What Gear Ratio Makes QDD Actuators Robust Against Impacts? A Theoretical Limit and Interactive Tool for Legged Robots

Kurzfassung

Impact robustness is critical when selecting and designing quasi-direct-drive (QDD) actuators for legged robots, yet currently used gear ratios vary widely. We derive a soft gear-ratio boundary beyond which reducing reflected inertia provides rapidly diminishing benefits for impact robustness. The boundary follows from factoring impact robustness into an energy-ratio term and an inertia-ratio term, with the latter exhibiting strong nonlinear behavior. Applying the resulting criterion to existing robots shows that proprioceptive designs with low collision energy can slightly exceed this boundary, whereas systems with larger link inertia remain below it. To support practical actuator selection, we also provide a browser-based calculator for real-time visualization of impact robustness across a wide parameter range. Together, these contributions enable rapid design exploration and provide a quantitative criterion for actuator selection in impact-prone legged robots.