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6.5 DEVELOPMENTS

– A development is the unfolded or unrolled, flat or plane figure of a 3-D object.
– Called a pattern, the plane figure 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.
– A true development is one in which no stretching or distortion of the surface occurs, and
every surface of the development is the same size and shape as the corresponding surface
on the 3-D object.
– Only polyhedrons and single-curved surfaces can produce true developments.
By the term development is meant a figure showing the true size and shape of the surface of
any given solid, when the surface has been rolled or spread out on a plane. A true development is
obtained when all parts of the surface is made to coincide with a plane, without overlapping or
folding. Such a development, when cut out of paper or thin sheet metal, and properly bent or rolled
up, will reproduce the original solid.
Some surfaces are truly developable, and others are not. Among the former are all surfaces
composed of planes, as those of prisms and pyramids, all cylindrical, and all conical surfaces. The
most familiar solid which has a non-developable surface is the sphere.

6.5.1 METHODS TO DEVELOP SURFACES

1. Parallel-line development: Prismatic objects (cylinder, prism)
2. Radial-line development: Non-prismatic objects (cone, pyramid). Apex as center and slant
edge as radius.
3. Triangulation development: Complex shapes are divided into a number of triangles and
transferred into the development
4. Approximation.
All lines are TRUE LENGTH
All planar surfaces are TRUE SIZE

Types of Developments
Parallel-line (Fig. 6.23)
Radial-line (Fig. 6.24)
Triangulation (Fig. 6.25)
Approximation (Fig. 6.26)

Figure 6.23

Figure 6.24

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