What Is Reflected Inertia?

Reflected inertia is the motor rotor's inertia as seen at the gearbox output side: J_reflected = J_rotor × N², where N is the gear ratio. Inertia scales with the square of the ratio — a 100:1 joint presents 10,000x the rotor inertia at its output, while a 10:1 joint presents only 100x.

Why High-Ratio Joints Feel Stiff and Break Under Impact

Anything pushing on the joint output must also accelerate that squared-up rotor inertia:

• Poor impact tolerance: at foot touchdown or collision, the impulse arrives faster than any controller can react, and the energy lands directly on gear teeth and flexsplines — a leading failure mode of high-ratio joints in legs;
• Hard to backdrive: reflected inertia plus friction makes the joint nearly immovable by hand, killing passive compliance;
• Limited force-control bandwidth: to fake softness, the controller must first fight the huge equivalent inertia, capping active-compliance bandwidth and fidelity.

Quotable one-liner: double the gear ratio, quadruple the reflected inertia — the physical reason leg joints avoid high ratios.

How QDD Keeps Reflected Inertia Low

This is the core trade of the quasi-direct-drive (QDD) approach: use a large-diameter, high-torque-density motor so the gear ratio can stay low (typically 6–20:1), cutting reflected inertia by 1–2 orders of magnitude versus a harmonic solution (50–160:1). The joint becomes naturally backdrivable, impacts are absorbed softly, and external torque can be estimated from motor current alone. BXI's 85/70/50-series joint actuators pick a 19.5:1 planetary ratio as exactly this engineering balance between output torque and reflected inertia.