## 3 Results and Discussion
The complete time evolution of the muscles' wrapping on the cylinder is available in Supplementary Materials--Video S2. A first quantitative comparison in the framework of the kinematical analysis is shown in Figure 12 on the muscles' fibre length \(l_{m}\), which also accounts for the muscle wrapping. Figure 11: Elbow wrapping in the (**a**) first and (**b**) the last time instants. Figure 12: Muscles’ fiber lengths comparison: (**a**) Matlab (**a**) and (**b**) OpenSim. Given that the comparison is satisfactory, the unique noticeable difference is related to the long biceps fibre length, probably due to a different wrapping algorithm used by the OpenSim software. After the kinematical analysis, the results of the inverse dynamics are shown in the Figure 13, in which the comparison between OpenSim and Matlab is made on the driving forces (rheonomic Lagrange multipliers \(\lambda_{r}\)). The inverse dynamics outputs result in a very satisfactory match between the Matlab model and the OpenSim software. The tool \"Static Optimization\" in OpenSim does not take into account the muscle passive force and allows choosing between the physiological criterion by using the muscle's force-length-velocity relationships or not. In the latter option the muscular activation \(a\) is intended as the ratio between the muscle force \(F_{m}\) and the maximum isometric force \(F_{0}\), bounded between 0 and 1. In the configuration of non-physiological criterion, the comparison on the muscles' activation is shown, respectively, in Figure 14. The comparison of the muscle forces is not shown because in this case the forces are proportional to the activations. The evaluated activations \(a\) calculated with the Matlab model are slightly underestimated with respect to the ones evaluated by OpenSim, which, moreover, show some discontinuities. The results obtained with the physiological criterion but not taking into account the passive muscle forces are shown in Figure 15, in terms of muscle activations \(a\), and in Figure 16, in terms of muscle forces \(F_{m}\). In this configuration there are small underestimations and overestimations in different parts of the time period and the OpenSim software returns some discontinuities, regarding both the activations and the muscle forces. Figure 13: Inverse dynamics comparison: (**a**) Matlab and (**b**) OpenSim. Figure 8:0 Muscles’ activations with non-physiological criterion and no passive forces: (**a**) Matlab and (**b**) OpenSim. Figure 8:1 Muscles’ activations with physiological criterion and no passive forces: (**a**) Matlab and (**b**) OpenSim. The \"Computed Muscle Control\" tool in OpenSim [36] allows evaluating the muscle activations, also considering the passive muscle forces, by calculating through PID controllers the muscle actions necessary to obtain the minimum difference between the trajectories of the degrees of freedom simulated with the forward dynamics and the ones known by inverse kinematics. The comparison results regarding the muscle activation \(a\) and the muscle forces \(F_{m}\) are shown respectively in Figure 17 and in Figure 8:2 In this last configuration, which includes all the analysed phenomena, despite the good qualitative match between the Matlab model and the OpenSim software, there are some discrepancies, probably due to the different approaches with respect to static optimization. While the muscle activations are underestimated, the muscle forces seems to be more similar to each other, except for the first instants of the time period discussed. Another interesting result is obtained regarding the residual actuators \(\lambda_{res}\) (which are the rheonomic Lagrange multipliers \(\lambda_{r}\) of Equation (33)), also provided in the OpenSim tools, in this configuration. With reference to Figure 19, the residual actuators show a similar behaviour, both quantitively and qualitatively.