PROJECTIONS OF SOLIDS
CLASS NOTES FOR ENGINEERING
Projection of solids is final aim of learning
projections. Projection of solids helps to
read industrial, commercial and domestic
WHAT IS A SOLID?
Every solid substance is 3-dimensional in the Universe. For example, book, wall, table, chair, fan, pen etc. These have different shapes. The solid shapes are: cubes, cuboids, prisms, pyramids, cone, cylinder, and sphere. A laptop is a cuboid. To represent a solid in orthographic projections, at least two views are essential for symmetrical solids. One view representing length and height is front view. The other view representing length and width is top view. Three or more views are required for complex solids.
TYPES OF SOLIDS
Fig. Cube, Triangular Tetrahedron and a Hexagonal prism
(a) Regular polyhedral
Have number of faces, equal and regular. Examples are Cube, Pentagon, Heptagon, Prism and Pyramid.
(b) Irregular polyhedral
Which have unequal faces.
Solids of revolution
Fig. Solids of revolution, Cylinder, sphere and a cone
Which obtained by rotating an object.
(i) Cylinders obtained by rotating a rectangle)
(ii) Cones obtained by rotating a right angle triangle
(iii) Spheres obtained by rotating a semi-circle
Definition of a prism
Square prism has two square bases bounded by four equal rectangles. Hexagonal prism has two hexagonal bases bounded by six rectangles
Definition of a Pyramid
A square pyramid has one square base and one vertex. Connect four corners of the square base to the vertex. There are Four isosceles triangles.
A hexagonal pyramid has one hexagonal base and one vertex. connect six corners of the base to the vertex. There are six isosceles triangles.
FRUSTUM OF A SOLID
It is a cut solid. Cutting plane is parallel to the base of the solid. The portion between the observer and the cutting plane is removed. The remaining solid is called frustum. Examples are Frustum of a cylinder, Frustum of a cone, Frustum of a pyramid.
Solid is cut by an inclined plane to the base of the solid. The portion between the observer and the cutting plane is assumed to be removed. The remaining solid is called Truncated solid.
PROJECTIONS OF SOLIDS
(a) Axis is perpendicular to HP or VP
Fig. Solids with axis Perpendicular to HP and parallel to VP
Draw the projection of the solid with axis perpendicular to HP. It gives the true shape and size of the base in HP (TOP VIEW). Projections completed only in one step.
Procedure for a cylinder
First draw the top view on the HP which is a circle in case of a cylinder. Project the front view by taking height of the cylinder.
Draw the projection of the solid with axis perpendicular to VP. It gives the true shape and size of the base in VP (FRONT VIEW). Projections completed only in one step.
(b). Axis parallel to HP & VP.
Fig. Projections of a triangular prism with base lying in HP and axis parallel to both HP & VP
Neither the front view nor the Top view gives the true shape and size. In this case, side view will give the true shape and size of the base of the solid.
Projections is completed in two steps.
(i) Axis inclined to HP and parallel to VP
(ii)Axis inclined to VP and parallel to HP
These projections are obtained by two methods.
First Method: By altering the positions of solids
projections completed in TWO STEPS.
(i) For axis inclined to HP
ASSUME FIRST AXIS IS PERPENDICULAR TO HP and DRAW THE PROJECTIONS. Axis is seen on VP (FRONT VIEW).
Tilt the front view to the required inclination and draw the final projections of the TOP VIEW.
(b) Similarly draw the projections for a solid axis inclined to VP.
Second Method: By altering the ground line x y
(i) Draw the top view and front view in simple position with axis perpendicular to HP.
(ii) Draw a line x1y1 as new ground line inclined to the axis at an angle θ. Draw projections perpendicular to new ground line x1y1 from front view. Cut the distances of all the points (in the auxiliary top view) below the ground line x y equal to corresponding distances below line x y.
(iii) Draw another line x2y2 inclined at angle φ with x1y1. Project the final front view by keeping the distances of all points from x2y2 equal to their respective distances the in the auxiliary to top view above x1y1 line.
Axis inclined to both HP AND VP
Fig. A right circular axis inclined at 450 HP and 300 VP
(a) By altering the position of solids
Projections completed in three steps.
Keep the axis perpendicular to HP, draw the projections.
Axis as vertical and top view will give true shape and size of the base. It gives FIRST FRONT VIEW AND FIRST TOP VIEW.
Make the axis in the front view inclined to HP at the required inclination. Redraw the front view and then the new top view. It gives SECOND FRONT VIEW AND THE SECOND TOP VIEW
Now tilt the axis of the top view at the required inclination with VP. Draw the top view in this position and then draw the new front view. This gives THIRD FRONT VIEW AND THIRD TOP VIEW.
These are final Front and Top views of a solid with axis inclined to both HP and VP.
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