Development of Multi-Axis Crank Linkage Motion System for Synchronized Flight Simulation with VR Immersion

: This paper developed a rotatable multi-axis motion platform combined with virtual reality (VR) immersion for ﬂight simulation purposes. The system could simulate the state of the ﬂight operation. The platform was mainly comprised of three crank linkage mechanisms to replace an expensive six degrees of freedom (DoF) Stewart platform. Then, an independent subsystem which could rotate ± 180 ◦ was installed at the center of the platform. Therefore, this platform exhibited 4-DoF movement, such as heave, roll, pitch, and yaw. In the servo motor control unit, Visual Studio C# was applied as the software to establish a motion control system to interact with the motion controller and four sets of servo motors. Ethernet Control Automation Technology (EtherCAT) was utilized to communicate the commands and orders between a PC and each servo motor. The optimum controller parameters of this system were obtained using Simulink simulation and veriﬁed by experiment. The multiple sets of servo motors and crank linkage mechanisms were synchronized with ﬂight VR imagery. For VR imagery, the software Unity was used to design the ﬂying digital content. The controller was used to transmit the platform’s spatial information to meet the direction of the pilot commands and to compensate the direction of the deviation in spatial coordinates. To achieve synchronized response and motion with respect to the three crank linkage mechanism platform and VR imagery on the tester’s goggle view, the relation of the spatial coordinate of VR imagery and three crank linkage mechanisms was transformed to angular displacement, speed and acceleration which were used to command the motor drive system. As soon as the position of the VR imagery changed, the computer instantly synchronized the VR imagery information to the multi-axis platform and performed multi-axis dynamic motion synchronously according to its commanded information. The testers can thus immerse in the VR image environment by watching the VR content, and obtain a ﬂying experience.


Introduction
The initial design of the parallel mechanism was proposed by Gough in 1962 [1]. Subsequently, Stewart proposed a Stewart platform with six Degrees of Freedom (DoF) for flight simulators based on a parallel mechanism in 1965 [2]. A few years later, a combination of parallel and series types were proposed to develop a quite wide range of applications in 1990 [3]. Research about the platform has been since developed in many ways [4,5].
Moreover, 3-DoF parallel mechanisms have been more widely studied than 6-DoF. Philip Ethelbert Smit designed a 3-DoF motion platform and analyzed electric drive and hydraulic drive motion control in 2010 [6]. Zhang et al. provided the basics about the selection

Specification of Platform
The specifications of the multi-axis platform were designed based on the movement freedoms of heave, roll, pitch, yaw angles. The definition of the platform motion is schematically shown in Figure 1. The roll motion was the angle transformation of the X direction, pitch motion was the angle transformation of the y-axis, and heave motion was the translation of the z-axis. The multi-axis platform also included yaw with a ±180 • rotation along the z-axis. The overall specifications of this study are shown in Table 1.
translation of the Z-axis. The multi-axis platform also included yaw with a ±1 along the Z-axis. The overall specifications of this study are shown in Table 1.

Design of the Platform
The platform design was not only based on the heave, roll, and pitch mot needed to consider the supporting weight and payload. Moreover, the inverse and mathematical calculation software Matlab was used to determine the mo tory and motor output angle of the multi-axis motion platform before the con sign. Based on the results of calculation, the lengths of proper crank linkage m could be obtained. After the preliminary design was completed, the mechan mance of the mechanisms was simulated and characterized through analysis

Design of the Platform
The platform design was not only based on the heave, roll, and pitch motion but also needed to consider the supporting weight and payload. Moreover, the inverse kinematics and mathematical calculation software Matlab was used to determine the motion trajectory and motor output angle of the multi-axis motion platform before the conceptual design. Based on the results of calculation, the lengths of proper crank linkage mechanisms could be obtained. After the preliminary design was completed, the mechanical performance of the mechanisms was simulated and characterized through analysis software to determine the required optimal dimension and geometry of the crank linkages. The platform designed in this paper contained four parts: a lower plate (motor and reducer), crank mechanism (crank and linkage), upper plate, and upper rotating disk in the middle (see Figure 1). Each motor was combined with reducer to increase the outputs and connected with the crank by Appl. Sci. 2021, 11, 3596 4 of 24 a revolute pair. Both of the cranks and the linkages were connected in the same way by rotating pair. A spherical pair was installed between the upper platform and the linkage. The crank mechanism transmitted input to the upper plate to produce the upper plate motion. The rotating disk above the upper plate could rotate independently by a motor to rotate ±180 • . The schematic illustration is shown in Figure 2.
determine the required optimal dimension and geometry of the crank linkage form designed in this paper contained four parts: a lower plate (motor and red mechanism (crank and linkage), upper plate, and upper rotating disk in the Figure 1). Each motor was combined with reducer to increase the outputs and with the crank by a revolute pair. Both of the cranks and the linkages were c the same way by rotating pair. A spherical pair was installed between the upp and the linkage. The crank mechanism transmitted input to the upper plate the upper plate motion. The rotating disk above the upper plate could r pendently by a motor to rotate ±180°. The schematic illustration is shown in F The DoF calculation is described by Equation (1). This platform had nine pairs, three spherical pairs, and six rotation pairs. This platform was contained tral axis of rotation, so DoF can be calculated by Equation (1), where indicated the amount of connecting rods, and was the amount o pairs which had i .

