The sweep holds the electromagnetics fixed (Bg=0.40 T, current density, fill, axial stack) and scales only the outer diameter. At constant airgap shear stress the four quantities that decide the actuator each scale as a clean power of D — which on the log plot below are four straight lines fanning out from the 110 mm baseline. There is no electromagnetic optimum: the binding constraint is elsewhere.
| OD | motor mass | T air (6) | T nom (9) | T peak (18) | Kₘ | TD peak | inertia |
|---|---|---|---|---|---|---|---|
| 100 mm | 0.70 kg | 22.2 | 33.3 | 66.6 | 0.87 | 13.9 | 2.4e-4 |
| 110 mm | 0.85 kg | 29.6 | 44.3 | 88.7 | 1.06 | 15.3 | 3.5e-4 |
| 120 mm | 1.01 kg | 38.4 | 57.6 | 115.1 | 1.26 | 16.7 | 5.0e-4 |
| 130 mm | 1.19 kg | 48.8 | 73.2 | 146.4 | 1.48 | 18.1 | 6.8e-4 |
| 140 mm | 1.38 kg | 60.9 | 91.4 | 182.9 | 1.71 | 19.5 | 9.2e-4 |
Torque ∝ D³, Km ∝ D², torque density ∝ D¹ — all monotonic. There is no peak to find; the physics never says "stop." Doubling the payoff costs only a squared growth in mass.
It also wins on your ledger: Km rising means less copper loss per newton-metre, so a larger machine is more joules-efficient per unit torque. Energy-optimal points the same way as torque-optimal — up.
Rotor inertia ∝ D⁴ — the steepest line. Reflected through the gearbox (×G² = 64), it dominates how fast the joint can accelerate. At 110 mm the reflected rotor inertia is ≈ 0.022 kg·m²; at 140 mm it is ~2.6× that. Past some diameter you add inertia faster than torque and the limb goes sluggish.
And the actuator sits at the joint, so its mass is distal load — every gram penalizes the limb it drives and the proximal joints that must swing it. The ceiling is a packaging + dynamics call, not a magnetics one.
Hip / knee (needs torque, tolerates mass): 120–130 mm is the sweet spot — 130 mm buys 73 N·m nominal / 146 N·m peak and clears the Km ≥ 1.3 datasheet target (crossed at 122 mm) at 1.19 kg, if it packages into the thigh. Ankle / wrist / elbow (needs low distal inertia): stay at 100–110 mm and accept less torque — the D⁴ inertia term matters more distally than the D³ torque gain.
So AXF-1 is not one motor — it is one design scaled per joint: same poles, same coils, same magnets, same process, only Do changes. That is the printability dividend — you re-slice, you don't re-engineer.