Engineering Graphics 2018-19-I DEPARTMENT OF CIVIL ENGINEERING Lecture 22 TA101A Engineering Graphics 2018-19-I By Dr. Mukesh Sharma Professor DEPARTMENT OF CIVIL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY KANPUR KANPUR-208016, INDIA

Intersection of Solid and a Plane BH 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

Object Projection Solution A 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)

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

Intersection of Plane (SEEN IN EV) and Cone b 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

Oblique plane Intersection a cone 4 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

Intersection of Cylinders - Concept 2 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

INTERSECTION OF CYLINDERS- AXES NOT INTERSECTING 13 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