1. The document describes various solids and their classification into two groups - Group A consisting of solids with bases and tops of the same shape, and Group B consisting of solids with bases of some shape and just a point as the top.
2. Dimensional parameters of different solids like cylinders, cones, prisms and pyramids are defined. Positions of solids relative to planes are also described.
3. Three step methods for solving problems involving solids inclined to horizontal and vertical planes are outlined. Various categories of illustrated problems involving different cases are listed.
Section of solids - ENGINEERING DRAWING/GRAPHICSAbhishek Kandare
Section of solids
THIS SLIDE CONTAINS WHOLE SYLLABUS OF ENGINEERING DRAWING/GRAPHICS. IT IS THE MOST SIMPLE AND INTERACTIVE WAY TO LEARN ENGINEERING DRAWING.SYLLABUS IS RELATED TO rajiv gandhi proudyogiki vishwavidyalaya / rajiv gandhi TECHNICAL UNIVERSITY ,BHOPAL.
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
Section of solids - ENGINEERING DRAWING/GRAPHICSAbhishek Kandare
Section of solids
THIS SLIDE CONTAINS WHOLE SYLLABUS OF ENGINEERING DRAWING/GRAPHICS. IT IS THE MOST SIMPLE AND INTERACTIVE WAY TO LEARN ENGINEERING DRAWING.SYLLABUS IS RELATED TO rajiv gandhi proudyogiki vishwavidyalaya / rajiv gandhi TECHNICAL UNIVERSITY ,BHOPAL.
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
Download the original presentation for animation and clear understanding. This Presentation describes the concepts of Engineering Drawing of VTU Syllabus. However same can also be used for learning drawing concepts. Please write to me for suggestions and criticisms here: hareeshang@gmail.com or visit this website for more details: www.hareeshang.wikifoundry.com.
Download the original presentation for animation and clear understanding. This Presentation describes the concepts of Engineering Drawing of VTU Syllabus. However same can also be used for learning drawing concepts. Please write to me for suggestions and criticisms here: hareeshang@gmail.com or visit this website for more details: www.hareeshang.wikifoundry.com.
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
Download the original presentation for animation and clear understanding. This Presentation describes the concepts of Engineering Drawing of VTU Syllabus. However same can also be used for learning drawing concepts. Please write to me for suggestions and criticisms here: hareeshang@gmail.com or visit this website for more details: www.hareeshang.wikifoundry.com.
Download the original presentation for animation and clear understanding. This Presentation describes the concepts of Engineering Drawing of VTU Syllabus. However same can also be used for learning drawing concepts. Please write to me for suggestions and criticisms here: hareeshang@gmail.com or visit this website for more details: www.hareeshang.wikifoundry.com.
This presentation gives the information about introduction to control systems
Subject: Control Engineering as per VTU Syllabus of Aeronautical Engineering.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
Disclaimer:
The contents used in this presentation are taken from the text books mentioned in the references. I do not hold any copyrights for the contents. It has been prepared to use in the class lectures, not for commercial purpose.
This template was created for DSCE, Aeronautical students. You have to replace the institution details.
Create a separate document for each chapter, so that under numbering, you can change the sequence of chapter main heading according to chapter wise. i.e., 2.1, 2.2 etc.
Same procedure is applicable to Figure caption and Table caption.
This template can be used to generate, BE seminar report, M.Tech and Ph.D thesis also.
This template is created to assist UG students in generating their thesis without much hassle.
Contents are taken from VTU website. I don’t hold any copyright for this document.
Hareesha N G
Assistant Professor
DSCE, Bengaluru
This document is an Instruction manual for Computer aided machine drawing
Subject: Computer aided machine drawing (CAMD)
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
This document gives the class notes of Unit-8: Torsion of circular shafts and elastic stability of columns. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
This document gives the class notes of Unit-8: Torsion of circular shafts and elastic stability of columns. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
This document gives the class notes of Unit 6: Bending and shear Stresses in beams. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
This document gives the class notes of Unit 5 shear force and bending moment in beams. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
This document gives the class notes of Unit 3 Compound stresses. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
This document gives the class notes of Unit 2 stresses in composite sections. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
This document contains: Mechanics of Materials: Question bank from old VTU Question papers ; Pprepared by Hareesha N G, DSCE, Bengaluru. These questions are picked from last 06 years of old VTU question papers.
