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RESEARCH PAPERS

A Novel Approach in the Direct Kinematics of Stewart Platform Mechanisms with Planar Platforms

[+] Author and Article Information
İ. D. Akçali

Mechanical Engineering Department, University of Çukurova, Adana 01330, Turkey

H. Mutlu

Mechanical Engineering Department, University of Mersin, Mersin 33160, Turkey

J. Mech. Des 128(1), 252-263 (Aug 03, 2004) (12 pages) doi:10.1115/1.1864114 History: Received April 10, 2003; Revised August 03, 2004

In handling the kinematic analysis of two rigid bodies connected to each other by six legs through the use of six double spherical joints, methods have been implemented both in the formulation and solution phases of the problem. A three-dimensional problem has been viewed, in fact, as a multitude of two-dimensional works on several planes, the intersections of which yield relationships allowing transition between adjacent planes. Thus formulation is purely based on the geometric structure consisting of eight planes of interest, ending in the three fundamental equations involving three angles between the base and side triangular planes. In solving the resulting three equations, an efficient strategy has been established to come up with 16 solution sets effectively. Extensions of the theory have been shown to include the analyses of other Stewart platform models. Efficiency and effectiveness of the approach has been verified on numerical examples.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

3-3 Stewart platform geometry

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Figure 2

Geometry of the base plane triangle

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Figure 3

6-3 Stewart platform reduced to 3-3 type

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Figure 4

5-3 Stewart platform and its equivalent 3-3

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Figure 5

4-3 Stewart platform and its equivalent 3-3

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Figure 6

A special case of 4-3 Stewart platform

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