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

Development of surfaces of a prism The surfaces (faces and bases) of a solid which is opened out and laid on a flat plane is called as the development of surfaces of that object. In square prism, when the faces are opened out, its faces are seen as four rectangles of same size and two square bases as shown in figure.

Parallel Line Method Parallel line method is used to draw development of prisms and cylinder. For example, in a square prism, two stretch-out lines whose length equal to perimeter of base are drawn parallel to each other with the gap between them equal to the axis length and rectangular faces are marked on the development. The bases are opened out and drawn in an arbitrary position.

Example 1: A hexagonal prism of base side 30 mm and height 50 mm rests vertically on HP with a side of base parallel to VP. Draw the development of the surfaces of the prism. Draw the TV and project the FV of the prism. Draw two stretch-out lines whose length equal to perimeter of base, parallel to each other with the gap between them equal to axis length and six faces are marked to complete the development. Bases, hexagon, are drawn in an arbitrary position.

Example 2: A pentagonal prism of base side 30 mm and axis length 60 mm rests with its base on HP and an edge of the base to inclined at 40° to VP. It is cut by a plane perpendicular to VP, inclined at 40° to HP and passing through a point on the axis, at a distance of 30 mm from the base. Develop the remaining surfaces of the truncated prism. Draw TV, project FV and the cutting plane at 40º to XY. Mark new corners on the longer edges. Draw two stretch-out lines, length equal to perimeter of base, parallel to each other, gap between them equal to axis length and faces are marked on it. Project and mark new corners on the development. Since top base is removed, bottom base, pentagon, is drawn.

Example 3: Draw the development of the lower portion of a cylinder of diameter 50 mm and axis 70 mm when sectioned by a plane inclined at 40º to HP and perpendicular to VP and bisecting the axis. Draw TV and divide it into 8 parts, project FV and draw the cutting plane at 40º to XY. Mark new corners on generators. Draw two stretch-out lines, length equal to circumference of base, parallel to each other, gap between them equal to axis length and show the 8 generators by dividing it into 8 equal parts. Project new corners to development. Since the top base is removed, bottom base, circle, is drawn.

Example 4: A vertical chimney of circular cross section of 400 mm diameter joins the roof of a room sloping at 35º to the horizontal. The shortest length of the chimney is 800 mm. Determine the shape of the sheet metal from which the chimney can be made. Use 1:10 scale. Understand the shape of the chimney from the figure. The cutting plane is at 35º to XY as shown. Use the same procedure as discussed in the previous problem to draw the development.

Draw TV, project FV of the chimney. Draw trace of the cutting plane at 35º to XY as shown. Mark the new corners in FV. Draw the development as discussed earlier and project the new corners to the development.

Example 5: A cube of 40 mm edge stands on one of its faces on HP with a vertical face making 45° to VP. A horizontal hole of 20 mm diameter is drilled centrally through the cube, such that the hole passes through the opposite vertical edge of the cube. Obtain the development of the lateral surface of the cube with the hole. Draw TV, project FV of cube. Draw the hole in FV as shown. Divide the circle in to 8 equal parts and project the points to the top view. Draw development of cube and mark the position of the points from TV to the development, then project them as shown. Join all points to complete the development of hole as an ellipse.

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.

REFERENCE BOOKS 1.Jeyapoovan T, “Lesson Plans for Engineering Graphics”, 2010, Vikas Publishing House Pvt Ltd, New Delhi. 2.Jeyapoovan T, “Engineering Drawing and Graphics”, 2011, Vikas Publishing House Pvt Ltd, New Delhi.

End of Lesson 9 Thank You