This presentation was prepared for a seminar. I have shared this with you. This is not related to curriculam. Please writre your criticisms to: hareeshang@gmail.com.
This presentation gives the information about Screw thread measurements and Gear measurement of the subject: Mechanical measurement and Metrology (10ME32/42) of VTU Syllabus covering unit-4.
This presentation gives the information about Force, Pressure and Torque measurements of the subject: Mechanical measurement and Metrology (10ME32/42) of VTU Syllabus covering unit-6.
This presentation gives the information about mechanical measurements and measurement systems of the subject: Mechanical measurement and Metrology (10ME32/42) of VTU Syllabus covering unit-5.
This CIM and automation laboratory manual covers the G-Codes and M-codes for CNC Turning and Milling operations. Some concepts of Robot programming are also introduced.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
How to Create Map Views in the Odoo 17 ERPCeline George
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Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Model Attribute Check Company Auto PropertyCeline George
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Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
2. SOLIDS
To understand and remember various solids in this subject properly,
those are classified & arranged in to two major groups.
Group A
Group B
Solids having top and base of same shape
Solids having base of some shape
and just a point as a top, called
apex.
Cylinder
Cone
Prisms
Triangular
Cube
Square
( A solid having
12/18/13
six square faces)
Pyramids
Pentagonal Hexagonal
Triangular
Square
Pentagonal Hexagonal
Tetrahedron
( A solid having
Four triangular faces)
Hareesha N G, DSCE, Blore
2
3. SOLIDS
Dimensional parameters of different solids.
Square Prism
Corner of
base
Cylinder
Slant
Edge
Base
Edge
of
Base
Base
Edge
of
Base
Cone
Apex
Apex
Top
Rectangular
Face
Longer
Edge
Square Pyramid
Triangular
Base
Face
Corner of
base
Base
Generators
Imaginary lines
generating curved surface
of cylinder & cone.
Frustum of cone & pyramids.
Sections of solids( top & base not parallel)
12/18/13
Hareesha N G, DSCE,top & base parallel to each other)
( Blore
3
4. STANDING ON H.P
On it’s base.
(Axis perpendicular to Hp
And // to Vp.)
F.V.
X
X
RESTING ON H.P
On one point of base circle.
(Axis inclined to Hp
And // to Vp)
F.V.
LYING ON H.P
On one generator.
(Axis inclined to Hp
And // to Vp)
F.V.
While observing Fv, x-y line represents Horizontal Plane. (Hp)
While observing Tv, x-y line represents Vertical Plane. (Vp)
T.V.
T.V.
Y
Y
T.V.
STANDING ON V.P
RESTING ON V.P
On it’s base.
On one point of base circle.
Axis inclined to Vp
12/18/13 Axis perpendicular to Vp
Hareesha N G, DSCE, Blore
And // to Hp
And // to Hp
LYING ON V.P
On one generator.
Axis inclined to Vp
And // to Hp
4
5. STEPS TO SOLVE PROBLEMS IN SOLIDS
Problem is solved in three steps:
STEP 1: ASSUME SOLID STANDING ON THE PLANE WITH WHICH IT IS MAKING INCLINATION.
( IF IT IS INCLINED TO HP, ASSUME IT STANDING ON HP)
( IF IT IS INCLINED TO VP, ASSUME IT STANDING ON VP)
IF STANDING ON HP - IT’S TV WILL BE TRUE SHAPE OF IT’S BASE OR TOP:
IF STANDING ON VP - IT’S FV WILL BE TRUE SHAPE OF IT’S BASE OR TOP.
BEGIN WITH THIS VIEW:
IT’S OTHER VIEW WILL BE A RECTANGLE ( IF SOLID IS CYLINDER OR ONE OF THE PRISMS):
IT’S OTHER VIEW WILL BE A TRIANGLE ( IF SOLID IS CONE OR ONE OF THE PYRAMIDS):
DRAW FV & TV OF THAT SOLID IN STANDING POSITION:
STEP 2: CONSIDERING SOLID’S INCLINATION ( AXIS POSITION ) DRAW IT’S FV & TV.
