Abstract: This paper introduces the structure and relatedresearch work of ``three-rings reducer'', including thestresses of the inner tooth plate, high speed eccentric shaft, low speedoutput shaft of ``offset three-rings reducer'', and thedisplacement compatibility principle for this kind ofover-restraint transmission system. Based on the ``SHQ40'' reducer,the principle and method of optimizing structural parameters areintroduced and the actual parameters of ``SHQ40'' reducer areoptimized. The amplitude of dynamic loads on the optimized reducerdecreases greatly and the distribution curve is very flat when theoptimization is considered.