In order to enhance the performance of rehabilitation robots, it is imperative to know both force and motion caused by the interaction between user and robot. However, common direct measurement of both signals through force and motion sensors not only increases the complexity of the system but also impedes affordability of the system. As an alternative of the direct measurement, in this work, we present new force and motion estimators for the proper control of the upper-limb rehabilitation Universal Haptic Pantograph (UHP) robot. The estimators are based on the kinematic and dynamic model of the UHP and the use of signals measured by means of common low-cost sensors. In order to demonstrate the effectiveness of the estimators, several experimental tests were carried out. The force and impedance control of the UHP was implemented first by directly measuring the interaction force using accurate extra sensors and the robot performance was compared to the case where the proposed estimators replace the direct measured values. The experimental results reveal that the controller based on the estimators has similar performance to that using direct measurement (less than 1 N difference in root mean square error between two cases), indicating that the proposed force and motion estimators can facilitate implementation of interactive controller for the UHP in robotmediated rehabilitation trainings.