Determine True Shape Of Plane Figure When Projections Are Given
Determine True Shape Of Plane Figure When Projections Are Given
BY USING AUXILIARY PLANE METHOD...
What will be the problem?
- Description of final FV & TV will be given.
- You are supposed to determine the true shape of that plane figure.
Follow the below-given steps:
- Draw the given FV & TV as per the given information in the problem.
- Then among all lines of FV & TV select a line showing true length (T.L.) (Its other view must be || to XY)
- Draw x-y perpendicular to this line showing T.L.
- Project view on x-y (it must be a line view)
- Draw x-y || to this line view & project new on it.
It will be the required answer i.e. True shape.
The facts you must know:
- If you carefully study and observe the solutions of all previous problems, You will find
- If one view is a line view & that too parallel to XY line, then and then its other view will show True shape:
Now final views are always some shape, not line views, So applying the above method:
We first convert one view in an inclined line view. (By using x1y1 aux. plane ) Then by making it || to x2-y2 we get true shape.
STUDY NEXT FOUR CASES :
1 ] TV is a triangle ABC. Ab is 50 mm long, angle cab is 300 and the angle CBA is 650. a' b' c' is a 25 mm, b' is 40 mm, and c' is 10 mm above HP respectively. Draw projections of that figure and find its true shape.
procedure
First draw FV & TV as per data.
Tv line ab is || to XY hence its other view a' b' is TL. So draw x1 y1 perpendicular to it. project view on x1y1.
- First draw projector from a' b' & c' on x1 y1.
- from XY take distance of a,b & c (TV) mark on these projectors from x1 y1. Name points a1b1 & c1.
- This line view is an Aux. TV. draw x2 y2 || to this line view and project Aux. FV on it. For that from x1 y1 take distance of a' b' & c' and mark from x1 y= on new projectors.
same points a1 ' b1 ' & c1 ' and join them. This will be the required true shape.
2 ] FV & TV of a triangular plate is shown. Determine its true shape.
Use same procedure steps of the previous problem:
But three is one difficulty:
- No one is || to XY in any view. This means no TL is available.
- In such cases draw one line || to XY in any view & its other view can be considered as TL for the purpose.
- Here a' 1' line in FV is drawn || to XY. Hence its TV a -1 becomes TL.
- Then follow the same steps and determine the true shape. (Study the illustration)
3] FV & TV both are circles of 50 mm in diameter. Determine the true shape of an elliptical plate.
Adopt the same procedure.
a c is considered as line || to XY. Then a' c' becomes TL for the purpose. Using steps properly true shape can be easily determined.
Study the illustration.
Always, for new FV take distance of previous FV and for new TV, Distances of previous TV.
4 ] Draw a regular pentagon of 30 mm sides with one side 30 inclined to XY. this figure is Tv of some plane whose FV is A-line 45ยบ inclined to XY. Determine its true shape.
In this case, also the true length is not available in any view.
But actually, we do not require Tl to find its True shape, as one view (FV) is already a line view. So just by drawing x1y1 || to this view we can project view on it and get true shape:
Study the illustration.
