5.Isometric Projections Solutions.pdf

Notes

1. 6.0 Isometric Projections (Using Solidworks)
SEMESTER: I/II
COURSE TITLE: COMPUTER AIDED ENGINEERING
GRAPHICS
COURSE CODE: 22MED13/23
Solution Manual
Prepared by :
Dr P R Venkatesh, Associate Professor
Room No 2, Ground Floor, Mech Engg Dept
RVCE, Bengaluru
Dr P R Venkatesh, Mech Dept, RVCE

2. Dr P R Venkatesh, Mech Dept, RVCE
WhatIsIsometricProjection?
•Isometricdrawing,alsocommonlycalledisometricprojection,isa
methodofgraphicrepresentationofthree-dimensionalobjects
throughdrawing.
•Inisometricprojection,theplanshowsthethreevisiblesidesofthe
objectfromthesameangletoeachother.Hence,theisometric
projectionshowsthesidesoftheobjectatanangleof120
0
toeach
other.Theselinesoftheobjectarecalledisometricaxes.
•Inisometricprojection,twoisometricaxesareheldatanangleof30
0
withthehorizontalplane.Whilethethirdaxisformsanangleof90
0
withthehorizontalplane.
•Graphicrepresentationsofthree-dimensionalobjectsusedby
engineers,technicalillustrators,andarchitectsaremadeusingthe
Isometricprojection.

3. Dr P R Venkatesh, Mech Dept, RVCE
Isometric Scale
Anisometricprojectionisformedusinganisometricscale.Usingthisscale,the
actualdimensionsoftheobjectareconvertedtoisometricdimensions.
Inthefig1,lineDPthelineshowsthetruescale,whilethelineDAgivesthe
isometriclength.
FromthesimilartrianglesDPOandDAO,ODisthecommonsidewhichmay
bewrittenasDPcos45
0
=DAcos30
0
Fig 2
Fig 11 3 2 2
0.816
232 23
DP DA DA DP DP DP

== == 


 Isometric length = 0.816 True length0.82 True length
Fig 2 shows the graphical method to obtain isometric length from true
lengths, which is based on the above relationship.

4. Dr P R Venkatesh, Mech Dept, RVCE
Lines in Isometric Projection
•Alinedrawnparalleltotheisometricaxisoftheobjectiscalledtheisometriclineand
itslengthisreducedby82%.
•Alineinisometricdrawingthatisnotparalleltotheisometricaxisiscalledanon-
isometricline.
•Verticallinesonanobjectarealsoverticalinisometricprojection,whilethe
horizontallinesonanobjectaredrawnatanangleof30
0
withthehorizontalin
isometricprojection.
•Themaindifferencebetweenorthographicandisometricprojectionisthatthe
orthographicdrawingrepresentsatwo-dimensionalviewoftheobject,while
isometricdrawingrepresentsthree-dimensionalviewsofthesameobject.

5. Dr P R Venkatesh, Mech Dept, RVCE
Theterm"isometric"comesfromtheGreekfor"equalmeasure",reflectingthatthescalealongeachaxisofthe
projectionisthesame.
IsometricProjectionof
circle.
Theisometricprojection
ofaisanellipse,whose
majoraxisisequalto
actualradiusofthecircle.

6. Dr P R Venkatesh, Mech Dept, RVCE
6.1Aregularpentagonalprismofbaseedge30mmandaxis60mmismountedcentrallyovera
cylindricalblockof80mmdiameterand25mmthick.Drawisometricprojectionofthecombinedsolids.
Solution:
1.Drawtheorthographicprojectionsofthecylinderandpentagonalprismcoaxialwithit.
2.Enclosethepentagonalprisminarectangle(intopview)touchingallcornersandouteredges.Thisisto
obtainboxwhichwillbearectangularprismwhoseheightisequaltothelengthofaxisoftheprism.
3.However,theenclosureforacylinderneednotbeshownasitwillbeasquareprismwithbasesideequal
todiameterofcylinderandheightequaltolengthofaxisofcylindricalblock.
4.Obtaintheisometricprojectionofcylindricalblockusing4centerapproximatemethod(toobtain
ellipticalshapeofthetop&bottomfacesinisometricprojection)
5.Obtaintheisometricprojectionofpentagonalprismbymarkingthecornersofthepentagonw.r.tthe
cornersoftherectangularboxandplaceitcoaxiallywiththecylinder.
Note:
•Toobtainisometricprojection,enclosethegivenobjectinaboxandtiptheboxonacornersuchthat
thehorizontaledgesoftheboxareat30
0
andtheverticaledgesoftheboxremainvertical,butthe
dimensionswillbe82%ofthetruedimensions(Scaleratio0.816canbeusedinsolidworks).The
cornersoftheobjectmustbemarkedw.r.tcornersofthebox.

