Directional efficiency in geared transmissions: Characterization of backdrivability towards improved proprioceptive control

This paper introduces the phenomenon of directional efficiency, a property of spur gear transmissions in which the coefficient of torque dependent efficiency is function of the power flow direction; the efficiency in the step-up direction differs from that of step-down. Understanding the directional efficiency is important in robot design where the mechanical impedance of the transmission significantly affects the dynamics of physical interaction with the environment. This paper is the first to address `backdrivability´ by investigating directional efficiency on a high gear ratio robotic actuator, industrial servo gearboxes and over a family of gears. The kinematic model shows that a single pair of gears operates at higher efficiency in step-down than in step-up and the effect is confirmed in experiment, albeit with discrepancy in the magnitude of difference. Experimental results show that step-down and step-up directional efficiency are 98% and 96% respectively for a PIC DESIGNS 6:1 gearbox over the range of tested velocities. Additionally the overall energy efficiencies of the Dynamixel robotic servo motor with a gear ratio of 248:1 are approximately 75% and 70% for step-down and step-up respectively over a range of tested velocities. For the Dynamixel servo actuator, modeling with directional efficiency coefficients reduces error in predicted output force to 2-4% compared to a 4-8% with a single efficiency coefficient and 30% for models without friction.