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A new closed-form solution to the forward displacement analysis of a 55 in-parallel platform

Y. Zhang
Qizheng Liao
Hai-Jun Su
Shimin Wei
Journal / Anthology

Mechanism and Machine Theory
Year: 2012
Volume: 52
Page range: 47-58

This paper presents a new solution procedure for the forward displacement analysis of a general 55 in-parallel platform, i.e., the connection points are not restricted to lie in planes. This paper is the continuation of Ref. [1] and its novelty lies in elimination strategy of the basic closure equations which were already derived in Ref. [1]. First of all, three kinematics constraint equations in two variables are derived from the basic closure equations by the vector algebraic elimination technique. Then, the greatest common divisor (GCD) of two constraint equations is symbolically factored out by using computer algebra system Mathematica 7.0. Finally, a 24th-degree univariant polynomial equation is reduced from this GCD polynomial together with the third constraint equation by constructing a 1010 Sylvester resultant matrix. At last, a numerical example is deployed to verify the procedure.