# Design Approaches of an Exoskeleton for Human Neuromotor Rehabilitation
## 4 Dynamic Analysis of the Proposed Exoskeleton
### Exoskeleton Virtual Prototyping with the Aid of MSC Adams Software  
By considering the kinematic scheme from Figure 8, an exoskeleton virtual prototype was built with the aid of SolidWorks program. This was a parameterized model and it was imported into the MSC Adams software environment. For this model were defined the mass properties and material characteristics (longitudinal elasticity module: E = 7.1 \(\times\) 10\({}^{10}\) Pa, density: 2770 kg/m\({}^{3}\) and Poisson ratio: 0.33), respectively, as well as kinematic links mobile reference systems and 15 kinematic joints. The virtual prototyping was performed in accordance with specific instructions provided by [32]. Moreover, 6 motor joints for hips, knees, and ankles were identified. By knowing the motion angle variations for hips, knees, and ankle joints, the drive joints angle variation laws \(\varphi_{01}\) and \(\varphi_{07}\) were obtained, according to Figure 8. These joints, as in the case of the mathematical model, actuate these two actuation mechanisms for the ankle and for knee joints, respectively. The angle variations for hips, knees, and ankle joints were established for a case study, through experimental analysis, as was shown in Figures 3-5. The imported exoskeleton prototype with proper revolute joints is shown in Figure 9. These drive joints, as in the case of the mathematical model, will actuate two mechanisms, one for the knee joint and other for ankle joint. Additionally, the contact force between ground and foot and the patient weight were introduced through the parameterized mannequin weighing 61.7 kg. Thus, an inverse dynamic analysis was processed with the aid of MSC Adams software, in order to obtain the proper connection forces variation over time of the analyzed kinematic joints. The obtained results were materialized through diagrams presented in a comparative analysis between computed mathematical models and the ones obtained through numerical simulations with MSC Adams software. For the proposed exoskeleton prototype, a parameterized mannequin was introduced, with anthropometric data similar to the healthy human subject used in the experimental analysis section. Thus, four sequences during virtual simulations processed under the MSC Adams environment are presented in Figure 10.  
In Figure 11, the connection force component in X-axis of the knee joint is represented, which corresponds to a complete gait sequence. This component has a high value when the analyzed models start walking and this reaches a value of 23. This component has a high value when the analyzed models start walking and this reaches a value of 23.567 Newton. This value was obtained when the contact between ground and foot occurs, for both analysed models (mathematical model and Adams model). It can be observed that the obtained trajectories for both models are appropriate, recording values between \(-10\) Newton and \(11.875\) Newton. The time interval also was appropriate, namely \(0\) to \(1.425\) s, respectively. An error of \(2.25\%\) was obtained, which is quite small. Figure 9: Exoskeleton parametrized virtual model with proper joints prepared for virtual simulations in a dynamic mode. The desired results, in order to validate this model, were given by the connection forces' variations over time; a comparative analysis can be seen in Figures 11-16. Figure 11: Connection forces component on x-axis for knee joint vs. time (without ground contact). Figure 10: A snapshot during virtual simulations in dynamic mode for a complete gait. Figure 14: Connection forces component on y-axis for ankle joint vs. time (without ground contact). Figure 13: Connection forces component on x-axis for ankle joint vs. time (without ground contact). Figure 15: Connection forces component on x-axis for knee joint vs. time (with ground contact). In the case of the connection force component on y-axis, for the same joint, high values can be observed in Figure 12 when gait starts and at the end of a complete gait.