2480b48c99ef4e3b94038d2680df02fe96bc196b029703c1929ec2575bed8eb9_Helloiitk Lecture 17 Lines and Planes Lecture three Oct 9 2023.pptx
- 1. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra TA 101: Engineering Graphics 2023 - 24 Sem – I Lecture 17 – Oct 9, 2023 Space Geometry Lines and Planes – III Sudhir Misra Department of Civil Engineering IIT Kanpur, Kanpur 208 016 1 Room No.: WLE 303 C; Phone – 7346 E-mail: sud@iitk.ac.in
- 2. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra LINE OF SIGHT AH BH A B BA AA AF BF F P A H Normal/Auxiliary View – Quick Review Notice the distances from the hinge lines d1 d2 d1 d2 TL BA AA AA BA 2
- 3. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra F H bH bF aH aF d aA1 bA1 Notice the direction of Projectors Notice the distance Measurements along Projectors bA2 , aA2 Normal View and PV of an Oblique Line Projected from the Top/Horizontal View PV d1 d1 3
- 4. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra Parallel Lines AH BH CH DH AF BF CF DF AP CP BP DP F H P Parallelism for Non-oblique lines needs to be checked in all three principal views
- 5. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra Perpendicular Lines Case A: Yes, AB and CD are perpendicular to each other Case B: Yes, AB and CD are perpendicular to each other Case C: May or may not be perpendicular to each other, need to check from an auxiliary view where one of these line is in TL
- 6. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra Review • By now, you must have learnt to find – Point view of a line – True length of a line – Edge view of a plane – True shape of a plane • You have also learnt that – If one sees any line of the plane in PV, the plane will be in EV – True Shape of a plane is available when line of sight is perpendicular to the EV – Correct slope of a line is visible when the line is in TL
- 7. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra Relationship between Lines and Planes • Any two lines in space can be intersecting, non-intersecting, parallel, perpendicular, or simply skewed to each other • Similarly, various relationships between a line and a plane are possible: line parallel to a plane, perpendicular to a plane, intersecting or non-intersecting with the plane and so on • Given the orthographic views of two lines, or lines and planes, we will learn to find relationship between them
- 8. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra We will learn about – Conditions for intersection, parallelism, and perpendicularity of lines – Shortest distance from a point to a line – Shortest distance from a line to a line – Conditions for intersection, parallelism, and perpendicularity of planes – Line piercing a plane and its visibility – Angle between two planes Relationship between Lines and Planes
- 9. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra A Line in a Plane • Is line AB in the plane 1-2-3-4? • How will you determine this? • Get EV of the plane & project the line in the same view. If no part of the line is outside of EV, then the line is in the plane • There is another easier way to establish this • Check for the ‘common point of intersection’ between plane & line • If the intersection of AB with lines 1- 2 and 3-4 stay aligned in both H and F view, then line AB is in the plane AH BH BF AF 2H 3H 2F 3F 1H 4H 4F F H 1F Line AB is in the Plane 1-2-3-4
- 10. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra AH BH CH AF BF CF DH DF PH QH PF QF AA1 BA1 CA1 DA1 PA1 QA1 H A1 F H A plane may be extended to check this Notice that AC is in TL in Top view So, we see that the line PQ is contained in the plane that contains the given plane ABC TL Get EV of plane, if line is in plane, line will completely lie within the EV Is there another way to check this? YES! Once the plane is extended, common points of intersection (between line & plane) may be checked if they are aligned or not A line in a plane
- 11. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra 𝐴𝑉 𝐵𝑉 𝐶𝑉 𝐴𝐻 𝐵𝐻 𝐶𝐻 𝐷𝐻 H V V A1 𝐷𝑉 𝐵𝐴1 𝐶𝐴1 𝑃𝐻 𝑃𝑉 𝐴𝐴1, 𝐷𝐴1 𝑃𝐴1 𝑄𝐴1 𝑄𝑉 𝑄𝐻 Line Parallel to A Plane 11
