Forward Displacement Analyses of the 4-4 Stewart Platforms

[+] Author and Article Information
W. Lin, M. Griffis, J. Duffy

Center for Intelligent Machines and Robotics, University of Florida, Gainesville, FL 32611

J. Mech. Des 114(3), 444-450 (Sep 01, 1992) (7 pages) doi:10.1115/1.2926572 History: Received March 01, 1990; Online June 02, 2008


A forward displacement analysis in closed-form is performed for each case of a class of Stewart Platform mechanisms. This class of mechanisms, which are classified into three cases, are called the “4-4 Stewart Platforms,” where each of the mechanisms has the distinguishing feature of six legs meeting either singly or pair-wise at four points in the top and base platforms. (This paper only addresses those 4-4 Platforms where both the top and base platforms are planar.) For each case, a polynomial is derived in the square of a tan-half-angle that measures the angle between two planar faces of a polyhedron embedded within the mechanism. The degrees of the polynomials for the first, second, and third cases are, respectively, eight, four, and twelve. All the solutions obtained from the forward displacement analyses for the three cases are verified numerically using a reverse displacement analysis.

Copyright © 1992 by The American Society of Mechanical Engineers
Topics: Displacement
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