Unit ii projection of lines

introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection

1. Dr.R. GANESAMOORTHY.B.E.,M.E.,Ph.d.
Professor –Mechanical Engineering
SaveethaEngineering College
Tandalam
Chennai.
30-Sep-18 1Dr.RGM PROF/MECH EG POINTS

2. What is Projections of Lines
Theshortestdistancebetweenanytwopointsis
calleda"straightline".Differentsurfacesandplanes
formtheconfigurationorshapeofanyobject.
Thusastraightlineisthebasicconceptualfigureusing
whichanyobjectlikeamachinecomponentora
structuralelementisrepresented.
Thusprojectionofastraightlineisthefoundationof
EngineeringDrawing.
Wehavestudiedtheprojectionsofgivenpoints,Joining
therespectiveprojectionsoftwopointstherefore
givestheprojectionofthestraightlinejoiningthe
twopoints
30-Sep-18 2Dr.RGM PROF/MECH EG POINTS

3. Objectives-Projection of Lines
Define straight line.
Draw the projections of a straight line located at
different positions with respect to the VP and the HP.
Position of line are arranged in planes
30-Sep-18 3Dr.RGM PROF/MECH EG POINTS

4. Coordinate System
30-Sep-18 4Dr.RGM PROF/MECH EG POINTS

5. Orientation of Line in Space
The position of straight line in space can be
described following
1.Lines parallel to VP and perpendicular to HP
2.Lines perpendicular to VP and parallel to HP
3.Lines parallel to both VP and HP
4.Lines parallel to VP and inclined to HP
5.Lines inclined to VP and parallel to HP
6.Lines inclined to both VP and HP
30-Sep-18 5Dr.RGM PROF/MECH EG POINTS

6. Notations of Lines in views
Following notations should be followed while
naming different views in projections.
Object Point
IT’S TOP VIEW a, b
IT’S FRONT VIEW a’, b’
IT’S SIDE VIEW a’’, b’’
30-Sep-18 6Dr.RGM PROF/MECH EG POINTS

7. 30-Sep-18 Dr.RGM PROF/MECH EG POINTS 7
Projection of straight line on its various positions
S.No Position of the line Front view Top view Traces
1
Lines parallel to both
VP and HP
True length and is
parallel to XY
True length and is
parallel to XY
NO
TRACES
2
Lines perpendicular to
VP and parallel to HP
Point
True length and is
Perpendicular to XY
Only VT
No HT
3
Lines parallel to VP and
perpendicular to HP
True length and is
Perpendicular to XY
Point
Only HT
No VT
4
Lines parallel to HP and
inclined to VP
Shorter than true
length and is parallel
to XY
Has true length and
true inclination
Only VT
No HT
5
Lines inclined to HP
and parallel to VP
Has true length and
true inclination
Shorter than true
length and is parallel
to XY
Only HT
No VT
6
Lines inclined to both
VP and HP
Shorter than true
length, inclined to XY
and angle is not true
inclination
Shorter than true
length, inclined to XY
and angle is not true
inclination
Has
Both HT
and VT

8. Projection of Lines in Different Quadrants
1.Perpendicular to the HP and Parallel to the VP
30-Sep-18 8Dr.RGM PROF/MECH EG POINTS

9. Projection of Lines in Different Quadrants
2.Perpendicular to the VP and Parallel to the HP
30-Sep-18 9Dr.RGM PROF/MECH EG POINTS

10. Projection of Lines in Different Quadrants
3.Parallel to the HP and Inclined to the VP
30-Sep-18 10Dr.RGM PROF/MECH EG POINTS

11. Projection of Lines in Different Quadrants
4.Parallel to the VP and Inclined to the HP
30-Sep-18 11Dr.RGM PROF/MECH EG POINTS

