CHAPTER 8 DEVELOPMENTS 8.21 Developments A development is a flat representation or pattern that when folded together creates a 3-D object. Sheet-metal construction is the most common application for developments and intersections. The resulting flat pattern gives the true size of each connected area of the form so that the part or structure can be fabricated. 8.22 Terminology The following terminology describes objects and concepts used in developments and intersections:
A ruled surface is one that may be generated by sweeping a straight line, called the generatrix, along a path, which may be straight or curved. Any position of the generatrix is an element of the surface. A face may be a plane, a single-curved surface, or a warped surface.
A plane is a ruled surface that is generated by a line, one point of which moves along a straight path while the generatrix remains parallel to its original position.
A single-curved surface is a developable ruled surface; that is, it can be unrolled to coincide with a plane. Examples are the cylinder and the cone.
A warped surface is a ruled surface that is not developable. Some examples are shown in Figure 8.20. No two adjacent positions of the generatrix lie in a flat plane. Warped surfaces cannot he unrolled or unfolded to lie flat. A warped surface is a ruled surface that is not developable. Some examples are shown in Figure 8.20. No two adjacent positions of the generatrix lie in a flat plane. Warped surfaces cannot he unrolled or unfolded to lie flat. A double-curved surface is generated by a curved line and has no straight- line elements. A surface generated by revolving a curved line about a straight line in the plane of the curve is called a double-curved surface of revolution. Common examples are the sphere, torus, ellipsoid, and hyperboloid.
A developable surface may be unfolded or unrolled to lie flat. Surfaces composed of single-curved surfaces, of planes, or of combinations of these types are developable. Warped surfaces and double-curved surfaces are not directly developable. 8.22 Solids Polyhedra are solids which are bounded entirely by plane surfaces - for exam pie cubes, pyramids, and prisms. Convex solids are ones that have no dents. Convex solids with all equal faces are called regular polyhedra. Examples of regular solids are shown in Figure 8.22. A solid generated by revolving a plane figure about an axis in the plane of figure is a solid of revolution.
Solids bounded by warped surfaces have no name – for example, the screw thread. 8.25 Developments
The development of a surface is that surface laid out on a plane. Practical applications of developments occur in sheetmetal work, stone cutting, pattern making, packaging, and package design. Single-curved surfaces and the surfaces of polyhedra can he developed. Developments for warped surfaces and double-curved surfaces can only be approximated. It is common practice to draw development layouts with the inside surfaces up. In this way, all folded and other markings are related directly to inside measurements, which are the important dimensions in all ducts, pipes, tanks, and other vessels.
The direction of development (i.e., unfolding or unrolling) must be perpendicular to the intersection and is called stretch-out line. 8.26 Hems and Joints for Sheetmetal and Other Materials Figure below shows a wide variety of hems and joints used in fabricating sheet-metal parts and other items. Hems are used to eliminate the raw edge as well as to stiffen the material. Joints and seams may be made for sheet-metal by bending, welding, riveting, and soldering and for package materials by gluing and stapling.
You must add materials for hems and joints to the layout or development. The amount of material to add depends on the thickness of the material and production equipment.
8.27 Developing a Prism
Figure below shows the intersection of a plane and a prism in the auxiliary view as true size. Step by Step 8.4 Developing a Prism Parallel Line Development
8.28 Developing a Cylinder
Figure below shows the intersection of a plane and a cylinder in the auxiliary view as true size. 8.29 More Examples of the Developments Radial Line Development
8.30 Transition Piece
A transition piece is one that connects two differently shaped, differently sized, or skewed-position openings. In most cases, transition pieces are composed of plane surfaces and conical surfaces, as shown in Figure 8.33. You will learn about developing conical surfaces by triangulation next. Triangulation can also be used to develop, approximately, certain warped surfaces. Transition pieces are used extensively in air conditioning, heating, ventilating, and similar construction. 8.31 Triangulation Triangulation is simply a method of dividing a surface into a number of triangles and transferring them to the development. To find the development of an oblique cone by triangulation, divide the base of the cone in the top view into any number of equal parts and draw an element at each division point, as shown in Figure 8.34. Find the true length of each element. If the divisions of; the base are comparatively small, the lengths of the chords may be used in the development to represent the lengths of the respective arcs. Since the development is symmetrical, it is necessary to lay out only half the development, as shown.