Measurement setup
Enter the minimum clear inside radius r (the distance from the ring center to the middle of an inner straight side), side count n, base width W and side height H. The result is a closed regular polygon made from straight channel sections, not a smooth rolled circle. There are n − 1 retained hinges and one final joint between the trimmed stock ends. The outside circumscribed diameter is the diameter of the circle through all outer vertices.
Geometry and cut equations
α = 360° / n; d = W × tan(π / n); outer-side length P = 2 × (r + W) × tan(π / n); inner-side length = 2r × tan(π / n); straight stock = nP; outside circumscribed diameter = 2 × (r + W) / cos(π / n). Each stock end has a half-miter setback d.
For each closing joint, d = span × tan(|α| / 2), and the full V opening is 2d. Span is tray width for horizontal cuts and wall height for vertical cuts. Downward vertical joints open the side-wall slit instead; their formed edge gap is 2H × sin(|α| / 2).
Every segment must contain its adjacent closing-notch setbacks plus a 10 mm margin. Impossible or overlapping layouts are rejected.
Default numerical example
W = 200 mm · H = 50 mm · Straight stock length = 6430.78 mm. Stock station: 535.90 mm / 1071.80 mm / 1607.70 mm / 2143.59 mm / 2679.49 mm / 3215.39 mm / 3751.29 mm / 4287.19 mm / 4823.09 mm / 5358.98 mm / 5894.88 mm. θ: 30.00° / 30.00° / 30.00° / 30.00° / 30.00° / 30.00° / 30.00° / 30.00° / 30.00° / 30.00° / 30.00°.
Inspect all four stages
- Inspect the uncut channel blank, including both end trims.
- Mark n − 1 retained fold axes and the half-miter on each stock end.
- Remove the inner V wedges and the two end half-wedges.
- Form the polygon and join the trimmed ends at the final seam; connection hardware is not specified.
Scope and method identity
This is a separately implemented TrayNeo method for the numbered entry. Exact correspondence with the reference product remains under review.
Ideal zero-radius geometry. Cut envelopes, retained folds and opening covers are shown explicitly; kerf, rolled lips, thickness allowances, cable clearance, springback and connection hardware are not specified.