Central Rotating Mechanism Design
In this study, a ±180° rotatable seat part was installed at the center of the form. The central rotating shaft could be rotated by a belt drive and the force the rotation also could be offset by the supporting unit, where the belt gear large and small pulleys was 45:15, the torque magnification was 3 times, and power loss was about 9%. In order to facilitate the calculation of the rotating s it was assumed there was no friction on the rotation of the central shaft. T torque required the driving force to be the product of the tangential frict applied to the support unit by the load and the distance from the support central axis of rotation. The free-body diagram is shown in Figure 3. The load The DoF calculation is described by Equation (1). This platform had nine component pairs, three spherical pairs, and six rotation pairs. This platform was contained at the central axis of rotation, so DoF can be calculated by Equation (1), where N indicated the amount of connecting rods, and C i was the amount of kinematic pairs which had i DoF.

Central Rotating Mechanism Design
In this study, a ±180 • rotatable seat part was installed at the center of the upper platform. The central rotating shaft could be rotated by a belt drive and the force applied for the rotation also could be offset by the supporting unit, where the belt gear ratio of the large and small pulleys was 45:15, the torque magnification was 3 times, and the output power loss was about 9%. In order to facilitate the calculation of the rotating shaft torque, it was assumed there was no friction on the rotation of the central shaft. The loading torque τ m required the driving force to be the product of the tangential friction force f applied to the support unit by the load F L and the distance from the support unit to the central axis of rotation. The free-body diagram is shown in Figure 3. The loading torque τ m was tangent to the support unit. The friction relationship is given by Equation (2). Finally, the torque demand of the central rotation was given by friction force conversion.
where τ m is the central load torque, f is the tangential friction of the support unit, x is the number of support units installed, µ is the friction coefficient of the support unit, N b is the positive force of the support unit relative to the load F L , and r is the distance of the axis.

= = =
where is the central load torque, is the tangential friction of the suppo the number of support units installed, is the friction coefficient of the supp is the positive force of the support unit relative to the load , and is the dis axis.

Stress Analysis
In this study, to consider tester safety and supporting a weight of ~400 kg stress simulation was carried out to verify the stress at a material safety facto this study, the material S45C was used. The stress simulation can be divided i pitch motion. Both of the roll and pitch motion were loaded with the downw the center point and set an upward support force at the three end points of th the same time to analyze the structural strength. The simulation model was sc shown in Figure 4a

Stress Analysis
In this study, to consider tester safety and supporting a weight of~400 kg, a platform stress simulation was carried out to verify the stress at a material safety factor (N = 2). In this study, the material S45C was used. The stress simulation can be divided into roll and pitch motion. Both of the roll and pitch motion were loaded with the downward force at the center point and set an upward support force at the three end points of the triangle at the same time to analyze the structural strength. The simulation model was schematically shown in Figure 4a where is the central load torque, is the tangential friction of the support unit, is the number of support units installed, is the friction coefficient of the support unit, is the positive force of the support unit relative to the load , and is the distance of the axis.

Stress Analysis
In this study, to consider tester safety and supporting a weight of ~400 kg, a platform stress simulation was carried out to verify the stress at a material safety factor (N = 2). In this study, the material S45C was used. The stress simulation can be divided into roll and pitch motion. Both of the roll and pitch motion were loaded with the downward force at the center point and set an upward support force at the three end points of the triangle at the same time to analyze the structural strength. The simulation model was schematically shown in Figure 4a

Motion Trajectory
In this part, the platform was divided into the upper platform and the motor output plane. The Cartesian coordinate was set to find the interrelationship of the initial upper platform coordinate , the upper platform coordinates after movement ′, and the motor output platform coordinate as the basis of the platform motion trajectory. The coordinate relationship was schematically shown in Figure 5.

