Implementing the Mexican Sign Language (LSM) system presents several challenges. One of the primary issues is ensuring the accuracy of the motion capture data, as even slight deviations can lead to misinterpretations. Additionally, the system must handle the vast variability in individual signing styles and regional sign language variations, which requires extensive and diverse training data. In the first phase, the motion capture system must collect data on the gestures executed by LSM users, using cameras to monitor hand and finger movements and sensors that record the position and movements of the forearms and hands. The second phase involves the real-time comparison of an individual's signs in front of a camera with the meanings of the signs stored in the repository. A pattern recognition algorithm, supported by machine learning techniques, identifies specific motion capture system data patterns. In the third phase, the results are evaluated to generate a text translated from sign language to natural language. A successful model promises a significant impact on the hearing-impaired community, facilitating communication and improving access to services. This computational approach has the potential to positively transform the lives of people with hearing disabilities by providing them with a more effective avenue for communication and improving their access to essential services.