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GE2111- Engineering Graphics

Prepared by K.S.Badrinathan, S.Ramesh Babu & V.Sridharan

Projection of Planes

Planes inclined to HP and VP

How to Start with

For the planes inclined to HP and VP, see the Surface / Plane inclination first.

Surface / Plane inclination with respect to HP,1. Start drawing the top view first and then project its front view. The front view

will be a line and it should be on XY line.2. Tilt the front view in anti clock wise direction to the given angle of inclination

with respect to HP and project its top view, which will measure an apparentshape.

3. Tilt the apparent shape of the polygon with respect to VP and then draw its frontview.

4. The final front view and top view should be drawn with continuous thick line(HB pencil).

Surface inclination with respect to VP,1. Start drawing the Front view first and then project its top view. The top view will

be a line and it should be on xy line.2. Tilt the top view in clock wise direction to the given angle of inclination with

respect to VP and project its front view, which will measure an apparent shape.

3.

Tilt the apparent shape of the polygon with respect to HP and then draw its Topview.4. The final front view and top view should be drawn with continuous thick line

(HB pencil).

Resting conditions

Case - 1 Surface inclination with respect to HP and the edge inclination with respectto VP

For this case, the planes may have one of its side/edge on HP or one of its corners onHP

When the plane is having one of its sides on HP, Construct the top view of the givenpolygon in such a way that one side / edge of the polygon is perpendicular to VP and itis on the left hand side.





When the plane is having one of its corners on HP, construct the top view of the givenpolygon in such a way that an imaginary line introduced through one corner of thepolygon is perpendicular to VP and on the left hand side. Also the two sides containingthe corner through which an imaginary line is introduced is equally inclined to that line.

Case - 2 Surface inclination with respect to VP and the edge inclination with respectto HP

For this case, the planes may have one of its sides/edges on VP or one of its cornerson VP

When the plane is having one of its sides on VP, construct the front view of the givenpolygon in such a way that one side / edge of the polygon is perpendicular to HP and itis on the left hand side.

When the plane is having one of its corners on HP, construct the top view of the givenpolygon in such a way that an imaginary line introduced through one corner of thepolygon is perpendicular to HP and on the left hand side. Also the two sides containingthe corner through which an imaginary line is introduced is equally inclined to that line.

Simple position Top view for the plane surface inclined to HP having one of its edges on HP

X Y

Simple position Top view for the plane surface inclined to HP having one of its Corners on HP

X Y





Simple position Front view for the plane surface inclined to VP having one of its edges on VP

X Y

Simple position Front view for the plane surface inclined to VP having one of its Corners on VP

X Y

Case – III (Refer problem no’s 12 and 13 in tutorial sheet no- 4): When theplane surfaces is inclined to both HP and VP , then their summation of their

angles will be 900. In this case the inclination angles can be seen only in the sideview. For this type of problems,





1. Start with either drawing the front view or top view first.2. Project its side view, which will be a line.3. Tilt the side view to the given angle of inclinations with respect to HP and VP4. Draw its final front view and final top view, which will measure an apparent

shape.

Indirect Problems

The problems for which the surface inclination with respect to HP and VP is not given,the apparent shape dimensions and in which view this apparent shape is obtained willbe given. For this kind of problems, the following hint will be useful

1. When the apparent shape is obtained in the top view, then the plane will beinclined to HP (eg. The top view of rectangular plane 50 X 30 mm resting on theHP on one of its shorter edges is a square of side 30 mm). For this type of

problem

a. Start drawing the top view first and then project is front view, whichwill be a line

b. Since the apparent shape dimensions are given, in the second stageconstruct the apparent shape of the polygon in the top view for thegiven dimensions and then find the angle of inclination in the frontview

c. Tilt the apparent shape of the polygon with respect to VP and thendraw its front view.

d.

The final front view and top view should be drawn with continuousthick line (HB pencil).

2. When the apparent shape is obtained in the front view, then the plane will beinclined to VP (eg. The front view of the circular lamina of 80 mm diameterhaving one of its corners on VP is an ellipse of major axis 80 mm and minor axis40 mm)

a. Start drawing the front view first and then project its top view, which willbe a line

b. Since the apparent shape dimensions are given, in the second stageconstruct the apparent shape of the polygon in the front view for the givendimensions and then find the angle of inclination in the top view

c. Tilt the apparent shape of the polygon with respect to HP and then drawits Top view.

d. The final front view and top view should be drawn with continuous thickline (HB pencil).



GE 2111 Engineering Graphics


Projection of Solids

I. Solid Axis “ Perpendicular to HP and Parallel to VP”

This case will be much useful for solving the projection of solids with axis inclined toHP and parallel to VP, section of solids, development of surfaces and isometricprojection.