Motion Trajectory
In this part, the platform was divided into the upper platform and the motor output plane. The Cartesian coordinate was set to find the interrelationship of the initial upper platform coordinate U, the upper platform coordinates after movement U , and the motor output platform coordinate G as the basis of the platform motion trajectory. The coordinate relationship was schematically shown in Figure 5. Both the motor output platform and the upper platform were designed as equilateral triangles: the length of the motor output platform assumes ℓ , the length of the upper platform assumes ℓ , and the distance H from the center of mass of the upper platform to the motor output platform were assumed. The upper platform coordinate after movement ′ can be converted by the Euler angle transformation matrix. It was assumed that the coordinate ′ was the coordinate turning angle to the axis and turning 2 angle to the axis as shown in Equation (3). Moreover, was shifted by h as shown in Equation (4). Then, the relationship of coordinate and coordinate was described by Equation (5). The distance from the center of mass to the three vertices was kept in the coordinate ′. The three vectors of the coordinate could be superimposed to obtain the vector of the coordinate and the final movement position { ′}.  Both the motor output platform and the upper platform were designed as equilateral triangles: the length of the motor output platform assumes G , the length of the upper platform assumes L , and the distance H from the center of mass of the upper platform to the motor output platform were assumed. The upper platform coordinate after movement U can be converted by the Euler angle transformation matrix. It was assumed that the coordinate U was the coordinate U turning α angle to the X U axis and turning I2 angle to the Y U axis as shown in Equation (3). Moreover, Z U was shifted by h as shown in Equation (4). Then, the relationship of coordinate U and coordinate U was described by Equation (5). The distance from the center of mass to the three vertices was kept in the coordinate U . The three vectors of the coordinate U could be superimposed to obtain the vector of the coordinate G and the final movement position U i .
After obtaining the position U i of the upper platform, the position of the crank connecting rod joint C i could be further derived. Assuming the position U i , position C i , crank length C , and the connecting rod length L were a known condition. The dimension of the platform is shown in Figure 6.
After obtaining the position { ′}, the vector of the connection point between { ′} and the upper platform was regarded as the connecting rod length ℓ and the motor output platform. The contact connection vector was regarded as the crank length ℓ and the vector relation, as shown in Equation (9). The crank length vector ℓ was projected to the motor output platform to obtain the vector ℓℓ , ⃑ , as shown in Figure 8. Finally, the motor output angle could be obtained by Equation (10). According to Figure 7a, the contact relationship is shown in Equations (6) and (7), and through the top view of the platform, the angle θ between the crank and the shaft X was a fixed value as shown in Figure 7b. The geometric relationship was shown in Equation (8).
Finally, the C i coordinate position can be calculated by Equations (6)- (8) to establish the motion trajectory.
FOR PEER REVIEW 7 of 23 After obtaining the position C i , the vector of the connection point between C i and the upper platform was regarded as the connecting rod length L and the motor output platform. The contact connection vector was regarded as the crank length C and the vector relation, as shown in Equation (9). The crank length vector C was projected to the motor output platform to obtain the vector C,i , as shown in Figure 8. Finally, the motor output angle could be obtained by Equation (10).

VR Image Design Method
VR content images can be designed according to customizable requirem ent content designs could produce different experiences. In this study, VR designed for flight training purposes. The design process was first to set the b size, and space. Second, the physical system, light field, and gravity condit internal environment were designed to meet the flight conditions of the aircra step was to set up the 3D model required in the virtual environment by using 3 software Blender and Autodesk 3Ds to create and set the dynamic conditions o The fourth step was to combine the joystick of the aircraft in the external co environment with the dynamic conditions of the aircraft. Finally, the VR equ integrated into the cockpit of the aircraft to complete the VR.

VR Image Design Method
VR content images can be designed according to customizable requirements. Different content designs could produce different experiences. In this study, VR content was designed for flight training purposes. The design process was first to set the basic terrain, size, and space. Second, the physical system, light field, and gravity conditions for the internal environment were designed to meet the flight conditions of the aircraft. The third step was to set up the 3D model required in the virtual environment by using 3D modeling software Blender and Autodesk 3Ds to create and set the dynamic conditions of the model. The fourth step was to combine the joystick of the aircraft in the external control virtual environment with the dynamic conditions of the aircraft. Finally, the VR equipment was integrated into the cockpit of the aircraft to complete the VR.

