surface development

MEHRAN UNIVERSITY OF ENGINEERING & TECHNOLOGY, JAMSHORO

B.E MECHANICAL ENGINEERINGBATCH-F16, 1ST YEAR,1ST SEMESTER

ENGINEERING DRAWING&

GRAPHICS

SURFACE DEVELOPMENT



A development is the unfold / unrolled flat / plane figure of a 3-D object. It is also called a pattern where the plane may show the true size of each area of the object. When the pattern is cut, it can be rolled or folded back into the original object as shown in figure. Surface development is a full size layout of an object drawn on a plane. Some objects are made of flat sheet metal. When the sheet is cut as per this layout, folded and joined together, it takes the shape of an object.

AN OBJECT HOLLOW AND MADE-UP OF THIN SHEET. CUT OPEN IT FROM ONE SIDE AND UNFOLD THE SHEET COMPLETELY. THEN THE SHAPE OF THAT UNFOLDED SHEET IS CALLED DEVELOPMENT OF LATERAL SURFACES OF THAT OBJECT OR SOLID.



APPLICATIONS:The knowledge of development of surfaces is very useful in the sheet metal industry, where products like utensils, cans, buckets, hoppers, domes, etc. are manufactured. Imagine an industry where domestic refrigerators are manufactured. The ultimate shape of a refrigerator is made from the sheet metal. Its door is first made on a plain sheet and then cut and folded to form the door.To make a funnel out of a sheet, what should be the shape of the sheet which, when folded, forms the final shape of the funnel? A tailor first prepares a development drawing on a cloth to cut and stitch the correct shape and size of a shirt. A development gives the shape and plane area of the material which enables the cost to be estimated. Development should be such as to allow the minimum waste of material when the shape is cut out.



EXAMPLES:-Boiler Shells & chimneys, Pressure Vessels, Shovels, Trays, Boxes & Cartons, Feeding Hoppers, Large Pipe sections, Body & Parts of automotive, Ships, Aero-planes and many more.



Types of development

1-Parallel line development: In this parallel lines are used to construct the expanded pattern of each three-dimensional shape. The method divides the surface into a series of parallel lines to determine the shape of a pattern.



Types of development2- Radial line development: In this, lines radiating from a central point to construct the expanded pattern of each three-dimensional shape is used. These shapes each form part of a cone and lines radiating from the vertex of the cone generate the expanded pattern of the curved surface as shown in the following explorations.



Types of development3-Approximate development: In this, the shapes obtained are only approximate. After joining, the part is stretched or distorted to obtain the final shape.4- Triangulation method: This is generally used for polyhedron, single curved surfaces, and warped surfaces.



Types of developmentParallel line development: In this parallel lines are used to construct the expanded pattern of each three-dimensional shape. The method divides the surface into a series of parallel lines to determine the shape of a pattern.Radial line development: In this, lines radiating from a central point to construct the expanded pattern of each three-dimensional shape is used. These shapes each form part of a cone and lines radiating from the vertex of the cone generate the expanded pattern of the curved surface as shown in the following explorations.Triangulation method: This is generally used for polyhedron, single curved surfaces, and warped surfaces.Approximate development: In this, the shapes obtained are only approximate. After joining, the part is stretched or distorted to obtain the final shape



Draw the development of a CIRCULAR CYLINDER



Draw the development of a PENTAGON PRISM



Draw the development of a SQUARE & HEXAGON PRISM



Draw the development of a CONE PYRAMID



Draw the development of a SQUARE PYRAMID



Draw the development of a PENTAGON PYRAMID



Draw the development of a NANOGON PYRAMID



Draw the development of a PENTAGON PYRAMID



Draw the development of a CYLINDER



Problem 1.

A cylinder made up of Aluminum sheet with base circle diameter 65 mm and height/length 75 mm is kept on its base on the ground.

The cylinder is cut at 45 degrees to make an ellipse, the lower edge of cut is 25 mm above the base. Develop the surface of the cone.



Problem 2(a). A cone made up of Aluminum sheet with base circle diameter 80 mm and height/length 75 mm is kept on its base on the ground. Develop the surface of the cone. Problem 2(b). A cone with base circle diameter 80 mm and axis length is 75 mm is kept on its base on the ground. The cone is cut at 25mm to make a circle. Develop the surface of the cone.



