A closed-form forward kinematics solution for the 6-6P Stewart platform

Ping Ji, Hongtao Wu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

73 Citations (Scopus)


This paper studies the forward kinematics of a special 6-6 Stewart platform, in which both the base and the mobile platforms are similar hexagons. A concise closed-form solution to the forward kinematics of the Stewart platform is obtained by introducing a quaternion to represent the transformation matrix. It is very interesting to find that the eight possible solutions have a very simple inner symmetry relationship. So, the solutions obtained from the approach presented in this paper are concise, represented as the squares of the four quaternion components. Besides, unnecessary complex roots are avoided automatically. Finally, only univariate quadratic equations are required to solve in this approach.
Original languageEnglish
Pages (from-to)522-526
Number of pages5
JournalIEEE Transactions on Robotics and Automation
Issue number4
Publication statusPublished - 1 Aug 2001


  • Closed form solution
  • Forward kinematics
  • Stewart platform

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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