Platform Integrated with VR
The completed platform was integrated with the flight VR image. To immerse in VR, the joystick was installed on the chair and combined with the multi-axis platform to make the experience more real. The tester sat in the middle of the platform and operated the joystick to control the VR image to perform three-axis direction and rotation. The schematic side view is shown in Figure 9.
pl. Sci. 2021, 11, x FOR PEER REVIEW Figure 9. Schematic side view of the seat platform.
The overall system correlation diagram is shown in Figure 10. The tes the roll, pitch, heave, and yaw motions of the aircraft through the joystic platform to make the corresponding action-angle. Then, the tester could more realistic flight experience.

Multi-Axis Motion Platform Mechanism
The platform design with multi-axis motion mainly consisted of thre The overall system correlation diagram is shown in Figure 10. The tester controlled the roll, pitch, heave, and yaw motions of the aircraft through the joystick to drive the platform to make the corresponding action-angle. Then, the tester could experience a more realistic flight experience.
ci. 2021, 11, x FOR PEER REVIEW 9 Figure 9. Schematic side view of the seat platform.
The overall system correlation diagram is shown in Figure 10. The tester contro the roll, pitch, heave, and yaw motions of the aircraft through the joystick to drive platform to make the corresponding action-angle. Then, the tester could experien more realistic flight experience.

Multi-Axis Motion Platform Mechanism
The platform design with multi-axis motion mainly consisted of three sets of c and linkage mechanisms. The servo motor was connected with a reducer to magnify torque output. In order to increase the stroke of the crank, the output setting position raised to 21 cm above the ground to avoid the cranks hitting the ground when the

Multi-Axis Motion Platform Mechanism
The platform design with multi-axis motion mainly consisted of three sets of crank and linkage mechanisms. The servo motor was connected with a reducer to magnify the torque output. In order to increase the stroke of the crank, the output setting position was raised to 21 cm above the ground to avoid the cranks hitting the ground when the platform moved to the lowest point. Then, the output shaft was linked with the crank. After that, the crank and the linkage were connected by a rotating pair, and the upper platform was assembled with a fish-eye joint to connect with the linkage to facilitate motion. The platform limitation of roll and pitch was ±20 • , heave stroke was ±20 cm, yaw was ±180 • and the supporting weight could not exceed~400 kg. According to the safety rule, the highest position of the single-person sports platform could not exceed 1.5 m. The prototype of the multi-axis motion platform was shown in Figure 11. The multi-axis motion platform specifications are shown in Table 2.
pl. Sci. 2021, 11, x FOR PEER REVIEW 10 of highest position of the single-person sports platform could not exceed 1.5 m. The prot type of the multi-axis motion platform was shown in Figure 11. The multi-axis motio platform specifications are shown in Table 2.

Central Rotating Mechanism
The design of the rotation mechanism was mainly by six universal wheels, pulle and belt, as shown in Figure 12. The supporting weight of this subsystem was ~250 k and the required torque was calculated by Equation (2). The result showed the requir torque was 188 • , and the rated torque of the motor was about 2.39 • . The reduc reduction ratio was 1:40. Finally, the drive was combined with the belt, and the reductio ratio was 1:120. Then, we found that the final torque was about 286.8 • .

Central Rotating Mechanism
The design of the rotation mechanism was mainly by six universal wheels, pulley, and belt, as shown in Figure 12. The supporting weight of this subsystem was~250 kg, and the required torque was calculated by Equation (2). The result showed the required torque was 188 N·m, and the rated torque of the motor was about 2.39 N·m. The reducer reduction ratio was 1:40. Finally, the drive was combined with the belt, and the reduction ratio was 1:120. Then, we found that the final torque was about 286.8 N·m. and belt, as shown in Figure 12. The supporting weight of this subsyste and the required torque was calculated by Equation (2). The result show torque was 188 • , and the rated torque of the motor was about 2.39 reduction ratio was 1:40. Finally, the drive was combined with the belt, an ratio was 1:120. Then, we found that the final torque was about 286.8 •

Stress Analysis Results
The support of the platform was input by total weight of~400 kg in the analysis. The stress simulation was divided into roll and pitch motion. Among them, the stress of roll motion simulation was analyzed at platform motion angles of 0 • , 10 • , and 20 • . The simulation results showed that the maximum stress was located at the angle of 20 • with a maximum stress of 129.63 MPa. The maximum stress analysis result is shown in Figure 13. The roll motion stress trend is shown in Figure 14.
For the pitch motion, the platform motion angles were 0 • , 10 • , and 20 • . The simulation results showed that the maximum stress was located at the angle of 20 • with a maximum stress of 119.79 MPa. The maximum stress analysis result is shown in Figure 15. The pitch motion stress trend is shown in Figure 16.

