## 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
For the flexion/extension module, as well as the adduction/abduction one, the connecting forces calculated from the couplings B and C, because these forces will be used later to perform the structural analysis with finite elements, are presented. For a good understanding and interpretation of the obtained results, in the case of the connection forces from the kinematic couplings of the robot's modules, Figure 10 presents the orientation of the local reference axis systems attached to the kinematic couplings of the ASPIRE robot in relation to the calculated components of the connecting forces. Figure 10: Positioning of the axes of the kinematic couplings of the ASPIRE robot. Figure 11a-c shows the time variation graphs for the components of the connecting force in the coupling A in relation to the local reference system attached to this coupling, oriented as in Figure 10. Through this rotation coupling, the module that performs the adduction/abduction movement is connected to the base of the robot with the help of a bearing. By means of an electric motor and a transmission with a worm gearbox, this module is operated and controlled. As previously detailed, the mass of this module is 24.3 kg, to which is added a part of the mass of the lower limb. The analysis of these graphs shows that the maximum value recorded along the X axis of the local reference system in coupling A is \(-\)34 N (Figure 11a). The component along the Y axis of the connecting force in coupling A reaches a maximum value of 23 N, and the minimum value is equal to 2.5 N (Figure 11b). Since the weight of 243 N of the adduction/abduction module is oriented along the Z axis, the component along this axis of the connecting force has the highest value, reaching \(-\)271 N (Figure 11c). The variation in the negative range of this component is explained by the orientation of the Z axis of the local reference system, which is oriented downwards, and the reaction transmitted to the base is oriented in the opposite direction. The connecting force in coupling A along the Z axis has an additional value of 31 N; this is as compared to the weight of this module of 243 N, which comes from the load given by the support of the patient's arm and from the interaction with the flexion/extension module. The resulting value of the connecting force in this coupling has a maximum of 274 N and a minimum of 263 N, according to Figure 11d. Figure 12 shows the variation laws of the connecting forces in the rotation coupling B, which is defined in ADAMS, between the flexion-extension module and the base. Quite high values are observed of 347 N for the vertical component of the connecting force, which is the one along the X axis of the local reference system from the coupling B (Figure 12a). The reaction along the Y axis has much lower values, reaching a maximum of 57 N (Figure 12b). The connecting force along the Z axis has much lower values, with a maximum of 10 N. This occurs due to the friction interaction between the flexion/extension module and slide 3, as well as due to the opposite resistance of the patient, in this case  
Figure 11: Connecting forces in the rotation coupling A connected to the base of the adduction/abduction module: (**a**) in the x direction; (**b**) in the y direction; (**c**) in the z direction; and (**d**) the resultant. only by the force of upper limb weight. The fact that the highest value is recorded by the component along the X axis of the connecting force in the coupling B is explicable, because of the weight of the flexion/extension module, equal to 175 N, to which is added both the weight of the upper limb and the interaction between the patient's upper arm and the robot module (opposite resistance of the upper limb), such that it acts in the opposite direction of the X axis of the local reference system.