projections of planes · projections of planes 1 1 an isosceles triangle abc with base ab = 42 mm...

Projections of planes

1

1 An isosceles triangle ABC with base AB = 42 mm and height 58 mm rests with AB on HP and 600 to VP with point A 18 mm in front

of VP. Complete the projections of triangular plate, its surface inclined at 450 to HP.

Initial Step: Assume triangular plane is simply kept

on H.P. True shape will be observed in T.V. Edge view

a’b’ on HP; draw side ab of triangle abc perpendicular

to VP. Point a should be 18 mm in front of VP.

Draw edge view in FV.

Inclination with HP: Surface i.e.

edge view makes 450 with HP.

Reproduce FV making an angle 450

with HP. Draw vertical projectors

from FV and horizontal projector

from TV of initial position and get

TV.

Inclination with VP: Resting edge ab

makes an angle 600 with VP. Reproduce TV

from second position as shown in third step.

Draw vertical projector from TV and

horizontal projectors from FV of second

position and get final FV.

M S Shinge


2

2 A regular hexagonal plate 50 mm side is resting on one of its corners in HP the diagonal through that corner is inclined at 400 to HP

and TV of that diagonal inclined to VP by 300. Draw its projections.

Initial position: Assume hexagonal plate is

laying on HP. True shape of plate will be

observed in TV. Corner is in HP; draw

hexagon as shown in TV. Accordingly draw

FV which is edge view of plate.

Inclination with HP: Reproduce

FV such that its diagonal ‘ad’

makes an angle 400 with HP.

Draw TV by drawing projectors.

Draw accordingly TV.

Inclination with VP: Reproduce TV such that ‘ad’

makes 300 with VP. Draw final FV.

M S Shinge


3

3 A 300-600 set square has its shortest side 50 mm long and is in the HP. The TV of the setsquare is an isosceles triangle and the

hypotenuse of the set square is inclined at an angle of 400 with the VP. Draw the projections of the setsquare and find its inclination

with the HP.

Initial position: 1) Plane is resting in HP: -

True shape will appear in HP. Draw first TV

2) Resting on shortest edge :-

Draw edge ab vertical at left side.

3) Draw FV

Inclination with HP:- 1) The TV

of the setsquare is an isosceles

triangle. Draw isosceles triangle in

TV (ab=ac=50) using horizontal

projectors from initial position.

2) Draw vertical projectors to draw

FV.

3) Draw FV. (a’-b’-c’)in first step

= a’-b’-c’)in second step

Inclination with VP:- 1) the hypotenuse of the set

square is inclined at an angle of 400 with the VP. As true

angle of hypotenuse is given and we have its apparent

length, find apparent angle. Apparent angle is 650. Draw

line making an angle 650 with VP. Mark hypotenuse cb

and reproduce TV from second position. 2) Draw final

FV by using vertical and horizontal projectors.

M S Shinge


4

4 A thin plate has a rhombus shape with its diagonals of 50 mm and 80 mm length. It rests on one of its corners on HP. with a shorter

diagonal to be perpendicular to VP and parallel to HP. The longer diagonal is inclined to HP in such a way that the top view of plate

looks likes a square. Draw FV, TV and LHSV and measure the inclination with HP.

Initial position: A thin plate has a rhombus shape rests

on one of its corners on HP, with a shorter diagonal to

be perpendicular to VP and parallel to HP.

1. Draw TV(diagonal ‘bd’ perpendicular to VP)

2. Draw FV

Inclination with HP: The longer diagonal is inclined

to HP in such a way that the top view of plate looks

likes a square.

1. Draw TV such that it is square. (bd=ac)

2. Draw FV using vertical and horizontal projectors.

𝜃 is inclination with HP.

Draw SV

M S Shinge


5

5 Triangle ‘abc’ carries ab=55, bc=65 and ca=50mm. ‘ab’ lies in HRP and point ‘a’ is 15 mm in front of FRP. Distance between

projectors of ‘a’ and ‘b’ is 45 mm. Complete the projections if point c is 45 mm above HRP.