Stress Analysis Results
The support of the platform was input by total weight of ~400 kg in the analysis. The stress simulation was divided into roll and pitch motion. Among them, the stress of roll motion simulation was analyzed at platform motion angles of 0°, 10°, and 20°. The simulation results showed that the maximum stress was located at the angle of 20° with a maximum stress of 129.63 MPa. The maximum stress analysis result is shown in Figure 13. The roll motion stress trend is shown in Figure 14.  For the pitch motion, the platform motion angles were 0°, 10°, and 20° tion results showed that the maximum stress was located at the angle of 20° mum stress of 119.79 MPa. The maximum stress analysis result is shown in F pitch motion stress trend is shown in Figure 16.   According to the analysis results, it can be seen that the multi-axis platfor nism was safe during movement, the overall stress was within the yield stren MPa of material S45C, and the material safety factor N was 2.

Motion Trajectory Results
In this study, the path of the platform was a mixture of roll and pitch motio fore, the motion trajectory of the platform would be calculated by mathematic tion analysis software Matlab. In addition, the motion sensor was used to me actual movement displacement, speed, and acceleration of the platform motion the consistency of the trajectory trend and platform movement.
The roll and pitch motions were analyzed based on harmonic curves, and cycle period of the path was 4 s. In addition, the motion angle was ±20°. The p of roll motion was a cosine curve, as shown in Figure 17a, and the pitch motion curve, as shown in Figure 17b. According to the analysis results, it can be seen that the multi-axis platform mechanism was safe during movement, the overall stress was within the yield strength 648.5 MPa of material S45C, and the material safety factor N was 2.

Motion Trajectory Results
In this study, the path of the platform was a mixture of roll and pitch motions. Therefore, the motion trajectory of the platform would be calculated by mathematical simulation analysis software Matlab. In addition, the motion sensor was used to measure the actual movement displacement, speed, and acceleration of the platform motion to verify the consistency of the trajectory trend and platform movement.
The roll and pitch motions were analyzed based on harmonic curves, and the singlecycle period of the path was 4 s. In addition, the motion angle was ±20 • . The preset path of roll motion was a cosine curve, as shown in Figure 17a, and the pitch motion was a sine curve, as shown in Figure 17b.
The trajectory of the crank and linkage positions of the roll and pitch motion were integrated and combined with the motor output angles of each action point to create a multi-axis motion platform trajectory model by Matlab, as shown in Figure 18. The maximum upward motor output angle was 58.3 • , the maximum downward angle was 58.6 • , and the total stroke angle was about 117 • , as shown in Figure 19. In addition, the maximum motor output velocity was about 7.8 rpm, as shown in Figure 20. The trajectory of the crank and linkage positions of the roll and pitch motion were integrated and combined with the motor output angles of each action point to create a multi-axis motion platform trajectory model by Matlab, as shown in Figure 18. The maximum upward motor output angle was 58.3°, the maximum downward angle was 58.6°, and the total stroke angle was about 117°, as shown in Figure 19. In addition, the maximum motor output velocity was about 7.8 rpm, as shown in Figure 20.   The trajectory of the crank and linkage positions of the roll and pitch motion w integrated and combined with the motor output angles of each action point to creat multi-axis motion platform trajectory model by Matlab, as shown in Figure 18. The ma mum upward motor output angle was 58.3°, the maximum downward angle was 58 and the total stroke angle was about 117°, as shown in Figure 19. In addition, the ma mum motor output velocity was about 7.8 rpm, as shown in Figure 20.  Moreover, in order to confirm the error between simulation and test, the roll and pitch motion path were input into the platform and performed for the actual measurement. In roll motion, the maximum angular velocity of the platform simulation was 15.71 rad/s, and the maximum angular velocity of the actual measurement was 14.55 rad/s. The comparison of the velocity for the simulation and the actual measurement is shown in Figure 21a. The maximum angular acceleration of the simulation was 24.67 rad/s 2 , and the maximum angular acceleration of the actual measurement was 22.8 rad/s 2 , as shown in Figure 21b. Moreover, in order to confirm the error between simulation and test, the roll and pitch motion path were input into the platform and performed for the actual measurement. In roll motion, the maximum angular velocity of the platform simulation was 15.71 rad/s, and the maximum angular velocity of the actual measurement was 14.55 rad/s. The comparison of the velocity for the simulation and the actual measurement is shown in Figure 21a. The maximum angular acceleration of the simulation was 24.67 rad/s 2 , and the maximum angular acceleration of the actual measurement was 22.8 rad/s 2 , as shown in Figure 21b. In pitch motion, the maximum angular velocity of the platform simulation was 1 rad/s, and the maximum angular velocity of the actual measurement was 14.36 rad/s velocity of the simulation and the actual measurement is shown in Figure 22a. The m mum angular acceleration of the simulation was 24.67 rad/s 2 , and the maximum ang acceleration of the actual measurement was 22.46 rad/s 2 , as shown in Figure 22b  In pitch motion, the maximum angular velocity of the platform simulation was 15.71 rad/s, and the maximum angular velocity of the actual measurement was 14.36 rad/s. The velocity of the simulation and the actual measurement is shown in Figure 22a. The maximum angular acceleration of the simulation was 24.67 rad/s 2 , and the maximum angular acceleration of the actual measurement was 22.46 rad/s 2 , as shown in Figure 22b.
In pitch motion, the maximum angular velocity of the platform simulation was 15 rad/s, and the maximum angular velocity of the actual measurement was 14.36 rad/s. T velocity of the simulation and the actual measurement is shown in Figure 22a. The m mum angular acceleration of the simulation was 24.67 rad/s 2 , and the maximum angu acceleration of the actual measurement was 22.46 rad/s 2 , as shown in Figure 22b. To sum up, the velocity error during the roll motion was about 7.41%, and the ac eration error was about 7.58%. Thus, the velocity error during the pitch motion was 8. and the acceleration error was about 8.96%. Obviously, the overall trend of those moti was in line with the actual measurement. The small error in the value could be judged the difference from the load above.

