# Analysis of Dynamic Behavior of ParReEx Robot Used in Upper Limb Rehabilitation
## 3 Dynamic Analysis in MSC.ADAMS of ParReEx-Wrist Robot  
Dynamic Analysis in MSC.ADAMS of ParReEx-Wrist Robot, Considering the Kinematic Elements as Rigid Solids without Considering Joint Friction  
Based on the structural scheme of the ParReEx robot, a virtual prototype is designed using Unigraphics NX software. The development of the virtual prototype is necessary from two aspects: it will be used to simulate the dynamic behavior of the robot, as well as for structural optimization with the finite element method. The development of the dynamic model in ADAMS involves the following steps:  
* Definition of the materials of the robot subassemblies. Robot element materials can be selected from the ADAMS database, or new materials can be defined by their properties. In this case, the materials of the component elements are defined in the database, and their mechanical properties are further explained. For each component element of the robot, we specify the material from which it is made. Thus, in the robot component, we have parts that are made of aluminum alloy with the following properties: density = 2470 kg/m\({}^{3}\), Young's Modulus = 7.17 \(\times\) 10\({}^{10}\) N/m\({}^{2}\) and Poisson's ratio = 0.33. The robot housing, the circular guide and the elements supporting the patient's hand are made of ABS. Acrylonitrile butadiene styrene, commonly known as ABS, is a polymer and opaque thermoplastic comprised of acrylonitrile, butadiene, and styrene. ABS is an incredibly versatile and durable plastic, making it an extremely popular material used in a variety of industries. The mechanical properties of this material are as follows: density = 1.15 \(\times\) 10\({}^{3}\) kg/m\({}^{3}\), Young's Modulus=1.6 \(\times\) 10\({}^{10}\) N/m\({}^{2}\) and Poisson's ratio = 0.340. * Kinematic joints related to the robot structure are defined. In the structure of the robot, there are rotational joints and upper rolling joints. In Figure 4, the kinematic joints defined in the ADAMS dynamic model are detailed, namely:  
* Joint A and Joint B are the rotational kinematic joints of the circular guide (4) with the robot housing. Joint A defines Motion 1, the law of motion for radial-ulnar deviation;
* Joint C is a rotational joint of the Hooke coupling structure;
* Joint D is a rotational joint of the level pinion with the system housing. This joint specifies Motion 2, the motion law for hand joint flexion-extension;
* Kinematic Joints R\({}_{1}\) and R\({}_{2}\), are superior joints that provide contact for a point on a curve. Special attention has been paid to the correct definition of the rolling joints between the circular guide and the slide. For this purpose, we have chosen to define a point-on-curve upper joint. In this case, for Joint R\({}_{1}\) we have specified the contact between the arc at the top of the guide and a point belonging to the slide. For Joint R\({}_{2}\), we have specified the contact between the arc of the circle at the bottom of the guide and a point belonging to the slide. These joints assure non-detaching contact between the circular guide (an arc of a circle) and the slide. All other kinematic joints are defined according to the structural schematic shown in Figure 1, as detailed in Figure 4 on the ADAMS dynamic model. * Another important step in the completion of the dynamic model is the definition of the toothed belt drive from the drive that performs ulnar-radial motion. For this purpose, we used the ADAMS machinery facility, which allows the definition of a toothed belt drive. * Another step in finalizing the ParReEx robot model is to define the bevel gear. For this purpose, we used the existing facility in Adams machinery to define gear drives. All the parameters required to define a level gear can be set in Table 1, namely: axis of rotation, number of teeth, face width, back cone distance, pitch angle, pitch apex, bore radius, outer module, addendum and dedendum factor.