Abstract: The rotary vector (RV) reducer is one of the most important transmission components inside the joints of robots. The high precision motion control of the robot can be realized in the normal operation and service life of agricultural robots. However, the complex structure of the RV reducer cannot fully meet the variable conditions in actual work and the harsh working environment. Mechanical, cracks, and pitting faults can often occur at the same time or successively in actual operation, due to lubrication, manufacturing errors, and unreasonable forces. The signals collected by the sensor are also the mutual coupling of multiple fault sources. Therefore, it is necessary to explore the composite fault diagnosis of the RV reducer. In this study, a blind fault separation was proposed from the compound signals of the RV reducer using time-frequency image ridge extraction and improved sparse component analysis. The fault feature of the RV reducer was then extracted from the core transmission component of agricultural robots. The composite fault diagnosis of the RV reducer was finally realized with the unknown number of fault sources under the reciprocating motion of the joint arm and the time-varying speed of the agricultural robot. Firstly, the ridge extraction from time-frequency images (RETF) was used to synchronously intercept the vibration signals of the manipulator in the constant speed period. Then, the blind source separation (SMF-DPC-OMP) was combined with the sinC function to improve morphological filtering (SMF), density peak clustering (DPC), and orthogonal matching pursuit (OMP), in order to separate and extract the composite faults of stationary signals. The sinC function was taken as a new structural element to construct the average combined morphological filter. The vibration signal in the constant speed period was subjected to morphological filtering for better impact characteristics and sparsity of the signal. The DPC was used to estimate the mixing matrix of sparse signals, and then the sensing matrix was constructed. The separation source signal was reconstructed to combine with the OMP algorithm in the frequency domain. Finally, the reconstructed time-domain signal was subjected to the fast Fourier transform for fault identification. The test bench was utilized to collect the composite fault signals of the sun gear and planetary gear wear of the RV reducer. The results show that the blind separation was effectively realized on the composite faults of the RV reducer. The RETE was used to identify the motion state of the RV reducer, when the time-frequency diagram was blurred, due to the variable speed condition. The SMF-DPC-OMP effectively completed the blind separation of composite faults when the number of fault sources was unknown. The SMF-DPC-OMP saved about 75% of the running time cost than before. A more concise spectrum was achieved to better suppress the fine side frequency and interference components. It is suitable for the composite fault diagnosis of the RV reducer in the articulated industrial robot. The finding can provide a strong reference for the fault feature extraction in the actual production.