This article proposes an automatic high-precision detection method for structure parameters of catenary cantilever devices (SPCCDs) using 3-D point cloud data. The steps of the proposed detection method are: 1) segmenting and recognizing the components of the catenary cantilever devices, 2) extracting the detection plane and backbone component axis of catenary cantilever devices, and 3) detecting the SPCCD. The effective segmentation of components is critical for structure parameter detection. A point cloud segmentation and recognition method based on three-dimensional convolutional neural networks (3-D CNNs) is introduced to determine the different components of the catenary cantilever devices. Compared with traditional unsupervised clustering procedures for point cloud segmentation, the proposed method can improve the segmentation accuracy, does not require complex tuning procedures of parameters, and improves robustness and stability. Additionally, the segmentation method defines a recognition function, facilitating the analysis of the structural relationship between objects. Furthermore, we proposed an improved projection random sample consensus (RANSAC) method, which can effectively divide the detection plane of catenary cantilever devices to solve the multicantilever device occlusion problem. With RANSAC, it is also possible to precisely extract the backbone component axis and enhance parameter detection accuracy. The experimental results show that the structure angle and steady arm slope's error accuracy can achieve 0.1029° and 1.19%, respectively, which indicates the proposed approach can precisely detect the SPCCD.