## 4 Dynamic Analysis of the ASPIRE Robot Using MSC.ADAMS Software
### Dynamic Analysis in MSC.ADAMS of the Robot, Considering the Kinematic Elements as Rigid Solids
Thus, the reaction resulting from coupling B shows an increase from the maximum value of 347 N to the value of 370 N, meaning an increase of 6.62%. The steeper change of the parameter's variation laws is noticed at the moment of the transition from the flexion movement to the extension for the module that realizes this movement of the arm from adduction to abduction. Dynamic Analysis in MSC_ADAMS of the Robot, Considering the Kinematic Elements as Deformable Solids and Joint Friction  
In the third stage of the simulation, the deformability of the kinematic elements of the ASPIRE robot are also considered (flexibility for the two modules of the ASPIRE robot, the flexion/extension and the adduction/abduction modules). The procedure for considering the kinematic elements as deformable solids involves their discretization in finite elements, the calculation of their own modes of vibrations, as well as the calculation of specific deformations and mechanical stresses. The second stage consists of establishing the connection points of the discretized element through kinematic connections with the other elements. Figure 17 shows a construction aspect of a deformable kinematic element in MSC_ADAMS. Figure 6:3 Connecting forces in the rotation coupling A of the adduction/abduction module, calculated assuming friction: (**a**) in the x direction; (**b**) in the y direction; (**c**) in the z direction; and (**d**) the resultant. Figure 6:4 Connecting forces in coupling B for the rotation of the flexion/extension module calculated assuming friction: (**a**) in the x direction; (**b**) in the y direction; (**c**) in the z direction; and (**d**) the resultant. Figure 6:5 Defining a deformable element in MSC.ADAMS. The purpose of this simulation is to obtain results of the dynamic operating parameters of the ASPIRE robot in real operating conditions. Through the dynamic analysis, considering also the flexibility of the kinematic elements, the friction from the kinematic couplings, as well as the external loads, results regarding the real variation of the dynamic parameters have been obtained. Thus, in this stage results will be presented, such as the specific deformation of the robot elements, deformation velocities and accelerations, own frequencies and normal modes of vibration, connection forces in the kinematic couplings and actuation moments. A first category of results of interest is represented by the moments of actuation of the flexion/extension module, as well as the adduction/abduction module. For this simulation, obviously we used the same loads, given by the weight of the upper limb, as well as the same laws of motion implemented in the motor torques. The dynamic simulation is performed only for a period of 10 s due to the complexity of the model. Thus, for this phase of the dynamic simulation, in Figure 18, the actuation moments corresponding to the flexion/extension and abduction adduction modules are presented. There are very abrupt variations of the dynamic parameters at the beginning of the robot's movement, which disappear after a second of operation. These aspects are also manifested in the real operation only in the initial phase of the robot's operation, so it does not affect the proper functioning of the robot and especially the patient. The other parameters of interest for the simulation in the dynamic regime, considering the deformability of the elements, are the translational deformations of some characteristic points of the ASPIRE robot kinematic elements. The variation graphs of the translational deformations for the centre of mass of the flexion/extension module are shown in Figure 6:6 From these graphs, it is found that the centre of mass of the flexion/extension module registers larger deformations in the first two seconds of operation. As expected, the largest deformation is recorded along the X and Z axes, because the loading produced by the movement of the robot takes place along these axes. The maximum value of the translational deformation of the marker detailed in Figure 19 reaches 0.08 mm.