1. Engineering Graphics 2018-19-I DEPARTMENT OF CIVIL ENGINEERING
Lecture 22
TA101A
Engineering Graphics I By
Dr. Mukesh Sharma
Professor
DEPARTMENT OF CIVIL ENGINEERING
INDIAN INSTITUTE OF TECHNOLOGY KANPUR
KANPUR , INDIA

2. Intersection of Solid and a PlaneBH
Cutting Plane parallel to cylinder axis UH SH RH TH CH AH BF TF UF XF SF RF ZF CF AF
The Cutting Plane will cut the elements of cylinder at T and U and will also cut a line RS from the plane ABC.
Point Z and X are then points common to the cutting plane, given plane and cylinder and are two point on the line of intersection being sought
Take more cutting planes for more points

3. Object Projection SolutionA
B,b A
C,c D B C 2
3,1 1 3 b c
B,b A
C,c D F G B XH C XF CI BI 2
3,1 1 3 b c 2 C
Object D ? 1 3
Visualize the object and its projections.
Observe BC, CD are EVs in top views (TV) and yield point
of intersections with line 2 and 3 as points F, G in TV.
B in TV is also point of intersection as line Bb is hit by line 1.
Transferring points of intersection (B,F,G) is straight
Forward in FV.
There will be a point of intersection from line Cc and
Plane 2-3. Catch is, plane 2-3 is not seen in EV so how
To get this point.
Take XH in TV on line 2 so that GC & X are in one line
– observe, line GX is on plane 2-3. Project the line GX in FV.
Wherever GX and Cc meet in FV is the required point
Of intersection (i.e. CI). Join lines of intersections in the order
and show visibility
Projection
Solution
Concept – moment you see a plane in EV and a line
Hitting it – you get point of intersection (in that view)

4. q1,q3, q2 q4 d P4 4 a c P3 1’3 P1 2 P2 b a’’ a’ c’ c’’ 1 1’ P1’ q1’ eg’ q 4 2 2’ 6
P4’
P2’
q2’
q4’ h f’ h’ f 3 3’
p3’
q3’
c’’
a’’ a’ c’

5. Intersection of Plane (SEEN IN EV) and Coneb c d e 1 2 3 4 5 6 7 11 10 9 8 v 4 5 3 c e 2 b 6 e f a v g 1 7 h l i 12 8 k j 11 9 10 v g
Plane Intersection Cone
Lines V-1, V-2 … called elements or generators of cone
If intersecting plane is seen in the EV, intersection curve is seen in the other view. f e h i
Intersecting plane
Seen in EV in front d j c k b a I 1 2 3 4 5 6 7 12 11 10 9 8
Intersection of Plane (SEEN IN EV) and Cone

6. Oblique plane Intersection a cone4 3 5 2 X 6 c b d e f a v 4 1 g 7 Y l h h 8 12 i k j
Cutting plane 11 9 10 v d e f g Y c X h i b a j l k 1 2 3 4 5 6 7 12 11 10 9 8
Oblique plane Intersection a cone
Make generators (V-1, V-2…) in TV and FV
Pass a vertical cutting plane through generators (e.g. V-2 and V-8), it will be in EV in TV
The cutting plane cuts the cone in half and cuts the oblique plane as well (at X , Y)
Transfer the points XY in the FV
Points of intersection of line X-Y with the generators (through which vertical cutting plane was passed) in FV
yield points of intersection of cone and the oblique plane – transfer the point in FV – similarly get all points

7. Intersection of Cylinders - Concept2 4’ 4 D 3’ 3 C B 2’ 2 A 1’ 1 1 2 2’ 2 3 4 4’ 3’ 3 4 A B C D
Intersection of Cylinders - Concept

8. INTERSECTION OF CYLINDERS- AXES NOT INTERSECTING13 12 A B 11 T T 10 9 C T 8 7 6 5 3 4 1 2 A F 8 8 6 7 9 9 5 10 10 5 6 7 4 11 11 4 3 12 3 12 C 2 2 F 13 1 1 13 B F