Social robots with the ability to empathize with users have the potential to enhance human-machine communication significantly. This article presents the design and construction of a robotic prototype capable of recognizing and imitating user emotions through a facial expression recognition algorithm. The aim is to foster empathy during interaction, making the system applicable to future research in fields such as healthcare, where social robots can support emotional identification and recognition particularly in individuals with cognitive disabilities. In this population, these skills are often impaired. The development methodology of the prototype was structured into three stages: planning, design, and implementation. The resulting robot can recognize five basic emotions: sadness, neutrality, anger, and surprise and imitate them using animated facial gestures reinforced by joint movements and facial tracking to enhance expressiveness. Among the key findings, the emotion recognition algorithm achieved high precision and specificity, with values of 86% and 87%, respectively. However, other performance metrics, such as accuracy and sensitivity, reached only 48%, highlighting areas for future improvement.