# Design and Implementation of Inverse Kinematics and Motion Monitoring System for 6 DoF Platform
## 1 Introduction  
Simulators continue to progress toward high performance, high fidelity, and complex, realistic scenes [1]. A motion platform with six degrees of freedom (DoF) simulates the dynamic motion of several vehicles to be perceived by passengers. In addition to visual effects, sound effects, and force, adding motion to professional training simulators can make the simulations more realistic as well as improving the effectiveness of training and exempting trainees from having to readapt to the motion of real vehicles. Regarding entertainment systems, adding motion can increase excitement, enhance interaction, and increase the value of the systems. Motion platforms with six DoF are commonly driven by one of the following devices: (1) A linear actuator, which is composed of motors, belts, and lead screws. This structure includes six electric cylinders, three pneumatic cylinders, upper and lower platforms, and a platform controller. (2) A 6 DoF crank arm platform, which is created by combining a crank arm mechanism--composed of a servo motor, a gear box, and a crank arm--with a reducer, a rocker arm, a platform support arm, upper and lower platforms, and a control system. Though they possess the advantages of simple control, high DoF, high efficiency, and high loading capacity (ton) [2], linear actuators have high production costs, and the height of the platform to be positioned in the center is overly high. With approximately half the development cost of linear actuators, 3 DoF and 4 DoF crank arm platforms have comparable high-fidelity motion, which reduces manufacturing costs, and can be applied in professional training simulators (e.g., of ships and vehicles) and entertainment simulators, which may serve as a point device at amusement parks [3, 4]. In 1965, [PERSON] from the United Kingdom proposed a 6 DoF, six-axis motion platform structure [5], which was first used as a flight simulator. The potential advantages and application prospects of parallel platforms received considerable attention and inspired numerous studies. In 1980, [PERSON] and [PERSON] proposed a parallel mechanism derivedfrom [PERSON]'s platform and discussed the inverse kinematics of said mechanism [6], which represented the earliest discussion of inverse kinematics. In 1985, [PERSON] and [PERSON] published a study on the relationship between the end effector speed of a six-axis motion platform and the drive input speed [7]. In 1992, [PERSON] clarified the relationship between the speed and acceleration of a six-axis platform and the drive. In 1993, [PERSON] proposed a comprehensive analysis of forward kinematics and inverse kinematics of a six-axis motion platform [8]. [PERSON] et al. analyzed the inverse kinematics of a 3-RRPS 6 DoF Stewart platform [9]. By that time, most kinematics problems related to the general type of 6 DoF Stewart platform had been resolved. Studies after 2010 have generally addressed means of controlling parallel architectures, such as artificial neural network control [10], and predictive control [11; 12; 13]. Studies after 2010 have also explored numerical solutions. For example, the spatial position and the center of the upper platform can be obtained by applying forward kinematics [14]. In addition, [15] proposed a real-time algorithm for solving the six motors' angular update command problem caused by multithreading. The algorithm is advantageous in that it increases the computing speed and reduces the running time, which enables the motors' angular update commands of the six-axis platform to provide more timely updates to the six servo drives. The current study applied the dynamic proprioception of real-life situations to achieve a motor sense that is identical or close to that created by real vehicles. Theoretically, the motion cueing effect most closely resembles reality when the motion state of the platform is exactly that of a real vehicle [16; 17]. The simulation of motion especially targeted the speed and acceleration perceptible by the human sensory system to achieve a realistic motor sense.