## 4 Conclusions and Future Work  
Most prior research focused on a 6 DoF electric linear actuator platform equipped with a monitor to design the simulator. This kind of design exhibited a smaller motion range than those developed in this study, and the monitor as an image output did not have an immersive feeling for testers. Therefore, this paper developed a rotatable multi-axis motion platform combined with VR digital content. The whole platform system included inverse kinematics, mechanical design, stress analysis, VR development, and interactive control. It allowed testers to achieve immersive VR flight training by watching and controlling VR imagery of a flight and experiencing the feedback brought by the multi-axis motion platform. The main contribution of this study was to design a simple 3-DoF crank linkage mechanism to replace the expensive 6-DoF electric linear actuator Stewart platform and to obtain a comparable movement experience to Stewart system. The three crank linkages with 3 DoF can work out a larger range of motion displacement and be able to support higher loading with lower folding height. Furthermore, the yaw axis with a \(\pm\)180\({}^{\circ}\) rotation was built at the center of the platform to obtain collectively 4-DoF of movement. VR replaced monitor output. The roll and pitch motions of the platform could obtain their overall motion trajectory through inverse kinematics and harmonic curves. Motion sensors were used to verify the position status of the simulated and actual platform. The velocity error  
-5.5%. This error might come from the mechanism machining accuracy or the errors at the motion of the motor. According to test results, the platform's motion angle return reliability was ~97.43%. In the final performance test, the maximum ultimate performance of the heave motion was ~0.34 G, the roll motion was ~0.51 G, and the pitch motion was ~0.53 G. In addition, the central rotation performance could achieve ~0.5 G. To sum up, this multi-axis motion platform can provide enough somatosensory feedback and a highly interactive realistic training system by combining the joystick and VR equipment. The testers can immerse in the VR content via movement with the platform to enjoy a flying experience.  
In the future, research will be focused on improving the installation methods of cranks, motors, and reducers to upgrade the rigidity of the platform and increase the wider range of motion. In the VR component, weather changes and design of a detailed scene could be added to make the operation more realistic. Through the establishment of different VR scenes and adjustment of the displacement, speed, and acceleration of the platform, this platform can be used not only for flight simulation, but also be applied in many different simulations.  
Conceptualization, P.-Y.S.; Data curation, H.-J.L. and Z.-Y.H.; Formal analysis, P.-Y.S., H.-J.L. and C.-H.H.; Funding acquisition, Z.-Y.H.; Investigation, P.-Y.S., H.-J.L. and C.-H.H.; Methodology, C.-T.P.; Project administration, C.-T.P.; Supervision, C.-T.P. and Y.-L.S.; Validation, Z.-Y.H. and Y.-L.S.; Writing--original draft, P.-Y.S.; Writing--review & editing, P.-Y.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded by grants KSVNSU110-004 from Kaohsiung Veterans General Hospital, MOST 108-2622-E-110-004-CC3 from Ministry of Science and Technology, and Kaohsiung Brogent Technologies Inc.  
Not applicable.  
This work was supported by grants KSVNSU110-004 from Kaohsiung Veterans General Hospital, MOST 108-2622-E-110-004-CC3 from Ministry of Science and Technology, and Kaohsiung Brogent Technologies Inc.  
We declare no competing interests.