Square-Throat Elbow: flat pattern
A rectangular elbow with a square inside corner, joined on one mitre, with or without turning vanes. A rectangular elbow with a square inside corner and a square heel, joined on one mitre, with or without turning vanes.
Open the square-throat elbow in SheetMorphConfigurations
- Without vanes. The elbow alone: two cheeks, a throat and a heel, each folded once at the mitre.
- With turning vanes. The same elbow with a number of single-thickness vanes set along the mitre; their blanks are listed.
A worked example
The without vanes configuration with the sizes SheetMorph opens with, in mm. 4 plates, each folded once at the mitre: 4 parts, 4 seams.
| Blank of P1 | 450.5 mm × 450.5 mm |
| Blank of P2 | 201.0 mm × 299.0 mm |
| Blank of P3 | 450.5 mm × 450.5 mm |
| Blank of P4 | 201.0 mm × 901.0 mm |
| Length of cut, every outline and hole | 6808.0 mm |
| Bend up, the pattern drawn outside face up | 90.0° |
| Bend down, the pattern drawn outside face up | 90.0° |
| Width (W) | 301.00 mm |
| Depth (D) | 201.00 mm |
| Bend angle | 90.00 ° |
| Mitre angle | 45.00 ° |
| Length of the mitre across a cheek | 425.68 mm |
| Throat, End A to the corner | 149.50 mm |
| Throat, corner to End B | 149.50 mm |
| Heel, End A to the corner | 450.50 mm |
| Heel, corner to End B | 450.50 mm |
| P1 Cheek 1, long | 450.50 mm |
| P1 Cheek 1, wide | 450.50 mm |
| P2 Throat, long | 201.00 mm |
| P2 Throat, wide | 299.00 mm |
| P3 Cheek 2, long | 450.50 mm |
| P3 Cheek 2, wide | 450.50 mm |
| P4 Heel, long | 201.00 mm |
| P4 Heel, wide | 901.00 mm |
| Plates | 4 |
| Triangular facets | 16 |
| Pattern extent X | 3465.40 mm |
| Pattern extent Y | 901.00 mm |
| Developed area | 602,400 mm² |
| Total cut length | 6808.00 mm |
| Longitudinal seam length | 0.00 mm |
How it is developed
Parallel-line development: flat cheeks, folded throat and heel. This is an exact development: the surface unfolds without stretching, so the pattern closes exactly.
- The throat and the heel are strips as wide as the depth, folded square across at the mitre. The cheeks are flat L shapes, cut to their true shape.
- Each plate is drawn as it is seen from outside the elbow, standing on its edge at End A, and every edge is dimensioned.
- Each side is a separate plate. The four corner edges of a duct are joints between plates, drawn as plain edges without allowance.
Checked before it can be exported
Every pattern SheetMorph draws is checked against the 3D part it comes from. For this example:
- Every station is a rectangle (passed): 3 stations: opposite sides and the two diagonals of each compared (max deviation 0).
- Plates flat, rolled or triangulated (passed): 2 flat, 2 folded or rolled from flat pieces (both develop exactly), 0 twisted and split along a diagonal.
- Surface connectivity (passed): 16 facets form one closed duct: every edge inside a part joins exactly two facets, every open edge one (V - E + F = 0).
- Developed edges equal true 3D lengths (passed): 48 facet edges compared between the 3D surface and the flat pattern (max deviation 1.14e-13).
- Shared edges and seam closure (passed): 12 internal edges are shared vertex-for-vertex between adjacent facets; 0 seam(s) have mating edges of equal true length (max deviation 0).
- 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 1.16e-10).
- Cut outlines closed and non-overlapping (passed): 4 closed outline(s); no outline crosses itself or another outline.
Assumptions
- The pattern is developed on the mid-thickness surface; inside or outside sizes are converted to it by one thickness across each opening.
- Folds are sharp lines; no bend allowance is applied.
- No seam, lap or weld allowance is added.
Limits of this module
- Vanes are single-thickness arcs; their blanks are plain rectangles and are listed, not drawn. Vane rails, tabs and double-thickness vanes are not modelled.
- The heel is square; a radius heel with a square throat is not modelled.
- No seam, lap, lock-seam, flange or weld allowance is added unless the module says so; corner joints are drawn as plain edges.
- Bend allowance and springback are not modelled; folds are sharp lines on the mid-thickness surface.
- No stiffening, tie rods, access doors or nesting onto stock sheets.
Conventions
Coordinate system. End A is at Z = 0, centred on the Z axis, with its width along X and its depth along Y. A duct that turns or is offset does so in the XZ plane, toward +X.
Corners and sides. Corners are numbered 0 (-X, -Y), 1 (+X, -Y), 2 (+X, +Y), 3 (-X, +Y), seen from +Z at End A. Rj_c is corner c of station j. Each of the four sides is its own plate; the plates are joined along the four corner edges.
Plates. Plates are drawn outside face up and stacked in the order of their numbers. The blank sizes listed are the bounding rectangle of each plate.
Material thickness. Say whether the sizes are inside, mid-thickness or outside sizes. The pattern is developed on the mid-thickness surface, one thickness larger or smaller across each opening; the views show the sizes as entered.
Elbow. Leg A is the length of the throat from End A to the inside corner, leg B from the corner to End B. The two legs meet on a mitre at half the bend angle. Vanes are spaced equally along the mitre and rolled to the radius entered, centred toward the throat.
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 square-throat elbowOther duct bends
- Elbow: Elbows of rectangular duct, rolled to a radius or in mitered segments: two cheeks, a throat and a heel.
- Reducing Elbow: A rectangular bend whose width, or width and depth, change steadily from one end to the other.
- Offset: A rectangular duct moved sideways between two parallel ends: an ogee of two curves, or a slanted piece on two mitres.
- Round to Rectangle: A square-to-round whose two ends are at an angle: it changes shape and direction in one piece.