Overview
This single‑page tool distills the MIT Biomimetic Robotics Lab design heuristics for quasi‑direct‑drive (QDD) leg actuators and the GOAT SEA analysis into practical calculators and plots. It emphasizes the impact of the motor air‑gap radius rg and low gear ratio n on torque density, bandwidth, and backdrivability.
- Efficiency metric:
K_m^2 = K_t^2 / R(torque² per watt of copper loss). - Scaling with gap radius (empirical):
τ/M ∝ r_g^0.8,τ/J ∝ r_g^-1.6,K_t^2/R ∝ r_g^4.1. - SEA/QDD bandwidth proxy:
ω_n = √(k_s / (n² I_m)); impact proxy:F∝√((k_s+k_g) n² I_m). - IMF (backdrivability proxy): here approximated by
ξ≈J_link/(n² I_m + J_link)(heuristic).
Note: These are simplified, educational models. Use full EM, thermal, and structural analyses before hardware commitments.
Key Models
Motor & Transmission
Copper loss for required joint torque: Pcu = τout² / ( (η n)² K_m² )
Current for required joint torque: I = τout / (η n K_t)
Reflected inertia: Jref = n² I_m
Scaling with gap radius (empirical): τ/M ∝ r_g^0.8, τ/J ∝ r_g^-1.6, K_t²/R ∝ r_g^4.1
Compliance & Impact
Bandwidth proxy (SEA/virtual): ωn = √(k_s / (n² I_m)), fn = ωn / 2π
Impact scaling proxy: F ∝ √((k_s + k_g) n² I_m)
IMF proxy: ξ ≈ Jlink / (n² I_m + Jlink)
Interactive Calculator
Task & Transmission
Motor & Compliance
Gap Radius Scaling
Objective Weights
References
- MIT Biomimetic Robotics Lab — Optimal Actuator Design
- Wensing et al. — Proprioceptive Actuator Design in the MIT Cheetah (see scaling with gap radius, IMF) — MIT DSpace
- Kalouche — GOAT actuator (SEA analysis & motivation for QDD) — IROS 2017 PDF
- MIT Cheetah Actuator note — CBA/MIT
- Additional MIT thesis on actuator/backdrivability — MIT DSpace
The calculator uses empirical exponents (0.8, −1.6, 4.1) observed in MIT analyses of Emoteq HT frameless motors and related catalog data; verify for your chosen motor family.