Direct Position Analysis of the 4–6 Stewart Platforms

[+] Author and Article Information
Ning-Xin Chen, Shin-Min Song

Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, IL 60680

J. Mech. Des 116(1), 61-66 (Mar 01, 1994) (6 pages) doi:10.1115/1.2919377 History: Received June 01, 1992; Online June 02, 2008


Although Stewart platforms have been applied in the design of aircraft and vehicle simulators and parallel robots for many years, the closed-form solution of direct (forward) position analysis of Stewart platforms has not been completely solved. Up to the present time, only the relatively simple Stewart platforms have been analyzed. Examples are the octahedral, the 3–6 and the 4–4 Stewart platforms, of which the forward position solutions were derived as an eighth or a twelfth degree polynomials with one variable in the form of square of a tan-half-angle. This paper further extends the direct position analysis to a more general case of the Stewart platform, the 4–6 Stewart platforms, in which two pairs of the upper joint centers of adjacent limbs are coincident. The result is a sixteenth degree polynomial in the square of a tan-half-angle, which indicates that a maximum of 32 configurations may be obtained. It is also shown that the previously derived solutions of the 3–6 and 4–4 Stewart platforms can be easily deduced from the sixteenth degree polynomial by setting some geometric parameters be equal to 1 or 0.

Copyright © 1994 by The American Society of Mechanical Engineers
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