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

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.

Point View of Line Viewing parallel to TL - Point

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

Shortest distance between two skew lines

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.

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

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.

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.

Plane Representation

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

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.

Location of a Point on a Plane Locate point 4 in the plane 1-2-3 IN Top view.

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.

Location of a Point on a Plane Locate Point 4 in Plane 1-2-3 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.

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.

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.

Edge View of Planes Given Plane 1-2-3. Find the edge view.

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.

Piercing Point – Edge view method Given Plane 1-2-3 and Line 4-5. Find piercing point between Line 4-5 and Plane 1-2-3.

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 1-2-3. Extend Line 4-5 until it crosses Plane EV. The intersection = piercing point.

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.

Piercing Point – Cutting Plane method Using CP method. Cutting plane AA containing Line 4-5. Cutting Line 6-7 in Plane 1-2-3. 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.

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

Intersection of Planes – EV method Given Plane 1-2-3 and Plane 4-5-6. 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.

Intersection of Planes – EV method Given Plane 1-2-3 and Plane 4-5-6. Project the two piercing points to TV and FV. Draw the line connecting the two piercing points.

Angle between line and plane Given Plane 1-2-3 and Line 5-6. Using EV and True size method.

Angle between line and plane Given Plane 1-2-3 and Line 5-6. Using EV and True size method. True length of Plane 1-2-3. Draw Edge View of Plane 1-2-3.. Draw True size of Plane 1-2-3. 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 1-2-3.

Angle between line and plane