## An actuator extension transformation for a motion simulator and an inverse transformation applying Newton-Raphson's methodJames E. Dieudonne, Russell V. Parrish, Richard E. Bardusch, Langley Research Center, United States. National Aeronautics and Space Administration A set of equations which transform position and angular orientation of the centroid of the payload platform of a six-degree-of-freedom motion simulator into extensions of the simulator's actuators has been derived and is based on a geometrical representation of the system. An iterative scheme, Newton-Raphson's method, has been successfully used in a real time environment in the calculation of the position and angular orientation of the centroid of the payload platform when the magnitude of the actuator extensions is known. Sufficient accuracy is obtained by using only one Newton-Raphson iteration per integration step of the real time environment. |

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actual magnitude actual position actuator extension transformation actuator i obtained Ai?m aircraft simulations angular orientation Center into extensions centroid degree of freedom desired accuracy equations which transform Euler angle fixed coordinate system freedom of input integration step INVERSE TRANSFORMATION APPLYING iteration per integration iterative scheme Langley Research Center load platform lower attachment point m/sec magnitude of actuator maximum error obtained maximum length Maximum rate maximum servo drive minimum number motion base moving coordinate system Moving payload platform neut neutral position Newton Newton-Raphson iterations number of Newton-Raphson optimal washout origin of fixed origin of moving pay load Performing Organization point of actuator position and angular position and orientation potentiometer rad/sec Raphson Raphson's method real-time environment real-time motion simulation RESULTS Actuator Extension servo drive rates simulator's actuators six-degree-of-freedom motion simulator system from origin system to upper TRANSFORMATION APPLYING NEWTON-RAPHSON'S TRANSFORMATION The actuator U.S. Customary Units upper attachment point vector in fixed yields