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

Lines Perpendicular to the Fold Line

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

Parallel Planes Edge View True length and then edge view.

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.

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

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’

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’

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.

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.

Plane Perpendicular to a Line Given View Method Line 1-2 perp. to Plane 2-3-4. 90 shown with one TL Line 1-2 not intersect with Lines 3-5 and 4-5.

Plane perpendicular to line Line through P3 perp. and intersecting Line 1-2 Find Plane 3-4-5 Perp. to Line 1-2 in (b) but not intersecting. Use CP method to find piercing point 8 between Line 1-2 and Plane 3-4-5. Line 3-8 perp. And intersecting line 1-2.

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

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

Line Perpendicular to a Plane -continued Line through P4 perp. To Plane 1-2-3. 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 1-2-3.

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 1-2-3. 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 4-5-6 perp. To Plane 1-2-3.

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

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.

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.

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.

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.

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 //.

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.

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