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Rectangle to round transition flat pattern
Enter the rectangle sides, the round diameter and the height. Offsets move the round away from the centre of the rectangle.
A rectangle-to-round transition is developed by triangulation: the surface is split into 4 flat triangles and 4 corner cones, and each triangle is laid flat from the true lengths of its sides. A 400 x 300 mm rectangle to a 250 mm round, 300 mm high, with 24 divisions per quarter, gives a one-piece pattern of 730.1 x 953.1 mm with 2,787.3 mm of cut and 100 bend lines.
| Piece | Qty | Flat size, mm | Area, mm² | Cut length, mm |
|---|---|---|---|---|
| Shell | 1 | 730.1 × 953.1 | 337,491.4 | 2,787.3 |
Patterns are developed at mid-thickness. An inside dimension is increased by the thickness, an outside dimension is reduced by it.
CutMeter is software. Check every result before you cut or bend. The person who approves the part is responsible for its dimensions.
Method
Rectangle corners C1 to C4 at height 0; round points Pj = (ex + r cos φj, ey + r sin φj, h) with φj = -90° + j x 90° / n, j = 0 to 4n. True length of a line = sqrt(Δx² + Δy² + Δz²). Each triangle Ci, Pj, Pj+1 and each side triangle is placed in the flat from its three true lengths. The seam runs from the middle of side A to the round point P0 (φ = -90°).
A, B = rectangle sides; r = round diameter / 2; h = height between the planes; ex, ey = offset of the round centre from the rectangle centre, at most half of each side; n = divisions per quarter circle.
The round is approximated by 4 x n straight facets. The lines from each corner to the round points are the bend lines of a press-braked part and go on layer BEND in the DXF; for a rolled part use more divisions.
Worked example
Side A = 400 mm, side B = 300 mm, round diameter 250 mm, height 300 mm, no offset, thickness 2 mm, mid-thickness dimensions, 24 divisions per quarter.
One shell, 730.1 x 953.1 mm, area 337,491.4 mm², cut length 2,787.3 mm, 100 bend lines. Entered as inside dimensions instead, the mean sizes become 402 x 302 mm and 252 mm, and the shell 732.2 x 959.2 mm.
True lengths for hand layout
| Round point | Angle on the round, ° | True length, mm |
|---|---|---|
| P0 | -90 | 361.4 |
| P1 | -75 | 344.9 |
| P2 | -60 | 332.6 |
| P3 | -45 | 326 |
| P4 | -30 | 325.7 |
| P5 | -15 | 331.8 |
| P6 | 0 | 343.7 |
Questions about transition flat patterns
How is a square to round transition developed?
By triangulation. The true length of every line from a rectangle corner to a point on the round is computed in 3D, and the triangles are laid out side by side in the flat, starting from the seam.
Can the round be off centre?
Yes. Enter offsets along side A and side B; each can be up to half of that side, so the centre of the round stays above the rectangle.
How many divisions should I use?
For a press-braked part, the number of bends per corner; each corner gets n + 1 bend lines, 4 x (n + 1) in all. For a rolled part, use more: the default is 24.
Can I get the pattern in two halves?
Not yet. The tool gives one piece with the seam in the middle of side A.
What is in the DXF?
The outline on layer CUT and the bend lines on layer BEND. CutMeter does not count layer BEND when it measures a file, so the pattern is measured and priced by the outline only.