1. Mechanical Engineering Drawing MECH 211/M
Lecture #5; Chapter 19
Dr. John Cheung

2. Lecture 4 summary Dihedral angle – Line – true length – point view.
Plane – true length- EV and TS.
Intersection line – validation.
Skew lines – validation – visibility.
Rotation method – true length – development work for cone.
Compass – Direction (no need to be true length). Slope (Horizontal angle) needs true length.
Distance between lines and point.

3. Point View of Line
Viewing parallel to TL - Point

4. Point View of Line Find True length. Project parallel to TL – Point.
Find the minimum distance between point and true length.

5. Shortest distance between two skew lines

6. Shortest distance between two skew lines
Draw folding line, obtain true length line 1-2.
Draw FL perpendicular to true length, obtain point view of Line 1-2.
Draw perpendicular line from Point 1,2 to line 3-4. This line = shortest distance between the two skew lines.

7. Line passing through two skew lines
Find a line through point A and intersecting skew lines 1-2 and 3-4.

8. Line through a point and intersecting two skew lines
Draw a line through Point ‘A’ and intersecting two skew lines.
Using edge view method.
T.L. of Line 1-2 then point view of line 1-2.
Draw line through Point view 1-2 and A to Line 3-4, form Line C-A-B.
Project Points B and C back to Auxiliary 1, Front and Top views.

9. Plane Representation A, Intersecting lines. B - Parallel lines.
C - Three points not in a straight lines.
D – A line and a point not on that line.

10. Plane Representation

11. Straight line in plane
Find the missing line 4-5 in front view. 2 3 7

12. Straight line in plane
Find the missing line 4-5 in front view using cutting plane method.
Given line 4-5 in top view.
Lines 4-5 and 1-2 not parallel, hence must intersect at Point 6.
Extend line 4-5 until it crosses line 2-3, then yield Point 7.
Cutting plane method – Project Point 6 to Line 1-2 and Point 7 to Line 2-3 in front view.
Joining points 4, 5, 6 and 7 to form the corresponding Line 4-5 in front view.

13. Location of a Point on a Plane
Locate point 4 in the plane IN Top view.

14. Location of a Point on a Plane
Locate Point 4 in Top View in Plane 1-2-3
Cutting plane method.
Extend Line 3-4 until it intersects Line 1-2 in Front view, then yield Point 5.
Project Point 5 to Line 1-2 in Top view.
Join Line 3-5 in Top view.
Project Point 4 in Line 3-5 in Front View to Line 3-5 in Top view. The intersection is Point 4 in Top View.

15. Location of a Point on a Plane
Locate Point 4 in Plane in Top View
Based on parallelism principle.
Draw a Line starting at Point 4 parallel to Line 2-3 in Front view. Intersection = P5.
Project P5 in Front View to Line 1-2 in Top View yields the corresponding P5 in TV.
Draw a line starting from P5 parallel to Line 2-3 in TV.
Project P4 in Front View to Line starting with P5. Intersection = P4 in TV.

16. Finding Point in Plane
Given: Point P 10mm above P2 and 12mm behind P3.
In Front view, Point P is somewhere along Line 4-5.
In Top View, Point P is somewhere along he line 12mm behind P3.

17. Finding Point in Plane - continued
Cutting plane method. Use Line 4-5 in Front view as Cutting plane.
Project P4 to Line 1-2 and P5 to Line 2-3 in TV .
Join P4 and P5 in Top view.
Use Line 6-7 (12mm behind P3) as CP.
Project P6 to Line 1-2 and P7 to Line 1-3 in FV.
Join P 6 and P7.
Intersection of Lines 4-5 and 6-7 is Point P.

18. Edge View of Planes
Given Plane
Find the edge view.

19. Edge View of Planes Given Plane 1-2-3. Find the edge view.
True length.
Draw auxiliary view looking parallel to TL. (Folding line perpendicular to TL)
Edge view with True length showing as a point, i.e., Points 2 and 4.

20. Piercing Point – Edge view method
Given Plane and Line 4-5.
Find piercing point between Line 4-5 and Plane

21. Piercing Point – Edge view method
Using edge view method.
Find TL in Front view.
Draw auxiliary view parallel to TL, i.e. Edge view of Plane
Extend Line 4-5 until it crosses Plane EV. The intersection = piercing point.

22. Piercing Point – Edge view method
Using edge view method.
Project piercing point back to Front View and Top view.
Check distance D1 between the auxiliary and Top views for accuracy.

23. Piercing Point – Cutting Plane method
Using CP method.
Cutting plane AA containing Line 4-5.
Cutting Line 6-7 in Plane
Line 6-7 and Line 4-5 in the sane plane – must intersect.
Project P6 and P7 to Front View. Draw Line 6-7.
Intersection between Line 4-5 and 6-7 in FV = Piercing point.
Project piercing point to TV.

24. Piercing Point – Cutting Plane method
Using CP method.
Determine the visibility of line and plane using the skew lines method learnt in Lecture 4.
View A, looking down to FV, see Line 2-3 first, So, Line 2-3 on top in TV .
View B, looking up to TV, see Line 2-3 first, so Line 2-3 is above and Line 4-5 hidden in FV. B A

25. Intersection of Planes – EV method
Given Plane and Plane
Find intersection of two plane = straight line containing all points common to the two planes.
TL of one plane and follow with its EV.
Intersection points = Piercing points.

26. Intersection of Planes – EV method
Given Plane and Plane
Project the two piercing points to TV and FV.
Draw the line connecting the two piercing points.

27. Angle between line and plane
Given Plane and Line 5-6.
Using EV and True size method.

28. Angle between line and plane
Given Plane and Line 5-6.
Using EV and True size method.
True length of Plane
Draw Edge View of Plane
Draw True size of Plane
Draw auxiliary view, looking perpendicular to Line 5-6. Line 5-6 parallel to folding line. Hence, line 5-6 = True length.
Measure the angle between True length Line 5-6 and the EV of plane

29. Angle between line and plane