## 4 Discussion  
In this study, the performance of a propeller on the holonomic vehicle is evaluated by both the performance experiments and the FEA simulation. To the current knowledge, this is the first attempt to evaluate the efficiency of propeller-induced propulsion ball-based wheels. Ball-based wheels indeed have many advantages over the Mecanum wheel design, such as reduced friction between the wheel and the ground and a higher motion velocity. Using the conventional method, the design and fabrication of a ball based system must consider details such as the complicated platform velocity kinematic relations, the cooperative work of the motor control system and the position precision of the fabricated three-dimensional structures [22; 37]. On the other hand, based on the design concept, not all complicated and basic mechanical design of components is necessary. Alternatively, a selection of commercially-available parts such as motors, propellers, ball wheels, etc., may be enough for the assembly of a holonomic vehicle. It can be said that the design is conceptually simple and therefore easy to manufacture. However, the concept may not be specific for the propulsion of a vehicle with ball-based wheels, but it may be suitable for the Mecanum wheels if only the propulsion method is considered. The universal design concept will thus promote the commercial use of the omnidirectional wheels, the application of which was said to be rarely found in commercial products [38]. From Equations (4) and (5) and Figure 4, it is not coincidental that for an applied propeller, a large efficiency value directly increases the motion velocity, and further increases the thrust exerted on the vehicle. As shown in Table 4, the theoretical velocity calculations confirmed the SolidWorks Motion velocity data. Therefore, the performance of the fabricated system suggests that the propeller is suitable for the holonomic vehicle driving, although the efficiency of the other type of propeller was not investigated. Even so, results from the simulation by SolidWorks supported the effectiveness of  
Figure 4: (**a**) Efficiency vs. Velocity; (**b**) Efficiency vs. Thrust; (**c**) Thrust vs. Velocity. the system design. Because the efficiency of the propeller is determinative for the velocity and thrust, a propeller design or a proper propeller selection is crucial to improve the efficiency. Propeller design and selection including parameters such as the propeller diameter and pitch should be based on experimental results such as performance data or a wind tunnel test. Because the basic propeller experimental data is important, [PERSON] had measured data (Blade number, thrust, torque and revolutions per minute, etc.) of small propellers with a diameter ranging from 6 to 22 inches, and the calculated results showed the efficiency of some propellers [27]. For example, a propeller with an 8.8 inch diameter and 8.75 inch pitch had an efficiency ranging from appropriate 0 to 60% as the Advance ratio (a parameter proportional to wind tunnel speeds and reversely proportional to Revolutions Per Second and Propeller Diameter) increased, and a large-sized propeller with a 12 inch diameter/pitch had a maximum efficiency of approximately 80% [27]. The actual efficiency of this study was 18.55% (Table 2). In the follow-up study, the velocity of the vehicle can be increased by improving the efficiency of the system through enlarging the propeller, and the velocity can be larger than 5 m/s when the efficiency is 70% according to Table 4.  
About the prototype developed in this study, there are some points to be improved. First, an improved program was necessary to control the vehicle conveniently and smoothly. In this study, in order to make the control simple and easy to understand, a series of operations of the forward/backward movement of the vehicle/fan were conducted by pushing up to 10 pairs of numbers on the universal television remote.