Rectangular Y (Trouser Piece): flat pattern

A rectangular trunk dividing into two rectangular legs side by side: a trouser piece, with equal or unequal legs. A rectangular trunk dividing into two rectangular legs side by side, equal or unequal.

Configurations

• Equal legs. Both legs have the same width and stand the same distance either side of the axis.
• Unequal legs. Each leg has its own width and its own distance from the axis.

A worked example

The equal legs configuration with the sizes SheetMorph opens with, in mm. 12 plates: the four sides of the trunk and of each of the two legs: 12 parts, 12 seams.

How it is developed

True-shape development of flat sides. This is an exact development: the surface unfolds without stretching, so the pattern closes exactly.

• The trunk divides in half across its width. Each leg starts on its half of the trunk and runs to its own end, so all its four sides are flat and are cut to their true shape.
• The two crotch sides meet along one line at the top of the trunk, across the depth.
• 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): 6 stations: opposite sides and the two diagonals of each compared (max deviation 0).
• Plates flat, rolled or triangulated (passed): 12 flat, 0 folded or rolled from flat pieces (both develop exactly), 0 twisted and split along a diagonal.
• Surface connectivity (passed): 24 facets form 3 closed ducts, set one onto another: every edge inside a part joins exactly two facets, every open edge one (V - E + F = 0).
• Developed edges equal true 3D lengths (passed): 72 facet edges compared between the 3D surface and the flat pattern (max deviation 2.27e-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 4.66e-10).
• Cut outlines closed and non-overlapping (passed): 12 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

• The trunk divides in half across its width, and the legs keep the depth of the trunk.
• The legs end level and parallel to End A; the crotch is a plain line where the two inner sides meet.
• 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.

Legs. The trunk runs from End A up the Z axis. At its top it divides across its width: leg B takes the +X half and leg C the -X half, each keeping the full depth. A leg ends level, at the leg height above the trunk, with its centre the distance entered from the axis. End B and End C are the ends of the legs.

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.
• Rectangle to Two Rounds: A rectangular inlet that divides into two round outlets side by side, as two square-to-rounds on one dividing edge.
• 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.