Robotic arm operation based on human-machine collaboration in manufacturing scenarios for the Internet of Things (IoT) has become an important research direction, especially in three-dimensional (3-D) scenarios that require high precision and flexible operation. However, owing to the complexity of operating robotic arms in 3-D scenarios, it is challenging for humans to perform tasks in pilot mode, leading to unnatural human-machine interactions. In this study, an embodied visual evoked potential (E-VEP) paradigm is proposed that can be used to control robotic arms in manufacturing scenarios in embodier mode. In addition, an incremental self-learning intention decoding (ISLID) algorithm is established to address the temporal variability in electroencephalography (EEG) signals. A brain-controlled robotic arm system was developed on the basis of the E-VEP paradigm and the ISLID algorithm. Online free grasping experiments revealed that the task time cost, output delay, and intention output ratio of the proposed system were 89.04 s, 2.22 s, and 46.59%, respectively. Compared with those of brain-controlled robotic arm systems based on the dynamic visual evoked potential (D-VEP) and SSVEP paradigms, the system based on the E-VEP paradigm achieved reductions in the average task time cost of 13.44% and 24.54%, respectively, and reductions in the average intention output ratio of 17.01% and 26.65%, respectively. The proposed brain-controlled robotic arm system holds significant application value in intelligent manufacturing scenarios for the IoT, advancing the integration of brain-machine interfaces and IoT technologies. The video (https://youtu.be/WtRHew4WGyo) demonstrates the utilization process of the proposed brain-controlled robotic arm.