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Therapist shortages make home-based rehabilitation an essential component of post-stroke care, yet patients often exhibit reduced adherence when functional gains are difficult to quantify and interpret. This study presents a cloud-enabled assessment framework centered on a dynamic reaching task for upper-limb rehabilitation in individuals with mild stroke. The proposed system combines wearable sensing and Internet of Things (IoT) connectivity to stream kinematic data to the cloud for near real-time analysis, and integrates a force-feedback rehabilitation robot to deliver motion guidance during training. The pipeline proceeds in three stages. First, smoothness-related kinematic descriptors are extracted and fed into a deep multi-class classifier to discriminate the affected side (left, right, or healthy). Second, movement quality is modeled using a Gaussian Mixture Model (GMM) trained on IoT-acquired trajectories to quantify performance via probabilistic similarity. Third, a calibrated scoring function transforms GMM log-likelihood into a normalized 0–1 quality index, producing visual reports that support interpretable feedback for patients and therapists. The framework is validated using motion data collected from stroke patients at Taipei Veterans General Hospital. Experimental results demonstrate that the neural network multi-classifier achieved an F1-score of 0.95. Incorporating robot-derived interaction signals further improved classification performance by approximately 5%. For movement quality assessment, the derived scores showed a significant positive correlation (Pearson correlation = 0.632, p = 0.02) with therapist-defined gold reference standards for right-affected patients. Additionally, integrating robot force-feedback signals and AIoT-enabled dynamic streams improved score accuracy by 8% and score responsiveness by 10%. These quantitative outcomes substantiate the efficacy of combining IoT-driven sensing and robot-assisted training for objective, interpretable, and remotely deployable motor assessment.