## 1 Introduction  
A precision reducer is the core component of an industrial robot and it directly affects the performance of a robot. RV reducers and harmonic reducers are widely used in robotics. The RV reducers have the higher rigidity and they are mostly applied in the parts of heavy loads, such as bases, arms, and shoulders, whereas the harmonic reducers are usually applied in forearms, wrists, and hands [1].  
Transmission error (TE) is the key index for characterizing the transmission precision of precision reducers. It has an important influence on the positioning precision of robots and it is also the main cause for vibration. The transmission error is listed as the precision index of precision reducers in GB/T35089/2018 [2]. It is necessary to measure and evaluate the transmission errors of precision reducers before leaving the factory. The measurement precision of transmission errors has a significant influence on the precision evaluation of the precision reducers.  
The transmission error of precision reducers has been extensively explored from the perspective of measurement and control. [PERSON] et al. decomposed the transmission error of a harmonic reducer into the transmission error \(\overline{\theta}_{p}\) that is related to manufacturing and installation errors and the transmission error \(\overline{\theta}_{s}\) related to speed, load, and stiffness. [PERSON] proposed to measure the transmission error component \(\overline{\theta}_{p}\) under the conditions of zero-load and low speed and set the measurement speed as 10 r/min [3; 4]. [PERSON] analyzed the internal and external factors that affect the transmission error of a harmonic reducer, divided the transmission error into the well-behaved transmission error and the poorly-behaved transmission error, and carried out the experimental study [5]. [PERSON] decomposed the transmission error of a RV reducer into static error and dynamic error. Taking RV-20E as an example, the static error was obtained at 30 r/min [6]. The measurement speeds in the above studies were different, although they all divided the transmission error of a precision reducer into two components. [PERSON] measured the transmission error of a new type of involute planetary gear transmission with double cranks and variable tooth thickness at 300 r/min [7]. [PERSON] measured the transmission error of a RV reducer and compared the result with the simulation transmission error under the actual machining error [8]. [PERSON] decomposed the transmission error of a harmonic reducer into the synchronous error \(\theta_{Symc}\) and nonlinear elastic error \(\theta_{Hys}\), established the mathematical models of each transmission error component, and explored the control strategy [9].  
In general, the transmission error is generally measured under the conditions of zero-load and low speed and the peak-to-peak value is treated as the evaluation basis of the transmission error of precision reduces in order to realize the transmission precision evaluation of the precision reducers. However, low speed is a general concept, and there is no uniform standard, and it thus results in the difference in the transmission precision evaluation results of the same precision reducer.  
From the perspective of transmission precision evaluation of precision reducers, the concept of optimal measurement speed was put forward in this paper in order to reduce the influence of the measurement speed on the dynamic measurement of transmission error. Subsequently, the calculation model of the optimal measurement speed of transmission error was established and the implementation steps were given based on the Stribeck friction model of precision reducers. Finally, taking a certain type of RV reducer as an example, with the RV reducer comprehensive performance tester that was developed by our research group, the transmission error measurement experiment was carried out to verify the proposed method.