12. Projection of Lines in Different Quadrants
5.The line both parallel VP and HP
30-Sep-18 12Dr.RGM PROF/MECH EG POINTS

13. Projection of Lines in Different Quadrants
6.The line both inclined VP and HP
30-Sep-18 13Dr.RGM PROF/MECH EG POINTS

14. Projection of Lines in Different Quadrants
6.The line both inclined VP and HP
30-Sep-18 14Dr.RGM PROF/MECH EG POINTS

15. Projection of Lines in Different Quadrants
6.The line both inclined VP and HP
30-Sep-18 15Dr.RGM PROF/MECH EG POINTS

16. S. NoPosition of the line Front view Top view Traces
1
Lines parallel to both
VP and HP
True length and is
parallel to XY
True length and is
parallel to XY
NO
TRACES
2
Lines perpendicular
to VP and parallel to
HP
Point
True length and is
Perpendicular to XY
Only VT
No HT
3
Lines parallel to VP
and perpendicular to
HP
True length and is
Perpendicular to XY
Point
Only HT
No VT
4
Lines parallel to HP
and inclined to VP
Shorter than true length
and is parallel to XY
Has true length and
true inclination
Only VT
No HT
5
Lines inclined to HP
and parallel to VP
Has true length and true
inclination
Shorter than true
length and is parallel
to XY
Only HT
No VT
6
Lines inclined to both
VP and HP
Shorter than true length,
inclined to XY and angle
is not true inclination
Shorter than true
length, inclined to XY
and angle is not true
inclination
Has
Both HT
and VT
Projection of straight line on its various positions
30-Sep-18 16Dr.RGM PROF/MECH EG POINTS

17. Problems in projection of Lines
1.Lines parallel to both VP and HP
1.A line CD 50mm long has its end C, 15mm above the HP
and 25 mm in front of the VP . The line is kept parallel to
both HP and VP .draw its projections
30-Sep-18 17Dr.RGM PROF/MECH EG POINTS

18. Problems in projection of Lines
2.Lines perpendicular to one plane and parallel to
another plane
2.A line 55 mm long has its end E 15 mm above the HP and 25
mm in front of the VP. The line is kept perpendicular to HP and
parallel to VP. Draw its projections
30-Sep-18 18Dr.RGM PROF/MECH EG POINTS

19. Problems in projection of Lines
2.Lines perpendicular to one plane and parallel to
another plane
3. A line GH 50 mm long has its end G 20 mm above the HP
and 25 mm in front of the VP. The line is kept perpendicular
to VP and parallel to HP. Draw its projections.
30-Sep-18 19Dr.RGM PROF/MECH EG POINTS

20. Problems in projection of Lines
3.Lines inclined to one plane and parallel to
another plane
4. A line AB 55 mm long is lying on the HP and makes an
angle of 35
0
with the VP. Its end A is 25mm in front of VP.
Draw the projections of the line .
30-Sep-18 20Dr.RGM PROF/MECH EG POINTS

21. Problems in projection of Lines
3.Lines inclined to one plane and parallel to
another plane
5. A line AB 50 mm long has its end A 30mm above HP and
25 mm in front of VP. The line is kept inclined at 40
0
to HP
and parallel to VP. Draw its projections and make its traces.
30-Sep-18 21Dr.RGM PROF/MECH EG POINTS

22. Problems in projection of Lines
3.Lines inclined to one plane and parallel to
another plane
6. A line AB 50 mm long has its end A25 mm above HP and
25 mm in front of VP. The line is inclined at 45
0
to VP and
parallel to HP. Draw its projections and also make its traces.
30-Sep-18 22Dr.RGM PROF/MECH EG POINTS

23. Problems in projection of Lines
3.Lines inclined to one plane and parallel to
another plane
7.A line AB 65 mm long has its end A 20 mm above HP and
30 mm in front of VP. Its top view has a length of 45 mm and
parallels to HP. Draw its projections and find the inclination
of the line with HP.
Answer: θ=46
0
30-Sep-18 23Dr.RGM PROF/MECH EG POINTS

