Open Access Open Access  Restricted Access Subscription or Fee Access

Dynamic Modeling of a Generalized Stewart Platform by Bond Graph Method Utilizing a Novel Spatial Visualization Technique

İ. Yıldız(1*), V. E. Ömürlü(2), A. Sağırlı(3)

(1) Yıldız Technical University, Mechanical Engineering Department, Turkey
(2) Yıldız Technical University, Mechanical Engineering Department, Turkey
(3) Yıldız Technical University, Mechanical Engineering Department, Turkey
(*) Corresponding author



This paper represents dynamic modeling of generalized Stewart Platform Manipulator by Bond Graph method with a new spatial visualization method and the state-space representation of the dynamic equations of the system. Dynamic model includes all the dynamics and gravity effects, linear motor dynamics as well as the viscous friction at the joints. Following modeling of actuation system and of main structure, unification of these two is accomplished. Linear DC motors are utilized and are modeled as the actuation system. Since overall system consists of high nonlinearity originated from geometric nonlinearity and gyroscopic forces, resultant derivative causality problem caused by rigidly coupled inertia elements is addressed and consequential system state-space equations are presented. A spatial visualization method is developed based on classic vector bond-graph method, due to the lack of representing overall kinematic bonds of the Stewart Platform Mechanism using classic vector bond-graph visualization.
Copyright © 2016 Praise Worthy Prize - All rights reserved.


Stewart Platform; Bond Graph; System Dynamics; Spatial Kinematics; State-Space

Full Text:



Stewart, D.,A Platform with Six Degrees-of-freedom, Proceedings of Mechanical Engineering Part I, Vol.180, pp 371-386, 1965-1966.

Karnopp, D.C., Rosenberg, R.C., Introduction to Physical System Dynamics McGraw Hill Inc., New York, 1983.

Thoma, J.U., Simulation by Bond Graphs: Introduction to a Graphical Method Springer-Verlag, Berlin, 1990.

Margolis, D. And Shim T., A Bond Graph Model Incorporating Sensors, Actuators, And Vehicle Dynamics For Developing Controllers For Vehicle Safety, Journal of the Franklin Institute, Vol. 338, n. 1, 21-34, 2001.

Allen, R.R., Dubowsky, S., Mechanisms as Components of Dynamic Systems: A Bond Graph Approach, ASME Journal of Engineering for Industry, Vol. 99, No. 1, pp: 104-111, 1977.

Bos, A.M., Tiernego, M.J.L., Formula Manipulating in the Bond Graph Modeling and Simulation of Large Mechanical Systems, Journal of Franklin Institute, Vol. 319, n. 1/2, pp. 51-55, 1985.

Fahrenthold, E.P., Worgo, J.D., Vector Bond Graph Analysis of Mechanical Systems, Transactions of ASME, Vol. 113, pp. 344-353, 1991.

Karnopp, D., Approach to Derivative Causality in Bond Graph Models of Mechanical Systems, Journal of the Franklin Institute, Vol. 329, n. 1, 1992.

Do, W. Q. D. and Yang, D. C. H., Inverse Dynamic Analysis and Simulation of a Platform Type of Robot, Journal of Robotic Systems , Vol. 5, n. 3, pp. 209-227, 1988.

Dasgupta B., Mruthyunjaya T.S., Closed-form dynamic equations of the general Stewart Platform through the Newton-Euler approach. Mechanism and Machine Theory, Vol. 33, n. 7, pp. 993-1012, 1998.

Geng, Z., Haynes, L. S., Lee, J. D. and Carroll, R. L., On the Dynamic Model and Kinematic Analysis of a Class of Stewart Platforms, Robotics and Autonomous Systems, Vol. 9, pp. 237-254, 1992.

Liu, K., Fitzgerald, M., Dawson, D. W. and Lewis, F. L., Modeling and control of a Stewart platform manipulator, ASME DSC Vol. 33, Control of Systems with Inexact Dynamic Models, 1991, pp. 83-89.

Sagirli A., Bogoclu M.E., Omurlu V.E., Modeling a Rotary Crane by Bond-Graph Method, Analysis of Dynamical Behavior and Load Spectrum Analysis (Part I), Nonlinear Dynamics, Vol. 33, pp. 337-351, 2003.

I. Davliakos, P. Chatzakos, and E. Papadopoulos, Development of a Model-based Impedance Controller for Electrohydraulic Servos, In L.A. Gerhardt (Ed.), Robotics and Applications, (ACTA Press, 2005, 498-061).

I. Davliakos, E. Papadopoulos, A Model-Based Impedance Control of a 6-dof Electrohydraulic Stewart Platform, Proceedings of the European Control Conference, Greece, 2007, pp. 3507-3514.


  • There are currently no refbacks.

Please send any question about this web site to
Copyright © 2005-2020 Praise Worthy Prize