Although the use of articulated robots and AGVs is common in many industrial sectors such as automotive or aeronautics, the use of mobile manipulators is not widespread nowadays. Even so, the majority of applications separate the navigation and manipulation tasks, avoiding simultaneous movements of the platform and arm. The capability to use mobile manipulators to perform operations on moving objects would open the door to new applications such as the riveting or screwing of parts transported by conveyor belts or AGVs. This paper presents a novel position-based visual servoing (PBVS) architecture for mobile manipulators for precise industrial operations on moving parts. The proposed architecture includes a state machine to guide the process through the different phases of the task to ensure its correct execution. The approach has been validated in an industrial environment for screw-fastening operations, obtaining promising results and metrics.