## 5 Discussion  
We have proposed two optimization methods based on grid search that consider the size and regularity of the workspace. The first one obtains the geometric parameters combination that results in the biggest and most regular workspace. The second method analyzes the geometric parameters combinations that result in an acceptable size of the workspace--even if it is not the biggest one--and find out which ones result in the lowest power consumption. The main advantages of these methods are their flexibility, the simplicity of the calculations and the visual results that allow us to compare the results easily.  
We have applied the two methods to the particular case of the 2 PRU-1 PRS parallel manipulator. We now summarize briefly to aide interpreting the results obtained.  
We applied the workspace optimization method to 1000 GP combinations and obtained the GP combinations that result in the biggest sphere in the useful workspace. The biggest sphere has a radius of seven discretization points. There are 15 GP combinations for which their useful workspace can house the biggest sphere. For six of those GP combinations, the biggest sphere can be placed in two positions, while the biggest sphere can be placed in four different positions in the useful workspace for the other nine. Thus, we obtained nine best GP combinations.  
We define the _StudyVariables_ of the power optimization method as the GP combinations that result in a useful workspace containing a sphere at least 0.5-\(S_{max}\). This provides us with 325 _StudyVariables_ to analyse in the power optimization method. The best GP combination of this method is the one that results in the lowest power consumption.  
The power consumption depends on the trajectory of the manipulator. We define three different harmonic trajectories to be studied: one rotation about the X-axis, one rotation about the Y-axis and one translation along the Z-axis. We observe that for the case of the rotations, the best GP combination is (H, L, R) = (0.35, 0.2, 0.2) m. For the translation along the Z-axis, we obtained two best combinations: (H, L, R) = (0.35, 0.2, 0.2) m and (H, L, R) = (0.3, 0.2, 0.2) m. Since (H, I, R) = (0.35, 0.2, 0.2) m is the optimal solution for the three trajectories, we define it as the best GP combination according to power consumption.  
Figure 10: Power consumption for all the suitable GP for the rotation about Y-axis.  
**Author Contributions:** Conceptualization, S.H. and C.P.; methodology, S.H.; software, S.H. and A.Z.; validation, S.H., C.P. and M.D.; formal analysis, S.H. and C.P.; investigation, S.H. and C.P.; data curation, S.H., M.D. and A.Z.; writing--original draft preparation, S.H.; writing--review and editing, C.P. and M.D.; supervision, C.P. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the Regional Government of the Basque Country (IT949-16) and the Science and Innovation Ministry of the Spanish Government (PID2019-105262 RB-I00).  
**Acknowledgments:** The authors wish to acknowledge the financial support received from the Science and Innovation Ministry of the Spanish Government (Project PID2019-105262 RB-I00) and the Regional Government of the Basque Country (Project IT949-16).  
**Conflicts of Interest:** The authors declare no conflict of interest.