ta101 2014 l2
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TA 101
Think and Analyze
Anupam SaxenaAssociate Professor
Mechanical EngineeringCompliant and Robotic Systems Lab
Indian Institute of Technology Kanpur
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Organization of Lectures and Laboratory AssignmentsTopic Week (No. of Lectures) Lab
Intro and Basic Constructions Week 1 (2)
Orthographic Projections Week 2 (2) Lab 1
Orthographic Projections Week 3 (2) Lab 2
Isometric Projections Week 4 (2) Lab 3
Missing Views Week 5 (2) Lab 4
Sectional and Assembly Week 6 (2) Lab 5
Oblique Projections Week 7 (2) Lab 6
Perspective Projections Week 8 (2) Lab 7
Lines and Planes Week 9 (2) Lab 8
Lines and Planes Week 10 (2) Lab 9
Auxiliary Projections Week 11 (2) Lab 10
Intersection of lines/planes/solids
Week 12 (2) Lab 11
Intersection and Development Week 13 (2) Lab 12
TOTAL 26 12
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Basic Construction and Conics
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ANUPAM SAXENATA101 LECTURE II
POLYGONS: HEXAGONS
d
Vertex-to-vertex distance Distance between flats
d
60
Circumscribing circle Inscribing circle
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ANUPAM SAXENATA101 LECTURE II
POLYGONS: PENTAGON
d
A B C
D
EF
rR
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ANUPAM SAXENATA101 LECTURE IIPOLYGONS: OCTAGON
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ANUPAM SAXENATA101 LECTURE II
POLYGONS: SEPTAGON OR ANY REGULAR POLYGON
Given a side
23 4
5
67
A B
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: CONCENTRIC CIRCLES
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: CONCENTRIC CIRCLES
(x, y)
q
P (bcosq, bsinq)
P
Q Q (acosq, asinq)
x = acosq y = bsinq
Exact Ellipse
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: CONCENTRIC CIRCLES
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: CONCENTRIC CIRCLES
P
Tangent-Normal at P
M
F G
|FM| + |MG| = 2a
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: CONCENTRIC CIRCLES
P
Tangent-Normal at P
M
F G
n
TA: Why is n the normal?
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: INTERSECTING ARCS
2a
2b
|FT| + |TG| = 2a
F G
M
QP
QP
T
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: INTERSECTING ARCS
2a
2b
F G
M
QP
QP
T
TA: What is the maximum radius of the arc possible
from F?
?
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: INTERSECTING ARCS
2l
2b
|FT| + |TG| = 2l
F G
M
QP
T
d1d2
(x, y)
= C
(a, 0)(a, 0)
+ = C
+ = 1 Ellipse if C 2a
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: STRING APPROACH
Source: wiki
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Trammel of Archimedes
2a
2b
QP
m
n
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Trammel of Archimedes
2a
2b
QP
m
n
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Trammel of Archimedes
2a
2b
QP
m
n
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Trammel of Archimedes
2a
2b
QP
m
n
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Trammel of Archimedes
2a
2b
QP
m
n
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Trammel of Archimedes
2a
2b
QP
m
n
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Trammel of Archimedes
2a
2b
QP
m
n
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Trammel of Archimedes
2a
2b
QP
m
n
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Trammel of Archimedes
2a
2b
QP
m
n
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Trammel of Archimedes
QP
m
n
y
x𝑦 1𝑥1
𝑙1❑
fl1
𝑥1𝑥
= 11+ 𝑓
;𝑦1𝑦
= 𝑓 ;𝑥2+𝑦2=𝑙1❑2
( 𝑥11+ 𝑓 )
2
+( 𝑦1𝑓 )2
=𝑙1❑2
R
Precise Ellipse!
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Parallelogram Method
1234567
0
8
1 2 3 4 5 6 7 8
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Parallelogram Method
1234567
0
8
1 2 3 4 5 6 7 8 1234567
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Parallelogram Method
1234567
0
8
1 2 3 4 5 6 7 8 1234567
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Parallelogram Method
1234567
0
8
1 2 3 4 5 6 7 8 1234567
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Parallelogram Method
1234567
0
8
1 2 3 4 5 6 7 8 1234567
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Parallelogram Method
1234567
0
8
1 2 3 4 5 6 7 8 1234567
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Parallelogram Method
1234567
0
8
1 2 3 4 5 6 7 8 1234567
TA: An exact or approximate Ellipse?TA: Can you identify the Conjugate Diameters?
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Conjugate Diameter Method
A
B
C
D
Q
AB, CD: Conjugate DiametersO: Center of Ellipse
O
OQ: Perpendicular to AB
TA: Exact Ellipse?
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: FOUR CENTER METHOD
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: FOUR CENTER METHOD
C1
C2 C3
C4
TA: An exact or approximate Ellipse?
Clue: The longest diagonal first
TA: Only withRhombus?
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ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF A PARABOLA
12
34 5
6 776
54
32
1
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Keep Thinking and Analyzing
Until next time...