In the era of Industry 4.0/5.0, collaborative robots (cobots) play a pivotal role in transforming manufacturing processes by enabling human-robot collaboration and adaptability. However, realizing the full potential of cobots necessitates advanced digital technologies. This paper introduces a digital twin framework specifically tailored for collaborative robots within the context of Industry 4.0 and 5.0. The framework leverages digital twin technology to create a virtual representation of physical cobots, enabling real-time monitoring and optimization of their performance. Emphasizing data flow, communication protocols, and visualization tools, the framework facilitates seamless integration of cobots into smart manufacturing environments. The digital twin application is implemented in the FlexSim software and it has been exploited to perform dynamic task allocation among UR3e cobots. Through the use case, the paper demonstrates the effectiveness and versatility of the proposed framework, offering a roadmap for harnessing the potential of digital twin for cobots management.