The study of the rehabilitation of the upper arm is an important issue in the Rehabilitation field due to: (i) the rapid growth of the older population [1, 2] and (ii) traumatic brain injury [3]. More specifically, the increase of the elderly at 2.4% per year and the increase in the probability of a stroke with age; in fact, this pathology is the first cause of invalidity in Europe where it occurs at a rate 60% higher than in the US. Moreover, it is necessary to take into account other degenerative pathologies, such as Parkinson’s. MIT-MANUS is the robotic system developed at the MIT Lab to rehabilitate the upper limb by means of exercises which guide or perturb the spontaneous movement of the brain-injured subject [4]. Its disadvantages are: (i) the loss of reality, because the patient reaches a visual target with the robot handle, which does not correspond to a 3D movement, and, especially, (ii) the high cost. The study of reaching is divided in two branches: reaching towards a still or a moving target. In the first case, it is preferable to explore the working space [5] to investigate the possible residual movements [6] and to recuperate the functions of the shoulder joint. Instead, as regards the moving target, there has been much research done because significant performance improvements were obtained in pathological patients [7]. So, the use of a ball projection machine is proposed [8]; it has the advantage to allow 3D trajectories but many disadvantages: (i) control only on initial impulse; (ii) not-reproducibility of trajectory; and (iii) risk in using with non-collaborative subjects. Instead, a system with magnetic coupling to move the object in 2D is proposed [7]; it allows the production of many trajectories and the control of dynamic parameters. The coordination between elbow and shoulder joints has been studied in the unconstrained reaching towards a still target [9].

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