Theoretical and Experimental Analysis of a Logarithmic Spiral Mechanical Reducer for Motion Assistance of Rolling Equipment

This study presents the design, theoretical modeling, and experimental validation of a novel mechanical reducer made up of three stages, including two logarithmic spiral gears, offering a continuously variable transmission ratio. Unlike conventional constant transmission ratio reducers (circular gears reducers), this reducer provides high transmission ratios during motion initiation and gradually decreases them per cycle, preventing abrupt torque transition. A comprehensive mechanical model was developed to predict transmission ratio, gear geometry, assistance distance and duration, motor torque, and energy consumption, providing a complete framework for reducer design according to target performance requirements. A proof-of-concept prototype manufactured by additive manufacturing was integrated into a trolley to validate the mechanical model. Experimental results demonstrated good agreement with theoretical predictions, with no difference in distance crossed and 13% difference in assistance duration. The model further predicts substantially lower energy consumption than conventional reducers, while maintaining progressive torque delivery throughout the assistance phase. These results demonstrate the potential of logarithmic spiral gears for variable-ratio mechanical transmissions and provide a predictive framework for the design and optimization of this type of mechanism. This reducer is hypothetically intended for applications requiring progressive torque assistance, such as manual trolleys, wheelchairs, or aircraft.