PROJECTIONS OF PLANES QUESTION ANSWERS-CLASS NOTES

PROJECTIONS OF PLANE 

QUESTION ANSWERS- 

CLASS NOTES

A plane is a 2-dimensional figure extending

infinite in the two dimensions. When two

dimensions are limited, it is a lamina. The

examples of lamina are rectangle, circle

and trapezium. It has negligible thickness

like the sheet of paper. Planes having

different positions are projected on HP and VP.

1. How to locate a plane?

It is located by any one of the followings:

(i) Three points not lying on the same line

(ii) A point and a straight line

(iii) Two parallel lines

(iv) Two intersecting lines

(v)  From its trace

2. Describe the types of planes.

There are two types.

(i) perpendicular planes

(ii) Oblique planes

3. Types of perpendicular planes

(i)Firstly Perpendicular to VP and parallel to HP

(ii) Secondly Perpendicular to HP and parallel to VP

(iii) Thirdly Perpendicular to VP and HP

(iv) Fourthly Perpendicular to VP and inclined to HP  (A.I.P)

(v) Fifthly Perpendicular to H and inclined to VP (A.I.V.)

4. Discuss oblique planes.

A plane inclined to both HP and VP.

5. Describe the traces of planes

There are two traces.

Vertical trace(V.T.)

The intersection of a plane with the vertical plane.

Horizontal Trace (H.T.)

The intersection of a plane with HP.

Discuss the representation of planes.

(i) Plane perpendicular to HP and parallel to VP

 H.T. represents this plane.

(ii) Plane perpendicular to VP and parallel to HP

 V.T. represents this plane.

(iii) Plane perpendicular to HP and VP.

 Bot H.T. and V.T. represent such a plane. Both are in the same straight line.

(iv) Plane perpendicular to VP and inclined to HP

 V.T. represents. VT is inclined to xy and above the xy. It has H.T. perpendicular to xy. The VT and HT meet at a point in xy.

(v) Plane perpendicular to HP and inclined to VP

 H.T. represents. HT is inclined to xy and below the xy. It has VT perpendicular to xy. The HT and VT meet at a point in xy.

General observations

Firstly Plane parallel to HP has no HT.

Secondly Plane parallel to VP has no VT.

Thirdly Plane perpendicular to HP has HT.

Fourthly Plane perpendicular to VP has VT

Fifthly Plane perpendicular to both HP and VP has HT and VT. These are is a straight line.

Sixthly Plane perpendicular to VP and inclined to HP

It has its VT inclined to xy and above xy. Its HT is perpendicular to xy. Both HT and VT at a point in xy.

Plane perpendicular to HP and inclined to VP

It has its HT inclined to xy and below  xy. Its VT is perpendicular to xy. Both HT and VT at a point in xy.

Name the principal planes of projections

Planes employed for projections of front view, top view and side view are principal planes of projections. These are also reference planes.  These planes intersect at right angles to each other. These are vertical plane, horizontal plane and the profile plane( Perpendicular to both HP and VP).  Assumed these transparent planes to help in the projection an object.

 What is the principle of projection?

Draw straight lines from various points on the contour of an object. These meet at points on the plane of projection. There points when joined form a shadow of the object on that plane. This shadow is the projection of the object on that plane. This gives front view, top view and side views.

PROJECTION OF PLANES

Sr. No.

Position of a plane

Front View

Top View

1

Perpendicular to VP and parallel to HP

Line parallel to xy & coincides with its VT

True shape of the plane

2.

Perpendicular to HP and parallel to VP

True shape of the plane

Line parallel to xy & coincides with its HT

3.

Perpendicular to VP and HP

Line perpendicular to xy and coincides with its VT

Line perpendicular to xy and coincides with its HT

4.

Perpendicular to VP and inclined to HP at angle θ

Line is inclined at an angle θ to xy , above xy and coincides with VT

Reduced shape of the plane

5.

Perpendicular to HP and inclined to VP at angle φ

Reduced shape of the plane

Line is inclined at an angle φ with xy, below xy and coincides with HT

6.

Inclined to both VP and HP

Reduced shape of the plane

Reduced shape of the plane

Fig. Orthographic Projections of planes

(1) Plane perpendicular to HP and parallel to VP

(2) Plane perpendicular to HP and parallel to VP

(3) Plane perpendicular to both HP and VP

(4) Plane perpendicular to VP and inclined to HP

(5) Plane perpendicular to HP and inclined to VP

Fig. HT & VT of Planes
(a) Plane perpendicular to HP & VP, HT and VT are perpendicular to XY
(b) Plane ↓ to HP and inclined at 300 to VP, HT is inclined to XY at 300 and VT is ↓ to XY, both the traces intersect at XY
(c)  Plane ↓ to VP and inclined at 450 to HP, HT is ↓ to XY  and VT is inclined at 450 to XY, both traces intersect at XY
(d) Plane parallel to HP and 40 mm from the HP, HT is parallel to XY at a distance of 40 mm and no VT.
(e) Plane parallel to VP and 45 mm from VP, No HT and VT is parallel to XY at a distance of 45 mm

(a)                          (b)             (c)

Fig. Projection of an inclined plane

Projection of a rectangle with a corner in HP, its diagonal AC inclined at 300 to HP and the diagonal BD inclined at 450 to VP and parallel to HP.

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