[{"data":1,"prerenderedAt":114},["ShallowReactive",2],{"\u002Fen\u002Fglossary\u002Freflected-inertia":3},{"id":4,"title":5,"alternateName":6,"body":7,"description":104,"extension":105,"keywords":106,"meta":107,"navigation":108,"path":109,"seo":110,"stem":111,"updated":112,"__hash__":113},"glossary\u002Fglossary\u002Fen\u002Freflected-inertia.md","Reflected Inertia","反射惯量",{"type":8,"value":9,"toc":98},"minimark",[10,15,35,40,43,65,71,75],[11,12,14],"h1",{"id":13},"what-is-reflected-inertia","What Is Reflected Inertia?",[16,17,18,22,23,26,27,30,31,34],"p",{},[19,20,21],"strong",{},"Reflected inertia"," is the motor rotor's inertia as seen at the gearbox output side: ",[19,24,25],{},"J_reflected = J_rotor × N²",", where N is the gear ratio. Inertia scales with the ",[19,28,29],{},"square"," of the ratio — a 100:1 joint presents ",[19,32,33],{},"10,000x"," the rotor inertia at its output, while a 10:1 joint presents only 100x.",[36,37,39],"h2",{"id":38},"why-high-ratio-joints-feel-stiff-and-break-under-impact","Why High-Ratio Joints Feel Stiff and Break Under Impact",[16,41,42],{},"Anything pushing on the joint output must also accelerate that squared-up rotor inertia:",[44,45,46,53,59],"ul",{},[47,48,49,52],"li",{},[19,50,51],{},"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;",[47,54,55,58],{},[19,56,57],{},"Hard to backdrive",": reflected inertia plus friction makes the joint nearly immovable by hand, killing passive compliance;",[47,60,61,64],{},[19,62,63],{},"Limited force-control bandwidth",": to fake softness, the controller must first fight the huge equivalent inertia, capping active-compliance bandwidth and fidelity.",[16,66,67,68],{},"Quotable one-liner: ",[19,69,70],{},"double the gear ratio, quadruple the reflected inertia — the physical reason leg joints avoid high ratios.",[36,72,74],{"id":73},"how-qdd-keeps-reflected-inertia-low","How QDD Keeps Reflected Inertia Low",[16,76,77,78,83,84,88,89,92,93,97],{},"This is the core trade of the ",[79,80,82],"a",{"href":81},"\u002Fen\u002Fglossary\u002Fquasi-direct-drive","quasi-direct-drive (QDD)"," approach: use a large-diameter, high-",[79,85,87],{"href":86},"\u002Fen\u002Fglossary\u002Ftorque-density","torque-density"," motor so the gear ratio can stay low (typically 6–20:1), cutting reflected inertia by ",[19,90,91],{},"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 ",[79,94,96],{"href":95},"\u002Fen\u002Fmotors\u002Fadvanced-motors","85\u002F70\u002F50-series joint actuators"," pick a 19.5:1 planetary ratio as exactly this engineering balance between output torque and reflected inertia.",{"title":99,"searchDepth":100,"depth":100,"links":101},"",2,[102,103],{"id":38,"depth":100,"text":39},{"id":73,"depth":100,"text":74},"Reflected inertia is rotor inertia multiplied by gear ratio squared at the output. It directly affects joint backdrivability and impact response.","md","reflected inertia, gear ratio squared, QDD reflected inertia, backdrivability, joint actuator inertia",{},true,"\u002Fglossary\u002Fen\u002Freflected-inertia",{"title":5,"description":104},"glossary\u002Fen\u002Freflected-inertia",null,"8-6CpndTia9NmkL5OpMklo45cRXWGU1NDmnWQHRnTGQ",1785156467347]