Motor Angle Trajectory Verification
This part was to verify the angle error between the motor output angle simulat and the actual motor output. In the first place, the motion sensor was installed on crank. Then, the motor trajectory measurement of the platform roll, and pitch motion w carried out. Among them, the roll and pitch motion were to let the upper platform to tain the actual crank output angle, the average value of the trajectory error, and the sta ard deviation of the measurement. The angle trajectory test of the platform is shown Figure 23. To sum up, the velocity error during the roll motion was about 7.41%, and the acceleration error was about 7.58%. Thus, the velocity error during the pitch motion was 8.6%, and the acceleration error was about 8.96%. Obviously, the overall trend of those motions was in line with the actual measurement. The small error in the value could be judged as the difference from the load above.

Motor Angle Trajectory Verification
This part was to verify the angle error between the motor output angle simulation and the actual motor output. In the first place, the motion sensor was installed on the crank. Then, the motor trajectory measurement of the platform roll, and pitch motion was carried out. Among them, the roll and pitch motion were to let the upper platform to obtain the actual crank output angle, the average value of the trajectory error, and the standard deviation of the measurement. The angle trajectory test of the platform is shown in Figure 23. Both of the roll and pitch motions tilted the platform at 0°, 5°, 10°, 15 the testers controlled the movement of the upper platform, the angle o driving motors was measured by the motion sensor. Figure 24a,b shows simulation trajectory of the roll and pitch motion. Both of the roll and pitch motions tilted the platform at 0°, 5°, 10°, 15°, and 20°. W the testers controlled the movement of the upper platform, the angle of the three set driving motors was measured by the motion sensor. Figure 24a,b shows the motor mo simulation trajectory of the roll and pitch motion. After that, comparing the motor output angle of actual and simulation of roll mot the error of the output angle of drive motor 1 was 2.95%, motor 2 was 8.5%, and mot was 6.5%. The overall motion error was 7.5%. The comparison chart is shown in Fig  25. Motor 1 during the roll motion was almost static. Therefore, the error of motor 1 relatively smaller than motor 2 and motor 3. Overall errors might come from mechan machining accuracy and errors at the moment of the motor start. After that, comparing the motor output angle of actual and simulation of roll motion, the error of the output angle of drive motor 1 was 2.95%, motor 2 was 8.5%, and motor 3 was 6.5%. The overall motion error was 7.5%. The comparison chart is shown in Figure 25. Motor 1 during the roll motion was almost static. Therefore, the error of motor 1 was relatively smaller than motor 2 and motor 3. Overall errors might come from mechanism machining accuracy and errors at the moment of the motor start. In the pitch motion, the error of the output angle of drive motor 1 was was 3.5%, and motor 3 was 3.5%. The overall motion error was 5.5%. The chart is shown in Figure 26. The motion angle during the pitch motion was sm errors were the same as roll motion. This might also come from mechanism accuracy and errors at the moment of the motor start. In the pitch motion, the error of the output angle of drive motor 1 was 4%, motor 2 was 3.5%, and motor 3 was 3.5%. The overall motion error was 5.5%. The comparison chart is shown in Figure 26. The motion angle during the pitch motion was small. Overall errors were the same as roll motion. This might also come from mechanism machining accuracy and errors at the moment of the motor start. was 3.5%, and motor 3 was 3.5%. The overall motion error was 5.5%. The co chart is shown in Figure 26. The motion angle during the pitch motion was sma errors were the same as roll motion. This might also come from mechanism accuracy and errors at the moment of the motor start.

