## 5 Discussion  
Traditionally, haptic rendering has only relied on virtual stiffness in order to render objects rigid in virtual scenarios, and rarely also included viscosity. However, the realism of any virtual contact can be greatly improved if all three effects are properly combined. To this end, two relevant issues have to be taken into account: the stability implications of combining the three haptic effects and the perception of each effect by the user. Stability control principles have been established in Section 2) and they do not require further discussion, rather than extending them to future analysis of other sources of instability (e.g., vibration modes of the mechanical device). As to how users are able to discriminate between these effects when they are displayed virtually, the results that are gathered in Table 3 are very open to further discussion. Inertia, viscosity, and stiffness are physical parameters that, once properly explained to users, would seem to be easily distinguishable from each other. However, when analyzing the results of \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Stiffness Evaluation** & **Trials** & **Failure** & **Success** & **Success Rate** \\ \hline Equal stiffness & 60 & 33 & 27 & 45\% \\ Different stiffness & 80 & 3 & 77 & 96.25\% \\ Total \(K\) (equal or different) & 140 & 36 & 104 & 74.29\% \\ \hline
**Damping Evaluation** & **Trials** & **Failure** & **Success** & **Success Rate** \\ \hline Equal damping & 60 & 15 & 45 & 75\% \\ Different damping & 80 & 3 & 77 & 96.25\% \\ Total \(B\) (equal or different) & 140 & 18 & 122 & 87.14\% \\ \hline
**Inertia Evaluation** & **Trials** & **Failure** & **Success** & **Success Rate** \\ \hline Equal inertia & 60 & 29 & 31 & 51.67\% \\ Different inertia & 80 & 19 & 61 & 76.25\% \\ Total \(M\) (equal or different) & 140 & 48 & 92 & 65.71\% \\ \hline
**All Effects Evaluation** & **Trials** & **Failure** & **Success** & **Success Rate** \\ \hline All trials & 420 & 102 & 318 & 75.71\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental results from the user-study. Table 3 for each haptic parameter independently, it can be seen that virtual damping is the effect that is best discriminated between trials, with a 87.14% success rate. This is quite a surprising result as users in general reported that virtual stiffness was the parameter that they felt to be most recognizable and were able to discriminate easier. In our opinion, this may be because stiffness is the physical parameter that is the easiest to understand, but, surprisingly, the results that were obtained from the experiment showed better discrimination rates for viscosity. Inertia was confirmed to be the most difficult haptic effect to recognize, although it should be noted that it was the only parameter that did not double the value among trials; rather, it only changed from 3 kg physical to 3 kg physical, plus 1 kg virtual. Analyzing the results more in-depth, the fact of whether it is easier to discriminate the equal or different values of the parameters between areas can be evaluated. According to the results, virtual stiffness was properly identified as remaining equal in 45% of the trials, while the success rate for identifying different stiffness values was 96.25%; for virtual damping, the successful identification of equal values in both areas was 75% and, for different values, it was 96.25%; lastly, for inertia, the results were 51.67% and 76.25% success rates for equal and different values between areas, respectively. Thus, most users were capable of detecting changes in the stiffness and viscosity with ease (both with 96.25% success rate). It is also remarkable that the least accurate discrimination was that of stiffness when it remains equal in both areas. We think that these results may be because variations in the other two parameters are mainly evaluated in free motion, while virtual stiffness is discriminated when colliding with virtual walls where the effect of all parameters is mixed.