Lecture 21 TA 101 A Engineering Graphics 2018

Lecture 21 TA 101 A Engineering Graphics 2018 -19 -I By Dr. Mukesh Sharma Professor DEPARTMENT OF CIVIL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY KANPUR-208016, INDIA

2 H 5 H ZH OH YH 1 H XH 4 H 3 H H F OF YF 5 F 4 F 1 F XF 2 F ZF 3 F Intersection of line and solid-cutting plane method

Intersection of a Plane and a Prism 6 H 11 H 5 H 10 H XH 3 H EV 2 H EV RH 7 H 12 H 9 H 14 H EV 1 H SH H F 5 F 9 F EV 4 H YH 8 H 13 H 8 F 6 F 7 F XF 2 F RF YF SF 1 F 10 F 14 F 13 F 11 F 4 F 3 F Connect Intersection points Move clockwise from intersection point to intersection point. Connect a line from where line 1 -4 hits plane 9 -8 -13 -14 to where line 9 -14 passes through plane 1 -2 -3 -4. Then go from this last point up to where line 2 -3 hits plane 5 -9 -14 -10. Repeat the process on the righthand side of the prism. Move from where line 2 -3 hits plane 6 -7 -12 -11 down to where line 7 -12 hits plane 1 -2 -3 -4. Finish by moving from this last point down to where line 1 -4 hits plane 8 -7 -12 -13 Visibility? 12 F Expected number of intersection points = 6 When an EV exists and a line hits it, intersection point is immediately available See the top view and immediately locate 4 intersection points Draw line R-S through point 9 -14 in top view – line R-S is on plane 1, 2, 3, 4 Look for point of intersection between line R-S and line 9 -14

Intersection of Solid and a Line XH QH YH ZH AH QF PF YF ZF AF XF

Intersection of a Cone and a Line v v X A N M B A Y 2 1 S Y R N V’ A’ M Y’ X B S N M P Q 2 1 X’ R B’ S P 2’ Pass a cutting plane (VXY) containing line (AB) and passing through apex (V) Sectioned part of cone (V 12) is shown in grey colour Line AB as it pierces the cone is seen at point M and N See V, X, B, 2, 1, Y, A, M, N, R, S are all in one plane 1’ Q R

Intersection of Solid and a Plane BH RH g UH SH Cuttin plane TH CH AH BF TF UF XF RF SF ZF CF AF