Forward kinematics of the general 6-6 Stewart platform using algebraic elimination

Tae Young Lee, Jae Kyung Shim

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112 Citations (Scopus)

Abstract

It is known that the number of solutions of the forward kinematics of the general 6-6 Stewart platform is up to 40 in the complex domain. Finding all the solutions is necessary when all the possible postures are of interest or a unique actual posture is to be determined by choosing the correct one out of the solutions. In such cases, algebraic elimination method can be a powerful tool. In this article, an elimination procedure for the forward kinematics of the general 6-6 Stewart platform is presented, which leads to a 40th-degree univariate equation without factoring out or deriving the greatest common divisor. In addition, the proposed method, when implemented in a computer language, requires less computation time than the existing algorithms do mainly because the size of the final Sylvester's matrix is relatively small. The algorithm is demonstrated by two numerical examples.

Original languageEnglish
Pages (from-to)1073-1085
Number of pages13
JournalMechanism and Machine Theory
Volume36
Issue number9
Publication statusPublished - 2001 Sep 1

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ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering
  • Mechanical Engineering

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