24. Problems in projection of Lines
3.Lines inclined to one plane and parallel to
another plane
8.A line AB 60 mm long has its end A 30 mm above HP and
15 mm in front of VP. Its front view has a length of 45 mm
and parallels to HP. Draw its projections and find the
inclination of the line with VP.
Answer: θ=46
0
30-Sep-18 24Dr.RGM PROF/MECH EG POINTS

25. Problems in projection of Lines
3.Lines inclined to one plane and parallel to
another plane
9. A line AB has its end A 30 mm above HP and 20 mm in
front of VP. It is inclined at 25
0
to the VP and parallels to HP.
Draw its projections, if the distance between the end
projectors to be 55 mm. Find the true length of the line also.
Answer : TL= 60mm
30-Sep-18 25Dr.RGM PROF/MECH EG POINTS

26. Problems in projection of Lines
4. Lines inclined to both the plane
10. A line 70 mm long has one end 15 mm above HP and 30
mm in front of VP. The line is inclined at 35
0
to the HP 45
0
to
the VP. Draw the projection of the line.
30-Sep-18 26Dr.RGM PROF/MECH EG POINTS

27. Problems in projection of Lines
4. Lines inclined to both the plane
11. One end of a line AB 70 mm long, is 10 mm above HP
and 25 mm in front of VP. The line is inclined at 25
0
to the HP
45
0
to the VP. Draw the projections and find its traces.
30-Sep-18 27Dr.RGM PROF/MECH EG POINTS

28. Problems in projection of Lines
4. Lines inclined to both the plane
12. A line AB 75 mm long has one end A 20 mm above HP
and 25 mm in front of VP. The end B is 50mm above the HP
and 60 mm in front of VP. Draw the projection of the line and
find its inclination with HP and VP.
Answer: θ= 24
0
ϕ = 28
0
30-Sep-18 28Dr.RGM PROF/MECH EG POINTS

29. Problems in projection of Lines
4. Lines inclined to both the plane
13.One end of a line AB is 10 mm above HP and 20 mm in
front of VP. The other end is 45 mm above HP and 65 mm in
front of VP the distance between the end projector is 40mm.
Draw the projection of the line and find its inclination and
length.
Answer : θ= 30
0
ϕ = 40
0
TL = 70 mm
30-Sep-18 29Dr.RGM PROF/MECH EG POINTS

30. Problems in projection of Lines
4. Lines inclined to both the plane
14. A line AB 65 mm long in the front view has its end A 20 mm above HP
and 15 mm in front of VP. The end B is 45 mm in front of VP. Draw the
projection of the line and find its inclination with HP and VP. The
distance between the ends projectors passing through the end point is
50 mm. Draw the projection of the line and find its inclination.
Answer: θ= 35
0
ϕ = 25
0
TL = 71 mm
30-Sep-18 30Dr.RGM PROF/MECH EG POINTS

31. Problems in projection of Lines
4. Lines inclined to both the plane
15. A line AB 80 mm long has its end A 10 mm above HP and in the VP.
Draw the projection of the line makes an angle of inclined at 50
0
to the
HP and 30
0
to the VP.
30-Sep-18 31Dr.RGM PROF/MECH EG POINTS

32. Problems in projection of Lines
4. Lines inclined to both the plane
16. One end A of a line AB is 60 mm long 30 mm above HP and 25 mm in
front of VP. The top and front view has a length of 35 mm and 55mm
respectively. Draw the projection of the line and find its inclination.
Answer: θ= 55
0
ϕ = 25
0
30-Sep-18 32Dr.RGM PROF/MECH EG POINTS

33. Problems in projection of Lines
4. Lines inclined to both the plane
17. A line AB 75 mm long has one of its ends 60 mm in front of the VP
and 20 mm above the HP and the other end is 20 mm in front of VP and
is above HP. The top view of the line is 55mm long. Draw the projection.
30-Sep-18 33Dr.RGM PROF/MECH EG POINTS

