Five-pointed star

The surface is developable and the flat pattern is solved in closed form. Cut the part to the drawing and it fits — the whole uncertainty sits in the K-factor, which belongs to the material and the machine, not to the geometry.

Dimensions are entered as: Outside dimensions. The flat pattern itself is always computed on the neutral fibre — at Ø800 in 3 mm sheet the difference between the inside and the outside dimension is 18.8 mm of developed width, and then the seam does not meet.

En konveks fem-takket stjerne skåret af en flad plade — ti omrids-punkter skiftevis på en ydre og en indre radius. Her vist let ekstruderet med blød kant, men selve mønstret er plant.

Dekorations- og skiltestjerner, ornamenter, julestjerner i metal og lasersnit-emner. En klassisk øvelse i nøjagtig passer- og vinkel-opmærkning af en regulær stjerneform.

Skiltetekniker, metalsmed og smed — dekorations- og skiltestjerner, ornamenter og lasersnit-emner.

Rustfri, cortenstål eller messing 1–3 mm; lasersnit eller vandskåret. Messing til pynt (metalsmed).

Source: Materialelære + samlinger: metalsmed-artikler i src/lib/skoler/indhold/data.ts. Fremstillingsfælder: docs/PLAN-UDFOLDNINGSBIBLIOTEK.md §9.2/§4.

Ydre radius — Ydre radius

Afstand fra centrum til en taks spids (mm). Sætter stjernens størrelse — de fem spidser ligger på denne cirkel.

Indre radius — Indre radius

Afstand fra centrum til de indadgående hjørner mellem takkerne (mm). Forholdet ydre/indre styrer hvor spidse eller buttede takkerne bliver.

Tykkelse — Plade-/godstykkelse

Materialets tykkelse (mm) — her vist som ekstruderingsdybde. Påvirker ikke det plane mønster, kun det færdige emnes dybde.

Step by step with compass and square — in cardboard first, in sheet metal after.

1. 01Slå en centerlinje og afsæt centrum; tegn med passer den ydre cirkel (ydre radius) og den indre cirkel (indre radius).
2. 02Del den ydre cirkel i 5 lige store dele med 72° — afsæt første punkt opad og drej 72° fem gange. Det giver de fem taks-spidser.
3. 03Del på samme måde den indre cirkel i 5 punkter, men forskudt 36° i forhold til spidserne — det giver de fem indadgående hjørner.
4. 04Forbind nu punkterne på kryds: ydre spids → nærmeste indre hjørne → næste ydre spids, hele vejen rundt (10 rette linjer i alt).
5. 05Kontrollér at figuren er symmetrisk om centerlinjen, og skær konturen ud i 1:1.

72°/36° kan slås rent med vinkelmåler eller ved at dele cirklen i 10 lige store buer (36° pr. bue) og bruge hvert andet punkt på ydre/indre cirkel. Tegn altid begge cirkler først — så bliver takkerne ens.

• ·Ren flad kontur i 1:1 — ingen udfoldning; ydre og indre radius sættes af med passer, tak-punkterne skiftevis på de to radier.
• ·Ved lasersnit lægges lead-in (start-tap) i de indadgående hjørner, hvor spændingen ellers koncentreres.
• ·Små tak-spidser < 30 mm kan tippe ned i skæresporet — hold dem sammenhængende.

The words and formulas the trade uses for a flat pattern. The symbols are the same throughout Discebo: α is the bend angle in degrees, R the inside bend radius, t the sheet thickness and K the K-factor — all in millimetres.

Flat pattern (development)

The part's surface laid out flat as one continuous cutting outline — the way the sheet looks BEFORE it is bent or rolled. Only a developable surface can be unfolded exactly; a doubly curved surface cannot be laid flat without stretching the material.

