# A Novel Kinematic Directional Index for Industrial Serial Manipulators
## 5 Experimental Setup and Performance Analysis in the Workspace  
In order to experimentally verify where the robots can achieve the maximum velocity, the end effector of each robot was equipped with an accelerometer, as shown in Figure 8. The chosen device was a piezometric accelerometer, DeltaTron Type 4508001 (manufactured by Hottinger Bruel & Kjaer, Naerum, Denmark), which did not require additional hardware for signal conditioning. The data were acquired by means of an LMS Pimento analyzer (manufactured by LMS International, Leuven, Belgium) at an acquisition frequency of 1000 Hz. The software supplied with the analyzer allowed directly computing the speed of the investigated movements.  
Figure 6: Point sets in which the experimental analyses were performed for the SCARA robot (**left**) and the articulated robot (**right**).  
Figure 7: KDI computed for SCARA (**left**) and articulated (**right**) robots.  
The experimental analysis was performed with the same set of points defined above and illustrated in Figure 6, in order to compare the results of the investigation with the values taken by the KDI. At each point, a back-and-forth movement with a length of 60 mm in the direction of interest was repeated five times so that the center of the displacement (where the maximum speed was reached) coincided with the investigated point. Using a data acquisition system, the signals of the accelerometers were gatherd, and the velocity of the robots was computed. In order to reduce the effect of measuring errors, the maximum experimentally measured speed was computed by calculating the average between the peaks of each repeated movement. In this way, the maximum speed reached in each point of the workspace could be collected. Such results have been normalized since the target of the work is to highlight the region of maximum speed without making performance comparisons between different robots. The experimentally gathered normalized performances are plotted in Figure 9 for both robots.  
It is now possible to appreciate that the values of the KDI perfectly matched the behavior of the robots; the best performance region identified by the KDI has a good correspondence with the measured region. Moreover, the trend of performance given by the KDI met the speed variation throughout the workspace. In fact, the comparison between Figures 7 and 9 highlights that the KDI can be adopted as a useful tool to foresee the regions where a robot can achieve its maximum speed with respect to a direction of interest. In order to better identify the correlation between the index and the real performance, the maximum value of the measured speed has been plotted in Figure 10 for each investigated point with respect to the value given by the KDI at the same point. Moreover, the linear regression between the KDI and the speed of each robot has been computed and plotted by means of a red line. In Figure 10, the proximity of the points on the scatter diagram to the red lines clearly shows a  
Figure 8: The end effectors of the robots equipped with accelerometers.  
Figure 9: Normalized maximum speeds of the SCARA (**left**) and the articulated (**right**) robots.  
strong correlation with the KDI values of the robots' velocities; therefore, it proves the effectiveness of the novel proposed index.