Manifold Header: flat pattern
A round run with a row of equal branches at an even pitch: the run unrolled with every hole marked, and the branches with their saddles. A round run with a row of equal branches set square onto it at an even pitch, on one side or on alternate sides: the run unrolled with every hole marked, and the branches with their saddles.
Open the manifold header in SheetMorphConfigurations
- Branches on one side. Every branch leaves the run on the same side.
- Branches on alternate sides. The branches leave the run on opposite sides in turn.
A worked example
The branches on one side configuration with the sizes SheetMorph opens with, in mm. 4 plates: the run with 3 holes, and 3 branches that are all alike: 4 parts, 11 seams.
| Blank of P1 | 1257.8 mm × 1500.0 mm |
| Blank of P2 | 630.4 mm × 276.5 mm |
| Blank of P3 | 630.4 mm × 276.5 mm |
| Blank of P4 | 630.4 mm × 276.5 mm |
| Length of cut, every outline and hole | 10828.6 mm |
| Diameter of the run | 401.00 mm |
| Diameter of a branch | 201.00 mm |
| Length | 1500.00 mm |
| Girth of the plate | 1259.78 mm |
| Number of branches | 3 |
| End A to the axis of the first | 300.00 mm |
| Pitch, axis to axis | 450.00 mm |
| End A to the axis of the last | 1200.00 mm |
| Length, from the axis of the run | 450.00 mm |
| Girth of the plate | 631.46 mm |
| Shortest line, along the run | 249.50 mm |
| Longest line, on the sides | 276.51 mm |
| Length along the run | 201.00 mm |
| Width round the run | 210.54 mm |
| Seam to the centres of the holes | 629.89 mm |
| P1 Run, long | 1257.76 mm |
| P1 Run, wide | 1500.00 mm |
| P2 Branch 1, long | 630.45 mm |
| P2 Branch 1, wide | 276.51 mm |
| Plates | 4 |
| Triangular facets | 256 |
| Pattern extent X | 4274.09 mm |
| Pattern extent Y | 1500.00 mm |
| Area of the blanks | 2,383,601 mm² |
| Area cut out | 98,069 mm² |
| Net area | 2,285,532 mm² |
| Total cut length | 12753.71 mm |
| Longitudinal seam length | 2248.50 mm |
How it is developed
Parallel-line development (unrolled cylinders). This is a triangulated approximation: the curved surface is divided into small flat triangles, each laid out at its true size. The finer the division, the closer the pattern is to the surface; SheetMorph states the deviation it found.
- The run is unrolled to a rectangle as long as its girth. Each hole is as long along the run as the diameter of a branch, and wider round it, because the wall of the run curves away under the branch.
- The holes are in one row down the middle of the plate, half the girth from the seam.
- Each line of a branch runs from its square end back to the run. It is shortest along the run and longest on the two sides. The branches are all alike: cut one and repeat it.
Checked before it can be exported
Every pattern SheetMorph draws is checked against the 3D part it comes from. For this example:
- Surface connectivity (passed): 256 facets form a run and 3 branches set onto it: every edge inside a part joins exactly two facets, every open edge one (V - E + F = 0).
- Developed edges equal true 3D lengths (passed): 768 facet edges compared between the 3D surface and the flat pattern (max deviation 1.61e-11).
- Shared edges and seam closure (passed): 252 internal edges are shared vertex-for-vertex between adjacent facets; 4 seam(s) have mating edges of equal true length (max deviation 2.27e-13).
- Developed facets consistently oriented (passed): All developed facets are counter-clockwise (outside face up); none is mirrored or degenerate.
- Developed area equals surface area (passed): Facet area in 3D and in the flat pattern agree (difference 1.76e-7).
- Cut outlines closed and non-overlapping (passed): 4 closed outline(s); no outline crosses itself or another outline.
- HOLE-B1 lies within its plate (passed): 48 points of the hole compared with the edges of the plate; its developed area is 32689.6117.
- HOLE-B2 lies within its plate (passed): 48 points of the hole compared with the edges of the plate; its developed area is 32689.6117.
- HOLE-B3 lies within its plate (passed): 48 points of the hole compared with the edges of the plate; its developed area is 32689.6117.
Assumptions
- The pattern is developed on the mid-thickness surface; inside or outside sizes are converted to it by the thickness.
- Curves are chains of chords between division points.
- No seam, lap, weld-preparation or pressing allowance is added.
Limits of this module
- The branches are equal, square to the run and on its centre; inclined, offset or unequal branches are not modelled. Use the tee for a single branch of that kind.
- A branch must be smaller than the run: under 0.95 of its diameter.
- The branches are set onto the run, not through it, and the saddles and holes are taken on the mid-thickness surfaces.
- Curves are chains of straight chords between division points.
- No seam, lap, weld-preparation or pressing allowance is added, and plates are not nested onto stock sheets.
Conventions
Coordinate system. The part stands on the Z axis with End A at Z = 0. Angles round the axis are measured from +X toward +Y, counter-clockwise seen from +Z.
Divisions and thickness. A circle is divided into 4N equal chords. Sizes are inside, mid-thickness or outside sizes; the pattern is developed on the mid-thickness surface and the views show the sizes as entered.
Run. The run stands on the Z axis from End A at Z = 0 to End B. With the branches on one side it is cut along the line at the back, opposite them, so the holes are down the middle of the plate; with the branches on alternate sides it is cut along the line midway between the two rows, on the -Y side.
Branches. The branches are square to the run and their axes cross its axis. Branch 1 is the nearest to End A and points toward +X; on alternate sides the even branches point toward -X. The first is measured from End A to its axis, and the pitch from one axis to the next along the run. A branch is measured from the axis of the run to its end, and is cut along the line toward End A. The ends of the branches are End C, End D and so on.
Change the sizes to your own in SheetMorph, check the drawing, add seam and flange allowances, and export DXF, PDF, SVG, CSV or G-code. Check every pattern against your own standards before cutting.
Open the manifold headerOther intersections
- Tee or Lateral: A branch set onto a run: equal or reducing tees and angled laterals, with the saddle cut and the hole in the run.
- Cross: Two branches set onto opposite sides of a run: equal, reducing or unequal, with both saddle cuts and both holes in the run.
- Cone on Pipe: A cone set onto a round pipe, square as a boot or hopper outlet, or at an angle as a conical lateral, with the hole in the pipe.
- Pipe on Cone: A round branch set square onto a conical shell, such as a nozzle on a hopper, with the hole in the cone.
- Cone on Cone: A cone set square onto a conical shell, such as a reducing branch on a hopper, with the hole in the main cone.
- Rectangular Tee: A rectangular branch set square onto a rectangular duct, straight or with a shoe, with the hole marked on the duct.
- Rectangle on Round: A rectangular branch set square onto a round run, on its centre or offset: the run with its hole, and the branch folded at its corners.