Flat length

The flat length the part must be cut to so the dimensions come out right once it is bent. It is either the sum of the outside dimensions minus the bend deductions, or the sum of the flat legs plus the bend allowances — both routes must give the same number.L = Σ(udvendige mål) − Σ(BD) = Σ(flade ben) + Σ(BA)

Bend allowance

The length of material that sits in the bend itself, measured along the neutral fibre. The bend allowance is always positive and is added to the flat legs.BA = (π/180) · α · (R + K · t)

Bend deduction

The amount subtracted from the sum of the outside dimensions, because the two outside dimensions between them count the corner twice. Here the bend deduction is taken as POSITIVE and subtracted; DIN 6935 writes the same quantity as the compensation value v with the opposite sign.BD = 2 · OSSB − BA

Outside setback

The distance from the theoretical outside corner point in to where the bend starts. Above 90°, tan(α/2) is clamped to at most 1 per DIN 6935, so the number does not explode towards 180°.OSSB = tan(α/2) · (R + t)

Compensation value v to DIN 6935

The standard's own way of writing the same corner loss: the flat length is a + b + v, where v is negative. Our bend deduction is therefore the same quantity with the opposite sign — never flip one without the other.L = a + b + v ⇒ v = −BD

K-factor

Where the neutral fibre sits in the sheet, given as a fraction of the sheet thickness. DIN 6935 writes the correction factor k, which applies to the neutral line in the form (R + t·k/2); the American CAD convention writes (R + K·t), so K = k/2.k = 0,65 + 0,5 · log₁₀(R/t), k ≤ 1,0 ⇒ K = k/2

Neutral fibre

The layer in the sheet that is neither stretched nor compressed when the part is bent. The flat pattern is always computed on the neutral fibre — which is why it matters whether the drawing's dimensions are inside or outside.

Bend angle

The angle the material is turned through, not the angle between the legs. The bend angle is 180° minus the included angle, so a square corner is 90° and a seam fold is 180°.α = 180° − åbningsvinklen

Inside bend radius

The radius on the inside of the bend. It is set by the tooling and the material, not by the drawing — too small a radius cracks the part in the outer fibre.

Sheet thickness

The thickness of the material. It enters every single bend allowance, so sheet delivered 0.2 mm thicker than ordered shifts the flat length at every bend.

Fold line

The line on the flat pattern where the part is to be bent. It is drawn but never cut through — in a laser file it therefore sits on its own layer.

Test bend

A strip of known raw length, bent in the material and the tooling that production will use. Measure the two outside legs afterwards and the bend deduction and K-factor can be worked back. The machine's own measured bend table beats any table.BD_målt = (A + B) − L₀

DIN 6935 covers only cold bending of flat products in structural steel. Stainless, aluminium, copper, brass and titanium zinc are not included — there the formulas are an extrapolation, and a test bend in the actual material settles it.

9 fields. The starting values belong to the figure itself — they live in one place in the code, so the tool, the share link and the smoke test can never disagree about what «default» means.

A preset sets every dimension at once. The name is often the word the part goes by in the workshop — the library's search knows them all.

Read them before the part is cut. They are here because they cannot be calculated away — not as legal text, but as craft.

• The figure draws GEOMETRY. The star is a decorative piece — load capacity, wind load, anchoring and the sheet's own deflection have not been calculated. If the star is mounted on a gable or facade, it is a wind-exposed building component and must be fixed in accordance with EN 1991-1-4 (wind load) and the facade's own instructions.
• The contour in the pattern and in the DXF is NOMINAL. The cut width has not been deducted: without kerf compensation on the machine, the whole star becomes one cut width too small all the way round. For plasma in 20 mm sheet that is 3.6 mm — not a rounding error, but a star that does not fit in its cut-out.
• The five points and five notches are SHARP internal and external corners. A sharp corner is a crack starter under dynamic or alternating load, and a laser or plasma cannot cut a sharper angle than its own kerf track — very sharp points become rounded. Fatigue and crack growth are not calculated here.
• Fixing and suspension are not covered. A centre hole is ONLY geometry — neither the hole's edge pressure, the suspension's load capacity, nor whether the star can hang from one point without distorting, has been calculated.
• Surface treatment, corrosion class and the sheet's flatness after cutting are not covered. Large, thin stars will warp from the heat of the many cuts and must be straightened — that is a finishing operation, not a tolerance.
• The figure draws a five-pointed star with STRAIGHT edges and sharp points. Curved points, rounded tips or a number of points other than five is a different geometry, which this figure does not cover.