Therapeutic exercises play an important role in physical therapy and rehabilitation. The use of robots has been increasing day by day in the practice of therapeutic exercises. This study aims to design and control a novel robotic platform named DIAGNOBOT for diagnosis and treatment (therapeutic exercise). It has three 1-degree-of-freedom robotic manipulators and a single grasping force measurement unit. It is able to perform flexion-extension and ulnar-radial deviation movements for the wrist and pronation-supination movement for the forearm. The platform has a modular and compact structure and is capable of treating two patients concurrently. In order to control the DIAGNOBOT, an impedance control-based controller was developed for force control, which was required for the exercises, as well as a proportional-integral-derivative controller for position control. To model the resistive exercise, an angle-dependent impedance control method different from traditional methods has been proposed. Experiments were made on five healthy subjects and it has been demonstrated that the proposed robotic platform and its controller can perform therapeutic exercises.