auxiliary planes
DESCRIPTION
Engineering GraphicsTRANSCRIPT
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