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Research Papers

Analytical Evaluation of the Double Stewart Platform Tensile Truss Stiffness Matrix

[+] Author and Article Information
Michael P. Hennessey

e-mail: mphennessey@stthomas.edu
School of Engineering,
University of St. Thomas,
100 O'Shaughnessy Science Hall,
2115 Summit Avenue,
St. Paul, MN 55105-1079

1Present address: Senior Engineer, at the 3M Company of Maplewood, MN.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received July 31, 2012; final manuscript received August 22, 2013; published online November 6, 2013. Assoc. Editor: Yuefa Fang.

J. Mechanisms Robotics 6(1), 011003 (Nov 06, 2013) (18 pages) Paper No: JMR-12-1113; doi: 10.1115/1.4025470 History: Received July 31, 2012; Revised August 22, 2013

The 6 × 6 stiffness matrix for a single Stewart platform tensile truss is well known. This work extends the methodology used to determine the stiffness matrix of a double Stewart platform system, in which one Stewart platform is stacked on top of another, in serial fashion. A double Stewart platform may offer advantages for some applications in terms of increased stiffness in certain directions. Using principles of statics and considering small displacement perturbations in three-dimensional space of both mobile platforms (middle and bottom) from their weighted equilibrium locations, displacements can be related in a linear manner to application loading, implying a stiffness matrix. Scripts are then developed and executed in matlabtm to determine the stiffness matrix of a specific system. The matlabtm result is validated using single and double Stewart platform physical models and measuring system compliance responses to external forces and moments.

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Copyright © 2014 by ASME
Topics: Cables , Stiffness
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References

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Figures

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Fig. 1

Three-dimensional platform representation of a double Stewart platform

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Fig. 2

Front view of initial configuration

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Fig. 3

Top view of movable platforms

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Fig. 4

Displaced middle and bottom platforms

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Fig. 5

Coordinate frame transformations

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Fig. 6

Weighted configuration front view

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Fig. 7

Weight and application loading effect on cable vectors

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Fig. 8

Coordinate frame shift due to weight

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Fig. 9

Free body diagrams for middle and bottom platforms, including weight and small magnitude application force and moment loads

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Fig. 10

Single Stewart platform model instrumented for yaw stiffness experiment

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Fig. 11

Double Stewart platform model instrumented for yaw stiffness experiment

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