Design Optimization of 3K Planetary Gear Train Based on Loose Constraints on Tooth Number

The 3K Planetary Gear Train (PGT) is a suitable transmission mechanism for back-drivable robot joints due to its higher bidirectional transmission efficiencies compared with harmonic drives. However, as the design constraints of a 3K PGT are strict, it is still a challenging issue to design a lightweight 3K PGT with much higher bidirectional transmission efficiencies. In this work, a design optimization approach is proposed based on Loose Constraints on Tooth Number (LCTN) and the equal strength theory. Utilizing the LCTN, the strict assembly and center distance conditions of traditional PGT designs are loosened, significantly increasing the feasible gear tooth number schemes and providing a large search space for the design optimization of the reducer. Based on the proposed design optimization method, a high-performance 3K PGT is designed for the knee joints of humanoid robots. Its forward and backward transmission efficiencies are as high as 94.30% and 94.07%, respectively, while its mass and the maximum output torque achieve 402g and 130Nm.