STEP 3: IN LAST STEP, CONSIDERING REMAINING INCLINATION, DRAW IT’S FINAL FV & TV.
GENERAL PATTERN ( THREE STEPS ) OF SOLUTION:
GROUP B SOLID.
CONE
AXIS
AXIS
VERTICAL INCLINED HP
AXIS
INCLINED VP
Three steps
If solid is 12/18/13 to Hp
inclined
AXIS
INCLINED HP
AXIS
AXIS
VERTICAL INCLINED HP
AXIS
INCLINED VP
GROUP A SOLID.
CYLINDER
GROUP B SOLID.
CONE
GROUP A SOLID.
CYLINDER
AXIS
er
TO VP
AXIS
INCLINED
VP
Three steps
Three steps
If solid is inclined to Vp
If solid is inclined to Hp N G, DSCE, Blore
Hareesha
AXIS
INCLINED HP
AXIS
er
TO VP
AXIS
INCLINED
VP
Three steps
If solid is inclined to Vp
5
Study Next Twelve Problems and Practice them separately !!
6. CATEGORIES OF ILLUSTRATED PROBLEMS!
PROBLEM NO.1, 2, 3, 4
GENERAL CASES OF SOLIDS INCLINED TO HP & VP
PROBLEM NO. 5 & 6
CASES OF CUBE & TETRAHEDRON
PROBLEM NO. 7
CASE
OF FREELY SUSPENDED SOLID WITH SIDE VIEW.
PROBLEM NO. 8
CASE
OF CUBE ( WITH SIDE VIEW)
PROBLEM NO. 9
CASE
OF TRUE LENGTH INCLINATION WITH HP & VP.
PROBLEM NO. 10 & 11
CASES OF COMPOSITE SOLIDS. (AUXILIARY PLANE)
PROBLEM NO. 12
CASE
12/18/13
OF A FRUSTUM (AUXILIARY PLANE)
Hareesha N G, DSCE, Blore
6
7. Problem 1. A square pyramid, 40
mm base sides and axis 60 mm long,
has a triangular face on the ground
and the vertical plane containing the
axis makes an angle of 450 with the
VP. Draw its projections. Take apex
nearer to VP
Solution Steps :
Triangular face on Hp , means it is lying on Hp:
1.Assume it standing on Hp.
2.It’s Tv will show True Shape of base( square)
3.Draw square of 40mm sides with one side vertical Tv &
taking 50 mm axis project Fv. ( a triangle)
4.Name all points as shown in illustration.
5.Draw 2nd Fv in lying position I.e.o’c’d’ face on xy. And project it’s Tv.
6.Make visible lines dark and hidden dotted, as per the procedure.
7.Then construct remaining inclination with Vp
( Vp containing axis ic the center line of 2 nd Tv.Make it 450 to xy as
shown take apex near to xy, as it is nearer to Vp) & project final Fv.
o’
a’b’
c’
d’
o
d1
a1
For dark and dotted lines
c1
c’1
d’1
a1
o1
c
o’1
d
o1 1
d1
b1
1.Draw proper outline of new view DARK. 2. Decide direction of an observer.
Hareesha N from it-dark.
3. Select 12/18/13
nearest point to observer and draw all lines starting G, DSCE, Blore
4. Select farthest point to observer and draw all lines (remaining)from it- dotted.
Y
a1
b
d
o’
a
c’d’
X a’b’
b’1
a’1
c1
b 1(APEX
c1
NEARER
TO V.P).
b
1
o
(APEX
AWAY
1
FROM V.P.)
7
8. Solution Steps:
Resting on Hp on one generator, means lying on Hp:
1.Assume it standing on Hp.
2.It’s Tv will show True Shape of base( circle )
3.Draw 40mm dia. Circle as Tv &
taking 50 mm axis project Fv. ( a triangle)
4.Name all points as shown in illustration.
5.Draw 2nd Fv in lying position I.e.o’e’ on xy. And
project it’s Tv below xy.
