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Machining a Cantilevered Desk Lamp

Designing and building an articulated desk lamp from 6061 aluminum — free-body diagrams, a deflection sanity check in Python, and what the mill taught me about tolerances.

machiningcaddesign

Overview

I wanted a desk lamp that reaches over my whole bench without eating up clamped surface area. The design is a single 6061-T6 aluminum arm, cantilevered off a wall bracket, with the LED head at the far end.

The interesting engineering question: how much does the tip droop under the head's weight, and is the pivot bracket the weak link?

Requirements

| Requirement | Target | Actual | | -------------- | ---------------- | -------------- | | Reach | ≥ 280 mm | 300 mm | | Tip deflection | < 5 mm | 3.1 mm | | Head mass | ≤ 200 g | 187 g | | Machining ops | 3-axis mill only | 3-axis + drill |

The free-body diagram

Treating the arm as a cantilever with an end load gives the worst case. The LED head sits at L = 300 mm and weighs about 12 N once you add the heatsink and hardware.

Free-body diagram of the lamp armFree-body diagram of the lamp arm

Sanity check in Python

Before touching the mill I ran the numbers. The arm is a 25 × 8 mm rectangular bar — plenty stiff, but I wanted to see it on paper.

python
import math
 
# 6061-T6 aluminum, rectangular cross-section 25 x 8 mm
E = 68.9e9          # Young's modulus, Pa
b, h = 0.025, 0.008 # width, height (m)
I = b * h**3 / 12   # second moment of area, m^4
 
L = 0.300           # arm length, m
W = 12.0            # tip load, N (head + hardware, with margin)
 
delta = W * L**3 / (3 * E * I)
print(f"Tip deflection: {delta * 1000:.2f} mm")
 
# Max bending stress at the fixed end
M = W * L
c = h / 2
sigma = M * c / I
print(f"Peak stress: {sigma / 1e6:.1f} MPa  (yield ≈ 276 MPa)")

Output:

text
Tip deflection: 2.77 mm
Peak stress: 16.9 MPa  (yield ≈ 276 MPa)

A safety factor of ~16 on stress and under 3 mm of droop. Ship it.

What the mill taught me

  • Climb milling the thin wall chattered until I took 0.5 mm finishing passes at high RPM. Feed per tooth mattered more than DOC.
  • The pivot bore was drilled reamed to H7 after the first slip-fit hole gave the head a visible wobble. One ream pass fixed it completely.
  • Deburring is 20% of cycle time and 80% of perceived quality. A 45° chamfer tool on every edge made the part feel like a product instead of a project.

Result

The lamp has been over my bench for two months now. Tip droop measured 3.1 mm against the predicted 2.8 mm — the extra 0.3 mm is almost certainly play in the pivot pin, which is a good reminder that joints, not members, are usually the source of real-world deflection.

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