Motions Performance Test
This platform performed the heave, pitch, roll, and rotation with limited G The G force could not exceed 0.9 G. In the heave part, the motion sensor would b at the center mass of the upper platform, and a maximum motor speed 7.8 rpm to make the upper platform motion from the highest point to the lowest point test, the heave limit G force of the platform was 0.34 G.
In the pitch and roll, the motion sensor was installed on the seat, and a motor speed 7.8 rpm was used to make the upper platform limit angle movem the test, the pitch limit G force was 0.53 G, and the roll limit G force was 0.51 G In the rotation part, the motion sensor was installed on the round edge of th platform and a maximum motor speed 30 rpm was set up to make seat platf ±180°. The maximum rotational G force was 0.5 G. The motion limit G force te is shown in Figure 27.

Motions Performance Test
This platform performed the heave, pitch, roll, and rotation with limited G forces test. The G force could not exceed 0.9 G. In the heave part, the motion sensor would be installed at the center mass of the upper platform, and a maximum motor speed 7.8 rpm was used to make the upper platform motion from the highest point to the lowest point. After the test, the heave limit G force of the platform was 0.34 G.
In the pitch and roll, the motion sensor was installed on the seat, and a maximum motor speed 7.8 rpm was used to make the upper platform limit angle movement. After the test, the pitch limit G force was 0.53 G, and the roll limit G force was 0.51 G.
In the rotation part, the motion sensor was installed on the round edge of the rotating platform and a maximum motor speed 30 rpm was set up to make seat platform rotate ±180 • . The maximum rotational G force was 0.5 G. The motion limit G force test method is shown in Figure 27.
1, x FOR PEER REVIEW 18 of 23 Figure 27. Heave, roll, and pitch limit G force test method.

Virtual Image Design
The image was designed for first-person perspective. Final VR content included the image of the aircraft, the outside environment, and the cockpit. The cockpit showed the Figure 27. Heave, roll, and pitch limit G force test method.

Virtual Image Design
The image was designed for first-person perspective. Final VR content included the image of the aircraft, the outside environment, and the cockpit. The cockpit showed the propulsion power, flight speed, and aircraft altitude, etc. The High Tech Computer (HTC) Vive Pro head-mounted display was set as the pilot's flight helmet. Therefore, testers could freely watch the outside scenes of the flight through the device, as shown in Figure 28. The content of the flight range was designed to be 1000 m × 1000 m, and the height was 1200 m. Figure 27. Heave, roll, and pitch limit G force test method.

Virtual Image Design
The image was designed for first-person perspective. Final VR content included the image of the aircraft, the outside environment, and the cockpit. The cockpit showed the propulsion power, flight speed, and aircraft altitude, etc. The High Tech Computer (HTC) Vive Pro head-mounted display was set as the pilot's flight helmet. Therefore, testers could freely watch the outside scenes of the flight through the device, as shown in Figure  28. The content of the flight range was designed to be 1000 m × 1000 m, and the height was 1200 m.