6.Make visible lines dark and hidden dotted,
as per the procedure.
7.Then construct remaining inclination with Vp
( generator o1e1 300 to xy as shown) & project final Fv.
Problem 2:
A cone 40 mm diameter and 50 mm axis
is resting on one generator on Hp
which makes 300 inclination with Vp
Draw it’s projections.
For dark and dotted lines
1.Draw proper outline of new vie
DARK.
2. Decide direction of an observer.
3. Select nearest point to observer
and draw all lines starting from
it-dark.
4. Select farthest point to observer
and draw all lines (remaining)
from it- dotted.
a’
h’b
’ c’
g’
a’ h’b’
h
c’ g
’
g
f’ d’ e’
o’
g1
f
f1
f’1
e e1
b
b’1
e’1
g1
h1
c’
d’1 1
a1
b
d1
d
Hareesha N G, DSCE,1 Blore
c
c1
o1
Y
a1
b1
e1
d1
o1
30
o1
h1
f1
a
12/18/13
h’1
a’1
g’1
d
’f’
e’
X
o’
c1
8
9. Solution Steps:
Problem 3:
Resting on Vp on one point of base, means inclined to Vp:
1.Assume it standing on Vp
A cylinder 40 mm diameter and 50 mm
will show
axis is resting on one point of a base 2.It’s Fv40mm dia.True Shape of base & top( circle ) project Tv.
3.Draw
Circle as Fv & taking 50 mm axis
0
circle on Vp while it’s axis makes 45 ( a Rectangle)
with Vp and Fv of the axis 350 with 4.Name all points as shown in illustration.
Hp.
5.Draw 2nd Tv making axis 450 to xy And project it’s Fv above xy.
Draw projections..
6.Make visible lines dark and hidden dotted, as per the procedure.
7.Then construct remaining inclination with Hp
( Fv of axis I.e. center line of view to xy as shown) & project final Tv.
4’
4’d’
d’
3’
c’ a’
1’ a’
4’
c’
d’
3’
c’
3’
1’
1’
a’
2’ b’
bd
c
2’
450
350
c
a
b’
d1
bd
X
2’
Y
b’
c1
b1
a1
3
a
3
24
3
Hareesha N G, DSCE, Blore
1
1
12/18/13
24
4
2
9
1
10. Solution Steps:
Problem 5: A cube of 50 mm long
edges is so placed on Hp on one
corner that a body diagonal is
parallel to Hp and perpendicular to
Vp Draw it’s projections.
1.Assuming standing on Hp, begin with Tv,a square with all sides
equally inclined to xy.Project Fv and name all points of FV & TV.
2.Draw a body-diagonal joining c’ with 3’( This can become // to xy)
3.From 1’ drop a perpendicular on this and name it p’
4.Draw 2nd Fv in which 1’-p’ line is vertical means c’-3’ diagonal
must be horizontal. .Now as usual project Tv..
6.In final Tv draw same diagonal is perpendicular to Vp as said in problem.
Then as usual project final FV.
a’
a’1
b’d
’
c’
c’1
1’
3’
1’
d
d1
d1
a
c
a1
1’
Y
c1
a1
X
c’
p’
3’
p’
b1
b’d’
d’1
c1
a’
d’1
12/18/13
b
b1
Hareesha N G, DSCE, Blore
10
11. Problem 6:A tetrahedron of 50 mm
long edges is resting on one edge on
Hp while one triangular face containing
this edge is vertical and 450 inclined to
Vp. Draw projections.
IMPORTANT:
Tetrahedron is a
special type
of triangular
pyramid in which
base sides &
slant edges are
equal in length.
Solid of four faces.
Like cube it is also
described by One X
dimension only..
Axis length
generally not given.
Solution Steps
As it is resting assume it standing on Hp.
Begin with Tv , an equilateral triangle as side case as shown:
First project base points of Fv on xy, name those & axis line.
From a’ with TL of edge, 50 mm, cut on axis line & mark o’
(as axis is not known, o’ is finalized by slant edge length)
Then complete Fv.
In 2nd Fv make face o’b’c’ vertical as said in problem.
