Analytical model of modular upper limb rehabilitation

This article presents a modular, reconfigurable robotic system for upper-limb rehabilitation that supports customizable therapy of the wrist, elbow, and shoulder – individually or in coordinated multi-joint modes. Unlike fixed-structure devices, the design features adjustable link lengths and a symmetric architecture that accommodates both left and right limbs and a wide range of patient anatomies. The current paper develops complete kinematic and dynamic models that include nonlinear inertial, Coriolis, and gravitational effects and integrates these models with real-time torque- and force-control strategies to achieve precise, safe motion tracking. The modular hardware and control stack facilitate instantaneous reconfiguration of the workspace, impedance, and safety limits to align with patient-specific protocols and progression. This research paper simulates the approach in detailed numerical modeling that demonstrates the robot’s kinematic reachability, dynamic controllability, and the effectiveness of fault-tolerant reconfiguration strategies under representative disturbance scenarios. Finally, the current analyses discuss practical considerations for implementation, friction and contact modeling – and outline how the system can accelerate translation for clinical trials. This work mathematically provides a practical, model-based platform for patient-tailored rehabilitation robotics and a foundation for further research in adaptive control and assistive therapy technologies.