How to start with

For the solid axis perpendicular to HP and parallel to VP, all the solids will be restingon the HP on its base.

The top view gives the true shape of the polygon. Hence draw the top view first and

then project its front view.

Various positions of the solid when its axis is “Perpendicular to HP andParallel to VP”

1. Prisms resting on the HP on its base and one of its base edges / lateral surfaces /

rectangular surfaces is parallel to VP

2. Pyramids resting on the HP on its base and one of its base edges is parallel to VP.

3. Prisms resting on the HP on its base and one of its base edges / lateral surfaces /

rectangular surfaces is perpendicular to VP.

4. Pyramids resting on the HP on its base and one of its base edges is perpendicular

to VP

5. Prism resting on the HP on its base and one of its base edge / lateral surface /

rectangular surface is inclined at some angle to VP

6. Pyramids resting on the HP on its base and one of its base edges is inclined at

some angle to VP



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3. Prisms resting on the HP on its base and one of its base edge / lateral surface / rectangular surface is perpendicular to VP.

While constructing the top view, see that one side of the given polygon isperpendicular to xy line

4. Pyramids resting on the HP on its base and one of its base edge isperpendicular to VP

While constructing the top view, see that one side of the given polygon is

perpendicular to xy line





5. Prism resting on the HP on its base and one of its base edge / lateral surface / rectangular surface is inclined at some angle to VP

While constructing the top view, see that one side of the given polygon isinclined to the given angle of inclination with respect to VP

6. Pyramids resting on the HP on its base and one of its base edges is inclined atsome angle to VP

While constructing the top view, see that one side of the given polygon isinclined to the given angle of inclination with respect to VP





II. Solid axis “ Inclined to HP and Parallel to VP”

How to start with

• When the solid axis is inclined to HP and parallel to VP, make the solid axisperpendicular to HP and parallel to VP, and the base of the solid should rest onthe HP.

• The top view gives the true shape of the polygon. Hence draw the top view firstand then draw its front view. While drawing the front view, see that the base ison the XY line.

• Tilt the front view in the clockwise direction with respect to the rightmost baseedge / corner for the given angle of inclination with respect to HP

• Then project its top view.

Hints for marking the visible and invisible edges –

1. Blindly connect the outermost boundary points with continuous thick lines.

2. In prisms, two end faces are there. The end face nearer to the observer will bevisible. So in the top view connect all the points of the end face nearer to theobserver with continuous thick line.

3. For the base, only one half will be visible. The visible base edges by default willbe the outside boundary of the solid and these edges would have been shown bystep 1. Connect the remaining points by chain dotted lines.

4. Among the N number of lateral edges (N- number of sides of the polygon), twolateral edges by default will be the outside boundary and these lateral edgeswould have been shown by step 1.

5. Now see the front view and see the position of the extreme lateral edges alreadyshown in the top view.

6. The remaining lateral edges between the observer and the extreme lateral edges(which forms the outside boundary in top view) will be visible always and henceshow these lateral edges by continuous thick lines

7. The remaining lateral edges between the extreme lateral edges (which forms theoutside boundary in top view) and the reference line will be invisible always andhence show these lateral edges by chain dotted lines





Resting conditions for the solids having its axis “Inclined to HP andParallel to VP”

1. Prisms will rest on the HP either on one of its corners or base side2. Pyramids will rest on the HP on one of its corners or base side or Triangular

surface or lateral edge3. Cylinder will rest on HP on one of its base circumferential points4. Cone will rest on HP on one of its base circumferential points or generator

1. Simple position top view for prisms resting on HP on one of its base edge / Simple position top view for the pyramids resting on HP on one of its base edge / Simple position top view for the pyramids having one of its triangular faces onHP

• While constructing the simple position top view of a given polygon, see that one

side of the polygon is perpendicular to VP (XY line) and is on the right hand side.Then project its front view.

• Tilt the front view with respect to the lower most right side edge (which will bethe resting edge on HP) in the clockwise direction to the given angle ofinclination with respect to HP. (Note:- while tilting see that the resting edge is onthe XY line)


• Refer the hints for marking the visible and invisible edges.

2. Simple position top view for prisms resting on HP on one of its corners / simpleposition top view for pyramids resting on HP on one of its corners / Simpleposition top view for the pyramids having one of its slant edges on HP

• Construct the top view of the given polygon in such a way that an imaginary lineintroduced through one corner of the polygon is perpendicular to VP and on theRight hand side. Also the two sides containing the corner through which animaginary line is introduced is equally inclined to that line. Then project its frontview.

• Tilt the front view with respect to the lower most right side corner(which will bethe resting corner on HP) in the clockwise direction to the given angle ofinclination with respect to HP. (Note:- while tilting see that the resting corner ison the XY line)


• Refer the hints for marking the visible and invisible edges.

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