TA 101: Technical Arts II Dr. Prishati Raychowdhury Department of Civil Engineering IIT Kanpur Office: FB 330; Phone:

Course Outline Week Lecture Lab AssignmentsHome Assignments 1Lettering and constructionNone 2Orthographic projectionsLettering and constructionNone 3 Orthographic projections with dimensioning Orthographic projectionsLettering and construction 4Isometric views and projection Orthographic projections with dimensioning Orthographic projections 5Pictorial viewsIsometric views and projection Orthographic projections with dimensioning 6Missing views and linesPictorial views Isometric views and projection 7Sectional viewsMissing views and linesPictorial views 8Perspective viewsSectional views (AUTOCAD)Missing views and lines 9Lines and planes 1Perspective viewsSectional views 10Lines and planes 2Lines and planes 1Perspective views 11Auxiliary viewsLines and planes 2Lines and planes 1 12Intersection of solidsAuxiliary viewsLines and planes 2 13Development of surfacesIntersection of solidsAuxiliary views 14ReviewDevelopment of surfacesIntersection of solids Total LA = 13Total HA = 12 Total Lecture = 27

Intersection of Solids Lecture 22

Intersection of Solids Why is it important? We will deal with intersection of: Solid with Line Solid with Plane Solid with Solid

Remember: Cutting Plane Method  POI should be on X H -Y H  Project the line X H -Y H in the FV  Look for POI between the projection of PQ and XY on FV  Check for visibility DHDH BHBH AHAH CHCH DFDF BFBF AFAF CFCF PHPH QHQH PFPF QFQF XHXH YHYH XFXF YFYF OFOF OHOH H F

Intersection of a Line and a Pyramid H F XHXH 4F4F 5F5F 4H4H 5H5H 1H1H 2H2H 3H3H OHOH 1F1F 2F2F 3F3F OFOF XFXF ZHZH ZFZF YFYF YHYH The points of intersection of line and pyramid should be located on the cutting plane Take a vertical cutting plane passing through 4-5 and cutting the pyramid edges at X, Y, and Z in HV Locate points X, Y, and Z in FV PFPF QFQF PHPH QHQH Visibility? Find intersection points P and Q in FV; then project PQ in HV Cutting Plane Method Note that it is not necessary to show line 4-5 inside the solid

AHAH QHQH BHBH XHXH YHYH PFPF QFQF AFAF BFBF XFXF YFYF Intersection of Line and Cylinder PHPH RFRF SFSF Given a line and a cylinder, find the points of intersection: 1)Pass a plane parallel to cylinder axis and containing the line AB 2)Locate the points of intersection of the ‘cutting plane’ and ‘base’/‘top’ of the cylinder (i.e., P, Q, R, and S) 3)One of the ‘point of intersection’ between line and cylinder is the intersection of PR and AB in FV (i.e. X F ) 4)Another ‘point of intersection’ is the intersection of QS and AB in FV (i.e. Y F ) 5)Points of intersection X F and Y F are projected in HV 6)Find visibility and complete the drawing Cutting Plane Method

Intersection of a Plane and a Pyramid ChCh BhBh AhAh OhOh CvCv BvBv AvAv OvOv SvSv QhQh PhPh RhRh ShSh RvRv QvQv PvPv 1v1v 2v2v 3v3v 4v4v 5v5v 5h5h 4h4h 2h2h 1h1h Cutting Plane Method Visibility needs to be found for: 1)Path of intersection 2)Plane and solid Complete Solution 3h3h F H

Intersection of a Line and a Cone SFSF RFRF BFBF AFAF BHBH AHAH VHVH XFXF YFYF 2F2F 1F1F 2H2H 1H1H VFVF YHYH SHSH RHRH XHXH F H PHPH QHQH Given a line and a cone, find the points of intersection 1)Take points X and Y on given line, get their projections in HV and FV 2)Pass a cutting plane passing through the points V, X, and Y 3)Extend the plane to base and locate points R and S in FV 4)Project RS in HV 5)RS cuts cone at 1 and 2 at the base in HV. Project 1 and 2 in FV. 6)Find intersection of AB with V-1 and V-2 in HV (P and Q, respectively). Project P and Q in FV. 7)Line AB pierces the cone at P and Q. 8)Note all points V, X, B, 2, 1, Y, A, P, Q, R, S are in one plane 9)Find visibility and complete drawing PFPF QFQF

Intersection of a plane and a cone Method 1: Selected Line Method (When an edge view of the plane is available) v v a b c l k d j e i f h g 1)In FV, the cone is seen as a triangle and the plane as EV. 2)Draw lines V-1, V-2, etc. called ‘elements’ or ‘generators’ in top and front views. 3)The points of intersection of ‘generators’ and EV give the ‘line of intersection’ of plane and cone in FV. 4)Locate the points of intersection (e & i) in the top view. 5)Similarly, locate all other points of intersection in top view and draw the ‘curve of intersection.’ 6)What will be the shape of the ‘curve of intersection’ in top view? Plane in EV i e a b c d f g h j k l

Intersection of a plane and a cone Method 2: Cutting Plane Method (When an oblique plane cuts the cone) Cutting plane )Draw generators in both top & front views. 2)Pass a ‘vertical cutting plane’ through generators V-2 & V-8, it will be in EV in top view. 3)The ‘cutting plane’ cuts the cone in half; and cuts the oblique plane at points X and Z. 4)Transfer the points X-Z in the front view. 5)Points of intersection of line X-Z with generators (V-2 & V-8) in front view yield desired ‘points of intersection of cone and the oblique plane’. 6)Transfer these ‘points of intersection’ (b & h) from front to top view. 7)Similarly, get all other points of intersection. v a b c d e f g h i j k l X Z v a b c d e f g h i j k l X Z 4

Intersection of Two Solids Two Methods: – Selected line method A sufficient number of lines are selected on a surface. Find the points where each of these lines pierces the other surface. A line joining the these piercing points would give the line of intersection between two surfaces. – Cutting plane method Pass a number of cutting planes through each of the given surfaces simultaneously. Each plane will cut a line (straight or curved) from each given surface. These lines will intersect in a point (or points) common to both surfaces. A line connecting those points will give the line of intersection of the given surfaces.

Thank You