Forward displacement analysis of the 6/6-SPS Stewart manipulator with two dissimilar semisymmetrical hexagons

This paper addresses the forward displacement of a special class of the 6/6-SPS Stewart manipulators in which the moving platform and the base one are two dissimilar semisymmetrical hexagons. After proposing a mathematical model of the forward displacement of this special class of the Stewart manipulators, a multivariate polynomial equations set in the moving platform position parameters and orientation parameters is constructed in which input-parameters are design parameters and the link-length of each limb of this special class of the 6/6-SPS Stewart manipulators. Based on this multivariate polynomial equations set, an algorithm has been developed in Mathematica language for solving the forward displacement of this special class of the Stewart manipulators by utilizing a symbolic computation software Mathematica. It is shown that the maximum number of the complete analytical solutions to the forward displacement of this special class of the 6/6-SPS Stewart manipulators is up to 28 in the complex domain for any given set of design parameters and six given link-lengths of this special class of the Stewart manipulators considered in the present paper and the number of real roots out of 28 groups of solutions to the forward displacement of this special class of the Stewart manipulators must be a even number. Numerical examples of the forward displacement analysis of a Stewart manipulator under investigation are given to demonstrate the above-mentioned theoretical results. Forward displacement analysis of this special class of the 6/6-SPS Stewart manipulators paves underlying theoretical grounds for the workspace analysis, path planning and control of this special class of the 6/6-SPS Stewart manipulators.