ta 101 t hink and a nalyze anupam saxena associate professor mechanical engineering compliant and...
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TA 101
Think and Analyze
Anupam SaxenaAssociate Professor
Mechanical EngineeringCompliant and Robotic Systems Lab
Indian Institute of Technology Kanpur
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
Basic Construction and Conics
ANUPAM SAXENATA101 LECTURE II
POLYGONS: HEXAGONS
d
Vertex-to-vertex distance Distance between flats
d
60
Circumscribing circle Inscribing circle
ANUPAM SAXENATA101 LECTURE II
POLYGONS: PENTAGON
d
A B C
D
EF
rR
ANUPAM SAXENATA101 LECTURE IIPOLYGONS: OCTAGON
ANUPAM SAXENATA101 LECTURE II
POLYGONS: SEPTAGON OR ANY REGULAR POLYGON
Given a side
23 4
5
67
A B
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: CONCENTRIC CIRCLES
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
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: CONCENTRIC CIRCLES
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: CONCENTRIC CIRCLES
P
Tangent-Normal at P
M
F G
|FM| + |MG| = 2a
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: CONCENTRIC CIRCLES
P
Tangent-Normal at P
M
F G
n
TA: Why is n the normal?
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: INTERSECTING ARCS
2a
2b
|FT| + |TG| = 2a
F G
M
QP
QP
T
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?
?
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
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: STRING APPROACH
Source: wiki
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Trammel of Archimedes
2a
2b
QP
m
n
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Trammel of Archimedes
2a
2b
QP
m
n
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Trammel of Archimedes
2a
2b
QP
m
n
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Trammel of Archimedes
2a
2b
QP
m
n
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Trammel of Archimedes
2a
2b
QP
m
n
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Trammel of Archimedes
2a
2b
QP
m
n
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Trammel of Archimedes
2a
2b
QP
m
n
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Trammel of Archimedes
2a
2b
QP
m
n
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Trammel of Archimedes
2a
2b
QP
m
n
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!
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Parallelogram Method
1234567
0
8
1 2 3 4 5 6 7 8
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Parallelogram Method
1234567
0
8
1 2 3 4 5 6 7 8 1234567
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Parallelogram Method
1234567
0
8
1 2 3 4 5 6 7 8 1234567
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Parallelogram Method
1234567
0
8
1 2 3 4 5 6 7 8 1234567
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Parallelogram Method
1234567
0
8
1 2 3 4 5 6 7 8 1234567
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: Parallelogram Method
1234567
0
8
1 2 3 4 5 6 7 8 1234567
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?
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?
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF ELLIPSE: FOUR CENTER METHOD
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?
ANUPAM SAXENATA101 LECTURE II
CONSTRUCTION OF A PARABOLA
12
34 5
6 776
54
32
1
Keep Thinking and Analyzing
Until next time...