Engineering Graphics 2018-19-I Lecture 21 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 line and solid-cutting plane method 1 2 3 O H 4 5 H Z H Y H X H F F 1 2 3 O F Y F 4 5 F X F Z Intersection of line and solid-cutting plane method

Intersection of a Plane and a Prism 5H10H 6H11H XH 3H EV 2H RH EV 7H12H 9H14H 4H EV EV YH 1H SH 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 right-hand 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? 8H13H H F 5F 9F 8F 6F 7F XF 3F 2F RF 4F YF SF 1F 10F 14F 13F 11F 12F 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 PF QF XF YF ZF AF

Intersection of a Cone and a Line v v Y A X N M A B 2 1 S R Y N V’ A’ M Y’ X N B M P Q S 2 X’ 1 R B’ S P 2’ 1’ Q R Pass a cutting plane (VXY) containing line (AB) and passing through apex (V) Sectioned part of cone (V12) 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

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