Engineering Graphics 2018-19-I Lecture 18 TA101A Engineering Graphics 2018-19-I By Dr. Mukesh Sharma Professor DEPARTMENT OF CIVIL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY KANPUR KANPUR-208016, INDIA

aH bH 1H 2H 3H 4H H F aF bF 1F 2F 3F 4F XH YH YF XF A Line in a plane – if a line is in the plane, all points of intersection should stay aligned in all views

Construct a line parallel to a plane bH 1H dH cH aH 2H H F aF dF 2F cF bF 1F Line 1-2 in top view and Point 1F is given See we forced the line 1-2 to be parallel to line b-d in front view As a result, line 1-2 is parallel to the given plane (abc)

A line perpendicular to a plane Very useful in finding shortest distance from a point to a plane pH 1H 2H 3H 4H H F oH oF pF TL EV 4F3F 1F2F 900 A line is perpendicular to plane when the line is in true length at a 900 angle to an edge view of the plane. Line OP is perpendicular to plane 1-2-3-4 How to draw a perpendicular from a point with this concept?

Draw a perpendicular to a plane from point – Recall edge view of plane and perpendicular at 900 needed PARALLEL OH 2H TL(?. Yes) Should be in TL OA 3H 3A2A pH 1H PA 900 H A d 4H EV H 4A1A F d 2F 3F pF Get the edge of plane See if any line in TL on the plane See through the line and project all points Line 2-3 in top view in TL in In aux view take distance from Front and locate points Draw a perpendicular from OA on EV ~ OA PA (in TL?) Project PA to Top view (see the arrows) Project PH to Front view see PF 1F 4F OF

Visibility of perpendicular OP OH In horizontal and front views Part of the OP can be behind the plane thus become dash Methodology: For Horz. View bring the point on OP drop it down to Front view And see which line you encounter first Line appearing first is above. The line appearing second is behind and thus should be dash A 2H TL 3H pH 1H 4H C B H F 2F 3F pF 1F 4F OF

Angle Between line and plane 5H 4C 2H TL True Angle TL EV 3H 3C IC 2C Sight ┴ to Line 4-5 IH 4H H 4F F 3F 3A C 5C 2F B H 3B A 2A 4A 5A 5B 2B IF 5F EV 4B A B TS IA IB Angle Between line and plane

Recap of Concept – Did you get this? IB 2B 3B 4B rB sB B A IA2A 4A3A rA sA TL EV 5B 6B 7B 8B tB uB B A 5A6A 8A7A tA uA EV NOT TL True Angle NOT True Angle A Recap of Concept – Did you get this?

Objective find angle between two planes 6H 4H 2H Line 1-2 is common to both the Planes. TL 3H 5H 1H H F 1F2F EV EV 5F6F True Angle 3F4F Concept – if we can project the planes in their EVs The angle between the EVs will be the true angle between the planes

Angle between Two Planes Get edge views of the planes Do you see common line to be in TL It is ab – see through it (e.g. hinge line Be perpendicular to TL) From EVs find true angle between planes dH aH bH cH H F cF dF aF F I TL cI dI bF True angle EV EV aI,bI

Angle between planes – General Case dI dI D2 DH H AH 1 True angle cH 1 2 EV DI A2B2 BH EV C2 AI TL H BI F DF d d CI BF AF CF Angle between planes – General Case

Concept: Shortest Distance from a point to a line 900 OH 900 H PH oH A 3H Parallel TL OA Parallel PH IH TL 4H TL H H 4APA3A F F PF IFPF2F 3F 4F A B TL OF OF Concept: Shortest Distance from a point to a line

Finding shortest Distance from a point to a line OH bH H pH I b2p2a2 bI aH TL pI 1 2 oI TL 900 aI Parallel oI H F aF pF bF oF Concept: Get the line in TL and keep projecting the point and then draw Perpendicular from the point on the obtained TL. Next step is to get the TL in point view and you will see the shortest distance (point to line) Project the perpendicular in Front and Top view

+ Concept – Shortest Distance between two lines What is the condition that should be met? 2H 3H OH PH TL 4H IH Parallel H F + 4F OF IF2F 900 TL PF 3F

Shortest Distance between two lines – most general case bH H oH I dH 1 2 aH d2 b2o2a2 cH pH dI bI TL TL oI 900 p2 aI Parallel pI c2 H F aF cI oF dF pF cF bF Shortest Distance between two lines – most general case

Intersection of a line and plane – EV method TL 2A 5H 1A 1H H 5A F 1F 2F 2’F 4F 5F 3F Intersection of a line and plane – EV method

Intersection of Line and Plane: Cutting Plane method XH 2H YH 1H 5H H F 1F C YF 4F 2F 5F XF B 3F