1. Mechanical Engineering Drawing MECH 211/M
Lecture #7, Chapter 11
Dr. John Cheung

2. Intersections of Plane and Vertical Prism – Edge view method

3. Intersection of Plane and Oblique Prism

4. Intersection of Plane and Oblique Prism
Use Prism edge as EV.
Cut Line 1-2 at Point 4 and Line 2-3 at 5.
Front view – Line intersects the EV at Point A.
Project Point A to Top view.

5. Intersection of Plane and Oblique Prism
Use parallelism theorem.
Use other prism edges as the cutting plane .
Repeat the procedure.

6. Intersection of Plane and Oblique Prism

7. Intersection of Plane and Pyramid

8. Intersection of Plane and Pyramid
Use pyramid edge W-Y as the cutting plane (EV).
Intersect Plane line 2-3 at Point 5 and Line 1-4 at Point 6.
Front view – Line intersects EV –WY at Point A.
Project Point A to Top View.
Other pyramid edges do not intersect with finite plane. W Y

9. Intersection of Plane and Pyramid
Use Plane edge 1-4 as EV, cutting pyramid edges WX and WY at Points 6 and 11 in Front view.
Project Points 6 and 11 to Top view.
Line 5-6 intersects Plane Edge 1-4 at Point E.
Repeat for pyramid edges WX and WZ.
Repeat for Plane edge 2-3. 11 11

10. Intersection of Plane and Pyramid

11. Intersection of Plane and Right-circular Cylinder – FIG. 21-5

12. Intersection of Plane and Inclined Cylinder - FIG 21-6
Divide circular section into a number of equal segments (30 degrees)
Draw auxiliary view - EV for Plane ABC.

13. Intersection of Plane and Inclined Cylinder – FIG 21-6
Plane EV intersects segments 6 and 10 in auxiliary view.
Project intersection point to segments 6 and 10 in Front view leading to 6’ and 10’.
Project 6’ and 10’ to Top view.
Use D1 to check accuracy
10’ 6’

14. Intersection of Plane and Inclined Cylinder – FIG.21-6

15. Intersection of Plane and Oblique Cylinder – FIG. 21-7
Use cutting plane method.
Divide the cylinder into a number of equal segments (30°)
Use the segment as the cutting plane.

16. Intersection of Plane and Oblique Cylinder –FIG.21-7
Use segment 0-0’ as cutting plane in Front view
Intersect Plane Line AB at d and Line BC at e.
Project Point d and e to Top view.
Line d-e intersects segment 0-0’ at Point 0” in TV.
Project 0” to FV.

17. Intersection of Plane and Oblique Cylinder – FIG 21-7
Use parallelism method .
To construct other intersection points based on Segment Line 0-0’ slope.

18. Intersection of Plane and Oblique Cone – FIG 21-8
Divide cone base into a number of equal segments.
Use Plane ABC EV as Cutting plane.

19. Intersection of Plane and Oblique Cone – FIG 21-8
Plane EV ABC in FV cut segments X-13 and X-5 at Points 13’ (front) and 5’ (back).
Project Points 13’ and 5’ to TV.

20. Intersection of Plane and Oblique Cone – FIG 21-8

21. Oblique Plane and Cone – FIG 21-9
Use parallelism method.
Cutting plane // to BC in both Front and Top views.
Draw EV 1-2 in FV.
Intersect cone side.
Draw circle diameter in TV = to intersected cone section.
TV – EV 1-2 intersects the circle of cone at Points 1” and 2”
Repeat for other cone sections. 1’ 2’

22. Oblique Plane and Cone –FIG. 21-9

23. Oblique Plane and Cone –FIG 21-9 USING EV METHOD

24. Intersection of Two Solids – FIG 21-10
Using solid edges as the cutting plane.

25. Intersection of Solids – FIG.21-10
Use edges 1-1’ and 4-4’ of the inclined prism as the cutting plane in TV.
EV 1-1’ intersects vertical prism edge DE at Point 5 and edge BA and Point 9 in TV.
Project P5 and P9 to FV the edge 1-1’ of the inclined prism.
Repeat for inclined prism edge 4-4’. – Yield Points 10 and 16.

