The paper proposes a novel method for an accurate and unobtrusive reconstruction of the upper-limb kinematics of stroke patients during robot-aided rehabilitation tasks with end-effector machines. The method is based on a robust analytic procedure for inverse kinematics that simply uses, in addition to hand pose data provided by the robot, upper arm acceleration measurements for computing a constraint on elbow position; it is exploited for task space augmentation. The proposed method can enable in-depth comprehension of planning strategy of stroke patients in the joint space and, consequently, allow developing therapies tailored for their residual motor capabilities. The experimental validation has a twofold purpose: (1) a comparative analysis with an optoelectronic motion capturing system is used to assess the method capability to reconstruct joint motion; (2) the application of the method to healthy and stroke subjects during circle-drawing tasks with InMotion2 robot is used to evaluate its efficacy in discriminating stroke from healthy behavior. The experimental results have shown that arm angles are reconstructed with a RMSE of 8.3 × 10−3 rad. Moreover, the comparison between healthy and stroke subjects has revealed different features in the joint space in terms of mean values and standard deviations, which also allow assessing inter- and intra-subject variability. The findings of this study contribute to the investigation of motor performance in the joint space and Cartesian space of stroke patients undergoing robot-aided therapy, thus allowing: (1) evaluating the outcomes of the therapeutic approach, (2) re-planning the robotic treatment based on patient needs, and (3) understanding pathology-related motor strategies.