Research Papers

Dynamic Modeling of a Six Degree-of-Freedom Flight Simulator Motion Base

[+] Author and Article Information
Mauricio Becerra-Vargas

Automation and Integrated
Systems Group—GASI,
UNESP-Univ Estadual Paulista,
Campus Sorocaba,
Sorocaba CEP,
São Paulo 18087-180, Brazil
e-mail: mauricio@sorocaba.unesp.br

Eduardo Morgado Belo

Department of Aeronautical Engineering,
University of São Paulo—EESC,
São Carlos, CEP,
São Paulo 13563-120, Brazil
e-mail: belo@sc.usp.br

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 28, 2014; final manuscript received February 22, 2015; published online June 25, 2015. Assoc. Editor: Javier Cuadrado.

J. Comput. Nonlinear Dynam 10(5), 051020 (Sep 01, 2015) (13 pages) Paper No: CND-14-1265; doi: 10.1115/1.4030013 History: Received October 28, 2014; Revised February 22, 2015; Online June 25, 2015

This paper presents a closed-form solution for the direct dynamic model of a flight simulator motion base. The motion base consists of a six degree-of-freedom (6DOF) Stewart platform robotic manipulator driven by electromechanical actuators. The dynamic model is derived using the Newton–Euler method. Our derivation is closed to that of Dasgupta and Mruthyunjaya (1998, “Closed Form Dynamic Equations of the General Stewart Platform Through the Newton–Euler Approach,” Mech. Mach. Theory, 33(7), pp. 993–1012), however, we give some insights into the structure and properties of those equations, i.e., a kinematic model of the universal joint, inclusion of electromechanical actuator dynamics and the full dynamic equations in matrix form in terms of Euler angles and platform position vector. These expressions are interesting for control, simulation, and design of flight simulators motion bases. Development of a inverse dynamic control law by using coefficients matrices of dynamic equation and real aircraft trajectories are implemented and simulation results are also presented.

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FAA-Federal Aviation Administration, 2012, 14 CFR FAR Part 60, Washington, DC.
Nahon, M., and Reid, L. D., 1990, “Simulator Motion Drive Algorithms—A Designer's Perspective,” J. Guid., Control, Dyn., 13(2), pp. 702–709. [CrossRef]
Stewart, D., 1965, “A Platform With 6 Degrees of Freedom,” Proc. Inst. Mech. Eng., 180(15), pp. 371–386. [CrossRef]
Dasgupta, B., and Mruthyunjaya, T., 1998, “Closed Form Dynamic Equations of the General Stewart Platform Through the Newton–Euler Approach,” Mech. Mach. Theory, 33(7), pp. 993–1012. [CrossRef]
Lebret, G., Liu, K., and Lewis, L., 1993, “Dynamic Analysis and Control of a Stewart Platform Manipulator,” J. Rob. Syst., 10(5), pp. 629–655. [CrossRef]
Liu, M.-J., Li, C.-X., and Li, C.-N., 2000, “Dynamics Analysis of the Gough-Stewart Platform Manipulator,” IEEE Trans. Rob. Autom., 16(1), pp. 94–98. [CrossRef]
Gallardo, J., Rico, J., Frisoli, A., Checcacci, D., and Bergamasco, M., 2003, “Dynamics of Parallel Manipulators by Means of Screw Theory,” Mech. Mach. Theory, 38(11), pp. 1113–1131. [CrossRef]
Guo, H., and Li, H., 2006, “Dynamics Analysis and Simulation of Six Degree of Freedom Stewart Platform Manipulator,” Proc. Inst. Mech. Eng., Part C, 220(1), pp. 61–72. [CrossRef]
Lopes, A., 2009, “Dynamic Modeling of a Stewart Platform Using the Generalized Momentum Approach,” Commun. Nonlinear Sci. Numer. Simul., 14(8), pp. 3389–3401. [CrossRef]
Becerra-Vargas, M., and Belo, E., 2011, “Robust Control of a Flight Simulator Motion Base,” J. Guid., Control, Dyn., 34(5), pp. 1519–1528. [CrossRef]
Becerra-Vargas, M., 2009, “Controle de uma Plataforma de Movimento de um Simulador de voo,” Ph.D. thesis, Doutorado em engenharia mecnica, Escola de Engenharia de Sao Carlos, Universidade de Sao Paulo, Sao Carlos, São Paulo, Brazil.


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Fig. 1

Flight simulator motion system

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Fig. 2

The UPS Stewart platform

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Fig. 3

Posicion analysis of one leg

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Fig. 4

Z-Y-X Euler angles

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Fig. 5

Velocity analysis of one leg

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Fig. 6

Axes of the universal joint

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Fig. 7

Acceleration analysis of one leg

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Fig. 8

Frames of references of one leg

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Fig. 9

Dynamic analysis of one leg

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Fig. 10

Dynamic analysis of the platform

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Fig. 11

Representation of the electromechanical servo-actuator

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Fig. 13

Rejected take-off maneuver: (a) acceleration components and (b) angular velocity components

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Fig. 14

Desired motion simulator-position: (a) linear position components and (b) Euler angles

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Fig. 15

Desired motion simulator-acceleration: (a) acceleration components and (b) Euler angles rates

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Fig. 16

Driving torques supplied by the servomotors

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Fig. 17

Motor angular velocities

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Fig. 18

Driving forces supplied by the actuators

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Fig. 19

Errors caused by simplification of leg acceleration

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Fig. 20

Platform and base leg points distribution




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