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Modeling and Experimental Validation of a Generalized Stewart Platform by Bond-Graph Method

  • Research Article - Mechanical Engineering
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Abstract

This paper represents modeling and experimental validation of a Stewart platform manipulator by Bond-Graph method. Dynamic model includes all dynamic and gravity effects, linear motor dynamics as well as viscous friction at the joints. Following the modeling of actuation system and of main structure, merging of these two is accomplished. Linear DC motors are utilized and are modeled as the main part of the actuation system. Since the 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 nonlinear system state-space equations are presented. Stability of the model is investigated by observing the variations of the system matrix eigen values which are utilized from the state-space equations. Four different trajectories are applied to the Bond-Graph model and to the experimental setup for validation purposes. Satisfactory close coordination between simulation and experimental system is achieved.

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Abbreviations

P i :

Connection point of the leg to the mobile plate

B i :

Connection point of the leg to the static plate

L i :

Length of the leg

m i :

Mass of the leg

mp :

Mass of the mobile plate

IP :

Inertia of the mobile plate

Ibi :

Inertia of the leg

rP :

Radius of the mobile plate

r B :

Radius of the static plate

θ i :

Angle of the leg

λ:

Angle between the neighbor connection points of the legs of the mobile plate

Λ:

Angle between the neighbor connection points of the legs of the static plate

\({\varepsilon_{\rm P}}\) :

Angle between the connection points of the legs and the x axis of the mobile plate

\({\varepsilon_B}\) :

Angle between the connection points of the legs and the x axis of the static plate

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Mechanical Engineering, Yildiz Technical University, Beşiktaş, Istanbul, 34349, Turkey

    İbrahim Yildiz & Ahmet Sağirli

  2. Department of Mechatronics Engineering, Faculty of Mechanical Engineering, Yildiz Technical University, Beşiktaş, Istanbul, 34349, Turkey

    Vasfi Emre Ömürlü

Authors
  1. İbrahim Yildiz
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  2. Vasfi Emre Ömürlü
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  3. Ahmet Sağirli
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Correspondence to İbrahim Yildiz.

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Yildiz, İ., Ömürlü, V.E. & Sağirli, A. Modeling and Experimental Validation of a Generalized Stewart Platform by Bond-Graph Method. Arab J Sci Eng 38, 2875–2890 (2013). https://doi.org/10.1007/s13369-012-0484-y

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  • DOI: https://doi.org/10.1007/s13369-012-0484-y

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