Mechanical Engineering Drawing MECH 211/M / Lecture #5; Chapter 19 - - PowerPoint PPT Presentation

Mechanical Engineering Drawing / MECH 211/M

• Lecture #5; Chapter 19

; p

• Dr. John Cheung

Lecture 4 summary Lecture 4 summary

• Dihedral angle – Line – true length – point view.

ed a a g e e t ue e gt po t e .

• Plane – true length‐ EV and TS.
• Intersection line – validation.

Intersection line validation.

• Skew lines – validation – visibility.
• Rotation method – true length – development

Rotation method true length development work for cone.

• Compass – Direction (no need to be true length).

p ( g ) Slope (Horizontal angle) needs true length.

• Distance between lines and point.

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Point View of Line Point View of Line

Viewing parallel to TL ‐ Point

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Point View of Line Point View of Line

Fi d T l th P j t ll l t TL P i t

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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

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Shortest distance between two skew lines Shortest distance between two skew lines

1 D f ldi li b i 1. Draw folding line, obtain true length line 1‐2. 2. Draw FL perpendicular to true length obtain point true length, obtain point view of Line 1‐2. 3. Draw perpendicular line from Point 1,2 to line 3‐4. from Point 1,2 to line 3 4. This line = shortest distance between the two skew lines.

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Line passing through two skew lines Line passing through two skew lines

Find a line through point A and intersecting skew lines 1 2 and 3 4 lines 1‐2 and 3‐4.

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Line through a point and intersecting two skew li lines

• 1. Draw a line through Point

g ‘A’ and intersecting two skew lines.

• 2. Using edge view method.

3 T L of Line 1 2 then point

• 3. T.L. of Line 1‐2 then point

view of line 1‐2.

• 4. Draw line through Point

view 1‐2 and A to Line 3‐4, form Line C‐A‐B.

• 5. Project Points B and C back

to Auxiliary 1, Front and Top views Top views.

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Plane Representation Plane Representation

• A Intersecting lines

A, Intersecting lines.

• B ‐ Parallel lines.

C h i i i h li

• C ‐ Three points not in a straight lines.
• D – A line and a point not on that line.

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Plane Representation Plane Representation

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Straight line in plane Straight line in plane

Find the missing line 4‐5 in front view Find the missing line 4 5 in front view.

2 3 7

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Straight line in plane Straight line in plane

Find the missing line 4‐5 in front view using cutting plane method plane method.

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

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Location of a Point on a Plane

Locate point 4 in the plane 1‐2‐3 IN Top view.

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Location of a Point on a Plane

Locate Point 4 in Top View in Plane 1 2 3

• 1. Cutting plane method.

Locate Point 4 in Top View in Plane 1‐2‐3

• 1. Cutting plane method.
• 2. Extend Line 3‐4 until it

intersects Line 1‐2 in Front view, then yield Point 5.

• 3. Project Point 5 to Line

1‐2 in Top view.

• 4. Join Line 3‐5 in Top

view.

• 5. Project Point 4 in Line

3 5 in Front View to 3‐5 in Front View to Line 3‐5 in Top view. The intersection is Point 4 in Top View

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Point 4 in Top View.

Location of a Point on a Plane

Locate Point 4 in Plane 1‐2‐3 in Top View Locate Point 4 in Plane 1 2 3 in Top View

• 1. Based on parallelism principle.
• 2. Draw a Line starting at Point 4

ll l parallel to Line 2‐3 in Front view. Intersection = P5.

• 3. Project P5 in Front View to Line 1‐2 in

Top View yields the corresponding P5 Top View yields the corresponding P5 in TV.

• 4. Draw a line starting from P5 parallel

to Line 2‐3 in TV to Line 2 3 in TV.

• 5. Project P4 in Front View to Line

starting with P5. Intersection = P4 in TV.

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Finding Point in Plane Finding Point in Plane

• 1. Given: Point P
• 1. Given: Point P

10mm above P2 and 12mm behind P3.

• 2. In Front view,

Point P is somewhere along Line 4‐5.

• 3. In Top View, Point

P is somewhere along he line along he line 12mm behind P3.

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Finding Point in Plane ‐ continued Finding Point in Plane continued

• 1. Cutting plane method.

g p Use Line 4‐5 in Front view as Cutting plane.

