## 3 Materials and Methods
### Experimental Setup  
A virtual environment was developed with two independent areas, referred to as 1 and 2 (Figure 8), with each area being of 200 \(\times\) 200 mm in size and having two virtual walls in the upper and lower zone. The users are able to move freely within wall limits, and they can also move from one area to the other. Virtual force law is implemented as a different combination of the three haptic parameters  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Workspace** & 800 \(\times\) 400 \(\times\) 400 mm \\
**Maximum force** & 14 N (cont.), 28 N (peak) \\
**Actuators** & Maxon DCX32L-GPX32, 128 mN\(\cdot\)m, 4:1 \\
**Transmission** & 20\(\cdot\)1 cable transmission \\
**Encoders** & Maxon ENX16, 1024 ppr \\
**Position resolution** & 6 \(\upmu\)m \\
**Weight** & 8.2 kg \\ \hline \hline \end{tabular}
\end{table}
Table 1: HomeRehab specifications.  
Figure 7: HomeRehab robotic tele-rehabilitation system.  
subject to analysis: stiffness, damping, and inertia. Note that, while stiffness is only felt when users collide with the virtual walls, damping and inertia are also felt within the complete area.  
Users feel a different combination of haptic effects in each area. Indeed, the aim of the experiment was to analyze whether they are able to discriminate between each haptic parameter and recognize differences. The values of the virtual stiffness coefficients that are tested in the experiments are 500 and 1000 N/m, the values of the virtual inertias are 0 and 1 kg, and the virtual viscous coefficients 0 and 10 N\(\cdot\)s/m (almost equal to the physical effect).  
At the beginning of the experiment, a brief report is given to all users describing the robotic device, configuration of the virtual environment, and the meaning of the three haptic parameters being tested. They also allowed for testing the virtual environment and trying out some haptic feedback effects. Afterwards, each of the twenty users carries out seven different trials, with haptic parameters of Area 1 being the same in all of the trials: virtual stiffness coefficient of the walls \(K=500\) N/m and no additional effects in free movement (\(M=0\) and \(B=0\)). However, the haptic parameters of Area 2 are modified between trials (Table 2), with the values being hidden from users and presented in randomized order.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Area 1**} & \multicolumn{3}{c}{**Area 2**} \\ \hline
**Trial** & **K (N/m)** & **M (kg)** & **B (N-s/m)** & **K (N/m)** & **M (kg)** & **B (N-s/m)** \\ \hline
1 & 500 & 0 & 0 & 1000 & 0 & 0 \\
2 & 500 & 0 & 0 & 500 & 0 & 10 \\
3 & 500 & 0 & 0 & 500 & 1 & 0 \\
4 & 500 & 0 & 0 & 1000 & 0 & 10 \\
5 & 500 & 0 & 0 & 1000 & 1 & 0 \\
6 & 500 & 0 & 0 & 500 & 1 & 10 \\
7 & 500 & 0 & 0 & 1000 & 1 & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Values applied in the experiment.  
Figure 8: Experimental setup.  
In each trial, the users are allowed to interact with the scene as many times as desired with no time restrictions, and it is explained to them that haptic parameters of Area 2 change (increase, decrease, or maintain), among trials. Whenever they feel confident, they are requested to answer whether stiffness, inertia, and viscosity of Area 2 are higher or lower than, or equal to, those of Area 1.