Planetary gear trains (PGTs), in addition to their typical advantages of high transmission efficiency and a wide gear ratio range, can achieve a reverse self-locking effect functionally equivalent to that of a worm gear mechanism. This is possible under specific gear tooth number combinations and component topological configurations. This study investigates the design of self-locking configurations for seven-member, 4K planetary gear trains. Initially, the analytical method of gear train efficiency is employed to derive the product of the forward and reverse efficiencies for eight distinct transmission cases of the 7420 (1, 2–4) model, based on the topological graph of a seven-member, 4K PGT. Subsequently, to manage the complexity of these numerous cases, this paper proposes a “variable approximation substitution method.” This method simplifies the eight transmission scenarios into three categories for a streamlined analysis of self-locking conditions, ultimately identifying all gear meshing combinations capable of achieving self-locking. Through this analysis, as many as 12 distinct self-locking configurations for the seven-link, 4K PGT are inversely derived. Two of these configurations are then selected for case study analysis, which successfully validates their self-locking properties and demonstrates a forward efficiency of nearly 50%. This research not only contributes to the development of novel gear transmission devices with self-locking characteristics, but also has significant implications for the transmission field that requires reverse self-locking.
Jiang et al. (2026) studied this question.