Edge computing refers to the use of an open platform on the side close to the object or data source to integrate network, computing, storage, and core application functions to provide the latest nearby services. With the development of edge computing, the cost of data acquisition has been reduced, and the efficiency has been improved. However, at present, there is no in-depth research on edge computing for robot arm behavior recognition. This paper aims to study the data acquisition and processing methods of robotic arm behavior recognition through edge computing technology. A gesture recognition method based on Cauchy distribution and grey correlation threshold is proposed, which improves the efficiency of data processing and has great research significance. In edge computing, the use of Cauchy distribution processing is more impressive; compared with empirical distribution, the algorithm optimization can reach at least 10%. Experiments show that the static gesture recognition method used in this paper is simple and high in recognition and has good robustness and the accuracy rate can basically reach more than 90%. In the case of different threshold values, when the gray correlation threshold is 0.75, the MAE value reaches the minimum value, which means that the gap between the predicted score and the actual score is the smallest, which means that the predicted result is accurate, which can prove that the recommendation of the algorithm has relatively superior performance.