34. Problems in projection of Lines
4. Lines inclined to both the plane
18.The top view of a line is 65mm long and is inclined at30
0
to the
reference line. One end is 20mm above the HP and 10mm in front of VP.
The other end is 60mm above the HP and is front view of VP. Draw the
projection of the line and find its inclination and length.
Answer: θ= 32
0
ϕ = 25
0
TL = 76 mm
30-Sep-18 34Dr.RGM PROF/MECH EG POINTS

35. Problems in projection of Lines
4. Lines inclined to both the plane
19. One end A of a line AB is 70 mm long 15 mm above HP and 20 mm in
front of VP. The top and front view has a length of 35 mm and 55mm
respectively. Draw the projection of the line and find its inclination.
Answer: θ= 21
0
ϕ = 41
0
30-Sep-18 35Dr.RGM PROF/MECH EG POINTS

36. Problems in projection of Lines
4. Lines inclined to both the plane
20.One end A of a line AB is 70 mm long 20 mm above HP and 25 mm in
front of VP. The line inclined at 50
0
to the HP and 30
0
to the VP. Draw the
projection of the line and mark the point O on it, which is 35 mm away
from one end of the line.
30-Sep-18 36Dr.RGM PROF/MECH EG POINTS

37. Problems in projection of Lines
4. Lines inclined to both the plane
21.A line AB 60 mm long has one of its ends 10 mm in front of the VP
and 20 mm above the HP. The line inclined at 40
0
to the HP and 50
0
to the
VP. Draw the projection.
30-Sep-18 37Dr.RGM PROF/MECH EG POINTS

38. Problems in projection of Lines
4. Lines inclined to both the plane
22. A straight line AB has one of its ends 25 mm in front of the VP and
20 mm above the HP and the other end is 60 mm above HP and is in
front of VP. The ends of the lines are on the same projector. Draw the
projection and find the true length, inclinations.
Answer: θ= 45
0
ϕ = 45
0
TL = 57 mm
30-Sep-18 38Dr.RGM PROF/MECH EG POINTS

39. Problems in projection of Lines
4. Lines inclined to both the plane
23.A line measuring 65mm long has one of its ends 45 mm in front of
the VP and 20 mm above the HP. The top view of the line is45mm long.
The other end is above HP and is 20mm in front of VP. The ends of the
lines are on the same projector. Draw the projection and find the true
length, inclinations
Answer: θ= 46
0
ϕ =23
0
30-Sep-18 39Dr.RGM PROF/MECH EG POINTS

40. Problems in projection of Lines
4. Lines inclined to both the plane
24. The front view of line AB measures 60mm and make an angle of
45
0
with XY line. The end A is in HP. The vertical trace of the line is 10mm
below XY. The top view is inclined 30
0
to XY. Draw the projections,
locate its traces.
Answer: θ= 41
0
ϕ =26
0
30-Sep-18 40Dr.RGM PROF/MECH EG POINTS

41. Problems in projection of Lines
4. Lines inclined to both the plane
Midpoints Problems
25. The midpoint of line AB 70mm long ,is 25 mm above the HP and
40mm in front of VP. It’s inclined at 35
0
to HP and 45
0
to the VP. Draw its
projections
30-Sep-18 41Dr.RGM PROF/MECH EG POINTS

42. Problems in projection of Lines
4. Lines inclined to both the plane
Midpoints Problems
26. The projection of line measuring 80 mm in the top view and 70 mm
in the front view the midpoint of the line is 45mm,in front of the VP and
35mm above HP .One end is 10 mm in front of VP and nearer to it. The
other end is nearer to HP. Draw the projection and find the true length,
inclinations
30-Sep-18 42Dr.RGM PROF/MECH EG POINTS

43. Problems in projection of Lines
4. Lines inclined to both the plane
Midpoints Problems
27.A straight line AB has one of its end A, 10 mm in front of the VP and
nearer to it. The midpoint m of the line is 50mm,in front of the VP and
40 mm above the HP. The front and top view measures 90mm and 120
mm respectively. Draw the projection and find the true length,
inclinations
30-Sep-18 43Dr.RGM PROF/MECH EG POINTS