# NURSE-2 DoF Device for Arm Motion Guidance: Kinematic, Dynamic, and FEM Analysis
## 6 Lab Prototype
### Repeattibility Test  
An experiment has been carried out in order to estimate the mechanism repeatability according with the Norm ISO 9283 available in [40], where the repeatability is defined as the measure of the ability of a robot to return to a same position and the accuracy is defined as the measure of the ability of a robot to reach a position with the minimum deviation with respect to the programed one. The experiment consists of sending the mechanism end-effector to five critical positions within its workspace during 30 times using a velocity of 396\({}^{\circ}\)/s and a load of 0.529 kg. Then, the reached positions are measured in order to apply the repeatability. The repeatability equation for a position [40], is defined as:  
\[R=\overline{L}+3S, \tag{22}\]  
where \(\overline{L}\) corresponds to the average of the mean square error (\(l_{i}\)) of the reached positions and \(S_{i}\) corresponds to the standard deviation of the reached positions. \(\overline{L}\), \(l_{i}\), and \(S\) are respectively defined [40] as:  
\[\overline{L}=\frac{1}{n}\sum\
olimits_{i=1}^{n}l_{i} \tag{23}\]  
\[l_{i}=\sqrt{\left(x_{i}\overline{X}\right)^{2}+\left(y_{i}\overline{Y} \right)^{2}} \tag{24}\]  
\[S=\sqrt{\frac{\sum\
olimits_{i=1}^{n}\left(l_{i}-\overline{L}\right)^{2}}{n-1 }}, \tag{25}\]  
where \(x_{i}\) is the \(X\) coordinate of a reached position; \(y_{i}\) is the \(Y\) coordinate of a reached position; \(\overline{X}\) is the average of the \(X\) coordinates of the reached positions, and \(\overline{Y}\) is the average of the \(Y\) coordinates of the reached positions.  
In order to determinate the five critical positions [24; 40], a rectangle figure is traced within the mechanism workspace covering most of the workspace and the Cartesian coordinates of the four corners and the central point represent the five critical positions (See Figure 11).  
Figure 11: The considered critical positions (\(A\), \(B\), \(C\), \(D\), and \(E\) points) within the mechanism workspace (in grey) with the reference rectangle.  
Figure 12 shows the mechanism end-effector reaching the five critical positions. The coordinates of the experimental reached positions have been obtained using red markers on the required positions that are tracked by image processing. Figure 13 shows the reached positions by the mechanism end-effector versus the programmed critical positions \(A\), \(B\), \(C\), \(D\), and \(E\). The repeatability has been successfully computed and it has been obtained that the mechanism has a repeatability of \(\pm\)1.3 cm. The mechanism repeatability is satisfactory considering that the lab prototype has a low precision manufacture. It is important to note that the encoder error has presented a maximum value of 50 counts (0.063\({}^{\circ}\) of motor rotation) which is negligible considering that 284,000 counts are equivalent to 360\({}^{\circ}\) of motor rotation.  
Figure 12: NURSE (cassiNo-qUeretaro unpeR-limb aSistive dEvice) end-effector on the two right critical positions in Figure 11: (**a**) Position \(A\) (-496, 700); (**b**) Position \(B\) (496, 700); (**c**) Position \(C\) (-496, 148); (**d**) Position \(D\) (496, 148); and (**e**) Position \(E\) (0, 424).  
An experimental characterization of NURSE device was carried out by the author using the lab prototype designed in this paper and since it comprised a detailed work it observed an individual report that can be consulted with free access in [41]. Trajectories, linear accelerations, torque, and power consumption were considered in [41] to check the mechanism behaviour during the reproduction of arm therapy exercises. The experimental results in [41] showed that the proposed mechanism design is capable of reproducing successfully exercises for the upper limb with smooth movements and low power consumption. It is important to note that the article in [41] exposes only experiments with arm therapy exercises, thus the authors have considered important to publish the current paper with the detailed design process to obtain the NURSE device.