26. Intersection of Solids – FIG.21-10
Use vertical prism edges as the cutting plane.
Use Edge D (EV) in TV. It intersects Line 1-2 at P6’ and Line 3-4 at P15’.
Project P6’ and P15’ Lines 1-2 AND 3-4 in FV.
Use parallelism theorem, draw line from P6’ and P15’ // to inclined prism edges.
Line from 6’ intersects Edge D at P6 and from P15’ at P15.
Repeat for edges C and B.

27. Intersection of Solids – Fig. 20-10
Figure of intersection: The intersection of two solids.

28. Intersection of a Prism and Cone

29. Intersection of a Prism and Cone

30. Intersection of a Prism and Cone

31. Intersection of Shortened Cone and Prism FIG. 21-13
Use EV parallel to cone base.
Cut horizontal circle in cone and straight line of prism.
Circle of cone intersects prism edge (vertical) at 2 points of each side in FV.

32. Intersection of Circular Cylinders – FIG. 21-14

33. Intersection of Circular Cylinders

34. Intersection of Circular Cylinder & Cone Axes Intersecting –FIG.21-15
Divide horizontal cylinder into a number of segments.

35. Intersection of Circular Cylinder & Cone Axes Intersecting –FIG.21-15
Locate P3 in cone at TV.
Line 3 intersects Edge D at 3’.
Project P3’ to FV.

36. Intersection of Circular Cylinder & Cone Axes Intersecting –FIG.21-15
Repeat for segments B,D and F.

37. Intersection of Circular Cylinder & Cone Axes Intersecting –FIG.21-15

38. Intersection of Circular Cylinder & Cone Axes Non-intersecting

39. Intersections of Circular Cylinders and Cones (Sphere Method)

40. Intersections of Circular Cylinders and Cones (Sphere Method) FIG

41. Intersections of Circular Cylinders and Cones (Sphere Method) FIG
Sphere B cuts two vertical circles in cylinder at C-C and B-B.
Sphere B Cut one horizontal circle in cone at A-A.
3, EV A-A intersects EV C-C at P2.

42. Intersections of Circular Cylinders and Cones (Sphere Method) FIG

43. Intersection of Oblique Cone & Cylinder (Constructing the Top View)

44. Intersection of Oblique Cone & Cylinder (Plane Cutting Elements) – FIG 21.19a
Determination of limiting plane in cone and cylinder.
Pass the vertex.
Cut or be tangent to the base.
Line V-P passes through vertex and intersects the extended cone base plane at Point P.
Line P-1 tangent to circular base at Point 1. Line of tangency –V-1.
Plane V-P-14 cuts the cone at P6 and P14.
Cutting elements – V-6 and V-14.

45. Intersection of Oblique Cone & Cylinder (Plane Cutting Elements) – FIG 21.19b
Cutting plane parallel to elements of axis.
Cut or be tangent to the base.
Line V-P in TV parallel to cylinder (any plane with VP line // to the cylinder).
Draw lines in TV tangent to and secant to the lower base P-14 and P12.
Element of tangency 13-13’.
Cutting elements 12-12’ and 14-14’.

46. Intersection of Oblique Cone & Cylinder FIG. 21-20
Cone – Limiting plane – V-P-9.
Cylinder – Limiting plane – V-P-13 (P13 Tangent point.)

47. Intersection of Oblique Cone & Cylinder FIG. 21-20
Number of system – important.
Starting from the limiting plane.
Number consecutively -anti-clockwise – must not continue beyond a secant limiting plane.
When secant limiting plane reached, direction reversed, placing only one number at the secant point.
On the other base, No 1 and 2.. Assigned on the same line.

48. Intersection of Oblique Cone & Cylinder FIG. 21-20

49. Intersection of Oblique Cone & Cylinder FIG. 21-20

50. Intersection of Oblique Cones

51. Intersection of Oblique Cylinders

52. Intersection of Cone & Cylinder Bases in Nonparallel Planes