Descriptive Geometry CH17 : DEVELOPMENTS

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

Developments

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.

Developable Surfaces

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. (Courtesy of Kessler Brewing Co.)

Developments

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

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

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.

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

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

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

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

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

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)

Problem 1 • Draw the given views and complete the development.