7. X Y
VP
HP
3
0
O
8
0
2
5
6
0
3
0
°
3
0
°
46.17
4
8
.5
4
6.1 A regular pentagonal prism of base edge 30 mm and axis 60mm is mounted centrally over a cylindrical block
of 80 mm diameter and 25mm thick. Draw isometric projection of the combined solids.
Iso 25
Iso 60
Iso 80
Iso 48.54
I
s
o

4
6
.
1
7 Dr P R Venkatesh, Mech Dept, RVCE
Note:1.Inisometricprojections,outervisibleedgesmustbethick,andthe
hiddenlines/curvesmustbethin.
2.Iso80meansIsometriclengthof80=(0.816x80)=65.28mmand
soon.

8. Q 6.2 A cone of base diameter 40mm and height 50mm rests centrally over a frustrum of a pentagonal pyramid
of base side 45mm, top side 35 mm and height 55 mm. Draw isometric projections of the combination of solids.
3
5
O
4 0
5
5
5
0
3
0
°
3
0
°
7
2
.8
1
Iso 72.81
69.25
I
s
o

6
9
.
2
5
I
s
o
5
5
I
s
o

5
0
Iso 40
4
5 Dr P R Venkatesh, Mech Dept, RVCE

9. Q 6.3 A hexagonal pyramid 30mm side and height 60mm rests on the center of the top of a square block of side
60mm and height 20mm. The base edge of the pyramid is parallel to the top edge of the square block. Draw the
isometric projection of the combination of the solids.
60q
3
0
2
0
6
0
5
1
.
9
6
3
0
°3
0
°
Iso 51.96
I
s
o
2
0
I
s
o
6
0
I
s
o

6
0 Dr P R Venkatesh, Mech Dept, RVCE

10. 6.4 The frustum of a square pyramid of sides of top face 20mm, bottom face 40mm and height 60mm rests
centrally on top of a square block of side 60mm and height 20mm. The base edges of the pyramid are parallel to
the top edges of the square block. Draw the isometric projection of combination of solids.
60q
40q
20q
2
0
6
0
3
0
°
3
0
°
I
s
o

6
0
I
s
o

2
0
Iso 40
Iso 20
I
s
o
6
0 Dr P R Venkatesh, Mech Dept, RVCE

11. Q 6.5 A sphere of diameter 60mm is placed centrally on the top face of a square
prism side 60mm and height 70mm. Draw the isometric projection of the
combination.
7
0
6
0
q
O
6
0
S
3
0
°3
0
°
I
s
o
7
0
I
s
o

6
0
I
s
o

3
0
A sphere, will appear as a circle of actual radius when looked at any angle, and hence isometric
projection of a sphere will be a circle. However, the center to center height will be a vertical dimension
and hence it will be isometric length of the radius of sphere.
O60S Dr P R Venkatesh, Mech Dept, RVCE

12. Q 6.6 Draw the isometric projection of a hexagonal prism of side
of base 40mm and height 60mm with a right circular cone of base
50mm diameter and height 60mm, resting on its top such that the
axes are collinear.
O
5
0
6
0
40
6
0
6
9
.
2
8
80
3
0
°
3
0
°
I
s
o

6
0
I
s
o

8
0
I
s
o

6
0
Iso 50 Dr P R Venkatesh, Mech Dept, RVCE

13. Dr P R Venkatesh, Mech Dept, RVCE
Q 6.7 Draw the isometric projection of the combination of solids shown in Figure 6.1. I
s
o
2
0
3
0
°
3
0
°
I
s
o
5
0
I
s
o

7
0
Iso 60
Iso 40