## 3 Results and Discussions
Additionally, time is saved in the manufacturing process, thanks to the 3D-printing Fused Deposition Modeling (FDM) technology used. The subsequent trajectory curves, shown in Figure 6, were obtained for subjects 1, 2, and 3 of the first and second DOFs after applying the parametric and kinematic models. On these plots, the blue line represents the theoretical trajectory described by the finger's tip. At the same time, the red dots are the experimental curves of the finger obtained using the MOCAP system. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Exp. Val. (mm)**} & \multicolumn{2}{c}{**Theor. Val. (mm)**} & \multicolumn{2}{c}{**Abs. Err. (mm)**} & \multicolumn{2}{c}{**Rel. Err. (\%)**} \\ \hline
**Phalanges** & **Dist.** & **Mid.** & **Prox.** & **Mid.** & **Prox.** & **Mid.** & **Prox.** & **Mid.** & **Prox.** \\ \hline Subj. 1 & 17 & 22.5 & 42 & 23.8 & 42.5 & \(-\)1.3 & \(-\)0.5 & \(-\)5.77 & 1.19 \\ Subj. 2 & 18.9 & 24.36 & 44.6 & 26.46 & 47.25 & 2.1 & 2.65 & 7.94 & 5.61 \\ Subj. 3 & 17.5 & 24.53 & 41.2 & 24.5 & 43.75 & \(-\)0.03 & 2.55 & \(-\)0.12 & 5.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Errors for the index’s phalanges lengths. Regarding the plots in Figure 6, it can be seen that the theoretical curve falls inside the cloud of points from the experimental values. Nevertheless, the experimental trajectories slightly differ from the theoretical one. This discrepancy between the results could be due to a series of factors, including the precision of the instruments and software used to track the phalanges' tips. There is also a human factor for when the patient is doing the desired movements, the forearm or wrist could move, therefore, producing an offset between each time the finger is flexed and extended. Another factor that possibly influences the results is the differences between the actual anatomy of the fingers' articulations and the kinematic model, which considers these articulations to be spherical. In addition, there are more anatomical limitations that make the experimental results differ from the theoretical ones, such as how the model considers the phalanges to be one-dimensional, disregarding the actual bone, muscle, and fat that add volume to the finger. In reality, the soft tissue of the finger limits the movement of the phalanges when they are contracted. Therefore, soft tissue is most likely the cause of the difference between trajectories at the end of the contraction movement. As can be observed in the plots in Figure 6b, the most significant deviation in the curves occurs at the end of the contraction movement. The parametric mechanism design was successful for the three subjects tested during this study. This model's success is confirmed because the natural trajectories of the subjects'  
Figure 6: Experimental vs. theoretical trajectories of the first and second DOF for: (**a**) subject 1, (**b**) subject 2, and (**c**) subject 3.  
phalanges tips were very similar to the ones produced by the mechanism, as shown in the plots in Figure 6.  
There are apparent anatomical differences between individuals that can affect the phalanges' ROM. Specifically, in this study, two subjects have very different ROM. While subjects one and two almost have the same theoretical and experimental movement ranges, subject two has a wider experimental ROM than the theoretical one. Addressing these anatomical differences could be an area of opportunity in order to adapt each mechanism for each individual better. Regarding how this work compares to previous ones, Table 3 summarizes the advantages of the proposed mechanism over other similar works in the literature. The first advantage is that the proposed mechanism has a double action, which can actively assist in flexion and extension motions. In contrast, other works only assist with flexion or extension but not both. On the same topic, some devices are passive, such as the one proposed in [14; 33].