Lecture 22 TA 101 A Engineering Graphics 2018

Lecture 22 TA 101 A Engineering Graphics 2018 -19 -I By Dr. Mukesh Sharma Professor DEPARTMENT OF CIVIL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY KANPUR-208016, INDIA

Intersection of Solid and a Plane BH UH SH RH TH l ne paralle la P g in tt Cu r axis to cylinde CH AH BF TF UF XF RF SF 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

B A D B, b 2 C ? Object C, c A 3 A B D D 1 2 XH F C, c 1 3 B, b 1 2 A A C G B 3 D D C F 2 XF 2 CI § 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. § § § 3, 1 b c Projection BI 3, 1 G b c Solution 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 Concept – moment you see a plane in EV and a line Hitting it – you get point of intersection (in that view)

v 4 5 3 c c e d 2 e b 6 e f b 4 3 a 2 v a 1 5 7 1 12 l i k 10 9 7 h 6 11 g 8 8 j 9 11 10 v 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. d c a 1 b Intersecting plane Seen in EV in front j k I 2 12 g f h e i 3 11 4 10 5 Intersection of Plane (SEEN IN EV) and Cone 6 9 8 7

4 3 2 X b v a 1 c d 5 6 e 4 f h Y l 12 7 g 8 i k j 11 Cutting plane 9 10 v c X b a l k 1 2 3 12 11 Oblique plane Intersection a cone § § § d e f i g h Y j 4 10 5 6 9 8 7 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

3’ C B A 4’ 3’ 2 4 4’ D 3 2’ 2 1’ 1 2 3 4 A BC D Intersection of Cylinders - Concept

INTERSECTION OF CYLINDERS- AXES NOT INTERSECTING 13 12 11 AT BT 10 9 CT 8 7 6 5 1 2 3 4 AF 6 7 8 4 3 2 CF 1 BF 8 9 10 11 5 5 7 9 10 11 4 3 12 13 6 12 2 1 13