Descriptive Geometry CH17 : DEVELOPMENTS

Developments A development is a flat representation or pattern that when folded together creates a 3D object.

Developable Surfaces 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.

Developments (Courtesy of Kessler Brewing Co.) The development of a surface is that surface laid out on a plane. Practical applications of developments occur in sheet metal work, stone cutting, pattern making, packaging, and package design.

Parallel Line Developments - Prism To develop the surface of a prism, three conditions must be known: 1. The true lengths of the lateral edges. 2. The relative positions of the parallel edges with respect to a right section (a plane figure formed by the intersection of a cutting plane perpendicular to the axis of a form). 3. The perimeter of the right section of the prism or perpendicular distances between the lateral edges.

Parallel Line Developments - Prism 1. Find the TL of the laterals (edges) 2. Construct a right section (in this eg: find the TS of the base) 3. Construct a stretch-out line starting with the shortest lateral, using the perimeter distances from the right section. 4. Draw the laterals using their TL. 5. Connect the endpoints of the laterals

Stretch-Out Line In the given example, the lower base plane is perpendicular to the lateral edges, and hence its perimeter unrolls into a straight line perpendicular to the parallel lateral edges in the development. This line is called the stretch-out line. Note that the stretch-out line is started on a line of symmetry and that for economy the seam is started at the shortest lateral edge. If the right section has a line of symmetry, only a half development needs to be drawn.

Problem 2 Draw the given views and complete the development.

Parallel Line Developments - Cylinder To develop the surface of a cylinder, three conditions must be known: 1. The true lengths of the lateral edges. 2. The relative positions of the parallel edges with respect to a right section (a plane figure formed by the intersection of a cutting plane perpendicular to the axis of a form). 3. The perimeter of the right section of the prism or perpendicular distances between the lateral edges.

Parallel Line Developments - Cylinder 1. Find the TL of the laterals (edges) 2. Construct a right section (in this eg: find the TS of the base) 3. Construct a stretch-out line starting with the shortest lateral, using the perimeter distances from the right section. 4. Draw the laterals using their TL. 5. Connect the endpoints of the laterals

Problem 1 Draw the given views and complete the development.