Control System
According to this study, the platform had to synchronize with VR images in realtime. Therefore, the control system needed to build on a high degree of synchronization and high transmission speed. In this study, the high transmission speed serial EtherCAT was selected to control the platform. EtherCAT was used to control 3 sets of 4.5 kW and 1 set of 750 W servo drive equipment in real-time, and collocation with planetary gear reducer with a reduction ratio of 1:50. The system was set up in the Visual Studio C# development environment, and the position control commands were compiled on the upperaxis control card. The compiled instructions were transmitted to the servo drive, and the drive sent the position control to the motors through the received instruction. Then, the

Control System
According to this study, the platform had to synchronize with VR images in real-time. Therefore, the control system needed to build on a high degree of synchronization and high transmission speed. In this study, the high transmission speed serial EtherCAT was selected to control the platform. EtherCAT was used to control 3 sets of 4.5 kW and 1 set of 750 W servo drive equipment in real-time, and collocation with planetary gear reducer with a reduction ratio of 1:50. The system was set up in the Visual Studio C# development environment, and the position control commands were compiled on the upper-axis control card. The compiled instructions were transmitted to the servo drive, and the drive sent the position control to the motors through the received instruction. Then, the motors would make the platform motions, and the multi-axis control was performed between the drives by using the master station and multiple sets of slave stations in series. The control architecture was a three-loop closed-loop system, and the position loop was the main control loop. The communication method is shown in Figure 29.
Appl. Sci. 2021, 11, x FOR PEER REVIEW 19 of 23 motors would make the platform motions, and the multi-axis control was performed between the drives by using the master station and multiple sets of slave stations in series. The control architecture was a three-loop closed-loop system, and the position loop was the main control loop. The communication method is shown in Figure 29.

System Reliability
To confirm the reliability of the overall platform in this study, the motion sensor was installed on the center of mass of the multi-axis motion platform and the passenger seat. The installation position is shown in Figure 30. The test method was to input trajectory of roll and pitch motion. After that, the platform motion angle was captured at each time

System Reliability
To confirm the reliability of the overall platform in this study, the motion sensor was installed on the center of mass of the multi-axis motion platform and the passenger seat. The installation position is shown in Figure 30. The test method was to input trajectory of roll and pitch motion. After that, the platform motion angle was captured at each time point in the overall trajectory. Finally, the average value with the simulated motion trajectory output by the trajectory kinematics was compared to confirm that the platform moves repeatedly reliability.

System Reliability
To confirm the reliability of the overall platform in this study, the motion sensor was installed on the center of mass of the multi-axis motion platform and the passenger seat. The installation position is shown in Figure 30. The test method was to input trajectory of roll and pitch motion. After that, the platform motion angle was captured at each time point in the overall trajectory. Finally, the average value with the simulated motion trajectory output by the trajectory kinematics was compared to confirm that the platform moves repeatedly reliability.

Rotatable Multi-Axis Motion Platform Combined with VR
Finally, the rotatable multi-axis motion platform and the VR image were integrated The angle data of the VR image was converted into the rotation angles of three sets o driving motors. The operating step of this system was that the tester wore a display of V

Rotatable Multi-Axis Motion Platform Combined with VR
Finally, the rotatable multi-axis motion platform and the VR image were integrated. The angle data of the VR image was converted into the rotation angles of three sets of driving motors. The operating step of this system was that the tester wore a display of VR and controlled the image in the virtual environment through the joystick, throttle, and foot rudder. Then the image's angle was caught to calculate the drive motor output. According to the angle, the multi-axis motion platform could be operated the heave, roll, pitch, and yaw motions. The comparison with the Stewart platform is shown in Table 3. The complete platform is shown in Figure 32. When the image moved in each direction, the tester would feel movement synchronously in the real world which enhanced real immersion in VR, as shown in Figure 33.

Conclusions and Future Work
Most prior research focused on a 6DoF electric linear actuator with a monitor to design the simulator. This kind of design exhibite range than those developed in this study, and the monitor as an im have an immersive feeling for testers. Therefore, this paper developed axis motion platform combined with VR digital content. The whole p cluded inverse kinematics, mechanical design, stress analysis, VR de teractive control. It allowed testers to achieve immersive VR flight tra and controlling VR imagery of a flight and experiencing the feedba

Conclusions and Future Work
Most prior research focused on a 6DoF 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 ±180 • 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 during the roll motion was about 7.41%, the acceleration error was about 7.58%, the velocity error during the pitch motion was 8.6%, and the acceleration error was about 8.96%. Due to the acceleration of the actual platform, the platform stress was analyzed at each movement. The result showed that the maximum stress obtained during the roll motion was~129.63 MPa, and the maximum stress during the pitch motion was~119.79 MPa. The above-mentioned maximum stress was lower than the yield strength~648.5 MPa of material S45C. Therefore, the design of the platform would not cause system crash during the motion. The error between the simulated motor output angle and the actual output angle of the overall roll motion error was~7.5%, and the overall pitch motion error was 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 multiaxis 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.