Collaborative robots have found a significant market in intelligent assembly, with human–robot collaboration being the primary application and research focus. Currently, serial robots are the main type of collaborative robot used, offering a large workspace and high dexterity. However, in certain industrial applications that require high precision, frequency response, and load capacity, particularly in industrial assembly and processing scenarios, traditional serial collaborative robots may not be capable of performing the specified tasks. Therefore, this paper introduces the concept of parallel collaborative robots. Under the framework of parallel collaborative robots, a basic unit of parallel collaboration is constructed. This unit is then used to cooperate and combine operations, resulting in a new parallel dual-collaboration operation mode of ‘machine-machine collaboration’ and ‘human–machine collaboration’. The concept of parallel collaborative robots can provide new robotic equipment for precision assembly operations. This includes exploring and expanding new operation modes to achieve high precision, speed, efficiency, reliability, stability, and lifespan in various industrial scenarios. This paper presents a comprehensive introduction to a parallel collaborative robot system. It covers the selection of the basic parallel unit configuration, the union and combination of basic units based on GF set theory, the kinematics of a single machine, the kinematics of the entire machine, system design, practical application cases, and more. The paper proposes a new exploration and expansion of collaborative robots through the concept and design theory of parallel collaborative robots. This provides a reference for new design and composition methods of collaborative robots.