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 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.
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:
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.