In'ei Spiral Gear: A Kinematically Constrained Low-Frequency Rectifier for 1/f Fluctuations

We introduce the In’ei Spiral Gear, a mechanically realizable rectification mechanism designed to harvest work from low-frequency components of 1/f-type fluctuations while rejecting high-frequency jitter through strict kinematic constraints. Using a minimal angular-domain model, we show that direct rectification of broadband 1/f fluctuations inevitably causes contact loss unless the effective bandwidth is explicitly limited. A systematic parameter sweep identifies a critical cutoff frequency of 11 cycles per revolution, beyond which continuous contact cannot be maintained. Within this limit, an optimal soft-rectification regime emerges, characterized by low stiffness and a high engagement threshold. The results establish a physical bandwidth limit for fluctuation-driven mechanical rectification and define the In’ei Spiral Gear as a mechanically enforced low-pass filter coupled with a kinematic rectifier.