Abstract
A logarithmic hollow shaft speed reducer comprising a compact, modular two-stage rotary system with independently selectable coupling paths. The first stage produces coaxial outputs directed to either the ring, sun, or carrier of a standalone second-stage differential planetary gear. This architecture enables multiple torque-speed modes—high-speed/low-torque, balanced, and high-torque/low-speed—without altering drive element configuration. The speed reducer's modularity and clarity support cost-effective manufacturing and flexible deployment.