Projectionoflines 140408110604 phpapp02, Lecture notes of Accounting

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• 08/05/15 Hareesha N G, DSCE, Bengaluru

SIMPLE CASES OF THE LINE

1. A VERTICAL LINE ( LINE PERPENDICULAR TO HP & // TO VP)

2. LINE PARALLEL TO BOTH HP & VP.

3. LINE INCLINED TO HP & PARALLEL TO VP.

4. LINE INCLINED TO VP & PARALLEL TO HP.

5. LINE INCLINED TO BOTH HP & VP.

PROJECTIONS OF STRAIGHT LINES

Information regarding a line means It’s length,

Position of it’s ends with hp & vp

It’s inclinations with hp & vp will be given.

Aim:- to draw it’s projections - means fv & tv.

A Line inclined to Hp

and

parallel to Vp

(Pictorial presentation)

X

Y

V.P.

A

B

b’

a’

b

a





F.V

T.V.

A Line inclined to Vp

and

parallel to Hp

(Pictorial presentation)

Ø

V.P.

a b

a’

b’

A B

Ø

F.V.^

T.V.

X Y

H.P.

V.P.

F.V.

a (^) T.V. b

a’

b’

X Y

H.P.

V.P.

a Ø

b

a’ b’

Tv

Fv

Tv inclined to xy

Fv parallel to xy.

Fv inclined to xy

Tv parallel to xy.

Orthographic Projections

X

Y

V.P.

a’ For Fv

b’

a b

B

A



For Tv

F.V

T.V.

X

Y

V.P.

a’

b’

a b



F.V

T.V.

For Fv

For Tv

B

A

X Y

H.P.

V.P.

a

b

FV

TV

a’

b’

A Line inclined to both

Hp and Vp

(Pictorial presentation)

Note These Facts:- Both Fv & Tv are inclined to xy. (No view is parallel to xy) Both Fv & Tv are reduced lengths. (No view shows True Length)

Orthographic Projections Fv is seen on Vp clearly.

To see Tv clearly, HP is

rotated 90^0 downwards,

Hence it comes below xy.

On removal of object i.e. Line AB Fv as a image on Vp. Tv as a image on Hp,

The most important diagram showing graphical relations among all important parameters of this topic. Study and memorize it as a CIRCUIT DIAGRAM And use in solving various problems.

True Length is never rotated. It’s horizontal component is drawn & it is further rotated to locate view.

Views are always rotated, made horizontal & further extended to locate TL,  & Ø

Also Remember

Important TEN parameters to be remembered with Notations used here onward

Ø

1. True Length ( TL) – a’ b 1 ’ & a b
2. Angle of TL with Hp -
3. Angle of TL with Vp –
4. Angle of FV with xy –
5. Angle of TV with xy –
6. LTV (length of FV) – Component (a-1)
7. LFV (length of TV) – Component (a’-1’)
8. Position of A- Distances of a & a’ from xy
9. Position of B- Distances of b & b’ from xy
10. Distance between End Projectors

X Y

H.P.

V.P.

a 1

b

b 1

Ø

Tv^ TL

LFV

a’

b’

b 1 ’

Fv TL

 LTV

Distance between End Projectors.

 &  Construct with^ a’

Ø &^  Construct with^ a

b & b 1 on same locus.

b’ & b 1 ’ on same locus.

NOTE this

a’

b’

a

b

X Y

b’ 1

b 1

Ø

GROUP (A)

GENERAL CASES OF THE LINE INCLINED TO BOTH HP & VP

PROBLEM 1)^ ( based on 10^ parameters).

Line AB is 75 mm long and it is 30^0 & 400 Inclined to Hp & Vp respectively. End A is 12mm above Hp and 10 mm in front of Vp. Draw projections. Line is in 1st^ quadrant.

SOLUTION STEPS:

1. Draw xy line and one projector.
2. Locate a’ 12mm above xy line & a 10mm below xy line.
3. Take 30^0 angle from a’ & 40^0 from a and mark TL I.e. 75mm on both lines. Name those points b 1 ’ and b 1 respectively.
4. Join both points with a’ and a resp.
5. Draw horizontal lines (Locus) from both points.
6. Draw horizontal component of TL a b 1 from point b 1 and name it 1. ( the length a-1 gives length of Fv as we have seen already.)
7. Extend it up to locus of a’ and rotating a’ as center locate b’ as shown. Join a’ b’ as Fv.
8. From b’ drop a projector down ward & get point b. Join a & b I.e. Tv.

LFV

TL

TL

FV

TV

X

a’

y

a

b’

FV

b

b 1

TL

b’ 1

TL

PROBLEM 3:

Fv of line AB is 50^0 inclined to xy and

measures 55 mm long while it’s Tv is 60^0

inclined to xy line. If end A is 10 mm

above Hp and 15 mm in front of Vp, draw it’s

projections,find TL, inclinations of line with Hp

SOLUTION STEPS:^ & Vp.

1.Draw xy line and one projector. 2.Locate a’ 10 mm above xy and a 15 mm below xy line. 3.Draw locus from these points. 4.Draw Fv 50^0 to xy from a’ and mark b’ Cutting 55mm on it. 5.Similarly draw Tv 60^0 to xy from a & drawing projector from b’ Locate point b and join a b. 6.Then rotating views as shown, locate True Lengths ab 1 & a’b 1 ’ and their angles with Hp and Vp.

X Y

a’

a

b’ 1

LTV

TL

b 1

b’

b

LFV

TV

FV

TL

PROBLEM 4 :-

Line AB is 75 mm long .It’s Fv and Tv measure 50 mm & 60 mm long respectively. End A is 10 mm above Hp and 15 mm in front of Vp. Draw projections of line AB if end B is in first quadrant.Find angle with Hp and Vp.

SOLUTION STEPS:

1.Draw xy line and one projector. 2.Locate a’ 10 mm above xy and a 15 mm below xy line. 3.Draw locus from these points. 4.Cut 60mm distance on locus of a’ & mark 1’ on it as it is LTV. 5.Similarly Similarly cut 50mm on locus of a and mark point 1 as it is LFV. 6.From 1’ draw a vertical line upward and from a’ taking TL ( 75mm ) in compass, mark b’ 1 point on it. Join a’ b’ 1 points.

7. Draw locus from b’ 1
8. With same steps below get b 1 point

and draw also locus from it.

9. Now rotating one of the components I.e. a-1 locate b’ and join a’ with it to get Fv.
10. Locate tv similarly and measure

Angles ^ & 