1. Mechanical Engineering Drawing MECH 211/M
Lecture #6; Chapter 20
Dr. John Cheung

2. Lines Perpendicular to the Fold Line

3. Lines Perpendicular to the Fold Line
Need third view to validate.

4. Parallel Planes Edge View
True length and then edge view.

5. Parallel Planes Intersecting Lines
If a pair of intersecting lines in a plane is parallel to a pair of intersecting lines in a second plane, the planes are parallel.

6. Determining if Planes are Parallel
Line 1-2 // 1’-6 and Line 1-3 // 3’-4.

7. Line Parallel to a Plane
A line is parallel to a plane if it is parallel to any line in the plane. Line 5-3 // line 4-5’

8. Plane Parallel to a Line
A plane is parallel to a line if it contains a line that is parallel to the given line.
Skew lines 1-2 and 3-4.
Form plane 3-4-2’.
Line 1-2 // 2’-4, hence, Line 1-2 // Plane 3-4-2’

9. Plane Parallel Through a Point and Parallel to Two Skew Lines
Skew lines 1-2 and 3-4 and Point 5. Plane through P5 // to skew lines 1-2 and 3-4. Line 1-2 // 2’-5 and Line 3-4 // 4’-5.

10. Perpendicular Lines
A dihedral angle appears true size when BOTH legs appear true size.
Right angles appear true size when one or both legs appear true size.
Lines 2-3, 2-4, 2-5 and 2-6 Perp. to line 1-2, not 90 in TV.
FV, TL of Line 1-2, 90 degree.

11. Plane Perpendicular to a Line Given View Method
Line 1-2 perp. to Plane shown with one TL
Line 1-2 not intersect with Lines 3-5 and 4-5.

12. Plane perpendicular to line
Line through P3 perp. and intersecting Line 1-2
Find Plane Perp. to Line 1-2 in (b) but not intersecting.
Use CP method to find piercing point 8 between Line 1-2 and Plane
Line 3-8 perp. And intersecting line 1-2.

13. Plane Perpendicular to a Line Auxiliary View Method
Line perp. To plane.
TL, EV, Point 4 and 5 in EV.
P4 and 5 anywhere along the projection line in top view.
Point perp. To Line

14. Line Perpendicular to a Plane
A line that is perpendicular to a plane is perpendicular to all lines in a plane

15. Line Perpendicular to a Plane -continued
Line through P4 perp. To Plane
Draw horizontal line in TV, get TL in FV and yield perp. Line from P4 in FV.
Draw horizontal line in FV, get TL in TV and yield perp. Line from P4 in TV.
Select any location for P5 along the projection line.
Use CP method to find the piercing point.
Find line 4-5 perp. To plane

16. Perpendicular Planes
If a line is perpendicular to a given plane, any plane containing the line is perpendicular to the given plane
Find Plane with Line 4-5 perp. To Plane
Add horizontal line to FV and find TL in TV. Draw perp. Line from P5.
Add horizontal line to TV at P3, find TL in FV. Draw perp. Line from P5 and locate P6 along the projection line.
Plane perp. To Plane

17. Line Perpendicular to Skew Lines
The shortest distance between two lines is measured along a line perpendicular to the two lines.

18. Line Perpendicular to Skew Lines Point View Method
Given two skew lines 1-2 and 3-4.
Draw a line perpendicular to both skew lines.
Select one of the line and draw a true length, Line 3-4.

19. Line Perpendicular to Skew Lines Point View Method
Line perp. To Point view 3-4 must be true length Line 5-6.
Line 1-2 not true length.
Project back to other view to find the common perpendicular line.

20. Line Perpendicular to Skew Lines Plane View Method
Line perpendicular to two skew lines.
Form a plane using one skew line.
Formed plane // to other skew line, hence perp. line can be drawn.
Find TL in plane and following with an EV of that plane.
Shortest distance = Perpendicular line.
But the location of the perpendicular line not known.
See part b.

21. Line Perpendicular to Skew Lines Plane View Method
True shape of Plane 1-2-X, but not drawn
Draw true shape of plane 1-2-X from EV
Draw Line 3-4 Perp. To Line 1-2 in Plane 1-2-X.

22. Shortest Horizontal Line (zero slope) Connecting Skew Lines EV method
Form Plane 1-2-X // to Skew line 3-4.
Draw edge view of both plane 1-2-X and line 3-4.
Plane and line //.

23. Shortest Horizontal Line (zero slope) Connecting Skew Lines EV method
Shortest horizontal line // to folding line H/1, must be true length (Line 5-6) in H/1.
Draw 2nd Auxiliary view perp. to folding line H/1, leading to Point view for Line 5-6.

24. Shortest Line Connecting Skew Lines at a Given Angle
Point view for finding perp. Line location