ENGINEERING GRAPHICS

AUXILIARY PLANES

Two views of an object (FV, TV) projected on the principal planes are sometimes not

sufficient to convey all information regarding object.

Additional views, called Auxiliary Views, are therefore, projected on other planes known

as Auxiliary planes.

Auxiliary views may also be used for determining True Length of a line Point-View of a line Edge-View of a plane Shortest Distance between point and a line Shortest distance between skew lines True Size and Form of plane True shapes of sections of solids

Very useful in finding solutions of problems in practical solid geometry.

AUXILIARY PLANES

Any plane perpendicular to an RP and inclined to the other RP is called an auxiliary plane.

The view of an object obtained on an auxiliary plane is called an auxiliary view.

In drawing practice, two auxiliary planes, viz., Auxiliary Inclined Plane (AIP) and Auxiliary

Vertical Plane (AVP), are used.

An AIP is a plane inclined to the HP and perpendicular to the VP.

AVP represents a plane inclined to the VP and perpendicular to the HP.

Obviously, AIP and AVP are seen as lines in FV and TV respectively.

These lines are called auxiliary reference lines and are shown by X1Y1, X2Y2, etc.

Auxiliary planes are used to obtain auxiliary views and true shapes of sections of solids.

AUXILIARY PLANE

AUXILIARY PLANEIMPORTANCE OF AUXILIARY VIEWS

Used to show true dimensions of an inclined plane.

AUXILIARY PLANEIMPORTANCE OF AUXILIARY VIEWS

AUXILIARY PLANEIMPORTANCE OF AUXILIARY VIEWS

AUXILIARY INCLINED PLANE

AIP

AUXILIARY INCLINED PLANE

AUXILIARY VERTICAL PLANE

AVP

AUXILIARY VERTICAL PLANE

A line AB has its end A, 10 mm above the HP and 24 mm in front of the VP. End B is 55 mm above the HP and 50 mm in front of the VP. The distance between the end projectors is 45 mm. Draw the projections of the line and find the TL and true inclinations. Also locate the traces.

TRUE LENGTH, TRUE INCLINATIONS AND TRACES OF A LINE

End D of line DE is 10 mm in front of VP, and 40 mm above HP. End E is 35 mm in front of VP and 5 mm above HP. Distance between end projectors is 55 mm. Draw the projections of the line. Also project (a) Auxiliary plan on an AIP, inclined 60° to HP; (b) Auxiliary elevation on an: AVP inclined 45° to VP.

AUXILIARY PLANES

Y2

YXX2

AVPY1

X1

AIP60o

45od

e

e’

d’

e1

d1

510

d2’

510

25

40 25

40

e2’

AIP

Aux. Plan

Aux. Elevation

AVP

End A of a line AB is 10 mm in front of VP and 40 mm above HP. End B is 50 mm in front of VP and 10 mm above HP. Distance between the end projectors is 50 mm. Draw the projections, determine its true length and find inclinations to HP and VP, using auxiliary plane method.

AUXILIARY PLANES

YX

Y2

X2

Y1

X1

10

10

a’

10

40

10

50

b’

a2’

b2’

a

b

a1 b1

50

40

50

TL=71

TL=71Aux. Plan

Aux. Elevation

AVP

AIP

End A of line AB is 35 mm above HP and 10 mm in front of VP. End B is 40 mm below HP and 25 mm behind VP. Distance between end projectors is 50 mm. Draw the projections. Determine its true length and find inclinations to HP and VP, using auxiliary plane method. Compare the true length obtained by auxiliary plane and by rotation method.

AUXILIARY PLANES

YX

a1

a’

50

35

10

25

40

b2’

a2’

b’

b1

Ɵ

b

a

TL=97

TL=97

Φ

Y1

X1

X 2

Y 2

10

25

40

35

AIP

AVP

End A of line AB is 35 mm above HP and 10 mm in front of VP. End B is 40 mm below HP and 25 mm behind VP. Distance between end projectors is 50 mm. Draw the projections. Determine its true length and find inclinations to HP and VP, using auxiliary plane method. Compare the true length obtained by auxiliary plane and by rotation method.

AUXILIARY PLANES

YX

b2

a’

50

35

10

25

40

b1’

b’

b

a

b1

b2’

TL=97

Find the shortest distance of the line connecting point R to the line AB as shown in fig. 1. Show the line of the shortest distance in plan and elevation.

AUXILIARY PLANES

YX

a’

b’r’

b

a

b1’r1’

a1’

Y2

a2, b2, s2

r2

r

TLS.D.

X2

Y1

X1

40

40

10

10

30

30

4030

s

s1’

s’

30

10

40TL

The centre lines of two pipes AB and CD are shown in fig. 2. Find the shortest distance between the two lines. Also project this shortest distance back on the front and top views.

AUXILIARY PLANES

YX

30o

60

b

3050

30

10

50 60

d’

c’ a’

a’

a

c

d

3030 60

60

30

30

50

X1

Y1

e’

e

e2

e1’TL

b1’

a1’

d1’

c1’

c2, d2,f2

b2

a2

f1’

f’

f

X2

Y2

Using auxiliary planes method, obtain the true shape of triangular lamina whose projections are given in fig 3. By projecting one side as a point

AUXILIARY PLANES

YX

b2 , c

2

a2

c1’

Y1c

b

a

c’

b’

a’

X1

Y2

X2

Y3

X3

b1’

a1’

b3’

a3’

c3’

TL

2030 74

10

70

50

4030

True Shape

Using auxiliary planes method, obtain the true shape of triangular lamina whose projections are given in fig 3. By projecting one side as a point

AUXILIARY PLANES

YX

Y1c

b

a

c’

b’

a’

X1

a3’TLY2

X2

b1’

c1’

a1’, d1’c2

d2

b2a2

d’

d

a’d’ ∕∕ XY

5070

7430

20

30 4010

TrueShape

Partial front view and complete end view

of a flat surface is given in fig. 4. Complete

the front view and finds its true shape

using auxiliary plane.

AUXILIARY PLANES

X2

Y1

Y2

T.S.

a1’, b1’

X1

g1’f1’

d1’c1’

e1’

ef g

e’f’

g’

g2

f2

e2

d2

c2b2

a2

TL