwelve equalregular pentagonal faces
Icosahedrontwenty equaequilateral triangular faces
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Prism a polyhedron formed by two equregular polygon, end faces connected bywhich are either rectangles or parallelogr
Different types of prisms
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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.
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Square pyramidTriangular pyramid Rectan
Pentagonal pyramid Hexagonal pyramid Obli
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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
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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.
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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
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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
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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
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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
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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
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Only one position in which a cylinder or a cone ma
with its base on HP.
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Four positions of a prism placed with its
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Four positions of a triangular pyram
placed with its base on HP
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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.
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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.
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Prism placed with their axis perpendicular to VP in thre
positions.
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Pyramid placed with their axis perpendicular to Vdifferent positions.
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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
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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.
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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
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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.
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Top and the front views of a hexagonal pyramid when it of its base edges with its axis or the base inclined to HP
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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.
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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.
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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.
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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.
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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.
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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
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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.
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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.
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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.
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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.
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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
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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.
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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.
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