Chapter-10Projections of Planar Surfaces

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Learning Objectives 2

2. Learn the projection of intersection of planesand with the principal planes.

1. Learn the projection of planes in a 3-D space.

Plane Surface under Study 3

Classification of Planar Surface 4

(A) Perpendicular Planes(a) Perpendicular to one referenceplane and parallel to the other(b) Perpendicular to one plane andinclined to the other

(B) Oblique Planes

Perpendicular Planes 5

Oblique Planes 6

Inclined PlanesHow to Determine True Shape or True Inclination

7Stage I: Assumption stageAssume plane surface parallel to that reference plane to which itis inclined and obtain the true shape and line view (L-view).Stage II: Surface inclination stageNow, rotate the line view of the surface through requiredinclination (θo) and obtain an apparent shape.

Oblique PlanesHow to Determine True Shape or True Inclination

8Stage I: Assumption stageAssume plane surface parallel to that reference plane to which it isinclined and obtain the true shape and line view (L-view).Stage II: Surface inclination stageNow, rotate the line view of the surface through required inclination (θo)and obtain an apparent shape.Stage III: Edge inclinationIn this stage, the edge of the apparent shape of plane surface is rotatedthrough required inclination (say αo) to obtain the final projections.

True Shape Stage Assumption 9

There are two options to draw a true shape:(a)If plane is resting on its edge, draw a true shape ofthe surface with the resting edge perpendicular tothe x-y line.(b)If the plane surface is resting on one of its corner,then draw the true shape of the plane surface suchthat line joining resting corner and the center of theplane parallel to the x-y line. In this stage, we obtaintrue shape in one view and line view of surface inanother view.

Model Solution-110

A rectangular plate of negligible thickness having 150mm length and 100 mm width is resting on one of itssmaller side on HP. The surface is perpendicular to VPand makes an inclination of 30o to HP. Draw projectionsof the plate.

Model Solution-211

A pentagonal plate of negligible thickness and havingedge length 100 mm is resting on one of its corners onVP. The plate is inclined 40o to VP and perpendicular toHP. Draw projections of the plate.

Model Solution-312

A circular plate is resting on its circumferential point onVP with surface perpendicular to HP. It is inclined to VPsuch that FV appears as an ellipse. Find the surfaceinclination at which the ellipse has minor axis 100 mmand major axis 150 mm.

Model Solution-413

A rectangular plate of negligible thickness having 150mm length and 100 mm width is resting on one of itssmaller side on HP. The surface makes an inclination of30o to HP and the smaller side makes an inclination of60o to VP. Draw projections of the plate.

Concluding Remarks When a plane is perpendicular to a reference plane, its projection on that plane is a straight line. When a plane is parallel to a reference plane, its projection on that plane is its true shape. When a plane is perpendicular to a reference plane and inclined to another , its inclination is the angle which its projection on the plane to which it is perpendicular, makes with line xy.

Solution for given oblique plane1. Initial Position

Assume the surface of a plane is parallel to thatreference plane to which it is inclined.2. Second PositionTo account the surface inclination rotatethe line view ofthe plane to required angle and get theapparent shape.3. Final PositionThis stage accounts the edge inclination.Inclined the edge togiven inclination and get the final projections

Problem :- A hexagonal lamina of L mm side; having its one of the edges in HP and inclined 0 to VP. Draw its projections when its surface makes an angle 0 with HP.

Draw the projections of a regular hexagon of 50mm side having one of its sides in the HP and inclined at 600 to the VP and its surface making an angle 450 with the HP.

Draw the top view of the hexagon with one side perpendicular to xy line. Project the front view a’c’ in xy. Rotate a’c’ by an angle 45 to xy keeping a’ in xy line and project the second top view. Reproduce the top view making a1f1 inclined at 600 to xy and project the final front view.

A circular plate of negligible thickness and 50mm diameter appears as an ellipse in the front view having a major axis 50mm and minor axis 30mm. Draw its top view when the major axis is horizontal.

As the front view is ellipse, its surface must be inclined to VP. Assume the plate to be parallel to VP and draw its FV and TV. Rotate the line ab (TV) so that its length in FV is 30mm and project the FV. Reproduce this view so that major axis c’d’ is horizontal and project the TV.

Problem :- A rectangle of 200 mm X 100 mm is resting on one of its smaller sides on the VP. It is tilted about that side so that, it appears as a square in the elevation. Find the inclination of the surface with VP.

Problem :- A pentagonal plate is resting on one of its corners on ground. The plate makes an angle 400 with ground. Draw its projections when edge opposite to the corner resting on the ground makes an angle 450 with VP

Find out the surface inclination that a square plate of 150 mm diagonal makes with the HP if it is resting on one of its corners on the HP and appears as rhombus with smaller diagonal 100 mm and longer diagonal 150 mm.

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A triangular lamina ABC (side 100 mm) having its corner C 50 mm above HP and 50 mm in front of the VP. Edge AB is 25 mm above HP and parallel to the VP. Draw the projections of the lamina and find its inclinations with HP and the VP.

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