Descriptive Geometry CH17 : DEVELOPMENTS
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1 Descriptive Geometry CH17 : DEVELOPMENTS
2 Developments A development is a flat representation or pattern that when folded together creates a 3D object.
3 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.
4 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.
5 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.
6 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
7 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
8 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
9 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.
10 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
11 Problem 2 Draw the given views and complete the development.
12 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.
13 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
14 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
15 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
16 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
17 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 For inclined surface use a spline (fit option)
18 Problem 1 Draw the given views and complete the development.
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