The development of exoskeletons for upper limb rehabilitation and assistance has garnered significant attention over the past decade, propelled by advancements in robotics and technologies such as digital twins. This paper presents a comprehensive kinematic and dynamic model, along with the formulation and implementation of a computed torque control (CTC) strategy for an upper-limb exoskeleton featuring three degrees of freedom. This exoskeleton was designed to replicate shoulder and elbow flexion-extension movements as well as forearm pronation and supination. A digital model was created using SolidWorks and subsequently validated in MATLAB’s Simscape multibody environment. Kinematic analysis was formalized using the Denavit-Hartenberg convention, and the workspace and manipulability indices were derived from the Jacobian. Additionally, a controller was developed based on the dynamic model, and its stability was assessed using Lyapunov theory. The simulation results demonstrate that CTC control offers robustness and ensures global stability, even in the presence of parametric disturbances. This approach lays a solid foundation for progressing towards a complete digital twin and its future application in assisted rehabilitation environments.