Problem 3.

A cone made up of Aluminum sheet with base circle diameter 65 mm and axis length 75 mm is kept on its base on the ground.

A circular hole of 30 mm diameter is cut through the cone such that its axis remains perpendicular to V.P.; 10 mm to the right of the axis of cone and 25 mm above the base of cone.

Develop the surface of the cone.



Problem 1. Procedure:Step-1 Draw a horizontal x-y line of some suitable length.Step-2 Draw a circle of radius 32.5 mm below the x-y line at some suitable distance from it. Divide this circle into 12 equal divisions as shown in the figure. Give notations on it. It is top view of the cone.

Step-3 From the center of the circle in the top view, draw a vertical center line of length 75 mm from the x-y line as shown in the figure. And from these notations of the circle draw vertical projectors up to x-y line, and then converge all these projectors at the end of the center line i.e. apex of the cone (point o’) as shown into the figure. It is a triangular shape. And Give the notations on it.

Step-4 Draw a horizontal center line at the distance 25 mm above the x-y line, and a vertical center line at the distance 10 mm on the right of the vertical center line as shown in the figure. From the intersection of the above two center lines, draw a circle of radius 15 mm.

Step-5 Give the cutting points name at the intersection of the previously drawn circle with the vertical projectors of the circle in front view, i.e., 1’, 2’, 3’ etc. as shown into the figure.



Problem 1. Procedure:Step-6 Now find out the angle covered by the cone when it is opened completely, by the equation , where L = Length of the last generator i.e., o’-a’ or o’-g’. = Angle subtended by the two extreme generators of the cone, when it is opened completely. r = Radius of the base circle of the cone. From this equation find out the value of in degree.

Step-7 Draw a line parallel to and equal to the length of the last generator i.e., o’-g’, at some suitable distance from the front view. Give that line the name O-A as shown in the figure. With O as center and radius equal to OA, draw an arc such that the angle subtended by the arc should be equal to , which you have found out from the previous equation. This is the full development of the vertical surface of the cone.

Step-8 Divide this developed surface of the cone in 12 equal divisions, angle wise, as shown in the figure. And give the notations in capital letters. i.e., A, B, C etc.

Step-9 Now in the front view, from the cutting points on the small circle of radius 15 mm, draw horizontal lines, parallel with x-y line, such that these lines should meet with the last generator i.e., o’-g’, in the front view.



Problem 1. Procedure:

Step-10 Then measure the distances of the end points of previously drawn respective lines from the point o’, and transfer these distances in the developed surface of the cone on respective generators, as shown in the figure.

Step-11 Now Connects all the points in sequence with medium dark smooth curve, as shown in the figure, and draw the boundary of the cone with dark curve with the use of a compass. This is the Development of the vertical surface of the cone.

Step-12 Give the dimensions by any one method of dimensions and give the notations as shown into the figure.



Problem 4 The square pyramid with the length of side of base 30 mm and length of axis 60 mm as shown in the figure. Develop the surface of the pyramid.



Problem 5 Development of Surfaces of Solids – The cylinder of diameter of base 50 mm and axis height 60 mm is resting on its base on H.P. as shown in the figure below. Develop the surface of the cylinder.



SYLLABUS• Introduction & Basics: Introduction to graphic language, Essential drawing

instruments and their correct use. Line types and lettering. Basic drafting techniques and standards. Curves used in engineering.

• Orthographic Projections: • Orthographic multi view projection of some simple and composite solids. • Sections: Sectioning and projection of auxiliary views. • Surface Development: Surface development of simple solids such as cylinder, cone,

prism and pyramid, surface development of intersecting solids. • Isometric Projections: Isometric projection / drawings of piping.• Freehand/Sketching : Sketching and basic rules of sketching. • Detail, assembly and Working Drawings: Preparing detail, assembly and working

drawings of various machine and engine parts such as, keys, cotters, foundation bolts, screws, pulleys, couplings, bearings riveted joints and nut and bolts. Fundamentals of geometric dimensioning and tolerancing.

• Computer Aided Drawing: Computer aided drafting (CAD). Auto CAD Software

surface development

Engineering