Slide 1

TA 101

Think and Analyze
Anupam Saxena
Associate Professor
Mechanical Engineering
Compliant and Robotic Systems Lab
Indian Institute of Technology Kanpur


Slide 2

Circle in Perspective
(PP)
(HL)
(Vp)

(SPt)

(GL)


Slide 3

Circle in Perspective
(PP)
(HL)
(Vp)

(SPt)

(GL)


Slide 4

Space Geometry
Lines and Planes


Slide 5

Organization of Lectures and Laboratory Assignments
Topic

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 (1)

Lab 6

Perspective Projections

Week 8 (3)

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


Slide 6

=0
𝑇𝐿 =

Y
(𝑥1 , 𝑦1 )

𝑦1 = 𝑦2

(𝑥1 − 𝑥2 )2 +(𝑦1 − 𝑦2 )2 +(𝑧1 − 𝑧2 )2

(𝑥2 , 𝑦2 )

X
Z

(𝑥2 , 𝑧2 )

(𝑥1 , 𝑧1 )
X

ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 7

(𝑥1 , 𝑦1 )

=0
𝑇𝐿 =

Y

(𝑥1 − 𝑥2 )2 +(𝑦1 − 𝑦2 )2 +(𝑧1 − 𝑧2 )2

(𝑥2 , 𝑦2 )

X
Z

𝑧1 = 𝑧2
(𝑥1 , 𝑧1 )

(𝑥2 , 𝑧2 )
X

ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 8

METHOD OF ROTATION

Y

X
Z

X

ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 9

METHOD OF ROTATION

Y

X
Z

X

ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 10

METHOD OF AUXILIARY PLANE

Y

X
Z

X
ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 11

METHOD OF AUXILIARY PLANE
TA: WOULD THE ACTUAL LINE ‘TL’ LIE ON THIS NEW PLANE?
Y

X
Z

X
ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 12

METHOD OF AUXILIARY PLANE

Y

X
Z

X
ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 13

METHOD OF AUXILIARY PLANE

Y

X
Z

X

ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 14

METHOD OF AUXILIARY PLANE

Y

X
Z

X

ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 15

METHOD OF AUXILIARY PLANE

Y

TL
X
Z

X

ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 16

METHOD OF AUXILIARY PLANE

Y

Y

TL

X
Z

X
Z

X

X
ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 17

POINT VIEW OF A LINE

Y

X
Z

X
ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 18

POINT VIEW OF A LINE

TA: LOOK AT A PLANE PERPENDICULAR TO ‘TL’

PV

ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 19

METHOD OF AUXILIARY PLANE

PV

TL

ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 20

AN EXAMPLE

TL1
TA: TAKE DISTANCES FROM THE VIEW WHICH IS
NOT COMMON
TA: AS MANY AUXILIARY PLANES CAN BE USED

TL2

TL2
TL1

ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 21

INTERSECTION OF TWO LINES
𝐴𝐻

𝐷𝐻
𝐵𝐻

𝐶𝐻

𝐵1
𝐶𝑉

𝐶1

𝐷1

𝑃𝑉 (𝐶𝐷)
𝐴2

𝐵𝑉

𝐴𝑉

𝐵2

𝐴1
𝐷𝑉
ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 22

INTERSECTION OF TWO LINES
𝐴𝐻

𝐷𝐻
𝐵𝐻

𝐶𝐻

𝐵1
𝐶𝑉

𝐶1

𝐷1

𝐵𝑉

𝐴𝑉

𝐵2

𝐴1

𝑃𝑉 (𝐶𝐷)

𝐴2

𝐷𝑉
ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 23

PARALLEL LINES
𝐴𝐻

𝐷𝐻

𝐶𝐻

𝐶𝑉

𝐶1
𝐷1
𝐴1

𝐴𝑉

𝐵1

𝐷𝑉
ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 24

PARALLEL LINES
𝐴𝐻

𝐷𝐻

𝐶𝐻

𝐶𝑉

𝐶1
𝐷1
𝐴1

𝐴𝑉

𝐵1

𝐷𝑉
ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 25

PERPENDICULAR TO A LINE FROM A POINT
𝐴𝐻

𝐷𝐻

𝐵𝐻
𝐶𝐻

𝐶𝑉

𝐵1

𝐶1

𝐷1
𝐴1
𝐵𝑉

𝐴𝑉

𝑃𝑉 (𝐶𝐷)

𝐴2

𝐷𝑉
ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 26

SHORTEST DISTANCE BETWEEN LINES

𝐴𝐻

𝑁𝐻

𝐷𝐻

𝑀𝐻

𝐵𝐻

𝐶𝐻
𝐵2
𝐵1
𝐶𝑉

𝐶1

𝑁1

𝑁𝑉

𝑀𝑉

𝑀1

𝐵𝑉
𝐷𝑉

𝑃𝑉 (𝐶𝐷)
𝐷1

𝑀2

𝑇𝐿 ?

𝐴2

𝐴1

𝐴𝑉
ANUPAM SAXENA
TA101 LECTURE XVII
LINES AND PLANES


Slide 27

Think and Analyze

Until next time...