In the contemporary era of information technology and Industry 4.0, digital twin technology is garnering widespread attention and experiencing extensive application worldwide. In the field of industrial manufacturing, the adoption of digital twins has significantly enhanced the efficiency of product design and elevated the intelligence level of production processes and service quality. Particularly in areas such as intelligent manufacturing, intelligent operation and maintenance and predictive maintenance, digital twin technology enables comprehensive lifecycle management of complex mechanical systems, which includes virtual debugging in the design stage, condition monitoring throughout the operational stage, fault diagnosis, and optimization process. We explore the utilization of digital twin technology for material gripping and transportation tasks performed by a robotic gripper in the inspection room of an assembly line and conducts comprehensive investigation on simulation modeling and virtual reality mapping. The focal point of the study lies in the proposed strategy of the virtual-reality mapping in the robot system, which ensures the consistency between the virtual model and the state of the physical equipment by real-time data acquisition and synchronous updating, so that the seamless integration of virtual and real can be achieved. The benefits of applying digital twin technology in real-time monitoring, remote manipulation, and fault prediction of the robot's operational status are illustrated with a practical case study.