# Analysis of Dynamic Behavior of ParReEx Robot Used in Upper Limb Rehabilitation
## 1 Introduction
The authors of [32] review the main wrist rehabilitation robots developed recently in terms of mechanical design and aspects of control, and highlight aspects of experimental tests of these robots on patients with neurological disorders. [PERSON] et al. studied a wrist rehabilitation robot that offers three DOFs [33], which, mounted on the accompanying robot, MIT-MANUS [34; 35], has become a very suitable tool for the rehabilitation of the shoulders and elbow. Another wrist robot [36] with three active DOFs was developed with a similar structure and an additional passive prismatic joint. RiceWrist [37], as an electrically operated forearm-wrist exoskeleton, uses a serial RRR manipulator and cable transmissions to rehabilitate the wrist and radio-ulnar joints. Robots presented in [38; 39] allow the rehabilitation of two movements: forearm supination/pronation and wrist flexion/extension, while in [40], the human wrist has been simplified to a single DOF--namely flexion/extension. A parallel wrist rehabilitation robot driven by two pneumatic actuators is developed in [41] to rehabilitate two DOFs: flexion/extension and radial/ulnar deviation. Patient safety is a critical milestone in the development of robotic systems for medical applications to avoid any unwanted damage. In this case, it can be achieved by implementing a dynamic model in the control system [42; 43] using various principles such as: the Lagrange-Euler formalism, the principle of virtual work [44] or the Newton-Euler equations [45; 46; 47]. ADAMS View, software designed for the analysis of mobile systems dynamics, with an increased accuracy of kinematic and dynamic results obtained from numerical simulationshas been used in several studies of robotic systems for rehabilitation of human movements, such as exoskeletons or flexible robotic structures for minimally invasive surgery [19; 27; 48; 49]. For structural optimization of a kinematic element, one of the most powerful software programs is ANSYS. In [19], we presented finite element analysis of a kinematic element in the ASPIRE robot structure. The aim of this study is to analyze from a kinematic, dynamic and experimental point of view a robotic system designed for the rehabilitation of the human wrist joint of post-stroke survivors. Numerical simulations are performed for the robot mounted on the wrist of a virtual patient. For validation of the dynamic model built in ADAMS, the results obtained by numerical simulation are compared with those obtained experimentally. Three distinct situations will be studied:  
* The kinematic elements are considered as rigid bodies, and the friction in the kinematic joints is not considered;
* The kinematic elements are considered as rigid bodies, and the friction in the robot joints is considered;
* The kinematic elements are considered as flexible bodies, and the friction in the robot joints is considered. The paper is structured as follows: after the introduction, a functional constructive description of the ParReEx robot for wrist rehabilitation is presented. Dynamic analysis is presented in ADAMS for the three considered operating hypotheses. Then, structural optimization is performed for the circular guidance of the ParReEx robot. At the end, experimental results, discussions, and conclusions are presented.