RV reducers contain multi-tooth contact characteristics, with high-impact resistance and a small backlash, and are widely used in precision transmissions, such as robot joints. The main parameters affecting the transmission performance include torsional stiffness and transmission errors (TEs). However, a cycloid tooth profile modification has a significant influence on the transmission accuracy and torsional stiffness of an RV reducer. It is important to study the multi-tooth contact characteristics caused by modifying the cycloid profile. The contact force is calculated using a single contact stiffness, inevitably affecting the accuracy of the result. Thus, a new multi-tooth contact model and a TE model of an RV reducer are proposed by dividing the contact area into several differential elements. A comparison of the contact force obtained using the finite element method and the test results of an RV reducer prototype validates the proposed models. On this basis, the influence of load on the different modification methods is studied, including a TE, the mechanical performance, and the transmission efficiency. In addition, the proposed reverse profile is particularly suitable for situations with a large clearance and torque. This study provides a reliable theoretical basis for a multi-tooth contact analysis of a cycloid profile modification.

Transmission error is the key index for characterizing the transmission precision of precision reducers, and its accurate measurement is significant for the precision evaluation of precision reducers. Transmission error is generally measured under the conditions of zero-load and low speed. However, low speed is a general concept and there is no general standard of measurement speed or solid scientific basis. Therefore, it is difficult to obtain consistent transmission precision evaluation results for the same precision reducer. The concept of optimal measurement speed in the transmission precision evaluation of precision reducers was put forward in order to reduce the influence of measurement speed. The determination method of optimal measurement speed was proposed and the calculation model of the optimal measurement speed was established, according to the Stribeck friction model of precision reducers. Taking a certain type of RV reducer as an example, the transmission error measurement experiments were carried out under different speeds. The friction torque of the RV reducer and the peak-to-peak value of the measured transmission error were the least under the optimal measurement speed. The influence of speed on the measurement results can be effectively reduced. The determination of optimal measurement speed of transmission errors could improve the measurement precision of the transmission errors for the objective evaluation of transmission precision of precision reducers.