## 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  
In order to analyze the dynamic behavior of the robot/mannequin assembly, harmonic laws of motion of the form: 0.4 \(\times\) cos (1 \(\times\) time), with an amplitude of 45 degrees and the period of 6.3 s were defined for the drive motors of each module. The time variation graph for the law of motion of the motors performing the rehabilitation movements is presented in Figure 7. In MSC.ADAMS, the implemented law of motion is defined as MOTION_1 or MOTION_2 for the second module, and in Figure 7, a measurement of the angle from the motor joint has been made. These parameters that define the amplitude and period of the movement were chosen because the laws of motion that will be done in the numerical simulation must be similar to the movement recommended for rehabilitation prescribed by the physiotherapist. A dynamic simulation was performed for the situation when the robotic system is used by the virtual patient dummy and all three modules of the ASPIRE robot are active simultaneously (flexion/extension, abduction/adduction, pronation/supination). The simulation was performed for a period of 20 s. Figure 8 shows the extreme operating positions of the ASPIRE robot corresponding to the situation when the flexion/extension and abduction/adduction movements are active, indicating a combined movement. The trajectories described by the elbow and shoulder joints are observed, which are spatial (spherical) circular portions. Figure 6: ASPIRE robot modules. Figure 7: Law of motion imposed in ADAMS on robot motor joints. In the first phase, a dynamic simulation with the specified laws of motion, without taking into account the friction in the kinematic joints of the robot, was performed. The results obtained for this simulation, meaning the variations of the motor moment calculated by numerical simulation in ADAMS when simultaneously performing those three types of movement--flexion-extension, adduction-abduction and pronation-supination of the arm--are presented in Figure 9.  
Figure 8: Extreme operating positions of the ASPIRE robot corresponding to a combined flexion-extension and abduction-adduction movement. Figure 9: ADAMS simulation computed torque for: (**a**) the flexion-extension module; (**b**) the adduction-abduction module; (**c**) the pronation-supination module. It is observed that the maximum value of the actuation moment of the flexion/extension module reaches a maximum value of 125 Nm, and the minimum is 110 Nm. It is important to note that these results are obtained when all three modules are active simultaneously. For the adduction-abduction movement, the motor moment obtained by numerical simulation in ADAMS is presented in Figure 9a. It is observed that its amplitude is around 22 Nm. For the pronation-supination movement, the value calculated by numerical simulation in ADAMS is equal to 0.023 Nm (Figure 9c). The results of the dynamic simulation conclude that, for the movement performed by the flexion-extension motion module, a very high actuation moment is required, namely 125 Nm (Figure 9a). In this case, it is necessary to use worm gearboxes to amplify the torque of the electric drive motor. The gear ratio of the planetary gearbox must be chosen in accordance with the size of the resistive torque but also with the angular velocity required at the output. For the flexion-extension module mechanism, a worm gearbox gear ratio I = 1:45 was used. For the adduction-abduction module mechanism a planetary gearbox with gear ratio I = 1:100 is implemented, and for the pronation-supination mechanism a planetary gearbox with gear ration I = 1:11 is required. As the flexion/extension module requires the greatest moment of actuation, it is clear that this module will be the most structurally stressed.