1. DEVELOPMENT OF SURFACES Part II
Prof.T.JEYAPOOVAN
Department of Mechanical Engineering
Hindustan Institute of Technology and Science Chennai , India

2. REFERENCE BOOKS
Jeyapoovan T, “Lesson Plans for Engineering Graphics”, 2010, Vikas Publishing House Pvt Ltd, New Delhi.
Jeyapoovan T, “Engineering Drawing and Graphics”, 2011, Vikas Publishing House Pvt Ltd, New Delhi.

3. Development of a pyramid
Consider a square pyramid, when the slant triangular faces are opened out, its faces are seen as four triangles of same size and shape, the base is a square as shown in fig.
Radial line method is used to draw development of pyramids and cone.

4. Radial Line Method
For example, consider a square pyramid and its development shown in fig.
An arc with true length of slant edge as radius and o as center is drawn. The base sides are marked along the arc and the triangular faces are drawn.
The base is opened out and drawn in an arbitrary position as shown.

5. Example 1: A square pyramid of side of base 45 mm, altitude 70 mm and resting with its base on HP with two sides of the base parallel to VP. The pyramid is cut by a section plane which is perpendicular to VP and inclined at 40° to the HP and bisects the axis of the pyramid. Draw the development of lateral surface of the truncated pyramid.
Draw TV, project FV of prism, the draw cutting plane and mark new corners.
An arc with true length of slant edge as radius and O as center is drawn. The base sides are marked along the arc and the triangular faces are drawn.
Measure true distance of new corners from o’ and mark from O to complete development of remaining portion of lateral surfaces.

6. Example 2: A cone of base diameter 40 mm and axis length 50 mm is resting on HP on its base cut by a plane inclined at 30° to HP and perpendicular to VP and is passing through a point on the circumference of the base. Draw the development of the remaining upper portion of the cone.
Draw TV and divide 8 parts, project FV and draw the cutting plane at 30º to XY. Mark the new corners on the generators. An arc with true length of generator as radius and o as center is drawn for the subtended angle as given below.

7. The chord length of each segment is marked along the arc and draw the generators.
Measure true distance of new corners from o’ and mark from O to complete development of remaining portion of lateral surfaces.

8. Example 3: A cone of base diameter 60 mm and height 70 mm is resting on its base on HP. It is cut by a plane perpendicular to both the HP and VP at a distance 15 mm to the left of the axis. Draw the development of the lateral surface of the right remaining portion.
Draw TV and divide 8 parts, project FV. Draw the cutting plane perpendicular to both HP and VP at 15mm to the left of axis. Mark the new corners on generators in FV and project to TV.
An arc with true length of generator as radius and o as center is drawn for the subtended angle

9. The chord length of each segment is marked along the arc and draw the generators.
Measure true distance of new corners from o’ and mark from O to complete development of remaining portion of lateral surfaces.

10. Draw the development of cylindrical portion as discussed earlier.
Example 4: Draw the development of the lateral surface of a funnel consisting of cylinder and a frustum of a cone. The diameter of the cylinder is 20 mm and the top diameter of the funnel is 70 mm. The height of frustum and cylinder are each equal to 40 mm.
Draw FV of the funnel, note that the upper portion is a frustum of a cone and lower portion is a cylinder.The frustum of the cone is produced to get as a cone to draw the development.
Draw the development of cylindrical portion as discussed earlier.

11. Tips to draw Development of Surfaces
Draw the projections of the solid, then draw the trace of the cutting plane. Carefully mark the new corners on the edges/generators which are cut by the cutting plane.
First draw the development with 2H pencil. Then project and mark new points on the development and darken the remaining portion with HB pencil to complete the development.
To draw the development of the lateral surfaces, bases need not be shown.

12. End of Lesson 10
Thank You