Due to the advantages of high durability, great repeatability and task orientation, the upper extremity rehabilitation robots have become a gospel for the rehabilitation treatment of stroke patients. The evaluation system for the comfort performance of rehabilitation robots has always been a research hotspot, and how to calculate the human-robot interaction forces is a challenge for the comfort evaluation. In this article, a four degrees of freedom (4-DOFs) upper extremity robot mechanism that is kinematically compatible with the upper limb is presented. Then, taking this mechanism as the research object, an algorithm for estimating human-robot interaction forces is addressed based on Newton-Euler dynamic. Subsequently, a prototype of the proposed robot is developed, and a comparison experiment of interaction forces is carried out on the prototype. The comparative experimental outcomes indicate that the presented algorithm for calculating the human-robot interaction forces is feasible. The findings of this paper provide a prerequisite for the evaluation of the robot comfort, which is of great practical significance.