PROJECTIONS AND TRACES OF A PLANE CLASS NOTES

 

PROJECTIONS AND TRACES OF

A PLANE CLASS NOTES

 

Plane projections a plane

help in the projection of solids.

Projection of oblique planes teach to

tackle difficult problems. Planes are

inclined to both HP and VP. In addition,

projection of oblique planes makes

more knowledgeable and more

confident. Projections and traces of planes makes

projection of solids simple & easy.

 

Projection of Planes

 Start with the projection of a point.

Number of points makes a line. Draw projections of a line.

Lines form planes. Draw projections of a plane.

Thus we achieve the final aim.

Definition of a plane

A plane is a 2-dimensional figure having length and breadth. Thickness is negligible. It is not a solid since a solid is always 3-dimensional. Projection of planes is drawing projections of a 2-dimensional figure on the principal planes of projections.  2-dimensional figures include various shapes of an area like a rectangle, square, circle, ellipse, pentagon, quadrilateral, hexagon etc. Project the Planes in the three positions given below.

  1. Perpendicular to both the Principal planes of projection

  2. Parallel to one and inclined to the other principal planes of projection ( ϴ to HP and⊥ to VP)

  3. Inclined to both the Principal planes of projection, called oblique planes (ϴ to HP and Ф to VP)

Fig. Projections of Planes

Plane perpendicular to the principal planes of projection

These perpendicular planes have two different positions.

(a) Perpendicular to both the Principal Planes of Projections

When such a plane is projected, the Front view & top view will appear as straight lines. These straight lines are perpendicular to reference line x y.

(b) Perpendicular to one and inclined to the other

       (i)    A Plane perpendicular to HP and inclined to VP

The Front view on VP will appear as apparent shape. It is smaller than the actual plane.  The top view on HP will appear as an inclined line to reference line x y.

(ii) Given Plane perpendicular to VP and inclined to HP

The top view on HP appears as an apparent shape. it is smaller than the actual plane.

Front view appears as inclined line to reference line x y on VP.

NOTE: When given plane is perpendicular to one and inclined to the other principal planes of projection.  Complete the projections in two steps.

 Case 1 Plane inclined to VP and perpendicular to HP

First step

   Given Plane inclined to VP. Take it parallel to VP. Draw the front view. It gives the true shape.  The top view  appears as a line parallel to x y.

Second step

 Tilt the plane till it becomes inclined to VP at the required angle. Make the line of top view as inclined to x y at the required angle. Draw its Front view on VP. It is the final projections of the given plane.

Case 2 Plane inclined to HP and perpendicular to VP 

Step 1

    Given plane inclined to HP. Take it parallel to HP.  Top view gives the true shape.  The Front view appears as a line parallel to x y.

Step 2

Now tilt the plane  till it becomes inclined to HP at the required angle. Make the Line of front view inclined to x y at the required angle. Draw the Top view on the HP. It becomes the final projections of the given plane.

OBLIQUE PLANE

A plane inclined to both HP and VP is an oblique plane. There are two different cases.

CASE 1

  Oblique plane inclines at ϴ to HP and Ф to VP. It has one edge or diameter or diagonal parallel to HP. Then do the projections in three steps.

STEP 1

Assume the plane to be parallel to HP with an edge perpendicular to VP and draw the projections. Front view will be a line and top view gives the true shape of the given plane.

STEP 2

Now tilt it make the required angle ϴ with HP.  In the front view the required angle ϴ will be visible and top view will become smaller in size.

STEP 3

Turn the plane to make angle Ф with the VP, draw the projections. Only the position of the Top View will change but  shape and size will not change.  Distances of the corners from x y will remain the same as in second front view.

 There are two more possibilities of this inclined plane.

(i) One of the edges is in HP

Here the plane is first assumed to be lying in HP with an edge perpendicular to VP.  Then complete the projections in three steps.

(ii) A corner of the given plane is in HP, then the starting position (STEP 1) is keep the line joining that corner and center of the plane parallel to VP and complete the projections.

CASE 2

 The oblique plane inclines at Ф to HP and at ϴ to VP. It has one edge or diameter or diagonal parallel to VP. Then complete the projections in three steps.

STEP 1

Assume the plane to be parallel to VP with an edge perpendicular to HP and draw the projections. Top view will be a line and Front view gives the true shape of the given plane. These are 1st front view and 1st top view.

STEP 2

Tilt it to make the required angle Ф with VP.  In the top view the required angle Ф will be visible and front view will become smaller in size. These will be 2nd front view and 2nd top view.

STEP 3

Turn the plane to make angle ϴ with the HP, draw the projections. Only the position of the Front View will change but its shape and size will not change. Distances of the corners from x y will remain the same as in second top view.

 There are two more possibilities of this inclined plane.

(i) One of the edges is in VP

Here the plane is first assumed to be lying in VP with an edge perpendicular to HP.  Then complete the projections in three steps.

(ii) A corner of the given plane is in VP, then the starting position (STEP 1) is keep the line joining that corner and center of the plane parallel to HP and complete the projections

Fig. Projections of a thin plate ABCD, measuring 40 mm x 30 mm. Diagonal AC is inclined at 300 HP & diagonal BD is inclined at 450 to VP.

In the initial stage, assume the plane parallel to HP.

First draw the top view with diagonal AC parallel to ground line xy.

Project the front view a’ b’ c’ d’.

Draw another front making diagonal a’c’ 300 to HP. Project the second top view as shown.

Tilt diagonal b1d1  to make an angle of 450 to VP. Draw the third front view as shown.

Traces of a plane

When a given plane when extended will meet the planes of projection in a straight line. This line is the TRACE of the plane. In the HP, it is a HORIZONTAL TRACE (HT).  In the vertical plane, it is the VERTICAL TRACE (VT). However there is an exception to the trace of a plane i.e. THERE WILL BE NO TRACE ON THE PRINCIPAL PLANE TO WHICH THE GIVEN PLANE IS PARALLEL. Obtain the final projections by one of the two methods.

        (i)   Change of Position method

         (ii) Change of reference line method

Draw the projections of planes for the following cases:

(i)             Firstly, given plane perpendicular to the both the principal planes of projection

(ii)          Secondly, given plane is parallel to one and perpendicular to the other principal planes of projection

(iii)         Thirdly, given plane is perpendicular to one and inclined to the other principal planes of projection

(iv)         Fourthly, given plane inclines to both the principal planes of projection

(v)          Find HT and VT of the given plane in each case.

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