Surface Dev

DEVELOPMENT OF SURFACES

The steps in making a finished development are:

  1. The object’s form is drawn on paper. This is the pattern development.
  2. The pattern or development is transferred to the flat material.
  3. The material is cut out.
  4. The material is formed to shape.
  5. The edges are joined.    LESSON 1 - SURFACES    A surface is the exterior face of any object, a geometric magnitude having two dimensions    (2D). It is the exterior of the four basic shapes: prism, cylinder, cones, and pyramids.    Surfaces of various geometrical objects may be classified as the following:

Plane Surface – objects like prism, pyramid, cube, and polyhedron are bounded by plane surfaces.

Singly Curved Surface – objects like cylinders and cone are bounded by singly curved surfaces.

Doubly Curved Surfaces – objects like sphere, paraboloid, ellipsoids, and hyperboloids are bounded by doubly curved surfaces. Surfaces, likewise, can be developable or non-developable. A developable surface is one that may be unfolded, or unrolled so as to coincide with a plane. Surfaces composed of singly curved surfaces, or of planes, or of combinations of these types are developable. A surface that is not developable – doubly curved surfaces are not developable. They may be developed approximately by dividing them into sections and substituting for each section a developable surface, that is, a plane or a single-curved surface. If the material is sufficiently pliable, the flat sheets may be stretched, pressed, stamped, spun, or otherwise forced to assume the desired shape. Non-developable surfaces are often produced by a combination of developable surfaces which are then formed slightly to produce the required shape. Articles or objects are first drawn on planes or flat surfaces for their 2D representation. When articles or objects are formed out of 2D surfaces they become three dimensional (3D) or solids. Solids bounded by plane surfaces are polyhedral, the most common of which are the pyramid and prism. Convex solids whose faces are all equal regular polygons are regular polyhedral. The simple regular polyhedral are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. Plane surfaces that bound polyhedral are called faces of the solids. Lines of intersection of faces are edges of the solids. A solid generated by revolving a plane figure about an axis in the plane of the figure is a solid of revolution.

  1. Tetrahedron – it has four equal equilateral triangular faces.
  2. Cube – it has six equal square spaces.
  3. Octahedron – it has eight equilateral triangular faces
  4. Dodecahedron - it has twelve equal pentagonal faces.
  5. Icosahedron – it has twenty equal triangular faces PRISM ◦ A prism is a polyhedron with two nsided polygonal bases which are parallel and congruent, and lateral faces are rectangles. All cross-sections parallel to the bases are congruent with the bases. An imaginary line that joins the center of the bases is called an axis. A right and regular prism has regular polygonal bases, axis perpendicular to the bases and all the faces are ◦ equal rectangles. Prisms are named according to the shape of their base, so a prism with a triangular base is called a triangular prism; a square base is called a square prism and so on. PYRAMID A pyramid is a polyhedron with n-sided polygonal base and lateral faces are triangle meeting at a point called the vertex or apex. An imaginary line that joins the apex with the center of the base is known as the axis. A right and regular pyramid has a regular polygon base, axis perpendicular to the case and all the faces are equal isosceles triangles. Pyramids are named according to the shape of their base, so a pyramid with a triangular base is called a triangular pyramid; a square base is called a square pyramid and so on. The center of gravity of pyramids lies on the axis at one-fourth of its height from the base.

\ Depending upon the basic forms of the object to be developed, methods of development may be classified as the following:

  1. Parallel Line Method – this method is adopted in the development of prisms and cylinders,    in which all the edges/generators of lateral surface are parallel in each other.
  2. Radial Line Method – this method is adopted in the development of pyramids and cones in    which the apex is taken as center and the slant edge or generator as radius of its development.
  3. Triangulation Method – this method is generally applied in the development of transition    pieces and oblique objects.
  4. Approximation Method – this method is adopted in the development of doubly curved surface like that of a sphere since the exact development of such surface is not possible.

\  LESSON 2 – SEAMS AND HEMS

\ The thickness of the material Seams can be joined by

  1. Welding
  2. Soldering
  3. Riveting
  4. Seaming
  5. Bolting
  6. Sewing
  7. Gluing
  8. Screwing Edging seams or exposed seams are folded or wired to strengthen them and remove sharp edges. The corners of the seams are cut at a 45 degree angle, so that when they are folded they will not overlap and become too thick. In the pattern or surface development, whenever possible, the seam must be placed on the shortest edge. Seams for patterns are also called tabs, laps, hems, or lips.

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