# Analysis of Dynamic Behavior of ParReEx Robot Used in Upper Limb Rehabilitation
## 1 Introduction  
Although there has been an increasing emphasis on prevention in recent decades, strokes are one of the leading causes of permanent disability worldwide [1]. In recent decades, strokes have led to the disability and even death of a very large number of people; in recent years, the number of people affected annually is about 13 million [2]. Globally, the leading causes of death are ischemic heart disease, with an incidence of 14.8%, and stroke, with an incidence of 11.8% [3]. Recent studies show that the number of stroke cases is increasing. Taking into account the aging of the population worldwide, there are advanced fears regarding the increasingly limited capacity of European and global medical systems to meet patient care requirements [4]. It is estimated that in the near future, strokes will affect an upper limb in over 85% of cases [5], and the success rate for arm rehabilitation will be only 10% [6] due to the complexity of upper limb movement [7]. In less than 10 years, the annual medical cost per stroke will increase rapidly; for example, in the USA, it will be 2.5 times higher than it was in 2012 [8]. Currently, in developed countries, 3-4% of medical costs are allocated to strokes [9]. Physical rehabilitation is becoming less and less effective as each patient hasto work with a physical therapist [10], but the use of robotic exoskeletons allows for more effective therapy through repetitive movements and adaptive training [11; 12]. The use of rehabilitation technology and robotics optimizes the results, minimizes costs by conserving labour and maximizing progressive repetitions, and improves the outcome compared to the high costs of conventional therapy performed as one-on-one training with a professional therapist [13; 14; 15]. Numerous articles have been dedicated to the study of robotic structures used for upper limb rehabilitation. Robotic systems for upper limb rehabilitation are the subject of much research. Thus, the design and performance evaluation of the RUPERT exoskeleton for upper limbs is presented in [16]. An innovative robotic system with a spherical architecture is developed and presented in [17]. A parallel robotic system based on a spherical architecture, ASPIRE, was designed for three degrees-of-freedom (DOFs) shoulder rehabilitation, as described in this study. In [18], a study of torque monitoring is performed for the ASPIRE robotic system. Clinical trials based on the use of ASPIRE on post-stroke patients are presented. Further, design optimization is studied based on therapist feedback following clinical evaluation. A study of the ASPIRE robot for upper limb rehabilitation is presented in [19], where, with the help of ADAMS software, the dynamic analysis of the robotic system is performed. The study of hand joint movements is also presented in [20]. Classifications and analyses of these structures can be found in [21]. Over the past decade, many robotic devices have been designed to enhance the motor rehabilitation process. In [22; 23; 24; 25], the authors noted an improvement in quality of life and concluded that robot-assisted therapy is beneficial for recovering the motor functions of the upper limbs in patients with early-stage stroke. Neurorehabilitation therapy including task-oriented training with the ARMin exoskeleton robot can enhance improvement of motor function in a chronically impaired paretic arm after stroke more effectively than conventional therapy [23]. A hybrid exoskeleton named EFW Exo II is developed for the motor function rehabilitation of elbow, forearm and wrist, and the ranges of motion meet the rehabilitation demands of daily living [24]. For clinical trials, an acquisition data system based on wearable sensors was used; due to their advantages, these systems are often used in evaluating biomechanical human data [25; 26; 27; 28; 29; 30; 31]. Several robotic devices have been developed to rehabilitate the wrist joint, which, after the shoulder, is the second-most complex joint of the human upper limb.