## 3 Results and Discussion
transitions, minimizing abrupt changes in angular velocity and reducing the mechanical strain on the manipulator's joints. These findings highlight the importance of integrating digital twin technology into the development cycle, enabling iterative design and testing processes that optimize performance before deployment. The proposed control architecture and human-machine interface enhanced the overall system performance by enabling real-time monitoring, bidirectional communication, and the seamless integration of simulated and experimental data. By leveraging the digital twin, trajectory errors were minimized through iterative adjustments, which were validated under various operational conditions, including different loads and friction levels. This adaptability demonstrates the robustness of the system for industrial applications, where dynamic environments demand precise and reliable control mechanisms. The application of statistical tools, such as variance and mean comparisons, not only provided quantitative validation of the system's performance but also established a rigorous framework for future evaluations of robotic systems. These results contribute to the existing body of knowledge on digital twin technology, emphasizing its potential to improve the accuracy, efficiency, and adaptability of modern robotic systems. To further validate the real-time adaptability of the digital twin, controlled external disturbances were introduced during the manipulator's operation. These disturbances included applying small external forces to the joints to assess how the system compensates for mechanical perturbations and varying the manipulator's loading conditions to analyze its response under different operational constraints. In both cases, the system successfully adjusted the control signals sent to the actuators, allowing the manipulator to correct deviations and maintain its planned trajectory within acceptable error margins. These findings confirm the system's ability to dynamically respond to unforeseen interferences, beyond just compensating for mechanical inaccuracies or servo drive signal processing errors. The developed digital twin presents high potential for implementation in industrial environments, particularly in tasks that require the precision and advanced control of parallel manipulators. To improve the accuracy and adaptability of the proposed system, it is feasible to propose the incorporation of computer vision-based methodologies that provide real-time feedback on the position of both the manipulator and its digital twin. In particular, implementing Eye-to-Hand visual servo control would enhance target localization, reducing execution errors and improving the correlation between the ideal trajectory generated in the virtual environment and the trajectory executed by the physical system. This integration would be especially valuable in automated manufacturing processes, where precision and stability in manipulator control are critical factors for performance. Beyond trajectory optimization, the digital twin can also support quality control, deviation detection, and predictive maintenance by enabling the continuous real-time monitoring of the manipulator. Additionally, this system can serve as a training tool, allowing operators to safely simulate and test robotic operations without risks, thus facilitating the adoption of Industry 4.0 technologies and improving overall efficiency in production environments.