- 12. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra 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 pH 1H 2H 3H 4H H F oH oF pF 4F3F 1F2F 900 How to draw a perpendicular from a point with this concept? A line perpendicular to a plane Very useful in finding shortest distance from a point to a plane
- 13. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra pH 1H 2H 3H 4H pF OH 900 2F 1F 3F 4F OA d 4A1A 3A2A PA H A d OF H F PARALLEL Draw a perpendicular to a plane from point 1. Get the edge of plane 2. See if any line in TL on the plane 3. See through the line and project all points 4. Line 2-3 in top view in TL in aux view. 5. Take distance from FV and locate points 6. Draw a perpendicular from OA on EV ~ OA PA (in TL?) 7. Project PA to Top view (see the arrows) 8. Project PH to Front view see PF Note: Edge view of plane and perpendicular at 900 needed
- 14. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra 𝐴𝑉 𝐵𝑉 𝐶𝑉 𝐴𝐻 𝐵𝐻 𝐶𝐻 𝐷𝐻 H V V A1 𝐷𝑉 𝐵𝐴1 𝐶𝐴1 𝑃𝐻 𝑃𝑉 𝐴𝐴1, 𝐷𝐴1 𝑃𝐴1 𝑄𝐴1 𝑄𝑉 𝑄𝐻 Line Perpendicular to A Plane 14
- 15. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra 𝐴𝑉 𝐵𝑉 𝐶𝑉 𝐴𝐻 𝐵𝐻 𝐶𝐻 𝐷𝐻 H V A1 𝐷𝑉 𝐵𝐴1 𝐶𝐴1 𝑃𝐻 𝑃𝑉 𝐴𝐴1, 𝐷𝐴1 𝑃𝐴1 𝑄𝐴1 𝑄𝑉 𝑄𝐻 𝐵𝐴2 𝐴𝐴2 𝐶𝐴2 TS A1 A2 𝑃𝐴2, 𝑄𝐴2 V Verification: PQ in PV 15
- 16. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra Intersection of two lines 16
- 17. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra 𝐴𝐻 𝐵𝐻 𝐴𝑉 𝐵𝑉 𝐶𝐻 𝐷𝐻 𝐶𝑉 𝐷𝑉 𝐶1 𝐷1 𝐴1 𝐵1 𝑃𝑉 (𝐶𝐷) 𝐴2 17 Intersection of two lines
- 18. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra 𝐴𝐻 𝐴𝑉 𝐶𝐻 𝐷𝐻 𝐶𝑉 𝐷𝑉 𝐶1 𝐷1 𝐴1 𝑃𝑉 (𝐶𝐷) 𝐴2 𝐵1 𝐵𝐻 𝐵𝑉 Perpendicular to a line from a point 18
- 19. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra Perpendicular Lines : Example Given: AB in Top and Front views; BC only in F view. Complete line BC in Top view such that AB and BC are perpendicular to each other F H bH bF aH aF aA1 bA1 cF cA1 cH If the lines are making a 90o angle in an auxiliary view where one of the lines in TL, the lines are perpendicular to each other
- 20. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra 𝐴𝑉 𝐶𝑉 𝐴𝐻 𝐵𝐻 𝐶𝐻 𝐷𝐻 H V V A1 𝐷𝑉 𝐵𝐴1 𝐶𝐴1 𝑃𝐻 𝑃𝑉 𝐴𝐴1, 𝐷𝐴1 𝑃𝐴1 𝑄𝐴1 𝑄𝑉 𝑄𝐻 A line is perpendicular to a plane when the line in its TL is at 90o with the EV of the plane Perpendicular from a point to a plane
- 21. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra • The concept of perpendicular lines can be used to determine shortest distance from a point to a line • Given: AB in TL and O and AB are in same vertical plane O F H A B TL P What is the shortest distance between O and AB? What is the TL of this shortest distance? OP! Because O and AB are in the same vertical plane Shortest Distance Between Two Lines
- 22. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra Shortest Distance from a Point to a Line Given: AB in TL and O is not in the vertical plane that contains AB O F H A B TL P Is OP perpendicular to AB? Yes! Is the TL of OP seen in F view? No, it needs to be found out in an auxiliary view
- 23. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra 𝐴𝐻 𝐴𝑉 𝐶𝐻 𝐷𝐻 𝐶𝑉 𝐷𝑉 𝐵𝐻 𝐵𝑉 𝐶1 𝐷1 𝐴1 𝐵1 𝑃𝑉 (𝐶𝐷) 𝐴2 𝐵2 𝑇𝐿 ? 𝑀2 𝑀1 𝑁1 𝑀𝐻 𝑁𝐻 𝑀𝑉 𝑁𝑉 Shortest Distance Between Two Lines 23
- 24. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra 5. Obviously, CD is not in TL in A2. OP is the required TL of the shortest distance between AB and CD (in A2) AH BH CH DH OH PH AF CF DF BF OF PF BA1 AA1 CA1 PA1 OA1 F H CA2 BA2,OA2,AA2 DA2 PA2 900 1. Get TL of AB and project CD in A1 2. Get PV of AB and project CD in A2 3. Drop perpendicular from PV of AB to CD in A2 4. In A2, which line is in TL? CD or OP? 7. Project OP back in A1, H, and F views (from A2) 8. Notice that P is in CD and O is in AB 9. How do you locate point O in A1? 10. Use another basic concept, OP will be parallel to hinge-line A1-A2, why? In TL 6. O is not fixed in space, somewhere in line AB
- 25. Department of Civil Engineering Indian Institute of Technology Kanpur TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra 25 :: THANK YOU ::