• 2. Project P4 to Line 1‐2

and P5 to Line 2 3 in and P5 to Line 2‐3 in TV .

• 3. Join P4 and P5 in Top

view.

• 4. Use Line 6‐7 (12mm

behind P3) as CP.

• 5. Project P6 to Line 1‐2

and P7 to Line 1‐3 in and P7 to Line 1‐3 in FV.

• 6. Join P 6 and P7.
• 7. Intersection of Lines

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4‐5 and 6‐7 is Point P.

Edge View of Planes Edge View of Planes

• 1. Given Plane 1‐2‐3.
• 2. Find the edge view.

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Edge View of Planes Edge View of Planes

• 1. Given Plane 1‐2‐3.
• 2. Find the edge view.
• 3. True length.

4 Draw auxiliary view

• 4. Draw auxiliary view

looking parallel to

• TL. (Folding line

perpendicular to TL)

• 5. Edge view with True

g length showing as a point, i.e., Points 2 and 4

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and 4.

Piercing Point – Edge view method Piercing Point Edge view method

1. Given Plane 1‐2‐3 and Li 4 5 Line 4‐5. 2. Find piercing point between Line 4‐5 and Plane 1 2 3 Plane 1‐2‐3.

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Piercing Point – Edge view method Piercing Point Edge view method

1. Using edge view h d method. 2. Find TL in Front view. 3. Draw auxiliary view parallel to TL i e Edge parallel to TL, i.e. Edge view of Plane 1‐2‐3. 4. Extend Line 4‐5 until it crosses Plane EV. The crosses Plane EV. The intersection = piercing point.

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Piercing Point – Edge view method Piercing Point Edge view method

1. Using edge view h d method. 2. Project piercing point back to Front View and Top view Top view. 3. Check distance D1 between the auxiliary and Top views for and Top views for accuracy.

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Piercing Point – Cutting Plane method Piercing Point Cutting Plane method

1. Using CP method. 2 C i l AA 2. Cutting plane AA containing Line 4‐5. 3. Cutting Line 6‐7 in Plane 1 2 3 Plane 1‐2‐3. 4. Line 6‐7 and Line 4‐5 in the sane plane – must intersect. intersect. 5. Project P6 and P7 to Front View. Draw Line 6‐7. 6. Intersection between Line 4‐5 and 6‐7 in FV = Piercing point.

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7. Project piercing point to TV.

Piercing Point – Cutting Plane method Piercing Point Cutting Plane method

1. Using CP method. 2 D i h i ibili f 2. Determine the visibility of line and plane using the skew lines method learnt in Lecture 4

A B

in Lecture 4. 3. View A, looking down to FV, see Line 2‐3 first, So, Line 2‐3 on top in TV .

A B

Line 2 3 on top in TV . 4. View B, looking up to TV, see Line 2‐3 first, so Line 2‐3 is above and Line 4‐5 hidden in FV.

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Intersection of Planes – EV method Intersection of Planes EV method

• 1. Given Plane 1‐2‐

3 d Pl 4 5 3 and Plane 4‐5‐ 6.

• 2. Find intersection
• f two plane =
• f two plane =

straight line containing all points common points common to the two planes.

• 3. TL of one plane

p and follow with its EV.

• 4. Intersection

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points = Piercing points.

Intersection of Planes – EV method Intersection of Planes EV method

• 1. Given Plane 1‐2‐

3 d Pl 4 5 3 and Plane 4‐5‐ 6.

• 2. Project the two

piercing points piercing points to TV and FV.

• 3. Draw the line

connecting the connecting the two piercing points.

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Angle between line and plane Angle between line and plane

• 1. Given Plane 1‐2‐

3 d Li 5 6 3 and Line 5‐6.

• 2. Using EV and

True size method method.

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Angle between line and plane Angle between line and plane

• 1. Given Plane 1‐2‐3 and Line 5‐6.
• 2. Using EV and True size method.
• 3. True length of Plane 1‐2‐3.
• 4. Draw Edge View of Plane 1‐2‐3..
• 5. Draw True size of Plane 1‐2‐3.
• 6. Draw auxiliary view, looking perpendicular to

Line 5‐6. Line 5‐6 parallel to folding line. Hence, line 5‐6 = True length line 5 6 True length.

• 7. Measure the angle between True length Line 5‐6

and the EV of plane 1‐2‐3.

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Angle between line and plane Angle between line and plane

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