For safety purposes, cooperative robots are installed with an actuator composed of a low-power servo motor, a reduction gearbox, and a torque sensor. When cooperative robots make contact with humans or the environment, they must detect the contact force with a force sensor, a contact sensor, or a joint torque sensor. Equipping these sensors increases the cost and size of the application, but can be avoided under sufficient backdrivability of the actuator. To this end, we propose a method that maximizes the power transmission efficiency of the 3K planetary reduction gearbox and develop a prototype of the backdrivable reduction gearbox called the bilateral drive gear. For this maximization, the profile shift coefficients and the number of teeth are decided under some conditions. The forward-and backward-driving efficiencies of the prototype gearbox were 89.0% and 85.3%, respectively, and the reverse-drive starting torque was 0.020 N•m. The drive efficiency of the same gearbox with uncorrected teeth is 68.5%. The forward-driving efficiency was 20.5% higher than the nonoptimized one. We confirmed that prototype gearboxes with different gear ratios are easily backdrivable by hand.