And like all previous problems solve completely.
o’1
o’
o’
TL
a’
90
b’
c’
a
a’1
b’ c’
c
a’
0
c1
o
b’1
c’1
450
a1
c1
o1
o1
b1
12/18/13
b
Hareesha N G, DSCE, Blore
b1
a1
11
Y
12. FREELY SUSPENDED SOLIDS:
Positions of CG, on axis, from base, for different solids are shown below.
CG
H
H/2
CG
H/4
GROUP A SOLIDS
( Cylinder & Prisms)
12/18/13
GROUP B SOLIDS
( Cone & Pyramids)
Hareesha N G, DSCE, Blore
12
13. Problem 7: A pentagonal pyramid
30 mm base sides & 60 mm long axis,
is freely suspended from one corner of
base so that a plane containing it’s axis
remains parallel to Vp.
Draw it’s three views.
Solution Steps:
In all suspended cases axis shows inclination with Hp.
1.Hence assuming it standing on Hp, drew Tv - a regular pentagon,corner case.
2.Project Fv & locate CG position on axis – ( ¼ H from base.) and name g’ and
Join it with corner d’
3.As 2nd Fv, redraw first keeping line g’d’ vertical.
4.As usual project corresponding Tv and then Side View looking from.
LINE
o’
d’g’ VERTICAL
d’
d”
c’e’
FOR SIDE VIEW
g’
H
e”
a’b’
g’
IMPORTANT:
When a solid is freely
suspended from a
corner, then line
joining point of
contact & C.G.
remains vertical.
( Here axis shows
inclination with Hp.)
So in all such cases,
assume solid standing
12/18/13
on Hp initially.)
X
H/4
c’ e’
a’ b’
a”
b”
o”
d’
Y
e1
e
a1
a
do
1
o
c”
d1
b
b1
c
Hareesha N G, DSCE, Blore
c1
13
14. Solution Steps:
1.Assuming it standing on Hp begin with Tv, a square of corner case.
2.Project corresponding Fv.& name all points as usual in both views.
3.Join a’1’ as body diagonal and draw 2nd Fv making it vertical (I’ on xy)
4.Project it’s Tv drawing dark and dotted lines as per the procedure.
5.With standard method construct Left-hand side view.
a’’
d’’
’
b’d
a’
b’d’
A cube of 50 mm long edges is so placed
on Hp on one corner that a body diagonal
through this corner is perpendicular to Hp
and parallel to Vp Draw it’s three views.
a’
( Draw a 450 inclined Line in Tv region ( below xy).
Project horizontally all points of Tv on this line and
reflect vertically upward, above xy.After this, draw
horizontal lines, from all points of Fv, to meet these
lines. Name points of intersections and join properly.
For dark & dotted lines
locate observer on left side of Fv as shown.)
Problem 8:
c’
c’
X
d
a
a1
Y
c1
Hareesha N G, DSCE, Blore
b
c’’
1’
d1
c
12/18/13
1’
1’
b’’
b
14
15. Problem 9: A right circular cone,
40 mm base diameter and 60 mm
long axis is resting on Hp on one
point of base circle such that it’s
axis makes 450 inclination with
Hp and 400 inclination with Vp.
Draw it’s projections.
This case resembles to problem no.7 & 9 from projections of planes topic.
In previous all cases 2nd inclination was done by a parameter not showing TL.Like
Tv of axis is inclined to Vp etc. But here it is clearly said that the axis is 40 0 inclined
to Vp. Means here TL inclination is expected. So the same construction done in those
Problems is done here also. See carefully the final Tv and inclination taken there.
So assuming it standing on HP begin as usual.
o’1
o’
o’
a’1
a’
h’1
b’1
h’b
’g’
’c
f’ d’ e’
450
g1
h1
f
a
e
b
d
c
f’1
a1
e’
g
h
o1
d’1
400
e’1
y
Axis True Length
f1
1
b1
e1
d1
Axis Tv Length
e1
o1
f1
d1
g1
c1
Axis Tv Length
12/18/13
c’1
’
c’ g’
d’f
X
a’ h’b’
g’1
Hareesha N G, DSCE, Blore
b1
1
h1
c1
Locus of
Center 1
a1
15