1. Side ‘ab’ of triangle ‘abc’ lies in HRP. Point

‘a’ is 15 mm in front of FRP. Assume triangle

is simply kept in HP. True shape will appear in

TV. Draw TV such that side ab is vertical and

point ‘a’ is 15 mm in front of FRP.

2. Draw FV.

1. Point c is 45 mm above HRP.

Reproduce FV such that c is 45 mm

above HP.

2. Draw TV using vertical and

horizontal projectors.

𝜃 is inclination with HP.

1. Distance between projectors of a and b is 45

mm.

Draw two projectors at distance 45 mm from

each other. Reproduce TV.

2. Draw FV by using vertical and horizontal

projectors.

M S Shinge


6

6 A rectangular plate 40×80 mm rests on one of its smaller side on FRP. Its front view appears like a square with all sides 40 mm.

Complete the projections of the plate if one of its diagonals is parallel to HP. Determine the inclination of the plate with FRP.

1. A rectangular plate rests on one of its smaller

side on FRP. Assume plate is kept in FRP and

draw true shape of plate in FV. Draw one smaller

side vertical.

2. Draw TV. by using vertical and horizontal

1. FV appears like a square. Draw square

in FV,

2. Reproduce TV by using vertical

projectors.

3. 𝜃 is inclination with FRP.

One diagonal is parallel to HP.

1. Reproduce FV such that diagonal bd is

parallel to HP.

2. Draw TV by using vertical and


M S Shinge


7

projectors.

7 A regular pentagon ‘abcde’ with all sides 40 mm has side ab in FRP and at 300 to HRP with corner ‘a’ 40 mm above HRP. Complete

its projection if‘d’ is 25 mm in front of FRP. Determine its inclination with FRP.

1. As one side of pentagon is in FRP, assume it

is simply kept in FRP. True shape will appear

in FRP i.e. FV. Draw pentagon in FRP with

one side vertical.(F.V.) Corner ‘a’ should be

40 mm above H.R.P. in all steps in F.V.

2. Draw T.V.

1. In second step reproduce T.V. such that‘d’

is 25 mm in front of FRP.(because corner ‘d’

is 25 mm in front of F.R.P.)

2. Draw F.V. by using vertical and horizontal

projectors.

1. In third step, draw F.V. such that side ab

is making 300 to xy line (edge ab is making

an angle 300 to HRP)

2. Draw TV by using vertical and


M S Shinge


8

8 A semicircular plate at has the 80 mm diameter straight edge in VP and inclined at 450 to HP. The surface of plate makes an angle of

300 to VP. Draw its projection.

Initial Position: 1) A semicircular plate has a

straight edge in VP. True shape will appear

in FV. Draw semicircle in FV. Straight edge

should be vertical as it is in VP.

Second position: 1) Surface makes an angle

of 300 to VP. Draw TV according to this

inclination. 2) Draw FV by using vertical

and horizontal projectors.

Final position: 1) Straight edge makes an

angle of 450 to HP. Draw a line 450 to XY

line, mark straight edge (bc) and reproduce

FV from FV in second position.

2) Draw TV by using vertical and horizontal

projectors

M S Shinge


9

9 Draw the projection of circular plane of negligible thickness of 50 mm diameter resting on HP on a point A on the circumference

with its plane inclined 450 to HP and the top view of the diameter passing through the resting point makes 450 to VP.

Initial Position: 1) A semicircular plate has a

straight edge in VP. True shape will appear in

FV. Draw semicircle in FV. Straight edge

should be vertical as it is in VP.

Second position: 1) Surface makes an angle

of 300 to VP. Draw TV according to this

inclination. 2) Draw FV by using vertical and


Final position: 1) Straight edge makes an

angle of 450 to HP. Draw a line 450 to XY

line, mark straight edge (bc) and reproduce

FV from FV in second position.

2) Draw TV by using vertical and horizontal

projectors

M S Shinge

projections of planes · projections of planes 1 1 an isosceles triangle abc with base ab = 42 mm...

Documents