Flat-pack lamp: kerf, bed size and stability
Year 12 student Mia is designing a flat-pack desk lamp for a local market stall. The brief: retail at NZ$45, ship flat in a 320 × 230 × 40 mm box, cut from 3 mm MDF on the school laser cutter (bed 300 × 420 mm), assemble without glue or fasteners, stand 350 mm tall, and hold the light head over a 200 mm-diameter work zone. Her first concept is cut from a single sheet: a 160 mm circular base, a 350 mm vertical column and an angled head, all joined with finger joints. Her test cut rattled - she measured a 0.2 mm gap at every joint. The 350 mm column will not fit on the bed in the orientation she drew it. When she stood the prototype up, it tipped over with a light nudge. She has two weeks and one sheet of 3 mm MDF per prototype.
1. Explain what the 0.2 mm gap reveals about the relationship between laser kerf and joint design, and describe exactly how Mia should find the right value for her file.
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The gap is not a drawing error - it is the kerf. A laser burns away roughly 0.1–0.2 mm of material along every cut line, so a slot is drawn at 3.0 mm but cuts at about 3.15 mm, while the tab that fits it shrinks to about 2.85 mm. The gap therefore equals roughly twice the kerf, which is why a 0.2 mm gap points to a kerf near 0.1 mm.
Mia should stop guessing and measure. Cut a kerf comb: a single strip with slots drawn at 2.6, 2.8, 3.0, 3.2 and 3.4 mm, then press-fit a cut tab into each. She wants the slot where the tab goes in with hand pressure and holds without a mallet - for MDF, slightly tighter than a sliding fit, because the compressed fibre springs back and swells with humidity.
Once found, she records the number on her drawing (e.g. 'slot = 2.8 mm for 3 mm MDF, kerf 0.1 mm') so every future file is repeatable. The judgement is that a rattle is data, not failure - the fix is a measured offset, not a thicker tab drawn by eye.
2. The 350 mm column will not fit the 300 × 420 mm bed as drawn. Evaluate two options and recommend one.
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Option A - split the column. Two 180 mm pieces joined by a half-lap. Workable, but it puts a joint exactly where bending moment is highest, adds a stacking tolerance, and doubles the part count in a flat-pack kit where assembly must be tool-free.
Option B - re-orient the part on the bed. Before redesigning, test whether the part actually fails to fit. A 350 × 60 mm strip laid diagonally at 30° needs a bounding box of about 333 mm along the bed and 227 mm across - inside 420 × 300. She never checked the diagonal; the bed's diagonal is over 500 mm, and strip parts usually fit once rotated.
Recommend B. It costs nothing, keeps the column as one continuous member (better for stiffness and for the 350 mm height), and preserves the single-sheet constraint that the $45 retail price depends on. Option A should stay as a fallback only if the head or base forces a tighter nest. The judgement is to check the cheap fix first: rotate and re-nest before you add a joint you cannot afford.
3. The prototype tipped when nudged. Explain how base size, mass distribution and the 200 mm work zone interact, and what Mia should change.
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A lamp tips when the vertical line through its combined centre of mass falls outside the edge of its base. The head hangs out over a 200 mm work zone, so it creates an overturning moment about the base rim; the base resists with its own weight acting at its centre and with its radius as a lever.
Three changes, in order of value:
- Add mass low. Rout a shallow pocket in the base and drop in steel washers or coins. A few hundred grams at floor level does more than doubling the base area, because it lowers the centre of mass as well as increasing the restoring moment.
- Offset the column back from the base centre, away from the head, so the overhang is partly counterbalanced.
- Widen the base to roughly 180–200 mm - enough that the centre of mass stays inside the footprint even with the head fully extended.
She should then test properly: a 200 g sideways push at head height, on a bench, with the lamp at full reach. The judgement is that stability is a ratio, not a base size - Mia must design the mass and the reach together.