Rectangle to Two Rounds: flat pattern

A rectangular inlet that divides into two round outlets side by side, as two square-to-rounds on one dividing edge. A rectangular inlet that divides into two round outlets side by side: two square-to-rounds that share the dividing edge of the rectangle.

Configurations

• Equal outlets. Both outlets have the same diameter; the two legs are a pair.
• Unequal outlets. The outlet on the +X side and the one on the -X side have their own diameters.

A worked example

The equal outlets configuration with the sizes SheetMorph opens with, in mm. 2 legs, each one plate: half the rectangle to a round; the two are a pair: 2 parts, 3 seams.

How it is developed

Triangulation (true-length development) of two transitions. 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.

• Each leg is developed as a transition from its half of the rectangle to its round: every edge of one end is joined to the point of the other that faces the same way, and the triangles are laid out from their true lengths.
• The two legs meet along the dividing edge of the rectangle, which is a joint between the two plates. Above it the inner flats lean apart.
• With equal outlets the two plates are mirror images: cut one and turn the second over.

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): 72 facets form two closed bands, one for each leg: every edge inside a part joins exactly two facets, every open edge one (V - E + F = 0).
• Developed edges equal true 3D lengths (passed): 216 facet edges compared between the 3D surface and the flat pattern (max deviation 3.80e-13).
• Shared edges and seam closure (passed): 70 internal edges are shared vertex-for-vertex between adjacent facets; 2 seam(s) have mating edges of equal true length (max deviation 1.14e-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 4.66e-10).
• Cut outlines closed and non-overlapping (passed): 2 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 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 two legs share the rectangle equally and the outlets are level and on the X axis; an outlet that is set forward, turned or inclined is made as two separate transitions.
• The legs are joined to each other along the dividing edge only: no saddle or gusset is drawn in the V between them.
• The curved parts are triangulated: narrow flat triangles between the corners of the rectangle and the divisions of the rounds.
• 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.

Inlet and outlets. End A is the rectangle at Z = 0, its width along X and its depth along Y. A line across it at X = 0, from front to back, divides it between the two legs. The outlets are level at Z = height, their centres on the X axis, half the spacing either side of the Z axis: End B on the +X side and End C on the -X side.

Legs. Each leg is a transition from its half of the rectangle to its round: four flat triangles, one on each side of the half, with a part of a cone between each pair. The inner flat of each leg rises from the dividing edge, so the two legs part there in a V. Each leg is one plate, cut down the middle of its outer flat.

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.

Other branches

• V-Piece: Breeches pieces: one round inlet dividing into two round branches, equal or unequal, level or angled.
• Y-Piece: A trunk dividing into two branches on flat miter cuts, symmetric or as a lateral, the branches of the trunk diameter or tapering to smaller ends.
• Twin Bend: A trunk dividing into two segmented bends that turn opposite ways: a bullhead at 90°, or any angle you give.
• Twin Bend to Rectangle: A round trunk dividing into two segmented bends that turn opposite ways and change to rectangular duct as they turn: a bullhead at 90°, or any angle you give.
• Three- or Four-Way: A round trunk that divides into three or four equal branches spaced evenly round it: a trifurcation or a four-way piece.
• Rectangular Y: A rectangular trunk dividing into two rectangular legs side by side: a trouser piece, with equal or unequal legs.
• Flat-Oval Tee: A round or flat-oval branch on the flat side of a flat-oval main: the main with its hole, and the branch cut to the main.